ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW379+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:07:33 AM UTC 2026

% Result   : Theorem 257.54s 262.89s
% Output   : Proof 257.81s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% 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_empty,axiom,
    ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_empty) ).

fof(fact_hoare__derivs_Oequations_I1_J,axiom,
    ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

fof(fact_triple_Oinject,axiom,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
      ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_cut,axiom,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ),
    file('theBenchmark.p',fact_cut) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ),
    file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_derivs__insertD,axiom,
    ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
        & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_derivs__insertD) ).

fof(fact_weak__Body,axiom,
    ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_weak__Body) ).

fof(fact_hoare__derivs_OBody,axiom,
    ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ),
    file('theBenchmark.p',fact_hoare__derivs_OBody) ).

fof(fact_BodyN,axiom,
    ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_BodyN) ).

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

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

fof(fact_Body__sound__lemma,axiom,
    ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2))
     => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ),
    file('theBenchmark.p',fact_Body__sound__lemma) ).

fof(fact_evalc_Oequations_I9_J,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
    <=> hBOOL(hAPP(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_MGT__BodyN,axiom,
    ! [V_Ga_2,V_pn_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_MGT__BodyN) ).

fof(fact_Body1,axiom,
    ! [V_pn_2,V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_Body1) ).

fof(fact_image__constant__conv,axiom,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_image__constant__conv) ).

fof(fact_insert__is__Un,axiom,
    ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2),
    file('theBenchmark.p',fact_insert__is__Un) ).

fof(fact_sup1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1CI) ).

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

fof(fact_bot__fun__def,axiom,
    ! [V_x_2,T_b,T_a] :
      ( class_Orderings_Obot(T_a)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_bot__fun__def) ).

fof(fact_equalityCE,axiom,
    ! [V_c_2,T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) )
       => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_equalityCE) ).

fof(fact_emptyE,axiom,
    ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_emptyE) ).

fof(fact_insertCI,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
       => V_a_2 = V_b_2 )
     => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertCI) ).

fof(fact_insertE,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
     => ( V_a_2 != V_b_2
       => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_insertE) ).

fof(fact_image__eqI,axiom,
    ! [T_a,V_A_2,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_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_image__eqI) ).

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

fof(fact_mem__def,axiom,
    ! [V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
    <=> hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_mem__def) ).

fof(fact_eq__mem,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_eq__mem) ).

fof(fact_pred__equals__eq,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
    <=> V_R_2 = V_S_2 ),
    file('theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_eqset__imp__iff,axiom,
    ! [V_x_2,T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_eqset__imp__iff) ).

fof(fact_eqelem__imp__iff,axiom,
    ! [V_A_2,T_a,V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eqelem__imp__iff) ).

fof(fact_eq__mem__trans,axiom,
    ! [V_A_2,T_a,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eq__mem__trans) ).

fof(fact_equals0D,axiom,
    ! [V_a_2,T_a,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_equals0D) ).

fof(fact_empty__iff,axiom,
    ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_empty__iff) ).

fof(fact_ex__in__conv,axiom,
    ! [V_A_2,T_a] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
    <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ex__in__conv) ).

fof(fact_all__not__in__conv,axiom,
    ! [V_A_2,T_a] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_insert__absorb,axiom,
    ! [V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ),
    file('theBenchmark.p',fact_insert__absorb) ).

fof(fact_insertI2,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertI2) ).

fof(fact_insert__ident,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
       => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)
        <=> V_A_2 = V_B_2 ) ) ),
    file('theBenchmark.p',fact_insert__ident) ).

fof(fact_insert__iff,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_insert__iff) ).

fof(fact_insertI1,axiom,
    ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_insertI1) ).

fof(fact_rev__image__eqI,axiom,
    ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_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_a,T_b,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_imageI,axiom,
    ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_imageI) ).

fof(fact_image__iff,axiom,
    ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
    <=> ? [B_x] :
          ( V_z_2 = hAPP(V_f_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_image__iff) ).

fof(fact_UnI2,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Un__iff) ).

fof(fact_bot__empty__eq,axiom,
    ! [V_x_2,T_a] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_singletonE,axiom,
    ! [V_a_2,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
     => V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singletonE) ).

fof(fact_singleton__iff,axiom,
    ! [V_a_2,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
    <=> V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singleton__iff) ).

fof(fact_insert__image,axiom,
    ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_insert__image) ).

fof(fact_image__constant,axiom,
    ! [V_c_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_image__constant) ).

fof(fact_hoare__sound,axiom,
    ! [V_ts_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
     => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ),
    file('theBenchmark.p',fact_hoare__sound) ).

fof(fact_insert__code,axiom,
    ! [V_x_2,V_A_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),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_insert__commute,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),
    file('theBenchmark.p',fact_insert__commute) ).

fof(fact_insert__absorb2,axiom,
    ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2),
    file('theBenchmark.p',fact_insert__absorb2) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_sup1I2,axiom,
    ! [V_A_2,T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I2) ).

fof(fact_sup1I1,axiom,
    ! [V_B_2,T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I1) ).

fof(fact_ball__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
           => hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_ball__Un) ).

fof(fact_bex__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
    <=> ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_bex__Un) ).

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

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

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

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

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

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

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

fof(fact_MGF__complete,axiom,
    ! [V_Q_2,V_P_2,V_c_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_MGF__complete) ).

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),hAPP(c_Natural_Oevalc,V_c_2)),
    file('theBenchmark.p',fact_MGT__def) ).

fof(fact_bot__apply,axiom,
    ! [V_x_2,T_b,T_a] :
      ( class_Orderings_Obot(T_a)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_bot__apply) ).

fof(fact_singleton__inject,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
     => V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_singleton__inject) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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__not__empty,axiom,
    ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_insert__not__empty) ).

fof(fact_empty__not__insert,axiom,
    ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2),
    file('theBenchmark.p',fact_empty__not__insert) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
      <=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_a)
          & V_x_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ),
    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_image__is__empty,axiom,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_image__is__empty) ).

fof(fact_image__empty,axiom,
    ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_image__empty) ).

fof(fact_empty__is__image,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_empty__is__image) ).

fof(fact_Un__empty,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Un__empty) ).

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

fof(fact_Un__empty__left,axiom,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('theBenchmark.p',fact_Un__empty__left) ).

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

fof(fact_Un__insert__left,axiom,
    ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__insert__left) ).

fof(fact_Un__insert__right,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_Un__insert__right) ).

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

fof(fact_image__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,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__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__Un) ).

fof(fact_the__elem__eq,axiom,
    ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2,
    file('theBenchmark.p',fact_the__elem__eq) ).

fof(fact_MGT__alternI,axiom,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_MGT__alternI) ).

fof(fact_triple_Osimps_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_triple_Orecs,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_escape,axiom,
    ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] :
      ( ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
         => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),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_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
     => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_escape) ).

fof(fact_MGT__alternD,axiom,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ostate__not__singleton
     => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_MGT__alternD) ).

fof(fact_hoare__derivs_Oequations_I7_J,axiom,
    ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

fof(fact_hoare__derivs_OSkip,axiom,
    ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_OSkip) ).

fof(fact_conseq1,axiom,
    ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => ( ! [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
           => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_conseq1) ).

fof(fact_conseq2,axiom,
    ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => ( ! [B_Z,B_s] :
            ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
           => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_conseq2) ).

fof(fact_Comp,axiom,
    ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_Comp) ).

fof(fact_LoopF,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_LoopF) ).

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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ),
    file('theBenchmark.p',fact_evalc_OWhileFalse) ).

fof(fact_evalc_OWhileTrue,axiom,
    ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(V_b_2,V_s0_2))
     => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s0_2),V_s1_2))
       => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
         => hBOOL(hAPP(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_OSemi,axiom,
    ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0),V_s0),V_s1))
     => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s1),V_s2))
       => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ),
    file('theBenchmark.p',fact_evalc_OSemi) ).

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

fof(fact_evalc__elim__cases_I1_J,axiom,
    ! [V_t,V_s] :
      ( hBOOL(hAPP(hAPP(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_Oequations_I7_J,axiom,
    ! [V_a2_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I7_J) ).

fof(fact_evalc_Oequations_I8_J,axiom,
    ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
              & hBOOL(hAPP(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_I4_J,axiom,
    ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
      ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1)) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I4_J) ).

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

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

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

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

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

fof(fact_com_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_I18_J,axiom,
    ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H),
    file('theBenchmark.p',fact_com_Osimps_I18_J) ).

fof(fact_com_Osimps_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_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_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_I6_J,axiom,
    ! [V_pname_H_2,V_pname_2] :
      ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
    <=> V_pname_2 = V_pname_H_2 ),
    file('theBenchmark.p',fact_com_Osimps_I6_J) ).

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

fof(fact_com_Osimps_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_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_the__elem__def,axiom,
    ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_the__elem__def) ).

fof(fact_MGF,axiom,
    ! [V_c_2] :
      ( c_Hoare__Mirabelle_Ostate__not__singleton
     => ( c_Com_OWT__bodies
       => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
         => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_MGF) ).

fof(fact_image__ident,axiom,
    ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__ident) ).

fof(fact_imageE,axiom,
    ! [V_A_2,V_f_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
     => ~ ! [B_x] :
            ( V_b_2 = hAPP(V_f_2,B_x)
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_imageE) ).

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

fof(fact_Loop__sound__lemma,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop__sound__lemma) ).

fof(fact_Loop,axiom,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop) ).

fof(fact_finite__pointwise,axiom,
    ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
     => ( ! [B_p] :
            ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_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_b),tc_HOL_Obool))))
           => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,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))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
         => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,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))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ),
    file('theBenchmark.p',fact_finite__pointwise) ).

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_MGF__lemma1,axiom,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ostate__not__singleton
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
           => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) )
       => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
         => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_MGF__lemma1) ).

fof(fact_vimage__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__insert) ).

fof(fact_vimageI,axiom,
    ! [T_b,V_B_2,T_a,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_a),V_b_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_vimageI) ).

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_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_vimage__code,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,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_o__eq__elim,axiom,
    ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2)
     => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ),
    file('theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ),
    file('theBenchmark.p',fact_o__eq__dest) ).

fof(fact_o__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,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_vimage__compose,axiom,
    ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)),
    file('theBenchmark.p',fact_vimage__compose) ).

fof(fact_vimage__ident,axiom,
    ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_vimage__ident) ).

fof(fact_o__assoc,axiom,
    ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2),
    file('theBenchmark.p',fact_o__assoc) ).

fof(fact_o__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,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_image__compose,axiom,
    ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)),
    file('theBenchmark.p',fact_image__compose) ).

fof(fact_finite__dom__body,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
    file('theBenchmark.p',fact_finite__dom__body) ).

fof(fact_vimageI2,axiom,
    ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_vimageI2) ).

fof(fact_vimageD,axiom,
    ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,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)) ),
    file('theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ),
    file('theBenchmark.p',fact_vimage__eq) ).

fof(fact_vimage__empty,axiom,
    ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__empty) ).

fof(fact_vimage__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Un) ).

fof(fact_peek__and__def,axiom,
    ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
    <=> ( hBOOL(hAPP(V_p_2,V_s_2))
        & hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_peek__and__def) ).

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

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

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

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

fof(fact_vimage__singleton__eq,axiom,
    ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
    <=> hAPP(V_f_2,V_a_2) = V_b_2 ),
    file('theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_finite__imageI,axiom,
    ! [V_h_2,T_b,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ),
    file('theBenchmark.p',fact_finite__imageI) ).

fof(fact_finite_OinsertI,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_finite_OemptyI,axiom,
    ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_hoare__derivs_OIf,axiom,
    ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_finite__Un,axiom,
    ! [V_Ga_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__Un) ).

fof(fact_finite__UnI,axiom,
    ! [V_Ga_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
    file('theBenchmark.p',fact_finite__UnI) ).

fof(fact_finite__insert,axiom,
    ! [V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_finite__insert) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_image__eq__fold__image,axiom,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,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_a),c_Set_Oinsert(T_b)),V_f_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))),V_A_2) ),
    file('theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_the__eq__trivial,axiom,
    ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    file('theBenchmark.p',fact_the__eq__trivial) ).

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(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(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_t_2)) )
       => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
           => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2_2),V_s_2),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_evalc__elim__cases_I5_J) ).

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

fof(fact_evalc_OIfFalse,axiom,
    ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_s1_2))
       => hBOOL(hAPP(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_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_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_fold__image__empty,axiom,
    ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__image__empty) ).

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(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(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I6_J) ).

fof(fact_evalc_Oequations_I5_J,axiom,
    ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(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(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(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_WT_OIf,axiom,
    ! [V_b_2,V_c1_2,V_c0_2] :
      ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
     => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
       => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ),
    file('theBenchmark.p',fact_WT_OIf) ).

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

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

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

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

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

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

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

fof(fact_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_Sup__fin_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_finite,axiom,
    ! [V_A_2,T_a] :
      ( class_Finite__Set_Ofinite(T_a)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [V_A_2,T_a] :
      ( class_Finite__Set_Ofinite(T_a)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_finite__code) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,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_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_Sup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_folding_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_DiffE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_DiffI) ).

fof(fact_finite__Diff,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff) ).

fof(fact_fun__diff__def,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( class_Groups_Ominus(T_a)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__diff__def) ).

fof(fact_Diff__idemp,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__idemp) ).

fof(fact_minus__apply,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( class_Groups_Ominus(T_a)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_minus__apply) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,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_DiffD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Diff__iff) ).

fof(fact_empty__Diff,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_empty__Diff) ).

fof(fact_Diff__empty,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Diff__empty) ).

fof(fact_Diff__cancel,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__cancel) ).

fof(fact_finite__Diff2,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Diff2) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__Diff) ).

fof(fact_vimage__Diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Diff) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ),
    file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_insert__Diff1,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_insert__Diff1) ).

fof(fact_insert__Diff__if,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    file('theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Diff__insert) ).

fof(fact_Diff__insert2,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2),
    file('theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_finite__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_folding__one_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_folding__idem_Oidem__left__comp,axiom,
    ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,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_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oremove) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [V_A_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ),
    file('theBenchmark.p',fact_insert__Diff) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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,axiom,
    ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,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,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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__one_Osingleton,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),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_comm__monoid__big_Oinfinite,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_Sup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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(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_b,tc_HOL_Obool)),V_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_folding__image__simple_Oremove) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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(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_b,tc_HOL_Obool)),V_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_folding__image__simple_Oinsert__remove) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),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_b,V_A_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__upd__image) ).

fof(fact_finite__empty__induct,axiom,
    ! [V_P_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(V_P_2,V_A_2))
       => ( ! [B_a,B_A] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
             => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
               => ( hBOOL(hAPP(V_P_2,B_A))
                 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,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_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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(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_setsum__diff1__ring,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( class_Rings_Oring(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_setsum__diff1,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1) ).

fof(fact_folding_Ounion,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion) ).

fof(fact_inf1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
         => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1E) ).

fof(fact_inf1I,axiom,
    ! [T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1I) ).

fof(fact_fun__upd__triv,axiom,
    ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_IntI,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_IntI) ).

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

fof(fact_finite__Int,axiom,
    ! [V_Ga_2,V_F_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ),
    file('theBenchmark.p',fact_finite__Int) ).

fof(fact_fun__upd__idem,axiom,
    ! [T_a,T_b,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_b,T_a),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_b,T_a,V_x_2,V_z_2] :
      ( V_z_2 != V_x_2
     => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_b,T_a,V_c_2,V_a_2] :
      ( V_a_2 != V_c_2
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_b,T_a,V_x_2,V_z_2] :
      ( ( V_z_2 != V_x_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_a,T_b),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_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),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_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_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_inf1D2,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => hBOOL(hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf1D2) ).

fof(fact_inf1D1,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_inf__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__apply) ).

fof(fact_inf__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_Int__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__assoc) ).

fof(fact_inf__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_Int__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Int__left__commute) ).

fof(fact_inf__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_Int__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_inf__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_Int__commute,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Int__commute) ).

fof(fact_inf__fun__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__fun__def) ).

fof(fact_inf__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_inf__idem) ).

fof(fact_inf_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_inf_Oidem) ).

fof(fact_Int__absorb,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Int__absorb) ).

fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,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__inf,axiom,
    ! [T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_setsum__commute,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ),
    file('theBenchmark.p',fact_setsum__commute) ).

fof(fact_fun__upd__def,axiom,
    ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
      ( ( V_x_2 != V_a_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_a,T_b),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__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
     => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).

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_sup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__distrib1) ).

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

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

fof(fact_Int__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__iff) ).

fof(fact_IntD1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_IntD1) ).

fof(fact_IntD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ),
    file('theBenchmark.p',fact_IntD2) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),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_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__right) ).

fof(fact_Int__empty__left,axiom,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__left) ).

fof(fact_insert__inter__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_insert__inter__insert) ).

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

fof(fact_Un__Int__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Int__Un__distrib2) ).

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

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

fof(fact_Diff__Int2,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    file('theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Int__Diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__Diff) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_vimage__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Int) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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(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__image__simple_Ounion__inter) ).

fof(fact_setsum__subtractf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_inf__Int__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_fun__upd__comp,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,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_setsum__diff1__nat,axiom,
    ! [V_f_2,V_A_2,V_a_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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(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_fun__left__comm__idem__insert,axiom,
    ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),
    file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_Int__insert__right,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__right) ).

fof(fact_Int__insert__left,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__left) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ),
    file('theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_Int__insert__left__if1,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ),
    file('theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_Diff__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_Diff__triv,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Diff__triv) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ),
    file('theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_Diff__Int,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Un) ).

fof(fact_Un__Diff__Int,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    file('theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_inf__Sup__absorb) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_folding__one_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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__one_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_Sup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,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_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_setsum__diff1_H,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_setsum_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,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_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_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))
         => ( ! [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) = V_z_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(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_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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_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(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_Sup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_setsum__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_setsum__Un) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,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_fold__empty,axiom,
    ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,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__empty) ).

fof(fact_setsum__addf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__addf) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_fold__image__def,axiom,
    ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_fold__image__def) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_setsum_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_union__fold__insert,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),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_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),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_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_setsum__Un__nat,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,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_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,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_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_setsum_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_minus__fold__remove,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_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,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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_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(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_setsum_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oclosed) ).

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

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

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_Sup__fold__sup,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_SUP1__I,axiom,
    ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_SUP1__I) ).

fof(fact_SUP2__I,axiom,
    ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__I) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,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_Ofun__left__comm__apply,axiom,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_finite__UN,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_finite__UN) ).

fof(fact_UN__o,axiom,
    ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2),
    file('theBenchmark.p',fact_UN__o) ).

fof(fact_finite__UnionD,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ),
    file('theBenchmark.p',fact_finite__UnionD) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

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

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

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

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

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

fof(fact_diff__eq__diff__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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_fun__left__comm_Ofold__fun__comm,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,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_sup__Sup__fold__sup,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__Sup__fold__sup) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_Sup__binary,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Sup__binary) ).

fof(fact_vimage__eq__UN,axiom,
    ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,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))))),
    file('theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_image__eq__UN,axiom,
    ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__eq__UN) ).

fof(fact_UN__I,axiom,
    ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_UN__I) ).

fof(fact_Sup__insert,axiom,
    ! [V_A_2,V_a_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ),
    file('theBenchmark.p',fact_Sup__insert) ).

fof(fact_Sup__singleton,axiom,
    ! [V_a_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Sup__empty,axiom,
    ! [T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_Sup__empty) ).

fof(fact_SUP__const,axiom,
    ! [V_M_2,T_a,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_SUP__const) ).

fof(fact_UnionI,axiom,
    ! [V_A_2,V_C_2,V_X_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ),
    file('theBenchmark.p',fact_UnionI) ).

fof(fact_UN__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_UN__insert) ).

fof(fact_SUP1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,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_a),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP1__iff) ).

fof(fact_Union__image__eq,axiom,
    ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_Union__def,axiom,
    ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Union__def) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2),
    file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_ball__UN,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
             => hBOOL(hAPP(V_P_2,B_xa)) ) ) ),
    file('theBenchmark.p',fact_ball__UN) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_SUP2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,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_a),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP2__iff) ).

fof(fact_Union__empty,axiom,
    ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__empty) ).

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

fof(fact_Un__eq__Union,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Un__eq__Union) ).

fof(fact_Union__insert,axiom,
    ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Union__insert) ).

fof(fact_UN__iff,axiom,
    ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_UN__iff) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_UN__empty2,axiom,
    ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__empty2) ).

fof(fact_UN__constant,axiom,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__constant) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_image__UN,axiom,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_image__UN) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)),
    file('theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_image__Union,axiom,
    ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),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_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)),
    file('theBenchmark.p',fact_image__Union) ).

fof(fact_UN__Un__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_UN__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_UN__Un) ).

fof(fact_Un__Union__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))),
    file('theBenchmark.p',fact_Un__Union__image) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_Int__Union2,axiom,
    ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Int__Union2) ).

fof(fact_Int__Union,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Int__Union) ).

fof(fact_SUPR__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_SUPR__apply) ).

fof(fact_SUP__commute,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ),
    file('theBenchmark.p',fact_SUP__commute) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_vimage__UN,axiom,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__UN) ).

fof(fact_vimage__Union,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)),
    file('theBenchmark.p',fact_vimage__Union) ).

fof(fact_Union__disjoint,axiom,
    ! [V_A_2,V_C_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Union__disjoint) ).

fof(fact_UN__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_UN__absorb,axiom,
    ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,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_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__singleton,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_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_UN__extend__simps_I1_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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)) ) ),
    file('theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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)) ) ),
    file('theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_a,tc_fun(T_b,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_finite__Union,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
     => ( ! [B_M] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ),
    file('theBenchmark.p',fact_finite__Union) ).

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_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__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__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__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_finite__UN__I,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__UN__I) ).

fof(fact_insert__partition,axiom,
    ! [V_F_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
           => ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)))
               => ( B_x != B_xa
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_insert__partition) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_UnionE,axiom,
    ! [V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
     => ~ ! [B_X] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    file('theBenchmark.p',fact_UnionE) ).

fof(fact_INF1__D,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__D) ).

fof(fact_INF1__E,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,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_a),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF1__E) ).

fof(fact_INT__D,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),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_a),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_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),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_INT__E) ).

fof(fact_INF2__D,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),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_INF2__E,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,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_a),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF2__E) ).

fof(fact_finite__INT,axiom,
    ! [V_A_2,T_b,V_I_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite__INT) ).

fof(fact_INFI__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_INFI__apply) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_INF__commute,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ),
    file('theBenchmark.p',fact_INF__commute) ).

fof(fact_INT__iff,axiom,
    ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__iff) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),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_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),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_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_INT__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2),
    file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_vimage__INT,axiom,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__INT) ).

fof(fact_INT__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_INT__absorb,axiom,
    ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ),
    file('theBenchmark.p',fact_INT__absorb) ).

fof(fact_INF__const,axiom,
    ! [V_M_2,T_a,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_INF__const) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_INT__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_INT__insert) ).

fof(fact_INT__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_INT__Un) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).

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_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_INFI__fold__inf,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_finite__induct,axiom,
    ! [V_P_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
       => ( ! [B_x,B_F] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
             => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
               => ( hBOOL(hAPP(V_P_2,B_F))
                 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) )
         => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ),
    file('theBenchmark.p',fact_finite__induct) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)
       => c_Nitpick_Ofold__graph_H(T_a,T_b,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_K__record__comp,axiom,
    ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2,
    file('theBenchmark.p',fact_K__record__comp) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,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_SUP2__E,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__E) ).

fof(fact_card__Un__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_setsum__restrict__set,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_UNIV__I,axiom,
    ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__I) ).

fof(fact_finite__Inter,axiom,
    ! [V_M_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ),
    file('theBenchmark.p',fact_finite__Inter) ).

fof(fact_InterE,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterE) ).

fof(fact_InterD,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterD) ).

fof(fact_Inter__UNIV,axiom,
    ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_INF1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__iff) ).

fof(fact_card_Oempty,axiom,
    ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_card_Oempty) ).

fof(fact_INF2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),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_zero__reorient,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_zero__reorient) ).

fof(fact_top__apply,axiom,
    ! [V_x_2,T_b,T_a] :
      ( class_Orderings_Otop(T_a)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_top__apply) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
       => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_card__infinite,axiom,
    ! [V_A_2,T_a] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__infinite) ).

fof(fact_finite__option__UNIV,axiom,
    ! [T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_Union__UNIV,axiom,
    ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__UNIV) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,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_a,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_Inf__UNIV,axiom,
    ! [T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Inter__def,axiom,
    ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Inter__def) ).

fof(fact_Sup__UNIV,axiom,
    ! [T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_Inter__empty,axiom,
    ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__empty) ).

fof(fact_Inf__empty,axiom,
    ! [T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_Inf__empty) ).

fof(fact_card__eq__0__iff,axiom,
    ! [V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__0__iff) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,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_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2),
    file('theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,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__fun__UNIVD2) ).

fof(fact_UNIV__not__empty,axiom,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_finite__UNIV,axiom,
    ! [T_a] :
      ( class_Finite__Set_Ofinite(T_a)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__UNIV) ).

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__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add__0__right) ).

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

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

fof(fact_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_Un__UNIV__left,axiom,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Un__UNIV__left) ).

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

fof(fact_Int__UNIV__left,axiom,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_right__minus__eq,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> 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_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( V_a_2 = V_b_2
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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_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_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_vimage__UNIV,axiom,
    ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,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_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,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_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,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_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2))
     => V_x_2 = V_z_2 ),
    file('theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_INF__INT__eq,axiom,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_INT__constant,axiom,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__constant) ).

fof(fact_INT__empty,axiom,
    ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_INT__empty) ).

fof(fact_range__composition,axiom,
    ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_range__composition) ).

fof(fact_setsum__0,axiom,
    ! [V_A_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_setsum__0) ).

fof(fact_Un__Inter,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Un__Inter) ).

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_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,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_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_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_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
      <=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_a)
          & V_x_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ),
    file('theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_Inter__image__eq,axiom,
    ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_range__eqI,axiom,
    ! [T_b,T_a,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_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_range__eqI) ).

fof(fact_rangeI,axiom,
    ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_rangeI) ).

fof(fact_Inf__fold__inf,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_Diff__UNIV,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_comp__surj,axiom,
    ! [V_g_2,T_c,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_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)) ) ),
    file('theBenchmark.p',fact_comp__surj) ).

fof(fact_setsum__empty,axiom,
    ! [V_f_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [V_g_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setsum__infinite,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_setsum__infinite) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_surj__image__vimage__eq) ).

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_fold__graph_OinsertI,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_setsum__eq__0__iff,axiom,
    ! [V_f_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_SUP__UN__eq,axiom,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_finite__range__imageI,axiom,
    ! [V_f_2,T_c,V_g_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) ) ),
    file('theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(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)) ) ),
    file('theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(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)) ) ),
    file('theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_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_B_2) ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_Inter__insert,axiom,
    ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__insert) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_Int__Inter__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,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_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Inf__insert,axiom,
    ! [V_A_2,V_a_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ),
    file('theBenchmark.p',fact_Inf__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [V_F_2,V_h_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
     => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__vimageD) ).

fof(fact_fold__def,axiom,
    ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)),
    file('theBenchmark.p',fact_fold__def) ).

fof(fact_image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,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_INT__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(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)) ) ),
    file('theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_vimage__const,axiom,
    ! [T_b,V_A_2,V_c_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_vimage__const) ).

fof(fact_setsum__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta) ).

fof(fact_setsum__delta_H,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_card_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_card__Diff__subset__Int) ).

fof(fact_Int__eq__Inter,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_Inf__binary,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Inf__binary) ).

fof(fact_setsum_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_triple_Osize_I1_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_fold1Set_Ointros,axiom,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_fold1Set_Ointros) ).

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_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => ? [B_y_H] :
              ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_setsum_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
             => ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(T_a),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_c) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_card__Diff__singleton,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_card_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_card_Oremove) ).

fof(fact_top1I,axiom,
    ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)),
    file('theBenchmark.p',fact_top1I) ).

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

fof(fact_fold1Set__nonempty,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
     => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_empty__fold1SetE,axiom,
    ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)),
    file('theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_a),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_card__eq__setsum,axiom,
    ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    file('theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_card__def,axiom,
    ! [V_A_2,T_a] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__def) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),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_fold1Set__sing,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_card_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_card_Oinsert) ).

fof(fact_card__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_triple_Osize_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_card_Ounion__inter__neutral,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).

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_b,T_a] :
      ( c_Nitpick_Ofold__graph_H(T_a,T_b,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_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_HOL_Obool)) ) ) ),
    file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

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_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_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_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_add__0__iff) ).

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

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_card__Plus__conv__if,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_card__Diff2__less,axiom,
    ! [V_y_2,V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_card__Diff1__less,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ),
    file('theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ),
    file('theBenchmark.p',fact_card__Suc__Diff1) ).

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

fof(fact_insert__fold1SetE,axiom,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2))
     => ~ ! [B_a,B_A] :
            ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
             => hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2))
    <=> ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
          & hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) ) ),
    file('theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [V_a_2,T_a] :
      ( class_Int_Oring__char__0(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => 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)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_Ints__odd__nonzero) ).

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_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_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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

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

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

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

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

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

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

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

fof(fact_Ints__mult,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ),
    file('theBenchmark.p',fact_Ints__mult) ).

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_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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv3) ).

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_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_mult__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_mult__idem) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_less__Suc__eq__0__disj,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( ? [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
            & V_m_2 = hAPP(c_Nat_OSuc,B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).

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

fof(fact_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_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__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( class_Rings_Oordered__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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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_a] :
      ( class_Rings_Oordered__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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
      <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

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

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

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

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

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

fof(fact_crossproduct__eq,axiom,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [V_b,V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

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

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

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

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

fof(fact_add__less__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,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_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_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_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__left) ).

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

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

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

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

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

fof(fact_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_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_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_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_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_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_diff__eq__diff__less,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

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_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

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

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

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

fof(fact_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_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_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_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_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_less__Sup__iff,axiom,
    ! [V_S_2,V_a_2,T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Complete__Lattice_Ocomplete__lattice(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Complete__Lattice_Ocomplete__lattice(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_fun__left__comm,axiom,
    ! [T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ),
    file('theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem) ).

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_setsum__product,axiom,
    ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( class_Rings_Osemiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),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_b,T_a] :
      ( class_Rings_Osemiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),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_b,V_r_2,T_a] :
      ( class_Rings_Osemiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_less__SUP__iff,axiom,
    ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Complete__Lattice_Ocomplete__lattice(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_INF__less__iff,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Complete__Lattice_Ocomplete__lattice(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_INF__less__iff) ).

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

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(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_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

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

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_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_even__less__0__iff,axiom,
    ! [V_a_2,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),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    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_less__iff__diff__less__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( class_Rings_Oring(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
      <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
    file('theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_eq__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( class_Rings_Oring(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

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

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

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

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

fof(fact_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_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_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_Ints__odd__less__0,axiom,
    ! [V_a_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(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_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_Ints__0,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ),
    file('theBenchmark.p',fact_Ints__0) ).

fof(fact_Ints__add,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ),
    file('theBenchmark.p',fact_Ints__add) ).

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

fof(fact_Ints__diff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ),
    file('theBenchmark.p',fact_Ints__diff) ).

fof(fact_Ints__1,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ),
    file('theBenchmark.p',fact_Ints__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_card__ge__0__finite,axiom,
    ! [V_A_2,T_a] :
      ( 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_a),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_nat__diff__split,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ( ! [B_d] :
            ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
           => hBOOL(hAPP(V_P_2,B_d)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_P_2,B_d))
              & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_a),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).

fof(fact_fold__image__distrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_card__insert__disjoint,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_card__insert__if,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ),
    file('theBenchmark.p',fact_card__insert__if) ).

fof(fact_fold__image__insert,axiom,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__insert) ).

fof(fact_card__gt__0__iff,axiom,
    ! [V_A_2,T_a] :
      ( 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_a),V_A_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [V_a_2,T_a] :
      ( class_Int_Oring__char__0(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
        <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__Plus,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,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_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_card__insert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card__insert) ).

fof(fact_card__Plus,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD1) ).

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_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_UNIV__Plus__UNIV,axiom,
    ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).

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_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_a] :
      ( class_Rings_Olinordered__ring__strict(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

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_Suc__eq__plus1__left,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    file('theBenchmark.p',fact_Suc__eq__plus1__left) ).

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

fof(fact_nat__mult__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_psubsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubsetD) ).

fof(fact_not__psubset__empty,axiom,
    ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_psubset__card__mono,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ),
    file('theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,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_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Plus__eq__empty__conv) ).

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

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

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

fof(fact_fold__image__Un__one,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_card__Suc__eq,axiom,
    ! [V_k_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),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_a,tc_HOL_Obool)) )
          & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
          & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) ) ),
    file('theBenchmark.p',fact_card__Suc__eq) ).

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

fof(fact_nat__mult__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_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_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_psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_psubset__trans) ).

fof(fact_comp__cong,axiom,
    ! [T_e,T_d,T_c,T_a,T_b,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_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ),
    file('theBenchmark.p',fact_comp__cong) ).

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_I5_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I5_J) ).

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

fof(fact_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_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_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_setsum__strict__mono,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__strict__mono) ).

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

fof(fact_nat__case__0,axiom,
    ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a] : c_Nat_Onat_Onat__case(T_a,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_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_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_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_fold1__eq__fold,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_fold1__Un,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un) ).

fof(fact_evaln_OBody,axiom,
    ! [V_s1,V_n,V_s0,V_pn] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(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_fold1__insert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
           => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__insert) ).

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_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

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_psubset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
            & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_setsum__SucD,axiom,
    ! [V_n_2,V_A_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum__SucD) ).

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_equalityI,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
       => V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_equalityI) ).

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_subsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subsetD) ).

fof(fact_empty__subsetI,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_empty__subsetI) ).

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))
     => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2))
       => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2))
         => hBOOL(hAPP(hAPP(hAPP(hAPP(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_evaln_OWhileFalse,axiom,
    ! [V_n_2,V_c_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(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__elim__cases_I5_J,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
         => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
       => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
           => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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))
     => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(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))
     => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ),
    file('theBenchmark.p',fact_evaln_OIfFalse) ).

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

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

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

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_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_INF__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_INF__subset) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_lessThan__subset__iff) ).

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

fof(fact_equalityE,axiom,
    ! [T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_equalityE) ).

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_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_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_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_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_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_subset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_subset__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__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_predicate1D,axiom,
    ! [V_x_2,V_Q_2,V_P_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_predicate1D) ).

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

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

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_equalityD2,axiom,
    ! [T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_equalityD2) ).

fof(fact_equalityD1,axiom,
    ! [T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_equalityD1) ).

fof(fact_rev__predicate1D,axiom,
    ! [V_Q_2,T_a,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate1D) ).

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

fof(fact_set__eq__subset,axiom,
    ! [T_a,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__eq__subset) ).

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

fof(fact_subset__refl,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)),
    file('theBenchmark.p',fact_subset__refl) ).

fof(fact_SUP__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_SUP__subset) ).

fof(fact_Union__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Union__mono) ).

fof(fact_Inter__anti__mono,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_card__lessThan,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2,
    file('theBenchmark.p',fact_card__lessThan) ).

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

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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
      <=> ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
      <=> ( V_x_2 != V_y_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_linorder__not__less) ).

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

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

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

fof(fact_add__le__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,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_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_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_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__left) ).

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

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

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

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

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

fof(fact_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_diff__eq__diff__less__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_subset__empty,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__empty) ).

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

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

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

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

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

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

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

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

fof(fact_le__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_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_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_le__sup__iff) ).

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

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

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

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

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

fof(fact_rev__finite__subset,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_finite__subset,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__subset) ).

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

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

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

fof(fact_le__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_le__infI) ).

fof(fact_inf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_inf__absorb2) ).

fof(fact_inf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_inf__absorb1) ).

fof(fact_le__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI2) ).

fof(fact_le__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI1) ).

fof(fact_le__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_le__inf__iff) ).

fof(fact_le__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_le__iff__inf) ).

fof(fact_inf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__le2) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_inf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_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_insert__mono,axiom,
    ! [V_a_2,V_D_2,V_C_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ),
    file('theBenchmark.p',fact_insert__mono) ).

fof(fact_subset__insertI2,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_subset__insertI2) ).

fof(fact_subset__insertI,axiom,
    ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_subset__insertI) ).

fof(fact_subset__UNIV,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_subset__UNIV) ).

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

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

fof(fact_Un__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),
    file('theBenchmark.p',fact_Un__upper1) ).

fof(fact_Int__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__lower1) ).

fof(fact_double__diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Diff__subset) ).

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

fof(fact_Sup__le__iff,axiom,
    ! [V_b_2,V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__le__iff) ).

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

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

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

fof(fact_thin,axiom,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,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_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ),
    file('theBenchmark.p',fact_weaken) ).

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

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] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
    <=> ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(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] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
    <=> ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(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_le__Inf__iff,axiom,
    ! [V_A_2,V_b_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ),
    file('theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_vimage__mono,axiom,
    ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_vimage__mono) ).

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

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

fof(fact_subset__psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubset__eq) ).

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_pred__subset__eq,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_fold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__belowI) ).

fof(fact_below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_SUP__le__iff,axiom,
    ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_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_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
    file('theBenchmark.p',fact_SUP__le__iff) ).

fof(fact_UN__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ),
    file('theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_le__INF__iff,axiom,
    ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_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_a),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_b,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_lessThan__iff,axiom,
    ! [V_k_2,V_i_2,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_lessThan__iff) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [V_n_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_lessThan__strict__subset__iff,axiom,
    ! [V_n_2,V_m_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(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_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

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

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

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [V_y_2,V_x_2,T_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_x_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
          <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
              & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_mult__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Olinordered__ring__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_2),V_b_2)),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(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_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__mult__iff) ).

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

fof(fact_add__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_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_le__iff__diff__le__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_le__iff__diff__le__0) ).

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

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

fof(fact_insert__subset,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__insert) ).

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

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

fof(fact_subset__singletonD,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
     => ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_subset__singletonD) ).

fof(fact_finite__surj,axiom,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a,T_b,V_f_2),V_A_2)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__surj) ).

fof(fact_image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,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_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))),
    file('theBenchmark.p',fact_image__Int__subset) ).

fof(fact_Sup__upper,axiom,
    ! [V_A_2,V_x_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ),
    file('theBenchmark.p',fact_Sup__upper) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    file('theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_image__diff__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,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_image__diff__subset) ).

fof(fact_Diff__subset__conv,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
    file('theBenchmark.p',fact_Diff__partition) ).

fof(fact_Inf__lower,axiom,
    ! [V_A_2,V_x_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Inf__lower) ).

fof(fact_image__vimage__subset,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)),
    file('theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_Union__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))),
    file('theBenchmark.p',fact_Union__Int__subset) ).

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

fof(fact_fold1__singleton__def,axiom,
    ! [V_a_2,V_f_2,T_a,V_g_2] :
      ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
     => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_fold1__singleton,axiom,
    ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2,
    file('theBenchmark.p',fact_fold1__singleton) ).

fof(fact_Inter__Un__subset,axiom,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Inter__Un__subset) ).

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

fof(fact_le__SUPI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ),
    file('theBenchmark.p',fact_le__SUPI) ).

fof(fact_INF__leI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
    file('theBenchmark.p',fact_INF__leI) ).

fof(fact_UN__upper,axiom,
    ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UN__upper) ).

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

fof(fact_INT__lower,axiom,
    ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_INT__lower) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_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(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_single__Diff__lessThan,axiom,
    ! [V_k_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold) ).

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

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

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

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

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

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

fof(fact_mult__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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).

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

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__squares__le__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_le__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( class_Rings_Oordered__ring(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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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_a] :
      ( class_Rings_Oordered__ring(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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
      <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

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

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_fold1__def,axiom,
    ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)),
    file('theBenchmark.p',fact_fold1__def) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_Sup__fin_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_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_diff__single__insert,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),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_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_setsum__diff,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff) ).

fof(fact_card__Diff__subset,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_card__psubset,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__psubset) ).

fof(fact_triple__valid__def,axiom,
    ! [V_t_2,V_n_2,T_a] :
      ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
    <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ),
    file('theBenchmark.p',fact_triple__valid__def) ).

fof(fact_setsum__diff__nat,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_Inf__le__Sup,axiom,
    ! [V_A_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_fold1__insert__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_fold1__Un2,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un2) ).

fof(fact_evaln_Oequations_I9_J,axiom,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2))
    <=> hBOOL(hAPP(hAPP(hAPP(hAPP(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_fold1__eq__fold__idem,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold__idem) ).

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_semilattice__big_OF__eq,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_evaln__elim__cases_I6_J,axiom,
    ! [V_s1,V_n,V_s,V_P] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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)
           => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_setsum__mono2,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
      ( class_Groups_Oordered__comm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_b] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono2) ).

fof(fact_flat__lub__def,axiom,
    ! [V_b_2,V_A_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) ),
    file('theBenchmark.p',fact_flat__lub__def) ).

fof(fact_arith__series__general,axiom,
    ! [V_n_2,V_d_2,V_a_2,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),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_fold1__in,axiom,
    ! [V_A_2,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__in) ).

fof(fact_setsum__mono3,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono3) ).

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

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_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_int__eq__0__conv,axiom,
    ! [V_n_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__eq__0__conv) ).

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

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

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

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

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

fof(fact_of__nat__le__iff,axiom,
    ! [V_n_2,V_m_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_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_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_le__0__eq,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_le__0__eq) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_termination__basic__simps_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_le__add2,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
    file('theBenchmark.p',fact_le__add2) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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_int__setsum,axiom,
    ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setsum) ).

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_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_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_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_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_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_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_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__less__iff) ).

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

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

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

fof(fact_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_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_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_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_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_less__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_less__diff__iff) ).

fof(fact_diff__less__mono,axiom,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_diff__less__mono) ).

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_Ints__of__nat,axiom,
    ! [V_n_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ),
    file('theBenchmark.p',fact_Ints__of__nat) ).

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_of__nat__setsum,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setsum) ).

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_card__insert__le,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ),
    file('theBenchmark.p',fact_card__insert__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_card__mono,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__mono) ).

fof(fact_card__seteq,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),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_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ),
    file('theBenchmark.p',fact_card__image__le) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_nat__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_setsum__constant,axiom,
    ! [V_A_2,V_y_2,T_b,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ),
    file('theBenchmark.p',fact_setsum__constant) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [V_n_2,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(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_nat__less__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff1) ).

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

fof(fact_diff__card__le__card__Diff,axiom,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
    file('theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_card__Diff1__le,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ),
    file('theBenchmark.p',fact_card__Diff1__le) ).

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

fof(fact_setsum__bounded,axiom,
    ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
      ( ( class_Rings_Osemiring__1(T_b)
        & class_Groups_Oordered__ab__semigroup__add(T_b) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_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_a),V_A_2))),V_K_2))) ) ),
    file('theBenchmark.p',fact_setsum__bounded) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,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_ord_OgreaterThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,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_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_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_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_zle__antisym,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
       => V_z = V_w ) ),
    file('theBenchmark.p',fact_zle__antisym) ).

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

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

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

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

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

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

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

fof(fact_zadd__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_zless__imp__add1__zle,axiom,
    ! [V_z,V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
    file('theBenchmark.p',fact_zless__imp__add1__zle) ).

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

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

fof(fact_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_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_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_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_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_pos__zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

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

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

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

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

fof(fact_int__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_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_of__nat__aux_Osimps_I1_J,axiom,
    ! [V_i_2,V_inc_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,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_of__nat__aux_Osimps_I2_J,axiom,
    ! [V_i_2,V_n_2,V_inc_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,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_zdiff__int__split,axiom,
    ! [V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) ) ),
    file('theBenchmark.p',fact_zdiff__int__split) ).

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

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

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

fof(fact_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_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_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_transfer__int__nat__relations_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_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_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_transfer__nat__int__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).

fof(fact_transfer__nat__int__set__relations_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_transfer__int__nat__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_Nat__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_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_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_transfer__nat__int__set__relations_I1_J,axiom,
    ! [V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_transfer__int__nat__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_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_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

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

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

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

fof(fact_ord_OatMost__iff,axiom,
    ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,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_OlessThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,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_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_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_Powp__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ),
    file('theBenchmark.p',fact_Powp__mono) ).

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_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_atLeastLessThan__inj_I2_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
           => V_b_2 = V_d_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
           => V_a_2 = V_c_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,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__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_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_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_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_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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_ivl__disj__un_I17_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_ivl__diff,axiom,
    ! [V_m_2,V_n_2,V_i_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,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_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).

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_setsum__add__nat__ivl,axiom,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( 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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),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_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( 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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),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_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_UN__UN__finite__eq,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_ivl__disj__un_I8_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [V_k_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( 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_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_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_setsum__op__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( ( ~ 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_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a) ) ) ),
    file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).

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_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_all__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_UN__finite2__subset,axiom,
    ! [V_B_2,V_k_2,V_A_2,T_a] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a] :
      ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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_a,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_a] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_ivl__disj__un_I3_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).

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__atLeastLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__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_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_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_greaterThanLessThan__empty,axiom,
    ! [V_k_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanLessThan__empty) ).

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__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_ivl__disj__int_I9_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).

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_ivl__disj__un_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b)
           => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
             => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
           => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

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_sum__diff__distrib,axiom,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ),
    file('theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( ( ~ 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_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) )
        & ( 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_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a),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_finite__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_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_greaterThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_greaterThan__eq__iff) ).

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_ivl__disj__un_I22_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,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_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_setsum__head,axiom,
    ! [V_P_2,V_n_2,V_m_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( 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_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head) ).

fof(fact_all__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less) ).

fof(fact_ex__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less) ).

fof(fact_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_ivl__disj__un_I5_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_H,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a_2 = V_b_2
       => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I19_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_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_greaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_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_greaterThan__iff,axiom,
    ! [V_k_2,V_i_2,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__subset__iff) ).

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_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_ivl__disj__un_I21_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2))
          & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).

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_setsum__head__Suc,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( 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_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_ivl__disj__int_I10_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_greaterThan__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_greaterThan__Suc) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( ( ~ 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_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a) ) ) ),
    file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( 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_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_ivl__disj__un_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_gauss__sum,axiom,
    ! [V_n_2,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),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_gauss__sum) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_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_I12_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_decr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_hom__fold1__commute,axiom,
    ! [V_N_2,V_h_2,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_incr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_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_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_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_atLeast__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_atMost__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atMost__eq__iff) ).

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

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

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

fof(fact_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_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_card__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_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_atMost__Int__atLeast,axiom,
    ! [V_n_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atMost__Int__atLeast) ).

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_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_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_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_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_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_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_nat__0__iff,axiom,
    ! [V_i_2] :
      ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_nat__0__iff) ).

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

fof(fact_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_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_atLeast__iff,axiom,
    ! [V_k_2,V_i_2,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_atLeast__iff) ).

fof(fact_atMost__iff,axiom,
    ! [V_k_2,V_i_2,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_atMost__iff) ).

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

fof(fact_nat__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_nat__0__le,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_nat__0__le) ).

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

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

fof(fact_zless__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_atMost__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_atLeast__subset__iff) ).

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_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_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_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [V_A_2,V_f_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_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_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_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__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_split__nat,axiom,
    ! [V_i_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [B_n] :
            ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
           => hBOOL(hAPP(V_P_2,B_n)) ) ) ),
    file('theBenchmark.p',fact_split__nat) ).

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

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

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

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

fof(fact_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__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_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),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_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_setsum__atMost__Suc,axiom,
    ! [V_n_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_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_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_ivl__disj__un_I14_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I14_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_ivl__disj__int_I8_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).

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_ivl__disj__un_I9_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_UN__le__add__shift,axiom,
    ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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_ivl__disj__int_I3_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).

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_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_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_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_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_ivl__disj__un_I2_J,axiom,
    ! [V_u_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ),
    file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [V_u_2,V_l_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).

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

fof(fact_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_aset_I6_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I6_J) ).

fof(fact_bset_I8_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I8_J) ).

fof(fact_aset_I4_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_aset_I4_J) ).

fof(fact_bset_I4_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_bset_I4_J) ).

fof(fact_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_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_bset_I3_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_bset_I3_J) ).

fof(fact_aset_I3_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_aset_I3_J) ).

fof(fact_aset_I5_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_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__int__nat__set__function__closures_I2_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_nat__set__def,axiom,
    ! [V_S_2] :
      ( c_Nat__Transfer_Onat__set(V_S_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    file('theBenchmark.p',fact_nat__set__def) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
    ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( V_A_2 = V_B_2
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_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_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_transfer__int__nat__set__relations_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_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_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_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__sum__prod_I1_J,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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_bset_I7_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I7_J) ).

fof(fact_aset_I8_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I8_J) ).

fof(fact_bset_I6_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I6_J) ).

fof(fact_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_periodic__finite__ex,axiom,
    ! [V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x,B_k] :
            ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
       => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        <=> ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) ) ) ),
    file('theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_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_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_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_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_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_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_aset_I7_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I7_J) ).

fof(fact_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_ex__least__nat__less,axiom,
    ! [V_n_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_P_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
            & ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
               => ~ hBOOL(hAPP(V_P_2,B_i)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_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_setsum__mono__zero__right,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_finite__subset__induct,axiom,
    ! [V_P_2,V_A_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
       => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
         => ( ! [B_a,B_F] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
               => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
                   => ( hBOOL(hAPP(V_P_2,B_F))
                     => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
           => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ),
    file('theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [V_a_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_inj__vimage__singleton) ).

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_inj__on__empty,axiom,
    ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__on__empty) ).

fof(fact_setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_b,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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),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_b,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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_abs__of__nat,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_abs__of__nat) ).

fof(fact_abs__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__eq__0,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_abs__eq__0) ).

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_inj__fun,axiom,
    ! [T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__fun) ).

fof(fact_inj__on__contraD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( V_x_2 != V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_a),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_inj__on__iff,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),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__onD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,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_a),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
           => V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_inj__onD) ).

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_inj__on__def,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),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__on__id2,axiom,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2),
    file('theBenchmark.p',fact_inj__on__id2) ).

fof(fact_inj__on__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_inj__on__diff) ).

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__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_inj__on__imageI2,axiom,
    ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_inj__on__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
       => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__on__Int) ).

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__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_inj__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,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_subset__inj__on,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
       => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_subset__inj__on) ).

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_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_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_abs__setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setsum__abs) ).

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_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_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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__not__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [V_a_2,T_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)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_zero__less__abs__iff) ).

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

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

fof(fact_finite__imageD,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
     => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__imageD) ).

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

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
      <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__inj__on,axiom,
    ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
       => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on) ).

fof(fact_inj__on__imageI,axiom,
    ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_inj__comp,axiom,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
       => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_inj__comp) ).

fof(fact_card__image,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ),
    file('theBenchmark.p',fact_card__image) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_inj__on__strict__subset) ).

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_inj__of__nat,axiom,
    ! [T_a] :
      ( class_Nat_Osemiring__char__0(T_a)
     => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__of__nat) ).

fof(fact_inj__int,axiom,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__int) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      <=> hBOOL(hAPP(hAPP(c_member(T_a),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_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_abs__mult__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_abs__mult__pos) ).

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

fof(fact_inj__on__iff__surj,axiom,
    ! [V_A_H_2,T_b,T_a,V_A_2] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
     => ( ? [B_f] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2))
            & c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) )
      <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_a,T_a,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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2))
       => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
         => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
       => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).

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

fof(fact_abs__triangle__ineq4,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_inj__on__image__Int,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_image__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__Int) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
       => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__set__diff) ).

fof(fact_setsum__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ),
    file('theBenchmark.p',fact_setsum__reindex) ).

fof(fact_pigeonhole,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
     => ~ c_Fun_Oinj__on(T_b,T_a,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_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_finite__vimageI,axiom,
    ! [V_h_2,T_b,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,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_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_inj__vimage__image__eq) ).

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_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_inj__singleton,axiom,
    ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__singleton) ).

fof(fact_setsum_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_card__bij__eq,axiom,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,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_a,T_b,V_f_2),V_A_2)),V_B_2))
       => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
               => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ),
    file('theBenchmark.p',fact_card__bij__eq) ).

fof(fact_vimage__subsetI,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ),
    file('theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_inj__on__insert,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
        & c_Fun_Oinj__on(T_a,T_b,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_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
        & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__Un) ).

fof(fact_card__inj__on__le,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,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_a,T_b,V_f_2),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(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_fold__image__reindex,axiom,
    ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( c_Fun_Oinj__on(T_a,T_b,V_h_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(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__reindex) ).

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_folding__image_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
     => ( 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(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_image__INT,axiom,
    ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
         => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,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_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_image__INT) ).

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_the__inv__into__comp,axiom,
    ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))
     => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))))
         => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_the__inv__into__into,axiom,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__into) ).

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_b,T_a] :
      ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),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_the__inv__into__f__f,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Fun_Othe__inv__into(T_a,T_b,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_the__inv__into__f__eq,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( hAPP(V_f_2,V_x_2) = V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,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_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_the__inv__f__f,axiom,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,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_the__inv__into__def,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))),
    file('theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
       => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ),
    file('theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => ( 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_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).

fof(fact_inj__on__Inter,axiom,
    ! [V_f_2,T_b,T_a,V_S_2] :
      ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [B_A] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
           => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
       => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,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_a] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Inter__subset) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_int__val__lemma) ).

fof(fact_inj__on__INTER,axiom,
    ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
      ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
           => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_inj__on__INTER) ).

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

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

fof(fact_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_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_CollectI,axiom,
    ! [T_a,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    file('theBenchmark.p',fact_CollectI) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [V_Q_2,V_P_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_empty__Collect__eq,axiom,
    ! [V_P_2,T_a] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [V_P_2,T_a] :
      ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_Collect__empty__eq) ).

fof(fact_Collect__def,axiom,
    ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2,
    file('theBenchmark.p',fact_Collect__def) ).

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

fof(fact_mem__Collect__eq,axiom,
    ! [V_P_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
    <=> hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_CollectD,axiom,
    ! [V_P_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectD) ).

fof(fact_CollectE,axiom,
    ! [V_P_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectE) ).

fof(fact_empty__def,axiom,
    ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)),
    file('theBenchmark.p',fact_empty__def) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [V_Q_2,V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ),
    file('theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_insert__Collect,axiom,
    ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    file('theBenchmark.p',fact_insert__Collect) ).

fof(fact_UNIV__def,axiom,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)),
    file('theBenchmark.p',fact_UNIV__def) ).

fof(fact_Collect__disj__eq,axiom,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    file('theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__conj__eq,axiom,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    file('theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)),
    file('theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_insert__compr__raw,axiom,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr) ).

fof(fact_Un__def,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    file('theBenchmark.p',fact_Un__def) ).

fof(fact_Int__def,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    file('theBenchmark.p',fact_Int__def) ).

fof(fact_Int__Collect,axiom,
    ! [V_P_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))))
    <=> ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__Collect) ).

fof(fact_Collect__conv__if,axiom,
    ! [T_a,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_Collect__conv__if2,axiom,
    ! [T_a,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_singleton__conv,axiom,
    ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv) ).

fof(fact_singleton__conv2,axiom,
    ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv2) ).

fof(fact_set__diff__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))),
    file('theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__not,axiom,
    ! [V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_insert__def,axiom,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    file('theBenchmark.p',fact_insert__def) ).

fof(fact_vimage__def,axiom,
    ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__def) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    file('theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ),
    file('theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_if__image__distrib,axiom,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))),
    file('theBenchmark.p',fact_if__image__distrib) ).

fof(fact_Collect__all__eq,axiom,
    ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Collect__all__eq) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [V_n_2,V_f_2,T_a,V_A_2] :
      ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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_a),V_A_2)) ),
    file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_setsum__image__gen,axiom,
    ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_dom__if,axiom,
    ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))),
    file('theBenchmark.p',fact_dom__if) ).

fof(fact_dom__override__on,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))),
    file('theBenchmark.p',fact_dom__override__on) ).

fof(fact_setsum__multicount,axiom,
    ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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),V_T_2))
             => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_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_b),V_T_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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),V_t_2))
             => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [V_Q_2,T_b,V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2)))))
      <=> ! [B_y] :
            ( hBOOL(hAPP(V_P_2,B_y))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_finite__image__set,axiom,
    ! [V_f_2,T_b,V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,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_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ),
    file('theBenchmark.p',fact_finite__image__set) ).

fof(fact_override__on__apply__in,axiom,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_a,T_b,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__apply__notin,axiom,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_a,T_b,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__emptyset,axiom,
    ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2,
    file('theBenchmark.p',fact_override__on__emptyset) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_override__on__def,axiom,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_a,T_b,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_a),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_a,T_b,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_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_add__Min__commute,axiom,
    ! [V_k_2,V_N_2,T_a] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Min__commute) ).

fof(fact_add__Max__commute,axiom,
    ! [V_k_2,V_N_2,T_a] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Max__commute) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
    <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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_pigeonhole__infinite,axiom,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
       => ? [B_x] :
            ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_pigeonhole__infinite) ).

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_not__neg__0,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__0) ).

fof(fact_not__neg__int,axiom,
    ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    file('theBenchmark.p',fact_not__neg__int) ).

fof(fact_not__neg__1,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__1) ).

fof(fact_Min_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Max_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [V_x_2] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    file('theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_neg__def,axiom,
    ! [V_Z_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_neg__def) ).

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

fof(fact_not__neg__nat,axiom,
    ! [V_z] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_not__neg__nat) ).

fof(fact_Max__ge,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Max__ge) ).

fof(fact_Min__le,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_Min__le) ).

fof(fact_Max__in,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__in) ).

fof(fact_Min__in,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__in) ).

fof(fact_Min__antimono,axiom,
    ! [V_N_2,V_M_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ),
    file('theBenchmark.p',fact_Min__antimono) ).

fof(fact_Max__mono,axiom,
    ! [V_N_2,V_M_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ),
    file('theBenchmark.p',fact_Max__mono) ).

fof(fact_Min_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oremove) ).

fof(fact_setsum__cases,axiom,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),V_P_2)),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_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ),
    file('theBenchmark.p',fact_setsum__cases) ).

fof(fact_setprod_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_card__partition,axiom,
    ! [V_k_2,V_C_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
       => ( ! [B_c] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
             => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
         => ( ! [B_c1] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
               => ! [B_c2] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
                   => ( B_c1 != B_c2
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ),
    file('theBenchmark.p',fact_card__partition) ).

fof(fact_inj__uminus,axiom,
    ! [V_A_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ),
    file('theBenchmark.p',fact_inj__uminus) ).

fof(fact_ComplI,axiom,
    ! [V_A_2,V_c_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_ComplI) ).

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

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_inf__min,axiom,
    ! [T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Lattices_Osemilattice__inf(T_a) )
     => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ),
    file('theBenchmark.p',fact_inf__min) ).

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__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__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_Compl__anti__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).

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_of__nat__setprod,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( ( class_Rings_Osemiring__1(T_a)
        & class_Groups_Ocomm__monoid__mult(T_a) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),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_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setprod) ).

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_minus__max__eq__min,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_minus__max__eq__min) ).

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

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

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

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

fof(fact_double__complement,axiom,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_double__complement) ).

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_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_uminus__apply,axiom,
    ! [V_x_2,V_A_2,T_b,T_a] :
      ( class_Groups_Ouminus(T_a)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_uminus__apply) ).

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_Compl__eq__Compl__iff,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)
    <=> V_A_2 = V_B_2 ),
    file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_compl__eq__compl__iff) ).

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_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_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_fun__Compl__def,axiom,
    ! [V_x_2,V_A_2,T_b,T_a] :
      ( class_Groups_Ouminus(T_a)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__Compl__def) ).

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

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

fof(fact_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__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__less__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__less__iff__conj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__conj) ).

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

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

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

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

fof(fact_less__max__iff__disj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_less__max__iff__disj) ).

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

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

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

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

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

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

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

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

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

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__le__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,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_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__le__iff__disj) ).

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

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_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_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_compl__le__compl__iff) ).

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

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

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

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

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_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_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_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__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_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_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_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__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,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_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).

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

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

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_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_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Compl__iff,axiom,
    ! [V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplE) ).

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_square__eq__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),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_minus__add__distrib,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__add__distrib) ).

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

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

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

fof(fact_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__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_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_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_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_vimage__Compl,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),
    file('theBenchmark.p',fact_vimage__Compl) ).

fof(fact_setprod__timesf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setprod__timesf) ).

fof(fact_setprod__1,axiom,
    ! [V_A_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_setprod__1) ).

fof(fact_abs__setprod,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setprod) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_setsum__negf,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__negf) ).

fof(fact_Collect__neg__eq,axiom,
    ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),
    file('theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [V_A_2,V_f_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Rings_Ocomm__semiring__1(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b)
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_setprod__zero) ).

fof(fact_setprod__zero__iff,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( ( class_Rings_Ono__zero__divisors(T_b)
        & class_Rings_Ocomm__semiring__1(T_b) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
        <=> ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b)
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_setprod__empty,axiom,
    ! [V_f_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oempty,axiom,
    ! [V_g_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ),
    file('theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ),
    file('theBenchmark.p',fact_setprod__infinite) ).

fof(fact_setprod__eq__1__iff,axiom,
    ! [V_f_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,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_a),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_neg__0__le__iff__le,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_neg__0__le__iff__le) ).

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

fof(fact_neg__le__0__iff__le,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),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_2)) ) ),
    file('theBenchmark.p',fact_neg__le__0__iff__le) ).

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

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

fof(fact_neg__less__0__iff__less,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),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_2)) ) ),
    file('theBenchmark.p',fact_neg__less__0__iff__less) ).

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

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

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

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

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

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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_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_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

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

fof(fact_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_square__eq__1__iff,axiom,
    ! [V_x_2,T_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
      <=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
          | V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_square__eq__1__iff) ).

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

fof(fact_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__top__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__top__eq) ).

fof(fact_compl__bot__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__bot__eq) ).

fof(fact_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_compl__sup__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__sup__top) ).

fof(fact_sup__compl__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__compl__top) ).

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

fof(fact_abs__le__iff,axiom,
    ! [V_b_2,V_a_2,T_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_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__le__iff) ).

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

fof(fact_abs__le__D2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ),
    file('theBenchmark.p',fact_abs__le__D2) ).

fof(fact_abs__less__iff,axiom,
    ! [V_b_2,V_a_2,T_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_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__less__iff) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_finite__compl,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__compl) ).

fof(fact_Compl__disjoint2,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__disjoint,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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_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_Compl__partition2,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition2) ).

fof(fact_Compl__partition,axiom,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition) ).

fof(fact_Compl__Un,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Un) ).

fof(fact_Compl__Int,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Int) ).

fof(fact_image__uminus__atLeastAtMost,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Diff__eq) ).

fof(fact_Diff__Compl,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__Compl) ).

fof(fact_setprod_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_Ints__minus,axiom,
    ! [V_a_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ),
    file('theBenchmark.p',fact_Ints__minus) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_Compl__eq,axiom,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),
    file('theBenchmark.p',fact_Compl__eq) ).

fof(fact_Compl__lessThan,axiom,
    ! [V_k_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ),
    file('theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_Compl__atLeast,axiom,
    ! [V_k_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Collect__imp__eq,axiom,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    file('theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_Compl__greaterThan,axiom,
    ! [V_k_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ),
    file('theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atMost,axiom,
    ! [V_k_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atMost) ).

fof(fact_Compl__INT,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__UN) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [V_f_2,V_S_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a,tc_Nat_Onat),V_f_2),V_S_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),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__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,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_b,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
         => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__reindex__cong) ).

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_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_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_setprod__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ),
    file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ),
    file('theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_Max_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [V_d_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [V_d_2,V_c_2,V_b_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [V_d_2,V_c_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Max_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_Min_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__atMost,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_setprod__insert,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setprod_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_setprod_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_setprod_Oeq__fold) ).

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_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_min__max_Osup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_fold1__below__iff,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_Max__insert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__insert) ).

fof(fact_Min__insert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__insert) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ),
    file('theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_Max__Un,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Max__Un) ).

fof(fact_Min__Un,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Min__Un) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_vimage__if,axiom,
    ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ),
    file('theBenchmark.p',fact_vimage__if) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_Max_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Min_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_fold1__antimono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_fold1__antimono) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [V_S_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [V_S_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_dual__min,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ),
    file('theBenchmark.p',fact_dual__min) ).

fof(fact_dual__max,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ),
    file('theBenchmark.p',fact_dual__max) ).

fof(fact_max__ord__max,axiom,
    ! [T_a] :
      ( class_Orderings_Oord(T_a)
     => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ),
    file('theBenchmark.p',fact_max__ord__max) ).

fof(fact_min__ord__min,axiom,
    ! [T_a] :
      ( class_Orderings_Oord(T_a)
     => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ),
    file('theBenchmark.p',fact_min__ord__min) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

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

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

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

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

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

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

fof(fact_nat__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_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_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_min__max_OSup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

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_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_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

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_min__max_OSup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [V_f_2,V_A_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),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__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

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_min__max_OInf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_Max_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Min_Oclosed,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_setprod__gen__delta,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__gen__delta) ).

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_setprod__diff1,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) )
            & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setprod__diff1) ).

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_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_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_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_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

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

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

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

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_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_divide__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__zero__left) ).

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

fof(fact_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

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

fof(fact_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_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_setsum__divide__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
      ( class_Fields_Ofield(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ),
    file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
        <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ),
    file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).

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

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

fof(fact_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_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
        <=> 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_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_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_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_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_Ints__power,axiom,
    ! [V_n_2,V_a_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
       => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ),
    file('theBenchmark.p',fact_Ints__power) ).

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

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

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

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

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

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

fof(fact_of__int__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_setprod__dividef,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__dividef) ).

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_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_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_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_Ints__of__int,axiom,
    ! [V_z_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ),
    file('theBenchmark.p',fact_Ints__of__int) ).

fof(fact_geometric__sum,axiom,
    ! [V_n_2,V_x_2,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ),
    file('theBenchmark.p',fact_geometric__sum) ).

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__int__setsum,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setsum) ).

fof(fact_setprod__constant,axiom,
    ! [V_y_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__constant) ).

fof(fact_of__int__setprod,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( ( class_Rings_Oring__1(T_a)
        & class_Groups_Ocomm__monoid__mult(T_a) )
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setprod) ).

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_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_of__int__0__le__iff,axiom,
    ! [V_z_2,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(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_of__int__le__0__iff,axiom,
    ! [V_z_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> 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__less__iff,axiom,
    ! [V_z_2,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)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> 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_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_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_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_one__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
    file('theBenchmark.p',fact_one__less__power) ).

fof(fact_power__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_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_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_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_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_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__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__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_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_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_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__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_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_a] :
      ( ( class_Rings_Ozero__neq__one(T_a)
        & class_Rings_Ono__zero__divisors(T_a)
        & class_Rings_Omult__zero(T_a)
        & class_Power_Opower(T_a) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    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_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_2))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_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_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_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_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__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,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_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_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,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_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_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_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__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__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_le__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_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_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_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_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__le__eq) ).

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__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__divide__divide,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_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_zero__le__divide__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(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_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__0__iff) ).

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

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

fof(fact_zero__less__divide__iff,axiom,
    ! [V_b_2,V_a_2,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)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),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_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),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_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_eq__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq) ).

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

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

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

fof(fact_frac__eq__eq,axiom,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_frac__eq__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_divide__strict__left__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).

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

fof(fact_neg__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
    file('theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_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_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_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_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq) ).

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_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_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_setprod__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un) ).

fof(fact_card__Pow,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),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_a),V_A_2)) ),
    file('theBenchmark.p',fact_card__Pow) ).

fof(fact_power__power__power,axiom,
    ! [T_a] :
      ( class_Power_Opower(T_a)
     => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ),
    file('theBenchmark.p',fact_power__power__power) ).

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_PowI,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ),
    file('theBenchmark.p',fact_PowI) ).

fof(fact_zdiv__zminus2,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b),
    file('theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),
    file('theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_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_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_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_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_Pow__top,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))),
    file('theBenchmark.p',fact_Pow__top) ).

fof(fact_image__Pow__surj,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
     => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ),
    file('theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_Union__Pow__eq,axiom,
    ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_Cantors__paradox,axiom,
    ! [V_A_2,T_a] :
      ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2),
    file('theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_Pow__not__empty,axiom,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Pow__INT__eq,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)),
    file('theBenchmark.p',fact_Pow__INT__eq) ).

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_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_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__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__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__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__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__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_Pow__bottom,axiom,
    ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))),
    file('theBenchmark.p',fact_Pow__bottom) ).

fof(fact_PowD,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Pow__iff) ).

fof(fact_Pow__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ),
    file('theBenchmark.p',fact_Pow__mono) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_zdiv__mono1,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_zdiv__mono2,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [V_i_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_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_Pow__def,axiom,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Pow__def) ).

fof(fact_finite__Pow__iff,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    file('theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_subset__Pow__Union,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))),
    file('theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_a,V_one_2,V_times_2),V_a_2),V_n_2)),
    file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_Pow__insert,axiom,
    ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))),
    file('theBenchmark.p',fact_Pow__insert) ).

fof(fact_Pow__UNIV,axiom,
    ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__UNIV) ).

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__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__add__self2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self2) ).

fof(fact_div__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_UN__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_Pow__Int__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ),
    file('theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_Pow__Compl,axiom,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))),
    file('theBenchmark.p',fact_Pow__Compl) ).

fof(fact_Pow__empty,axiom,
    ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_Pow__empty) ).

fof(fact_Un__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ),
    file('theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_split__zdiv) ).

fof(fact_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_min__max_OSup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ohom__commute) ).

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

fof(fact_div__mult__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_nat__mult__div__cancel1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel1) ).

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

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

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

fof(fact_split__div,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

fof(fact_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_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_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_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_split__div_H,axiom,
    ! [V_n_2,V_m_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_split__div_H) ).

fof(fact_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_Min_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ohom__commute) ).

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_strong__setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).

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_setprod__mono__one__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__mono__one__right) ).

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_transfer__nat__int__sum__prod__cong_I2_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
      ( ( class_Groups_Ocomm__monoid__mult(T_a)
        & class_Groups_Ocomm__monoid__add(T_a) )
     => ( 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_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_split__pos__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_split__neg__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_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_zmod__zminus2,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
    file('theBenchmark.p',fact_zmod__zminus2) ).

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

fof(fact_mod__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_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_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_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_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_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_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_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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_mod__mult__self2__is__0,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_mod__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__by__1) ).

fof(fact_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_zmod__le__nonneg__dividend,axiom,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ),
    file('theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

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

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

fof(fact_zmod__eq__0__iff,axiom,
    ! [V_d_2,V_m_2] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
    file('theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_zmod__zminus2__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(fact_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_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_div__mod__equality,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality) ).

fof(fact_div__mod__equality2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_mod__div__equality,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__equality2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ),
    file('theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

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

fof(fact_neg__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__mod__conj) ).

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

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

fof(fact_pos__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ),
    file('theBenchmark.p',fact_pos__mod__conj) ).

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

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

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

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

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

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

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

fof(fact_sgn__1__pos,axiom,
    ! [V_a_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = 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_2)) ) ),
    file('theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [V_y,V_q_1,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_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_split__zmod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__zmod) ).

fof(fact_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_zdiv__zminus2__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

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

fof(fact_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__1__neg,axiom,
    ! [V_a_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = 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_2),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_sgn__1__neg) ).

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_setprod__pos__nat,axiom,
    ! [V_f_2,V_S_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
    file('theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
       => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ),
    file('theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_fold__image__1,axiom,
    ! [V_f_2,V_S_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
             => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_fold__image__1) ).

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_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__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__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_quotient__empty,axiom,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,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_a] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty) ).

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

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

fof(fact_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_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_mod__if,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ),
    file('theBenchmark.p',fact_mod__if) ).

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

fof(fact_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_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_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_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_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_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_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_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_mod__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)),
    file('theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_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_quotient__diff1,axiom,
    ! [V_a_2,V_A_2,V_r_2,T_a] :
      ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ),
    file('theBenchmark.p',fact_quotient__diff1) ).

fof(fact_mod__lemma,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_mod__lemma) ).

fof(fact_split__mod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_j)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__mod) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_Suc__times__mod__eq) ).

fof(fact_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_quotient__def,axiom,
    ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_quotient__def) ).

fof(fact_singleton__quotient,axiom,
    ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__quotient) ).

fof(fact_quotientI,axiom,
    ! [V_r_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ),
    file('theBenchmark.p',fact_quotientI) ).

fof(fact_card_Oneutral,axiom,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_card_Oneutral) ).

fof(fact_Image__eq__UN,axiom,
    ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,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))))),
    file('theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_Image__INT__subset,axiom,
    ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))),
    file('theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_Image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))),
    file('theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_Image__UN,axiom,
    ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)),
    file('theBenchmark.p',fact_Image__UN) ).

fof(fact_Image__empty,axiom,
    ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Image__empty) ).

fof(fact_Image__mono,axiom,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_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_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_Image__mono) ).

fof(fact_Image__Un,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)),
    file('theBenchmark.p',fact_Image__Un) ).

fof(fact_Un__Image,axiom,
    ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Image) ).

fof(fact_quotientE,axiom,
    ! [V_r_2,V_A_2,V_X_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
     => ~ ! [B_x] :
            ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_quotientE) ).

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_min__max_Ofold__sup__le__sup,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_less__by__empty,axiom,
    ! [V_B_2,T_a,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_less__by__empty) ).

fof(fact_mod__induct__0,axiom,
    ! [V_i_2,V_P_2,V_p_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
         => ( hBOOL(hAPP(V_P_2,B_i))
           => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
     => ( hBOOL(hAPP(V_P_2,V_i_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_mod__induct__0) ).

fof(fact_InterI,axiom,
    ! [V_A_2,V_C_2,T_a] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
         => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
     => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ),
    file('theBenchmark.p',fact_InterI) ).

fof(fact_fold__image__cong,axiom,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),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_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__cong) ).

fof(fact_Max__eqI,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max__eqI) ).

fof(fact_Min__eqI,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min__eqI) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),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_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_expand__Suc,axiom,
    ! [V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_expand__Suc) ).

fof(fact_eq__number__of,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( ( class_Int_Oring__char__0(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( class_Int_Onumber(T_a)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
      <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ),
    file('theBenchmark.p',fact_number__of__reorient) ).

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_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_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_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_le__number__of__eq__not__less,axiom,
    ! [V_w_2,V_v_2,T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Int_Onumber(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ),
    file('theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_left__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
    file('theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_right__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_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_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_less__number__of,axiom,
    ! [V_y_2,V_x_2,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_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_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_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_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_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_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_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_Ints__number__of,axiom,
    ! [V_w_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ),
    file('theBenchmark.p',fact_Ints__number__of) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).

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_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_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_less__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of1) ).

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_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_divide__le__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( class_Int_Onumber(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of1) ).

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_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__number__of__odd__number__of,axiom,
    ! [V_v_2,V_w_2,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_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_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_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd__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_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_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_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_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_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_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_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_rel__simps_I34_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I34_J) ).

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

fof(fact_rel__simps_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__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_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_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_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_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_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__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_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_power__number__of__odd,axiom,
    ! [V_z_2,V_w_2,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_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_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_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd) ).

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

fof(fact_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_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_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_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_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_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_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_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_succ__Pls) ).

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

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

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

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

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

fof(fact_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_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_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_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_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_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_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_nat__1__add__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__1) ).

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

fof(fact_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_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_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_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_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_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_eq__number__of__0,axiom,
    ! [V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [V_v_2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('theBenchmark.p',fact_number__of2) ).

fof(fact_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_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_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_divide__Numeral1,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ),
    file('theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_divide__numeral__1,axiom,
    ! [V_a,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_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_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_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_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_le__special_I3_J,axiom,
    ! [V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [V_x_2,T_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_2)),c_Groups_Ozero__class_Ozero(T_a)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_less__0__number__of,axiom,
    ! [V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ),
    file('theBenchmark.p',fact_less__0__number__of) ).

fof(fact_numeral__1__eq__Suc__0,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_numeral__3__eq__3,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_numeral__3__eq__3) ).

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

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

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

fof(fact_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_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_number__of__succ,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ),
    file('theBenchmark.p',fact_number__of__succ) ).

fof(fact_number__of__pred,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__pred) ).

fof(fact_le__special_I4_J,axiom,
    ! [V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
      <=> 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_le__special_I2_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_less__special_I2_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_less__special_I4_J,axiom,
    ! [V_x_2,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_2)),c_Groups_Oone__class_Oone(T_a)))
      <=> 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_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_nat__number__of__mult__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_mult__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_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_mod__Suc__eq__mod__add3,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_div__Suc__eq__div__add3) ).

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

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

fof(fact_nat__case__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))),
    file('theBenchmark.p',fact_nat__case__number__of) ).

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

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

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

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

fof(fact_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_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_nat__case__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_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_nat__rec__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),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_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,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_eq__special_I4_J,axiom,
    ! [V_x_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
      <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
      <=> c_Int_Oiszero(T_a,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_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_iszero__def,axiom,
    ! [V_z_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( c_Int_Oiszero(T_a,V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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_nat__rec__0,axiom,
    ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a,V_f1_2,V_f2_2),V_nat_2)),
    file('theBenchmark.p',fact_nat__rec__Suc) ).

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_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_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_eq__number__of__eq,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
      <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_eq__special_I1_J,axiom,
    ! [V_y_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
      <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_nat__rec__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_neg__zmod__mult__2) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_zmod__number__of__Bit1) ).

fof(fact_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_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_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_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_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_Bit0__def,axiom,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    file('theBenchmark.p',fact_Bit0__def) ).

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

fof(fact_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_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_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_less__eq__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).

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

fof(fact_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_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_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_iszero__number__of__Bit0,axiom,
    ! [V_w_2,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_OBit0(V_w_2)))
      <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ),
    file('theBenchmark.p',fact_iszero__number__of__Bit0) ).

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

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

fof(fact_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_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_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_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__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_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_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_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_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_power__number__of__even,axiom,
    ! [V_w_2,V_z_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ),
    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_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_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_power__number__of__even__number__of,axiom,
    ! [V_w_2,V_v_2,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),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ),
    file('theBenchmark.p',fact_power__number__of__even__number__of) ).

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_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    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_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_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_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_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_half__gt__zero__iff,axiom,
    ! [V_r_2,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)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r_2),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_2)) ) ),
    file('theBenchmark.p',fact_half__gt__zero__iff) ).

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_a] :
      ( class_Rings_Olinordered__idom(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_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_a) ) ),
    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_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    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_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
          | V_a_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
    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_a] :
      ( class_Rings_Olinordered__idom(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_Power_Opower__class_Opower(T_a),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_a),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_a)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    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_sum__power2__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_not__sum__power2__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__sum,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__sum) ).

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

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

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

fof(fact_power__minus1__even,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__minus1__even) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ),
    file('theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_mod2__gr__0,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_mod2__gr__0) ).

fof(fact_div__2__gt__zero,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_div__2__gt__zero) ).

fof(fact_power2__diff,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__diff) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ),
    file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

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

fof(fact_power__minus1__odd,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_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_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_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_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_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_of__int__num,axiom,
    ! [V_k_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( ( 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_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),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_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),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_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_of__int__num) ).

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_rel__simps_I45_J,axiom,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I45_J) ).

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

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

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

fof(fact_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_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_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_rel__simps_I47_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OMin
    <=> V_k_2 = c_Int_OMin ),
    file('theBenchmark.p',fact_rel__simps_I47_J) ).

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

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

fof(fact_bin__less__0__simps_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_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_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_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_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_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_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_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_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_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_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('theBenchmark.p',fact_pred__Pls) ).

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_pred__Min,axiom,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    file('theBenchmark.p',fact_pred__Min) ).

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

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_inj__graph,axiom,
    ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__graph) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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_Nitpick_Oprod__def) ).

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_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_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_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_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_Nats__number__of,axiom,
    ! [V_w_2,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ),
    file('theBenchmark.p',fact_Nats__number__of) ).

fof(fact_sup__Un__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_bot__empty__eq2,axiom,
    ! [V_y_2,V_x_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_inf__Int__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_pred__equals__eq2,axiom,
    ! [V_S_2,V_R_2,T_b,T_a] :
      ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_rev__ImageI,axiom,
    ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,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_a,T_b,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__ImageI) ).

fof(fact_Image__iff,axiom,
    ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_Image__iff) ).

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_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_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_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_SUP__UN__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_INF__INT__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq2) ).

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_Nats__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ),
    file('theBenchmark.p',fact_Nats__0) ).

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_Nats__add,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ),
    file('theBenchmark.p',fact_Nats__add) ).

fof(fact_Nats__mult,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
         => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ),
    file('theBenchmark.p',fact_Nats__mult) ).

fof(fact_Nats__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ),
    file('theBenchmark.p',fact_Nats__1) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [V_n_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ),
    file('theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Image__singleton__iff,axiom,
    ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,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(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Image__singleton__iff) ).

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_Image__singleton,axiom,
    ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,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_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)),
    file('theBenchmark.p',fact_Image__singleton) ).

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_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_pair__imageI,axiom,
    ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_pair__imageI) ).

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_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_sup2CI,axiom,
    ! [T_b,T_a,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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2CI) ).

fof(fact_sup2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,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_inf2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
         => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2E) ).

fof(fact_inf2I,axiom,
    ! [T_b,T_a,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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2I) ).

fof(fact_mem__splitI,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ),
    file('theBenchmark.p',fact_mem__splitI) ).

fof(fact_splitI,axiom,
    ! [T_b,T_a,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_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_splitI) ).

fof(fact_prod__caseI,axiom,
    ! [T_b,T_a,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_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_prod__caseI) ).

fof(fact_bot2E,axiom,
    ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)),
    file('theBenchmark.p',fact_bot2E) ).

fof(fact_splitD_H,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_swap__inj__on,axiom,
    ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2),
    file('theBenchmark.p',fact_swap__inj__on) ).

fof(fact_sup2I2,axiom,
    ! [V_A_2,T_b,T_a,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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I2) ).

fof(fact_sup2I1,axiom,
    ! [V_B_2,T_b,T_a,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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I1) ).

fof(fact_rev__predicate2D,axiom,
    ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_predicate2D,axiom,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_predicate2D) ).

fof(fact_inf2D2,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_inf2D2) ).

fof(fact_inf2D1,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,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_Pair__inject,axiom,
    ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
     => ~ ( V_a = V_a_H
         => V_b != V_b_H ) ),
    file('theBenchmark.p',fact_Pair__inject) ).

fof(fact_Pair__eq,axiom,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2)
    <=> ( V_b_2 = V_b_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_Pair__eq) ).

fof(fact_split__paired__All,axiom,
    ! [T_b,T_a,V_P_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ),
    file('theBenchmark.p',fact_split__paired__All) ).

fof(fact_split__weak__cong,axiom,
    ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] :
      ( V_p_2 = V_q_2
     => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),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_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2),
    file('theBenchmark.p',fact_split__twice) ).

fof(fact_split__conv,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_split__conv) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_splitD,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_splitD) ).

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

fof(fact_split__paired__The,axiom,
    ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))),
    file('theBenchmark.p',fact_split__paired__The) ).

fof(fact_The__split__eq,axiom,
    ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2),
    file('theBenchmark.p',fact_The__split__eq) ).

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_in__rel__def,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ),
    file('theBenchmark.p',fact_in__rel__def) ).

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_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__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_negDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_negDivAlg__minus1) ).

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

fof(fact_negDivAlg__eqn,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_Nitpick_Orefl_H__def,axiom,
    ! [V_r_2,T_a] :
      ( c_Nitpick_Orefl_H(T_a,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

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

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

fof(fact_posDivAlg__0,axiom,
    ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_posDivAlg__0) ).

fof(fact_posDivAlg__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_posDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_posDivAlg__div__mod) ).

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

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

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

fof(fact_apsnd__compose,axiom,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apsnd__compose) ).

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

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_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_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_divmod__nat__div__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_divmod__nat__div__mod) ).

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

fof(fact_divmod__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_pdivmod__def,axiom,
    ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),
    file('theBenchmark.p',fact_pdivmod__def) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [V_k,V_l] :
      ( ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) )
      & ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) ),
    file('theBenchmark.p',fact_pdivmod__posDivAlg) ).

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

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opsimps) ).

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

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
    file('theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ),
    file('theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_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_mod__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ),
    file('theBenchmark.p',fact_mod__eq) ).

fof(fact_div__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ),
    file('theBenchmark.p',fact_div__eq) ).

fof(fact_divmod__nat__rel,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
    file('theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
            & ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_accp__subset,axiom,
    ! [V_R2_2,V_R1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ),
    file('theBenchmark.p',fact_accp__subset) ).

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_snd__eqD,axiom,
    ! [V_a,V_y,V_x,T_a,T_b] :
      ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
     => V_y = V_a ),
    file('theBenchmark.p',fact_snd__eqD) ).

fof(fact_snd__conv,axiom,
    ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
    file('theBenchmark.p',fact_snd__conv) ).

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

fof(fact_snd__apsnd,axiom,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),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_a,T_b,T_c] :
      ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ),
    file('theBenchmark.p',fact_apsnd__eq__conv) ).

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

fof(fact_accp_Oequations,axiom,
    ! [V_a_2,V_r_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,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_a,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Oequations) ).

fof(fact_accp_Osimps,axiom,
    ! [V_a_2,V_r_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,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_a,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Osimps) ).

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

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_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_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_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_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_in__measure,axiom,
    ! [V_f_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),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_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_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_irrefl__def,axiom,
    ! [V_r_2,T_a] :
      ( c_Relation_Oirrefl(T_a,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_irrefl__def) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Opinduct) ).

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

fof(fact_prod__eqI,axiom,
    ! [V_q,V_p,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
     => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
       => V_p = V_q ) ),
    file('theBenchmark.p',fact_prod__eqI) ).

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

fof(fact_fst__conv,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    file('theBenchmark.p',fact_fst__conv) ).

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

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

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

fof(fact_div__int__def,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    file('theBenchmark.p',fact_div__int__def) ).

fof(fact_split__comp__eq,axiom,
    ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_split__comp__eq) ).

fof(fact_split__beta,axiom,
    ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)),
    file('theBenchmark.p',fact_split__beta) ).

fof(fact_split__def,axiom,
    ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)),
    file('theBenchmark.p',fact_split__def) ).

fof(fact_split__comp,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)),
    file('theBenchmark.p',fact_split__comp) ).

fof(fact_The__split,axiom,
    ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))),
    file('theBenchmark.p',fact_The__split) ).

fof(fact_div__neg__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__neg__pos) ).

fof(fact_div__pos__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__pos__pos) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_div__pos__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_div__pos__neg) ).

fof(fact_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_prod__size__simp,axiom,
    ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,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_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),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_a,T_b,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
     => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ),
    file('theBenchmark.p',fact_exI__realizer) ).

fof(fact_conjI__realizer,axiom,
    ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_p_2))
     => ( hBOOL(hAPP(V_Q_2,V_q_2))
       => ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2))))
          & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ),
    file('theBenchmark.p',fact_conjI__realizer) ).

fof(fact_div__nat__def,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_div__nat__def) ).

fof(fact_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_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_nat__gcd_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
           => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_inv__image__def,axiom,
    ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,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_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),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_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))),
    file('theBenchmark.p',fact_inv__image__def) ).

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_in__inv__image,axiom,
    ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),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),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_rp__inv__image__def,axiom,
    ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))),
    file('theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_Union__quotient,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ),
    file('theBenchmark.p',fact_Union__quotient) ).

fof(fact_equiv__class__self,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__self) ).

fof(fact_quotient__disj,axiom,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            | V_X_2 = V_Y_2 ) ) ) ),
    file('theBenchmark.p',fact_quotient__disj) ).

fof(fact_equiv__class__eq,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
       => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_quotient__eqI,axiom,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
               => V_X_2 = V_Y_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eqI) ).

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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
             => ( V_X_2 = V_Y_2
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_eq__equiv__class,axiom,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
      ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
         => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
      <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
          & hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_UN__equiv__class,axiom,
    ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_UN__equiv__class2,axiom,
    ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,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_in__finite__psubset,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
     => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
         => c_Equiv__Relations_Ocongruent(T_b,T_c,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_c,T_b,T_a] :
      ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),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_b,T_a] :
      ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
           => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_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)) ) ) ) ),
    file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_finite__psubset__def,axiom,
    ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))),
    file('theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
             => ( ! [B_x] :
                    ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
                   => ! [B_y] :
                        ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2)))
             => ( ! [B_x1] :
                    ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
                   => ! [B_x2] :
                        ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),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_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,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_b,V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_mlex__leq,axiom,
    ! [V_R_2,T_a,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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_mlex__leq) ).

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_mlex__less,axiom,
    ! [V_R_2,T_a,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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ),
    file('theBenchmark.p',fact_mlex__less) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [V_code__numeral_H_2,V_code__numeral_2] :
      ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
    <=> V_code__numeral_2 = V_code__numeral_H_2 ),
    file('theBenchmark.p',fact_code__numeral_Oinject) ).

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

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

fof(fact_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_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_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_prod_Orecs,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_nat__size,axiom,
    ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
    file('theBenchmark.p',fact_nat__size) ).

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

fof(fact_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_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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_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_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_in__lex__prod) ).

fof(fact_equivp__equiv,axiom,
    ! [V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
    <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ),
    file('theBenchmark.p',fact_equivp__equiv) ).

fof(fact_apfst__apsnd,axiom,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))),
    file('theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_apfst__compose,axiom,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apfst__compose) ).

fof(fact_identity__equivp,axiom,
    ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal),
    file('theBenchmark.p',fact_identity__equivp) ).

fof(fact_equivp__def,axiom,
    ! [V_R_2,T_a] :
      ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
        <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
    file('theBenchmark.p',fact_equivp__def) ).

fof(fact_equivp__reflp,axiom,
    ! [V_x_2,V_R_2,T_a] :
      ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
     => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_equivp__reflp) ).

fof(fact_equivp__symp,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_a] :
      ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_equivp__symp) ).

fof(fact_equivp__transp,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
      ( c_Equiv__Relations_Oequivp(T_a,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_snd__apfst,axiom,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2),
    file('theBenchmark.p',fact_snd__apfst) ).

fof(fact_apfst__eq__conv,axiom,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ),
    file('theBenchmark.p',fact_apfst__eq__conv) ).

fof(fact_fst__apfst,axiom,
    ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)),
    file('theBenchmark.p',fact_fst__apfst) ).

fof(fact_apfst__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2),
    file('theBenchmark.p',fact_apfst__conv) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)),
    file('theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_apsnd__apfst,axiom,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))),
    file('theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_same__fstI,axiom,
    ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_same__fstI) ).

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_ImageE,axiom,
    ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ImageE) ).

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_pair__leqI2,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ),
    file('theBenchmark.p',fact_pair__leqI2) ).

fof(fact_smax__insertI,axiom,
    ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ),
    file('theBenchmark.p',fact_smax__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ),
    file('theBenchmark.p',fact_smin__insertI) ).

fof(fact_smin__emptyI,axiom,
    ! [V_X_2] :
      ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    file('theBenchmark.p',fact_smin__emptyI) ).

fof(fact_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_pair__leqI1,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ),
    file('theBenchmark.p',fact_pair__leqI1) ).

fof(fact_wmin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
    file('theBenchmark.p',fact_wmin__insertI) ).

fof(fact_wmax__insertI,axiom,
    ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
    file('theBenchmark.p',fact_wmax__insertI) ).

fof(fact_Field__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)),
    file('theBenchmark.p',fact_Field__insert) ).

fof(fact_Field__Union,axiom,
    ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)),
    file('theBenchmark.p',fact_Field__Union) ).

fof(fact_Field__empty,axiom,
    ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Field__empty) ).

fof(fact_mono__Field,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ),
    file('theBenchmark.p',fact_mono__Field) ).

fof(fact_Field__Un,axiom,
    ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)),
    file('theBenchmark.p',fact_Field__Un) ).

fof(fact_finite__Field,axiom,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Field) ).

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_wmin__emptyI,axiom,
    ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    file('theBenchmark.p',fact_wmin__emptyI) ).

fof(fact_min__weak__def,axiom,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_min__weak__def) ).

fof(fact_max__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_Id__on__def,axiom,
    ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Id__on__def) ).

fof(fact_Id__on__def_H,axiom,
    ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)),
    file('theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_Id__on__empty,axiom,
    ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Id__on__empty) ).

fof(fact_Image__Id__on,axiom,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Image__Id__on) ).

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

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

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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,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__extp__max__ext__eq,axiom,
    ! [V_xa_2,V_x_2,V_R_2,T_a] :
      ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ),
    file('theBenchmark.p',fact_max__extp__max__ext__eq) ).

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_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_rp__inv__image__rp,axiom,
    ! [V_f_2,T_b,V_P_2,T_a] :
      ( c_FunDef_Oreduction__pair(T_a,V_P_2)
     => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ),
    file('theBenchmark.p',fact_rp__inv__image__rp) ).

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_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_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_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_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_measure__def,axiom,
    ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_measure__def) ).

fof(fact_mlex__prod__def,axiom,
    ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))),
    file('theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_of__int,axiom,
    ! [V_j_2,V_i_2,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_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_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_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_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_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_Id__onE,axiom,
    ! [V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ),
    file('theBenchmark.p',fact_Id__onE) ).

fof(fact_Rep__Integ,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)),
    file('theBenchmark.p',fact_Rep__Integ) ).

fof(fact_type__definition__Integ,axiom,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    file('theBenchmark.p',fact_type__definition__Integ) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,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_accp__acc__eq,axiom,
    ! [V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_acc__subset,axiom,
    ! [V_R2_2,V_R1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ),
    file('theBenchmark.p',fact_acc__subset) ).

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

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

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,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_type__definition_ORep__range,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_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_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
          <=> V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,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_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_type__definition_ORep,axiom,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),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_b,T_a] :
      ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),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_rel__comp__def,axiom,
    ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),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_a,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(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_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(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_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),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_s_2))))),
    file('theBenchmark.p',fact_rel__comp__def) ).

fof(fact_max__extp_Oequations,axiom,
    ! [V_a2_2,V_a1_2,V_R_2,T_a] :
      ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
       => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
               => ? [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2))
                    & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_rel__compI,axiom,
    ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_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_b_2),V_c_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__compI) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),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_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)),
    file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_rel__comp__empty2,axiom,
    ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_rel__comp__empty1,axiom,
    ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),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_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)),
    file('theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_rel__comp__mono,axiom,
    ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_O__assoc,axiom,
    ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)),
    file('theBenchmark.p',fact_O__assoc) ).

fof(fact_union__comp__emptyR,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_union__comp__emptyL,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_max__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),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_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ),
    file('theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),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_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ),
    file('theBenchmark.p',fact_min__ext__compat) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),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_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
       => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_reduction__pairI) ).

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_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_c,T_b,T_a,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_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_wf__empty,axiom,
    ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_wf__empty) ).

fof(fact_wf__inv__image,axiom,
    ! [V_f_2,T_b,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_wf__inv__image) ).

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

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

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

fof(fact_wf__not__refl,axiom,
    ! [V_a_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__not__sym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__asym) ).

fof(fact_wf__irrefl,axiom,
    ! [V_a_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__irrefl) ).

fof(fact_max__ext__wf,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_max__ext__wf) ).

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_pred__comp_Oequations,axiom,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,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__subset,axiom,
    ! [V_p_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2))
       => c_Wellfounded_Owf(T_a,V_p_2) ) ),
    file('theBenchmark.p',fact_wf__subset) ).

fof(fact_wf__Int1,axiom,
    ! [V_r_H_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    file('theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [V_r_H_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    file('theBenchmark.p',fact_wf__Int2) ).

fof(fact_wf__finite__psubset,axiom,
    ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)),
    file('theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_wf__mlex,axiom,
    ! [V_f_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
     => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__mlex) ).

fof(fact_min__ext__wf,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_min__ext__wf) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_wf__less) ).

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

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

fof(fact_wf__no__loop,axiom,
    ! [V_R_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
     => c_Wellfounded_Owf(T_a,V_R_2) ),
    file('theBenchmark.p',fact_wf__no__loop) ).

fof(fact_wf__union__merge,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
    <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ),
    file('theBenchmark.p',fact_wf__union__merge) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
    <=> ~ ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ),
    file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_wfE__pf,axiom,
    ! [V_A_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2)))
       => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_wfE__pf) ).

fof(fact_wf__union__compatible,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
     => ( c_Wellfounded_Owf(T_a,V_S_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
         => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_wf,axiom,
    ! [T_a] :
      ( class_Orderings_Owellorder(T_a)
     => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ),
    file('theBenchmark.p',fact_wf) ).

fof(fact_reduction__pair__def,axiom,
    ! [V_P_2,T_a] :
      ( c_FunDef_Oreduction__pair(T_a,V_P_2)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
        & c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) ) ),
    file('theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [V_S_2,V_R_2,V_P_2,T_a] :
      ( c_FunDef_Oreduction__pair(T_a,V_P_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
         => ( c_Wellfounded_Owf(T_a,V_S_2)
           => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ),
    file('theBenchmark.p',fact_reduction__pair__lemma) ).

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

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

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)),
    file('theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_pred__nat__def,axiom,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    file('theBenchmark.p',fact_pred__nat__def) ).

fof(fact_wf__lenlex,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lenlex) ).

fof(fact_wf__same__fst,axiom,
    ! [T_a,V_R_2,T_b,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
     => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__same__fst) ).

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_wf__lex,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lexn,axiom,
    ! [V_n_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ),
    file('theBenchmark.p',fact_wf__lexn) ).

fof(fact_wf__if__measure,axiom,
    ! [T_a,V_g_2,V_f_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
     => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ),
    file('theBenchmark.p',fact_wf__if__measure) ).

fof(fact_lex__def,axiom,
    ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)),
    file('theBenchmark.p',fact_lex__def) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_Range__Collect__split,axiom,
    ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))),
    file('theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_wfP__def,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_r_2)
    <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__def) ).

fof(fact_wfP__empty,axiom,
    ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))),
    file('theBenchmark.p',fact_wfP__empty) ).

fof(fact_SigmaI,axiom,
    ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_SigmaI) ).

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

fof(fact_Times__eq__cancel2,axiom,
    ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
     => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_wfP__accp__iff,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_r_2)
    <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ),
    file('theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_accp__wfPD,axiom,
    ! [V_x_2,V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_r_2)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ),
    file('theBenchmark.p',fact_accp__wfPD) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),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_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),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_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_Range__Id__on,axiom,
    ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Range__Id__on) ).

fof(fact_Sigma__Union,axiom,
    ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Union) ).

fof(fact_Sigma__empty1,axiom,
    ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_card__cartesian__product,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),
    file('theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ),
    file('theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_Times__empty,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,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_a,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Times__empty) ).

fof(fact_Sigma__empty2,axiom,
    ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty2) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),
    file('theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ),
    file('theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_wfP__subset,axiom,
    ! [V_p_2,V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2))
       => c_Wellfounded_OwfP(T_a,V_p_2) ) ),
    file('theBenchmark.p',fact_wfP__subset) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),
    file('theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_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))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ),
    file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_swap__product,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)),
    file('theBenchmark.p',fact_swap__product) ).

fof(fact_finite__cartesian__product,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ),
    file('theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_equiv__type,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ),
    file('theBenchmark.p',fact_equiv__type) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),
    file('theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))),
    file('theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_Range__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Range__Diff__subset) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),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_a),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD1,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_SigmaD1) ).

fof(fact_SigmaD2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_SigmaD2) ).

fof(fact_SigmaE2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),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_SigmaE2) ).

fof(fact_Range__Union,axiom,
    ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)),
    file('theBenchmark.p',fact_Range__Union) ).

fof(fact_Range__empty__iff,axiom,
    ! [V_r_2,T_a,T_b] :
      ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_Range__empty,axiom,
    ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__empty) ).

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

fof(fact_finite__Range,axiom,
    ! [V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Range) ).

fof(fact_snd__eq__Range,axiom,
    ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2),
    file('theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2),
    file('theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),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)) ) ),
    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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,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_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),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_a),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_Collect__split,axiom,
    ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))),
    file('theBenchmark.p',fact_Collect__split) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)),
    file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_fst__image__times,axiom,
    ! [V_A_2,T_b,T_a,V_B_2] :
      ( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 )
      & ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_fst__image__times) ).

fof(fact_snd__image__times,axiom,
    ! [V_B_2,T_b,T_a,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_snd__image__times) ).

fof(fact_Range__iff,axiom,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Range__iff) ).

fof(fact_Range__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)),
    file('theBenchmark.p',fact_Range__insert) ).

fof(fact_Range__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))),
    file('theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_insert__times__insert,axiom,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),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_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ),
    file('theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_vimage__Times,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__Times) ).

fof(fact_UN__Times__distrib,axiom,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),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(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,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_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Sigma__def) ).

fof(fact_finite__quotient,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ),
    file('theBenchmark.p',fact_finite__quotient) ).

fof(fact_wf__in__rel,axiom,
    ! [V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
     => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ),
    file('theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wfP__wf__eq,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
    <=> c_Wellfounded_Owf(T_a,V_r_2) ),
    file('theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
      ( class_Rings_Osemiring__0(T_c)
     => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),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_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),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_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),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))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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_setsum__mult__setsum__if__inj) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ),
    file('theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [V_A_2,V_I_2,T_b,T_a] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_RangeP_Ointros,axiom,
    ! [T_b,T_a,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_a,T_b,V_r_2),V_b_2)) ),
    file('theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_image__id,axiom,
    ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__id) ).

fof(fact_apfst__id,axiom,
    ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_apfst__id) ).

fof(fact_apsnd__id,axiom,
    ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_apsnd__id) ).

fof(fact_vimage__id,axiom,
    ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_vimage__id) ).

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_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_RangeP_Oequations,axiom,
    ! [V_a2_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,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_inj__on__id,axiom,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2),
    file('theBenchmark.p',fact_inj__on__id) ).

fof(fact_id__o,axiom,
    ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2,
    file('theBenchmark.p',fact_id__o) ).

fof(fact_o__id,axiom,
    ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = 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_a,T_b,T_c] :
      ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),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_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_surj__id,axiom,
    ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_surj__id) ).

fof(fact_folding_Oempty,axiom,
    ! [V_F_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ),
    file('theBenchmark.p',fact_folding_Oempty) ).

fof(fact_split__Pair,axiom,
    ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_split__Pair) ).

fof(fact_setsum__reindex__id,axiom,
    ! [V_B_2,V_f_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,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_a,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_setprod__Sigma,axiom,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__Sigma,axiom,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),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_b,V_A_2,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),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)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_card__SigmaI,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__SigmaI) ).

fof(fact_finite__SigmaI,axiom,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_RangeE,axiom,
    ! [V_r_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
     => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_RangeE) ).

fof(fact_SigmaE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
               => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ),
    file('theBenchmark.p',fact_SigmaE) ).

fof(fact_wfP__acyclicP,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_r_2)
     => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_wf__Un,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ( c_Wellfounded_Owf(T_a,V_s_2)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
         => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_wf__Un) ).

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

fof(fact_Domain__Id__on,axiom,
    ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_acyclic__subset,axiom,
    ! [V_r_2,V_s_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,V_s_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
       => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__acyclic,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Oacyclic(T_a,V_r_2) ),
    file('theBenchmark.p',fact_wf__acyclic) ).

fof(fact_Domain__empty__iff,axiom,
    ! [V_r_2,T_b,T_a] :
      ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Domain__empty,axiom,
    ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__empty) ).

fof(fact_Domain__mono,axiom,
    ! [V_s_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ),
    file('theBenchmark.p',fact_Domain__mono) ).

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

fof(fact_finite__Domain,axiom,
    ! [V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Domain) ).

fof(fact_fst__eq__Domain,axiom,
    ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2),
    file('theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_Domain__iff,axiom,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_Domain__iff) ).

fof(fact_Domain__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),
    file('theBenchmark.p',fact_Domain__insert) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
       => c_Wellfounded_Owf(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_wf__iff__acyclic__if__finite,axiom,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
     => ( c_Wellfounded_Owf(T_a,V_r_2)
      <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_Domain__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Field__def,axiom,
    ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)),
    file('theBenchmark.p',fact_Field__def) ).

fof(fact_Domain__Union,axiom,
    ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)),
    file('theBenchmark.p',fact_Domain__Union) ).

fof(fact_Domain__Collect__split,axiom,
    ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)),
    file('theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ),
    file('theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [V_r_2,T_a] :
      ( c_Nitpick_Owf_H(T_a,V_r_2)
    <=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) )
        & c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).

fof(fact_DomainE,axiom,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
     => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_DomainE) ).

fof(fact_DomainP_Ointros,axiom,
    ! [T_b,T_a,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_a,T_b,V_r_2),V_a_2)) ),
    file('theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_DomainP_Oequations,axiom,
    ! [V_a1_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,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_map__pair__surj,axiom,
    ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_map__pair__surj) ).

fof(fact_map__pair__inj__on,axiom,
    ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
       => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ),
    file('theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_map__pair__imageI,axiom,
    ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ),
    file('theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,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_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,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_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)),
    file('theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)),
    file('theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)),
    file('theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_fst__map__pair,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),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_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_map__pair__simp,axiom,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2,
    file('theBenchmark.p',fact_map__pair__ident) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_apsnd__def,axiom,
    ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2),
    file('theBenchmark.p',fact_apsnd__def) ).

fof(fact_apfst__def,axiom,
    ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)),
    file('theBenchmark.p',fact_apfst__def) ).

fof(fact_map__pair_Oid,axiom,
    ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair__def,axiom,
    ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,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_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),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_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
     => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,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))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ),
    file('theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_wf__map__pair__image,axiom,
    ! [V_f_2,T_b,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
       => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_prod__fun__imageE,axiom,
    ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2)))
     => ~ ! [B_x,B_y] :
            ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ),
    file('theBenchmark.p',fact_refl__on__def) ).

fof(fact_refl__on__Id__on,axiom,
    ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)),
    file('theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_refl__on__empty,axiom,
    ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),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_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Un) ).

fof(fact_refl__on__Int,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__onD2,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD2) ).

fof(fact_refl__onD1,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_refl__onD) ).

fof(fact_reflp__def,axiom,
    ! [V_r_2,T_a] :
      ( c_Predicate_Oreflp(T_a,V_r_2)
    <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_reflp__def) ).

fof(fact_refl__onI,axiom,
    ! [V_A_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
       => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_refl__onI) ).

fof(fact_reflpE,axiom,
    ! [V_x_2,V_r_2,T_a] :
      ( c_Predicate_Oreflp(T_a,V_r_2)
     => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_reflpE) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
       => hBOOL(hAPP(V_P_2,V_y_2)) ) ),
    file('theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ),
    file('theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_refl__on__def_H,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) ) ) ),
    file('theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [V_x_2,V_P_2] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
         => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
     => hBOOL(hAPP(V_P_2,V_x_2)) ),
    file('theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_ball__UNIV,axiom,
    ! [V_P_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
    file('theBenchmark.p',fact_ball__UNIV) ).

fof(fact_INFI__bool__eq,axiom,
    ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a),
    file('theBenchmark.p',fact_INFI__bool__eq) ).

fof(fact_Powp__def,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
         => hBOOL(hAPP(V_A_2,B_x)) ) ),
    file('theBenchmark.p',fact_Powp__def) ).

fof(fact_ball__empty,axiom,
    ! [V_P_2,T_a,B_x] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
     => hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_ball__empty) ).

fof(fact_Collect__ball__eq,axiom,
    ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_congruent__def,axiom,
    ! [V_f_2,V_r_2,T_b,T_a] :
      ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ),
    file('theBenchmark.p',fact_congruent__def) ).

fof(fact_INTER__def,axiom,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))),
    file('theBenchmark.p',fact_INTER__def) ).

fof(fact_Sup__Inf,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ),
    file('theBenchmark.p',fact_Sup__Inf) ).

fof(fact_Inf__Sup,axiom,
    ! [V_A_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ),
    file('theBenchmark.p',fact_Inf__Sup) ).

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_wfP__SUP,axiom,
    ! [T_a,V_r_2,T_b] :
      ( ! [B_i] : c_Wellfounded_OwfP(T_b,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_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ),
    file('theBenchmark.p',fact_wfP__SUP) ).

fof(fact_triples__valid__Suc,axiom,
    ! [V_n_2,V_ts_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
         => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
     => ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
         => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ),
    file('theBenchmark.p',fact_triples__valid__Suc) ).

fof(fact_hoare__valids__def,axiom,
    ! [V_ts_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
    <=> ! [B_n] :
          ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2))
             => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
         => ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
             => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ),
    file('theBenchmark.p',fact_hoare__valids__def) ).

fof(fact_Inter__eq,axiom,
    ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,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_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))),
    file('theBenchmark.p',fact_Inter__eq) ).

fof(fact_mem__splitI2,axiom,
    ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] :
      ( ! [B_a,B_b] :
          ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
         => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
     => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    file('theBenchmark.p',fact_mem__splitI2) ).

fof(fact_mem__splitE,axiom,
    ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2)))
     => ~ ! [B_x,B_y] :
            ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
           => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
    file('theBenchmark.p',fact_mem__splitE) ).

fof(fact_Eps__split,axiom,
    ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))),
    file('theBenchmark.p',fact_Eps__split) ).

fof(fact_wfI__pf,axiom,
    ! [V_R_2,T_a] :
      ( ! [B_A] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A)))
         => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(T_a,V_R_2) ),
    file('theBenchmark.p',fact_wfI__pf) ).

fof(fact_exE__some,axiom,
    ! [T_a,V_c_2,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
       => hBOOL(hAPP(V_P_2,V_c_2)) ) ),
    file('theBenchmark.p',fact_exE__some) ).

fof(fact_someI,axiom,
    ! [T_a,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ),
    file('theBenchmark.p',fact_someI) ).

fof(fact_tfl__some,axiom,
    ! [T_a,B_P] :
      ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
     => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ),
    file('theBenchmark.p',fact_tfl__some) ).

fof(fact_someI__ex,axiom,
    ! [T_a,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ),
    file('theBenchmark.p',fact_someI__ex) ).

fof(fact_some__eq__ex,axiom,
    ! [T_a,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
    <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
    file('theBenchmark.p',fact_some__eq__ex) ).

fof(fact_some__eq__trivial,axiom,
    ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,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_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_Eps__split__eq,axiom,
    ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2),
    file('theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_split__paired__Eps,axiom,
    ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))),
    file('theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_LeastM__def,axiom,
    ! [V_P_2,V_m_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ),
    file('theBenchmark.p',fact_LeastM__def) ).

fof(fact_GreatestM__def,axiom,
    ! [V_P_2,V_m_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ),
    file('theBenchmark.p',fact_GreatestM__def) ).

fof(fact_LeastM__nat__lemma,axiom,
    ! [V_m_2,T_a,V_k_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_k_2))
     => ( ! [B_y] :
            ( hBOOL(hAPP(V_P_2,B_y))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) )
        & hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ),
    file('theBenchmark.p',fact_LeastM__nat__lemma) ).

fof(fact_LeastM__nat__le,axiom,
    ! [T_a,V_m_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ),
    file('theBenchmark.p',fact_LeastM__nat__le) ).

fof(fact_Greatest__def,axiom,
    ! [T_a] :
      ( class_Orderings_Oord(T_a)
     => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ),
    file('theBenchmark.p',fact_Greatest__def) ).

fof(fact_Sigma__mono,axiom,
    ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),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)),hAPP(V_D_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Sigma__mono) ).

fof(fact_LeastM__natI,axiom,
    ! [V_m_2,T_a,V_k_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_k_2))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ),
    file('theBenchmark.p',fact_LeastM__natI) ).

fof(fact_acc_OaccI,axiom,
    ! [V_r_2,V_x_2,T_a] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_acc_OaccI) ).

fof(fact_not__acc__down,axiom,
    ! [V_R_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
     => ~ ! [B_z] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2))
           => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ),
    file('theBenchmark.p',fact_not__acc__down) ).

fof(fact_max__ext_Osimps,axiom,
    ! [V_R_2,V_a2_2,V_a1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [V_f_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_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_WTs__elim__cases_I3_J,axiom,
    ! [V_c_2,V_a_2,V_Y_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
     => hBOOL(hAPP(c_Com_OWT,V_c_2)) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I3_J) ).

fof(fact_com_Osimps_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_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_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_com_Osimps_I40_J,axiom,
    ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2),
    file('theBenchmark.p',fact_com_Osimps_I40_J) ).

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

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

fof(fact_com_Osimps_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_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_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_I36_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I36_J) ).

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

fof(fact_setsum__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
         => ( ! [B_a] :
                ( hBOOL(hAPP(hAPP(c_member(T_a),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_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_scomp__unfold,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))),
    file('theBenchmark.p',fact_scomp__unfold) ).

fof(fact_scomp__scomp,axiom,
    ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)),
    file('theBenchmark.p',fact_scomp__scomp) ).

fof(fact_Pair__scomp,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    file('theBenchmark.p',fact_Pair__scomp) ).

fof(fact_scomp__Pair,axiom,
    ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2,
    file('theBenchmark.p',fact_scomp__Pair) ).

fof(fact_scomp__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),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_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_scomp__def) ).

fof(fact_iterate_Osimps,axiom,
    ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,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_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) ) ),
    file('theBenchmark.p',fact_iterate_Osimps) ).

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_a,T_b] :
      ( ( class_Orderings_Oord(T_a)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( V_a_2 = V_c_2
       => ( V_b_2 = V_d_2
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__ivl__cong) ).

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_minus__shift__def,axiom,
    ! [V_r,V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) ),
    file('theBenchmark.p',fact_minus__shift__def) ).

fof(fact_inc__shift__def,axiom,
    ! [V_k,V_v] :
      ( ( V_v != V_k
       => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
      & ( V_v = V_k
       => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
    file('theBenchmark.p',fact_inc__shift__def) ).

fof(fact_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_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_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_wf__trancl,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
     => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_wf__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_a] :
      ( c_Wellfounded_Oacyclic(T_a,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_acyclic__def) ).

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

fof(fact_trancl__subset__Field2,axiom,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))),
    file('theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_r__into__trancl_H,axiom,
    ! [V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_trancl__empty,axiom,
    ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),
    file('theBenchmark.p',fact_trancl__empty) ).

fof(fact_trancl__domain,axiom,
    ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2),
    file('theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2),
    file('theBenchmark.p',fact_trancl__range) ).

fof(fact_finite__trancl,axiom,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__trancl) ).

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

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

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

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

fof(fact_trancl__mono,axiom,
    ! [V_s_2,V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ),
    file('theBenchmark.p',fact_trancl__mono) ).

fof(fact_trancl__unfold,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [V_A_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_trancl__Int__subset,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,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_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_trancl__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))),
    file('theBenchmark.p',fact_trancl__insert) ).

fof(fact_reflcl__set__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ),
    file('theBenchmark.p',fact_reflcl__set__eq) ).

fof(fact_r__into__rtrancl,axiom,
    ! [V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_IdI,axiom,
    ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))),
    file('theBenchmark.p',fact_IdI) ).

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

fof(fact_trancl__unfold__left,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_trancl__unfold__right,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_reflcl__trancl,axiom,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    file('theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_trancl__reflcl,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    file('theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [V_r_2,V_s_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,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_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rtrancl__subset,axiom,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
       => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ),
    file('theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_rtrancl__mono,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))),
    file('theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_Image__closed__trancl,axiom,
    ! [V_X_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2))
     => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ),
    file('theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_refl__rtrancl,axiom,
    ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    file('theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_rtrancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl__idemp,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    file('theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),
    file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [V_S_2,V_R_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
    file('theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_r__comp__rtrancl__eq,axiom,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(fact_rtrancl__unfold,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_rtrancl__empty,axiom,
    ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a),
    file('theBenchmark.p',fact_rtrancl__empty) ).

fof(fact_Range__rtrancl,axiom,
    ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__rtrancl) ).

fof(fact_Domain__rtrancl,axiom,
    ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_R__O__Id,axiom,
    ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2,
    file('theBenchmark.p',fact_R__O__Id) ).

fof(fact_Id__O__R,axiom,
    ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2,
    file('theBenchmark.p',fact_Id__O__R) ).

fof(fact_Image__Id,axiom,
    ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Image__Id) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a)))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).

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

fof(fact_rtrancl__into__trancl1,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_rtranclD,axiom,
    ! [V_R_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
     => ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
          & V_a_2 != V_b_2 )
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_rtranclD) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,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_Domain__Id,axiom,
    ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__Id) ).

fof(fact_Range__Id,axiom,
    ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__Id) ).

fof(fact_refl__Id,axiom,
    ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)),
    file('theBenchmark.p',fact_refl__Id) ).

fof(fact_pair__leq__def,axiom,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    file('theBenchmark.p',fact_pair__leq__def) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [V_y_2,V_R_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Not__Domain__rtrancl) ).

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

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

fof(fact_wf__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
        & c_Wellfounded_Owf(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__insert) ).

fof(fact_acyclic__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
        & c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__insert) ).

fof(fact_refl__reflcl,axiom,
    ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))),
    file('theBenchmark.p',fact_refl__reflcl) ).

fof(fact_Id__def,axiom,
    ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))),
    file('theBenchmark.p',fact_Id__def) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))),
    file('theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
          | V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_irrefl__tranclI,axiom,
    ! [V_x_2,V_r_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_sequence__trans,axiom,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
      ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,V_r_2))) ),
    file('theBenchmark.p',fact_sequence__trans) ).

fof(fact_rtrancl__converse,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    file('theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_converse__Id,axiom,
    ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a),
    file('theBenchmark.p',fact_converse__Id) ).

fof(fact_converse__INTER,axiom,
    ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)),
    file('theBenchmark.p',fact_converse__INTER) ).

fof(fact_refl__on__converse,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
    <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_refl__on__converse) ).

fof(fact_converse__UNION,axiom,
    ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)),
    file('theBenchmark.p',fact_converse__UNION) ).

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

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

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

fof(fact_Field__converse,axiom,
    ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2),
    file('theBenchmark.p',fact_Field__converse) ).

fof(fact_finite__converse,axiom,
    ! [V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__converse) ).

fof(fact_converse__converse,axiom,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_converse__converse) ).

fof(fact_converse__Int,axiom,
    ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)),
    file('theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__Id__on,axiom,
    ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2),
    file('theBenchmark.p',fact_converse__Id__on) ).

fof(fact_converse__Un,axiom,
    ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)),
    file('theBenchmark.p',fact_converse__Un) ).

fof(fact_converse__rel__comp,axiom,
    ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)),
    file('theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_acyclic__converse,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
    <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ),
    file('theBenchmark.p',fact_acyclic__converse) ).

fof(fact_trancl__converse,axiom,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),
    file('theBenchmark.p',fact_trancl__converse) ).

fof(fact_wf__converse__trancl,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
     => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_equiv__comp__eq,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ),
    file('theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_Range__def,axiom,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),
    file('theBenchmark.p',fact_Range__def) ).

fof(fact_Domain__converse,axiom,
    ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2),
    file('theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2),
    file('theBenchmark.p',fact_Range__converse) ).

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

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

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

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

fof(fact_Image__subset__eq,axiom,
    ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ),
    file('theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ),
    file('theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_comp__equivI,axiom,
    ! [V_A_2,V_r_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2
     => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
       => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_comp__equivI) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
       => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_converse__def,axiom,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),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_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))),
    file('theBenchmark.p',fact_converse__def) ).

fof(fact_Image__INT__eq,axiom,
    ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_total__on__diff__Id,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))
    <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_single__valued__Id,axiom,
    ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)),
    file('theBenchmark.p',fact_single__valued__Id) ).

fof(fact_single__valued__Id__on,axiom,
    ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),
    file('theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [V_s_2,T_c,V_r_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
     => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
       => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_single__valued__subset,axiom,
    ! [V_s_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
       => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_single__valued__subset) ).

fof(fact_total__on__empty,axiom,
    ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2),
    file('theBenchmark.p',fact_total__on__empty) ).

fof(fact_total__on__converse,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
    <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__converse) ).

fof(fact_single__valuedD,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2))
         => ! [B_z] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2))
             => B_y = B_z ) ) ),
    file('theBenchmark.p',fact_single__valued__def) ).

fof(fact_total__on__def,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
             => ( B_x != B_xa
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_total__on__def) ).

fof(fact_single__valued__confluent,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ),
    file('theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_Image__Int__eq,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
     => hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ),
    file('theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [V_R_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ),
    file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_acyclicI,axiom,
    ! [V_r_2,T_a] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
     => c_Wellfounded_Oacyclic(T_a,V_r_2) ),
    file('theBenchmark.p',fact_acyclicI) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [V_n_2,V_R_2,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
     => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ),
    file('theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_comp__funpow,axiom,
    ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_comp__funpow) ).

fof(fact_funpow__swap1,axiom,
    ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_funpow__swap1) ).

fof(fact_funpow__mult,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),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_wf__exp,axiom,
    ! [V_R_2,V_n_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))
     => c_Wellfounded_Owf(T_a,V_R_2) ),
    file('theBenchmark.p',fact_wf__exp) ).

fof(fact_rel__pow__commute,axiom,
    ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_rel__pow__imp__rtrancl,axiom,
    ! [V_R_2,V_n_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ),
    file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_rtrancl__power,axiom,
    ! [V_R_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
    <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ),
    file('theBenchmark.p',fact_rtrancl__power) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a),
    file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_rel__pow__0__E,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
    file('theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_funpow__add,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow__add) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a),
    file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_trancl__power,axiom,
    ! [V_R_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
    <=> ? [B_n] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)),
    file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_funpow__code__def,axiom,
    ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a),
    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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2))
               => B_x = B_y ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2))
               => B_y = B_x ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_tranclD2,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
    file('theBenchmark.p',fact_tranclD2) ).

fof(fact_tranclD,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) ) ),
    file('theBenchmark.p',fact_tranclD) ).

fof(fact_IdE,axiom,
    ! [V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
     => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ),
    file('theBenchmark.p',fact_IdE) ).

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_wf__eq__minimal,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
    <=> ! [B_Q] :
          ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
         => ? [B_x] :
              ( ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
                 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) )
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) ) ) ),
    file('theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [V_P_H_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
     => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_Int__Collect__mono,axiom,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_Q_2,B_x)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ),
    file('theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_rel__compE,axiom,
    ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2)))
     => ~ ! [B_x,B_y,B_z] :
            ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_rel__compE) ).

fof(fact_converseE,axiom,
    ! [V_r_2,V_yx_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
     => ~ ! [B_x,B_y] :
            ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_converseE) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),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_a),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_a),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_a),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_a),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
    file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_Nitpick_Oof__frac__def,axiom,
    ! [V_q,T_a,T_b] :
      ( ( class_Rings_Oring__1(T_b)
        & class_Rings_Oinverse(T_b) )
     => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ),
    file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_Nitpick_Oinverse__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
    file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).

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

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

fof(fact_Nitpick_Odenom__def,axiom,
    ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)),
    file('theBenchmark.p',fact_Nitpick_Odenom__def) ).

fof(fact_Nitpick_Onum__def,axiom,
    ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)),
    file('theBenchmark.p',fact_Nitpick_Onum__def) ).

fof(fact_setprod__pos,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_setprod__pos) ).

fof(fact_internal__split__def,axiom,
    ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),
    file('theBenchmark.p',fact_internal__split__def) ).

fof(fact_internal__split__conv,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_setprod__nonneg,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
       => 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__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_setprod__nonneg) ).

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

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

fof(fact_finite__less__ub,axiom,
    ! [V_u_2,V_f_2] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
     => 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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ),
    file('theBenchmark.p',fact_finite__less__ub) ).

fof(fact_lenlex__def,axiom,
    ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))),
    file('theBenchmark.p',fact_lenlex__def) ).

fof(fact_lexn__length,axiom,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_lexn__length) ).

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_lenlex__conv,axiom,
    ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))),
    file('theBenchmark.p',fact_lenlex__conv) ).

fof(fact_length__sublist,axiom,
    ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,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_a)),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_lexn_Osimps_I2_J,axiom,
    ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),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_list_Oinject,axiom,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),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_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_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_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_Cons__in__lex,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_set__Cons__def,axiom,
    ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))),
    file('theBenchmark.p',fact_set__Cons__def) ).

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_select__weight__cons__zero,axiom,
    ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2),
    file('theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_lexord__cons__cons,axiom,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_lexord__lex,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__lex) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),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_a,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_Cons__acc__listrel1I,axiom,
    ! [V_xs_2,V_r_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ),
    file('theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_listrel1__mono,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ),
    file('theBenchmark.p',fact_listrel1__mono) ).

fof(fact_listrel1__converse,axiom,
    ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)),
    file('theBenchmark.p',fact_listrel1__converse) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))),
    file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_in__listrel1__converse,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ),
    file('theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_listrel1I1,axiom,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_listrel__Cons,axiom,
    ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_listrel__Cons) ).

fof(fact_lexord__irreflexive,axiom,
    ! [V_y_2,V_r_2,T_a] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))),
    file('theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_listrel__mono,axiom,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ),
    file('theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))),
    file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_listrel__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ),
    file('theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)),
    file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ),
    file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [V_r_H_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2))
     => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ),
    file('theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_listrel_OCons,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_listrel_OCons) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [V_xa_2,V_x_2,V_r_2,T_a] :
      ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_listrel__Cons2,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2)))
     => ~ ! [B_x,B_xs] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
      ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2))
    <=> ( c_List_Olistrelp(T_a,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_a,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_a,V_r_2,V_xs_2,V_ys_2)
       => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_listrel__Cons1,axiom,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
     => ~ ! [B_y,B_ys] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_listrel__subset,axiom,
    ! [V_A_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ),
    file('theBenchmark.p',fact_listrel__subset) ).

fof(fact_lists__UNIV,axiom,
    ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lists__UNIV) ).

fof(fact_lists__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ),
    file('theBenchmark.p',fact_lists__mono) ).

fof(fact_equiv__listrel,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_equiv__listrel) ).

fof(fact_listrel__refl__on,axiom,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
     => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [V_A_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_lists__accI,axiom,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accI) ).

fof(fact_lists__accD,axiom,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accD) ).

fof(fact_listrel__iff__nth,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,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_a)),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_lexord__linear,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_a] :
      ( ! [B_a,B_b] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2))
          | B_a = B_b
          | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2)))
        | V_x_2 = V_y_2
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__linear) ).

fof(fact_infinite__UNIV__listI,axiom,
    ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__listI) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [T_a,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_a)),V_xs_2)))
           => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
    file('theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_nth__Cons__0,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
    file('theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_nth_Osimps,axiom,
    ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_nth_Osimps) ).

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_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_lexord__take__index__conv,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
    <=> ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_set__sublist,axiom,
    ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),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_finite__set,axiom,
    ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_finite__set) ).

fof(fact_set__subset__Cons,axiom,
    ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))),
    file('theBenchmark.p',fact_set__subset__Cons) ).

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_set__take__subset__set__take,axiom,
    ! [V_xs_2,T_a,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_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_set__take__subset,axiom,
    ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_set__take__subset) ).

fof(fact_set__sublist__subset,axiom,
    ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_set__sublist__subset) ).

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_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_set__ConsD,axiom,
    ! [V_xs_2,V_x_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_set__ConsD) ).

fof(fact_in__set__sublistD,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_in__set__takeD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__takeD) ).

fof(fact_notin__set__sublistI,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ),
    file('theBenchmark.p',fact_notin__set__sublistI) ).

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__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_sublist__upt__eq__take,axiom,
    ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2),
    file('theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_card__length,axiom,
    ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    file('theBenchmark.p',fact_card__length) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ),
    file('theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_list__size__estimation,axiom,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),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_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),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_a,V_f_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_in__lists__conv__set,axiom,
    ! [V_A_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),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_a)),V_xs_2))) ),
    file('theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_nth__mem,axiom,
    ! [V_xs_2,T_a,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_a)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_nth__mem) ).

fof(fact_in__set__conv__nth,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
    <=> ? [B_i] :
          ( hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_lists__eq__set,axiom,
    ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)),
    file('theBenchmark.p',fact_lists__eq__set) ).

fof(fact_set__conv__nth,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))))),
    file('theBenchmark.p',fact_set__conv__nth) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [V_n_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_finite__lists__length__le,axiom,
    ! [V_n_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__le) ).

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_listrel__iff__zip,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__zip) ).

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__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_zip__Cons__Cons,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    file('theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [T_a,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_zip__same,axiom,
    ! [V_xs_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2))))
    <=> ( V_a_2 = V_b_2
        & hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),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_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ),
    file('theBenchmark.p',fact_in__set__zipE) ).

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_set__zip,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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)),tc_prod(T_a,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)),tc_prod(T_a,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(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))),
    file('theBenchmark.p',fact_set__zip) ).

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_listsum__setsum__nth,axiom,
    ! [V_xs_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__setsum__nth) ).

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_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_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_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_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_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_list__size__pointwise,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),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_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ),
    file('theBenchmark.p',fact_list__size__pointwise) ).

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_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_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_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_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_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_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_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_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__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__update_Osimps_I2_J,axiom,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2),
    file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs),
    file('theBenchmark.p',fact_list__update__code_I2_J) ).

fof(fact_in__set__butlastD,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_set__update__subsetI,axiom,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ),
    file('theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_set__update__subset__insert,axiom,
    ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))),
    file('theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_nth__list__update__eq,axiom,
    ! [V_x,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_list__update__same__conv,axiom,
    ! [V_x_2,V_xs_2,T_a,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_a)),V_xs_2)))
     => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
      <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_nth__list__update,axiom,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( ( V_i != V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) )
        & ( V_i = V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) ) ),
    file('theBenchmark.p',fact_nth__list__update) ).

fof(fact_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_set__update__memI,axiom,
    ! [V_x_2,V_xs_2,T_a,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_a)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ),
    file('theBenchmark.p',fact_set__update__memI) ).

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_listrel1__iff__update,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
    <=> ? [B_y,B_n] :
          ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,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_a)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_distinct__list__update,axiom,
    ! [V_i_2,V_a_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ),
    file('theBenchmark.p',fact_distinct__list__update) ).

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_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_distinct__sublistI,axiom,
    ! [V_I_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ),
    file('theBenchmark.p',fact_distinct__sublistI) ).

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_distinct_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_card__distinct,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
     => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_card__distinct) ).

fof(fact_distinct__card,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_distinct__card) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),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_a)),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_a)),V_xs_2)))
         => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2)
          <=> V_i_2 = V_j_2 ) ) ) ),
    file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__conv__nth,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),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_a)),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_a)),V_xs_2)))
             => ( B_i != B_j
               => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ),
    file('theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [V_xs_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [V_A_2,T_a] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) ),
    file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_dom__map__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)),
    file('theBenchmark.p',fact_dom__map__upds) ).

fof(fact_map__upds__apply__nontin,axiom,
    ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => hAPP(c_Map_Omap__upds(T_a,T_b,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__upds__list__update2__drop,axiom,
    ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,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_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_b)),V_ys_2)))
       => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upds__list__update2__drop) ).

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_restrict__map__upds,axiom,
    ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2))
       => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_restrict__map__upds) ).

fof(fact_restrict__map__insert,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,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__restrict,axiom,
    ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_restrict__restrict) ).

fof(fact_restrict__in,axiom,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ),
    file('theBenchmark.p',fact_restrict__in) ).

fof(fact_dom__restrict,axiom,
    ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2),
    file('theBenchmark.p',fact_dom__restrict) ).

fof(fact_fun__upd__restrict,axiom,
    ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2),
    file('theBenchmark.p',fact_fun__upd__restrict) ).

fof(fact_fun__upd__restrict__conv,axiom,
    ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ),
    file('theBenchmark.p',fact_fun__upd__restrict__conv) ).

fof(fact_restrict__fun__upd,axiom,
    ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
       => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
       => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ),
    file('theBenchmark.p',fact_restrict__fun__upd) ).

fof(fact_set__remove1__eq,axiom,
    ! [V_x_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_set__remove1__eq) ).

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_lists_ONil,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))),
    file('theBenchmark.p',fact_lists_ONil) ).

fof(fact_listrel__Nil2,axiom,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_listrel__Nil1,axiom,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_listrel__Nil1) ).

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_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__nonempty,axiom,
    ! [V_x_2,V_k_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_set__empty2,axiom,
    ! [V_xs_2,T_a] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_set__empty) ).

fof(fact_length__0__conv,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    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_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_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_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_listrelp_Oequations_I1_J,axiom,
    ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_listrelp_ONil,axiom,
    ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_list_Osize_I1_J) ).

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_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_sublist__nil,axiom,
    ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_sublist__nil) ).

fof(fact_take__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_a] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_take__0,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__0) ).

fof(fact_take__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__Nil) ).

fof(fact_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_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_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_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_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_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_in__set__remove1,axiom,
    ! [V_xs_2,T_a,V_b_2,V_a_2] :
      ( V_a_2 != V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2))))
      <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__remove1) ).

fof(fact_notin__set__remove1,axiom,
    ! [V_y_2,V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_remove1__idem,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__idem) ).

fof(fact_map__upds__Nil1,axiom,
    ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),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_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2,
    file('theBenchmark.p',fact_map__upds__Nil2) ).

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_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_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_sublist__empty,axiom,
    ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_sublist__empty) ).

fof(fact_set__remove1__subset,axiom,
    ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_length__greater__0__conv,axiom,
    ! [V_xs_2,T_a] :
      ( 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_a)),V_xs_2)))
    <=> V_xs_2 != c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_length__greater__0__conv) ).

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_not__listrel1__Nil,axiom,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))),
    file('theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))),
    file('theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_listrel_ONil,axiom,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))),
    file('theBenchmark.p',fact_listrel_ONil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))),
    file('theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))),
    file('theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_Nil__notin__lex,axiom,
    ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))),
    file('theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_take__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2),
    file('theBenchmark.p',fact_take__Cons) ).

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_a,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_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ),
    file('theBenchmark.p',fact_sublist__singleton) ).

fof(fact_lists__empty,axiom,
    ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_lists__empty) ).

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_listrel__Nil,axiom,
    ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listrel__Nil) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2),
    file('theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_length__remove1,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,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_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_length__remove1) ).

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_select,axiom,
    ! [V_s_2,T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_select) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_zip__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_zip__Cons) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),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_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = 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_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)),
    file('theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_zip__Cons1,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2),
    file('theBenchmark.p',fact_zip__Cons1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_upto_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_i,B_j] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
             => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_anamorph_Osimps,axiom,
    ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,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(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) ),
    file('theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_sublist__Cons,axiom,
    ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),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_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,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_append__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
    <=> ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ),
    file('theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)
    <=> ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ),
    file('theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append1__eq__conv,axiom,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))
    <=> ( V_x_2 = V_y_2
        & V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_append1__eq__conv) ).

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_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_set__append,axiom,
    ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)),
    file('theBenchmark.p',fact_set__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_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_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_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_append__same__eq,axiom,
    ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_append__same__eq) ).

fof(fact_same__append__eq,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_same__append__eq) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)
    <=> ? [B_us] :
          ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2)
            & hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 )
          | ( hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2
            & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv2) ).

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__in__lists__conv,axiom,
    ! [V_A_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ),
    file('theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_fun__upds__append2__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append2__drop) ).

fof(fact_fun__upds__append__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append__drop) ).

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_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_Nil__is__append__conv,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_a)
        & V_xs_2 = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_Nil__is__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_self__append__conv,axiom,
    ! [V_ys_2,T_a,V_xs_2] :
      ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_self__append__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [V_xs_2,T_a,V_ys_2] :
      ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_self__append__conv2) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_a)
        & V_xs_2 = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_append__self__conv,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
    <=> V_ys_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_append__self__conv) ).

fof(fact_append__self__conv2,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_append__self__conv2) ).

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_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_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_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_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_remove1__append,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_remove1__append) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2))))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) )
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),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_append__listrel1I,axiom,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,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_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_append__listrel1I) ).

fof(fact_lexord__append__leftI,axiom,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_distinct__append,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
        & hBOOL(hAPP(c_List_Odistinct(T_a),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_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,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_a)),V_l_2)))),V_A_2)))),
    file('theBenchmark.p',fact_sublist__append) ).

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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
     => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2))
       => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel1I) ).

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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_listrel1E,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
     => ~ ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
           => ! [B_us,B_vs] :
                ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
               => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ),
    file('theBenchmark.p',fact_listrel1E) ).

fof(fact_lexord__append__leftD,axiom,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2)))
     => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rotate1__def,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2),
    file('theBenchmark.p',fact_rotate1__def) ).

fof(fact_map__upds__append1,axiom,
    ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))
     => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ),
    file('theBenchmark.p',fact_map__upds__append1) ).

fof(fact_image__map__upd,axiom,
    ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ),
    file('theBenchmark.p',fact_image__map__upd) ).

fof(fact_set__rotate1,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    file('theBenchmark.p',fact_set__rotate1) ).

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_dom__const,axiom,
    ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_dom__const) ).

fof(fact_domI,axiom,
    ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ),
    file('theBenchmark.p',fact_domI) ).

fof(fact_insert__dom,axiom,
    ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ),
    file('theBenchmark.p',fact_insert__dom) ).

fof(fact_distinct1__rotate,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_map__upd__eqD1,axiom,
    ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))
     => V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_map__upd__eqD1) ).

fof(fact_map__upd__triv,axiom,
    ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
      ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ),
    file('theBenchmark.p',fact_map__upd__triv) ).

fof(fact_map__upd__Some__unfold,axiom,
    ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
    <=> ( ( hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),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_rotate1__is__Nil__conv,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_map__upds__Cons,axiom,
    ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2),
    file('theBenchmark.p',fact_map__upds__Cons) ).

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_finite__range__updI,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__updI) ).

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_map__upds__twist,axiom,
    ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
     => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ),
    file('theBenchmark.p',fact_map__upds__twist) ).

fof(fact_restrict__upd__same,axiom,
    ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_restrict__upd__same) ).

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_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_map__upd__upds__conv__if,axiom,
    ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upd__upds__conv__if) ).

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

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

fof(fact_inj__Some,axiom,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2),
    file('theBenchmark.p',fact_inj__Some) ).

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

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_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_Option_Oset_Osimps_I2_J,axiom,
    ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).

fof(fact_elem__set,axiom,
    ! [V_xo_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
    <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ),
    file('theBenchmark.p',fact_elem__set) ).

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_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_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_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__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_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_take__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    file('theBenchmark.p',fact_take__drop) ).

fof(fact_drop__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__take) ).

fof(fact_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_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_in__set__dropD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__dropD) ).

fof(fact_set__drop__subset,axiom,
    ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_set__drop__subset) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs),
    file('theBenchmark.p',fact_drop__Suc__Cons) ).

fof(fact_drop__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_nth__via__drop,axiom,
    ! [V_ys,V_y,V_xs,V_n,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
     => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ),
    file('theBenchmark.p',fact_nth__via__drop) ).

fof(fact_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_set__drop__subset__set__drop,axiom,
    ! [V_xs_2,T_a,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_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_drop__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = 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_2)),V_n_2)) ),
    file('theBenchmark.p',fact_drop__eq__Nil) ).

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__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_append__eq__conv__conj,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
    <=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)
        & V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),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_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
         => ( hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
         => ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_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_zip__append2,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    file('theBenchmark.p',fact_zip__append2) ).

fof(fact_zip__append1,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    file('theBenchmark.p',fact_zip__append1) ).

fof(fact_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_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__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__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__in__set,axiom,
    ! [T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),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_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_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_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_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_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_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_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_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_tl__append,axiom,
    ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_tl__append) ).

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_fold1__set,axiom,
    ! [V_xs_2,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => ( V_xs_2 != c_List_Olist_ONil(T_a)
       => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ),
    file('theBenchmark.p',fact_fold1__set) ).

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_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_foldl__append,axiom,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,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_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,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_set__rotate,axiom,
    ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    file('theBenchmark.p',fact_set__rotate) ).

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_rotate0,axiom,
    ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)),
    file('theBenchmark.p',fact_rotate0) ).

fof(fact_foldl__absorb0,axiom,
    ! [V_zs_2,V_x_2,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),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_a] :
      ( class_Groups_Osemigroup__add(T_a)
     => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ),
    file('theBenchmark.p',fact_foldl__assoc) ).

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__add,axiom,
    ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)),
    file('theBenchmark.p',fact_rotate__add) ).

fof(fact_distinct__rotate,axiom,
    ! [V_xs_2,V_n_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rotate) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [V_xs_2,V_n_2,T_a] :
      ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_foldl__Nil,axiom,
    ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2,
    file('theBenchmark.p',fact_foldl__Nil) ).

fof(fact_rotate__def,axiom,
    ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)),
    file('theBenchmark.p',fact_rotate__def) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
    file('theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_rotate__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_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_listsum__foldl,axiom,
    ! [T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_listsum__foldl) ).

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_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_fun__left__comm__idem_Ofold__set,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),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_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [V_xs_2,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( class_Lattices_Olattice(T_a)
     => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),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_a] :
      ( class_Lattices_Olattice(T_a)
     => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),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_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_INFI__set__fold,axiom,
    ! [V_f_2,V_xs_2,T_b,T_a] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_a)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_map__upds__fold__map__upd,axiom,
    ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),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_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_ran__def,axiom,
    ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))),
    file('theBenchmark.p',fact_ran__def) ).

fof(fact_lexord__append__rightI,axiom,
    ! [V_r_2,V_x_2,T_a,V_y_2] :
      ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_ranI,axiom,
    ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
     => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ),
    file('theBenchmark.p',fact_ranI) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_lexord__Nil__left,axiom,
    ! [V_r_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2)))
    <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ),
    file('theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_length__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ),
    file('theBenchmark.p',fact_length__insort) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [V_x_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_set__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort) ).

fof(fact_insort__key__left__comm,axiom,
    ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,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_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ),
    file('theBenchmark.p',fact_insort__left__comm) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ),
    file('theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_remove1__insort,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__insort) ).

fof(fact_insort__not__Nil,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_distinct__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)))
      <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__insort) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_insort__insert__insort,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_distinct__insort__insert,axiom,
    ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
       => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),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_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort__insert) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__key__triv) ).

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_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_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__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__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__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__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_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__in__set,axiom,
    ! [T_a,V_as_2] :
      ( V_as_2 != c_List_Olist_ONil(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),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_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_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2
    <=> ( c_List_Olast(T_a,V_ys_2) = V_x_2
        & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
        & V_ys_2 != c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_lists_Osimps,axiom,
    ! [V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
    <=> ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_lists_Osimps) ).

fof(fact_map__of__zip__upd,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_zs_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(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2))
           => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__upd) ).

fof(fact_finite__dom__map__of,axiom,
    ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))),
    file('theBenchmark.p',fact_finite__dom__map__of) ).

fof(fact_map__of__zip__inject,axiom,
    ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_zs_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))
         => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))
           => V_ys_2 = V_zs_2 ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__inject) ).

fof(fact_body__def,axiom,
    c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),
    file('theBenchmark.p',fact_body__def) ).

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(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(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) )
      & ( V_l = V_k
       => hAPP(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_map__of__eq__dom,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
     => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ),
    file('theBenchmark.p',fact_map__of__eq__dom) ).

fof(fact_finite__range__map__of,axiom,
    ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_finite__range__map__of) ).

fof(fact_map__of__is__SomeD,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ),
    file('theBenchmark.p',fact_map__of__is__SomeD) ).

fof(fact_map__of__SomeD,axiom,
    ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ),
    file('theBenchmark.p',fact_map__of__SomeD) ).

fof(fact_dom__map__of__conv__image__fst,axiom,
    ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)),
    file('theBenchmark.p',fact_dom__map__of__conv__image__fst) ).

fof(fact_map__of__zip__is__Some,axiom,
    ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__Some) ).

fof(fact_dom__map__of__zip,axiom,
    ! [V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
       => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ),
    file('theBenchmark.p',fact_dom__map__of__zip) ).

fof(fact_map__of_Osimps_I2_J,axiom,
    ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))),
    file('theBenchmark.p',fact_map__of_Osimps_I2_J) ).

fof(fact_ran__distinct,axiom,
    ! [V_al_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2)))
     => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ),
    file('theBenchmark.p',fact_ran__distinct) ).

fof(fact_set__map__of__compr,axiom,
    ! [V_xs_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
     => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ),
    file('theBenchmark.p',fact_set__map__of__compr) ).

fof(fact_inj__mapI,axiom,
    ! [V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapI) ).

fof(fact_listsum__abs,axiom,
    ! [V_xs_2,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(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ),
    file('theBenchmark.p',fact_listsum__abs) ).

fof(fact_foldl__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    file('theBenchmark.p',fact_foldl__map) ).

fof(fact_zip__map2,axiom,
    ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map2) ).

fof(fact_map__zip__map2,axiom,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),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_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_map__zip__map) ).

fof(fact_zip__map1,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),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_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map__map) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_map__comp__map,axiom,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_map__comp__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2),
    file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_map__map,axiom,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2),
    file('theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)),
    file('theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_List_Omap_Oid,axiom,
    ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)),
    file('theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_list__size__map,axiom,
    ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2),
    file('theBenchmark.p',fact_list__size__map) ).

fof(fact_nth__map,axiom,
    ! [V_f_2,T_b,V_xs_2,T_a,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_a)),V_xs_2)))
     => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ),
    file('theBenchmark.p',fact_nth__map) ).

fof(fact_map__fun__upd,axiom,
    ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ),
    file('theBenchmark.p',fact_map__fun__upd) ).

fof(fact_map__tl,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__tl) ).

fof(fact_length__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
    file('theBenchmark.p',fact_length__map) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_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) ),
    file('theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_set__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_set__map) ).

fof(fact_map__append,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)),
    file('theBenchmark.p',fact_map__append) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_map__update,axiom,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),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__eq__conv,axiom,
    ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
    file('theBenchmark.p',fact_map__eq__conv) ).

fof(fact_listsum__0,axiom,
    ! [V_xs_2,T_b,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_listsum__0) ).

fof(fact_listsum__mult__const,axiom,
    ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] :
      ( class_Rings_Osemiring__0(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2) ),
    file('theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_listsum__const__mult,axiom,
    ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] :
      ( class_Rings_Osemiring__0(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_listsum__subtractf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_listsum__addf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__addf) ).

fof(fact_map__ident,axiom,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2,
    file('theBenchmark.p',fact_map__ident) ).

fof(fact_take__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_take__map) ).

fof(fact_map__butlast,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__butlast) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_inj__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_map__injective,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__injective) ).

fof(fact_hd__map,axiom,
    ! [V_f_2,T_b,T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_hd__map) ).

fof(fact_drop__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_drop__map) ).

fof(fact_map__inj__on,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_b,T_a,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)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
     => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_rotate__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_rotate__map) ).

fof(fact_distinct__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
    <=> ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__map) ).

fof(fact_last__map,axiom,
    ! [V_f_2,T_b,T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ),
    file('theBenchmark.p',fact_last__map) ).

fof(fact_uminus__listsum__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ),
    file('theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_inj__on__mapI,axiom,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2)))
     => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_map__fst__zip,axiom,
    ! [V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),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_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ),
    file('theBenchmark.p',fact_map__snd__zip) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2,
    file('theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_inj__map,axiom,
    ! [V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__map) ).

fof(fact_inj__mapD,axiom,
    ! [V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapD) ).

fof(fact_pick__member,axiom,
    ! [V_xs_2,T_a,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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ),
    file('theBenchmark.p',fact_pick__member) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [V_f_2,V_xs_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ),
    file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2
          & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_listsum__triv,axiom,
    ! [V_xs_2,V_r_2,T_b,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ),
    file('theBenchmark.p',fact_listsum__triv) ).

fof(fact_map__of__inject__set,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)))
       => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
        <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ),
    file('theBenchmark.p',fact_map__of__inject__set) ).

fof(fact_listsum__map__remove1,axiom,
    ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,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_a] :
      ( 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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ),
    file('theBenchmark.p',fact_select__weight__member) ).

fof(fact_select__weight__def,axiom,
    ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,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_a,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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))),
    file('theBenchmark.p',fact_select__weight__def) ).

fof(fact_map__of__mapk__SomeI,axiom,
    ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2)
       => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,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_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ),
    file('theBenchmark.p',fact_map__of__mapk__SomeI) ).

fof(fact_Some__eq__map__of__iff,axiom,
    ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
     => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2)
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ),
    file('theBenchmark.p',fact_Some__eq__map__of__iff) ).

fof(fact_map__of__eq__Some__iff,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
     => ( hAPP(hAPP(c_Map_Omap__of(T_a,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_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ),
    file('theBenchmark.p',fact_map__of__eq__Some__iff) ).

fof(fact_map__of__is__SomeI,axiom,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
       => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ),
    file('theBenchmark.p',fact_map__of__is__SomeI) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
         => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) ) ),
    file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_listsum__mono,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
        & class_Groups_Omonoid__add(T_b) )
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__mono) ).

fof(fact_zip__same__conv__map,axiom,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2),
    file('theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,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_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),
    file('theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [V_l_2,V_k_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [V_j_2,V_i_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
    file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_map__of__map__restrict,axiom,
    ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)),
    file('theBenchmark.p',fact_map__of__map__restrict) ).

fof(fact_map__of__map__keys,axiom,
    ! [V_m_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
     => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ),
    file('theBenchmark.p',fact_map__of__map__keys) ).

fof(fact_select__weigth__select,axiom,
    ! [T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ),
    file('theBenchmark.p',fact_select__weigth__select) ).

fof(fact_pick__same,axiom,
    ! [V_xs_2,T_a,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_a)),V_xs_2)))
     => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),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_a),V_xs_2),V_l_2) ),
    file('theBenchmark.p',fact_pick__same) ).

fof(fact_map__of__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)),
    file('theBenchmark.p',fact_map__of__map) ).

fof(fact_option__map__comp,axiom,
    ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2),
    file('theBenchmark.p',fact_option__map__comp) ).

fof(fact_Option_Omap_Ocompositionality,axiom,
    ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2),
    file('theBenchmark.p',fact_Option_Omap_Ocompositionality) ).

fof(fact_Option_Omap_Ocomp,axiom,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_Option_Omap_Ocomp) ).

fof(fact_option__map__o__map__upd,axiom,
    ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))),
    file('theBenchmark.p',fact_option__map__o__map__upd) ).

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_Option_Omap_Oidentity,axiom,
    ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)),
    file('theBenchmark.p',fact_Option_Omap_Oidentity) ).

fof(fact_Option_Omap_Oid,axiom,
    ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)),
    file('theBenchmark.p',fact_Option_Omap_Oid) ).

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_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_option__map__Some,axiom,
    ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),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_a,T_b] :
      ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
    <=> ? [B_z] :
          ( hAPP(V_f_2,B_z) = V_y_2
          & V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) ) ),
    file('theBenchmark.p',fact_option__map__eq__Some) ).

fof(fact_dom__option__map,axiom,
    ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2),
    file('theBenchmark.p',fact_dom__option__map) ).

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_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_zero__code__numeral__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_zero__code__numeral__def) ).

fof(fact_one__code__numeral__def,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_one__code__numeral__def) ).

fof(fact_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_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_select__def,axiom,
    ! [V_xs_2,T_a] : c_Random_Oselect(T_a,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_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))),
    file('theBenchmark.p',fact_select__def) ).

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

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

fof(fact_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,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_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_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_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_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_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_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_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_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_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_weak__map__of__SomeI,axiom,
    ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2)))
     => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ),
    file('theBenchmark.p',fact_weak__map__of__SomeI) ).

fof(fact_map__of__zip__map,axiom,
    ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_map__of__zip__map) ).

fof(fact_partition__set,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
      ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ),
    file('theBenchmark.p',fact_partition__set) ).

fof(fact_option__map__o__empty,axiom,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_option__map__o__empty) ).

fof(fact_option__map__is__None,axiom,
    ! [V_opt_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
    <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_option__map__is__None) ).

fof(fact_option__map__None,axiom,
    ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_option__map__None) ).

fof(fact_map__of__Cons__code_I1_J,axiom,
    ! [V_k,T_a,T_b] : hAPP(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_set__empty__eq,axiom,
    ! [V_xo_2,T_a] :
      ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ),
    file('theBenchmark.p',fact_set__empty__eq) ).

fof(fact_Option_Oset_Osimps_I1_J,axiom,
    ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).

fof(fact_empty__upd__none,axiom,
    ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_empty__upd__none) ).

fof(fact_dom__def,axiom,
    ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,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_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))),
    file('theBenchmark.p',fact_dom__def) ).

fof(fact_domIff,axiom,
    ! [V_m_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
    <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_domIff) ).

fof(fact_dom__empty,axiom,
    ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_dom__empty) ).

fof(fact_dom__eq__empty__conv,axiom,
    ! [V_f_2,T_b,T_a] :
      ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
    <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ),
    file('theBenchmark.p',fact_dom__eq__empty__conv) ).

fof(fact_restrict__map__def,axiom,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
       => hAPP(c_Map_Orestrict__map(T_a,T_b,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__out,axiom,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
     => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ),
    file('theBenchmark.p',fact_restrict__out) ).

fof(fact_restrict__map__empty,axiom,
    ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_restrict__map__empty) ).

fof(fact_restrict__map__to__empty,axiom,
    ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_restrict__map__to__empty) ).

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

fof(fact_map__upd__nonempty,axiom,
    ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),
    file('theBenchmark.p',fact_map__upd__nonempty) ).

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

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

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

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

fof(fact_ran__empty,axiom,
    ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    file('theBenchmark.p',fact_ran__empty) ).

fof(fact_map__of_Osimps_I1_J,axiom,
    ! [V_x_1,T_b,T_a] : hAPP(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_Option_Omap__def,axiom,
    ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)),
    file('theBenchmark.p',fact_Option_Omap__def) ).

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

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

fof(fact_dom__minus,axiom,
    ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_dom__minus) ).

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_partition__P,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
      ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
           => ~ hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_partition__P) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_ran__map__upd,axiom,
    ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
      ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
     => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ),
    file('theBenchmark.p',fact_ran__map__upd) ).

fof(fact_map__of__zip__is__None,axiom,
    ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b)
      <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__None) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)),
    file('theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_dom__fun__upd,axiom,
    ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
      ( ( V_y_2 != c_Option_Ooption_ONone(T_a)
       => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) )
      & ( V_y_2 = c_Option_Ooption_ONone(T_a)
       => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,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)))) ) ),
    file('theBenchmark.p',fact_dom__fun__upd) ).

fof(fact_restrict__complement__singleton__eq,axiom,
    ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)),
    file('theBenchmark.p',fact_restrict__complement__singleton__eq) ).

fof(fact_map__of__eq__None__iff,axiom,
    ! [V_x_2,V_xys_2,T_a,T_b] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
    <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ),
    file('theBenchmark.p',fact_map__of__eq__None__iff) ).

fof(fact_UNIV__option__conv,axiom,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__option__conv) ).

fof(fact_dom__eq__singleton__conv,axiom,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
    <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ),
    file('theBenchmark.p',fact_dom__eq__singleton__conv) ).

fof(fact_fun__upd__None__restrict,axiom,
    ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ),
    file('theBenchmark.p',fact_fun__upd__None__restrict) ).

fof(fact_lists__Int__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))),
    file('theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_lists__IntI,axiom,
    ! [V_B_2,V_A_2,V_l_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
       => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ),
    file('theBenchmark.p',fact_lists__IntI) ).

fof(fact_listsp_ONil,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_listsp_ONil) ).

fof(fact_append__in__listsp__conv,axiom,
    ! [V_ys_2,V_xs_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2))
        & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [V_a2_2,V_a1_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2))
        & hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
    file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [V_xs_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_A_2,B_x)) ) ),
    file('theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_listsp__conj__eq,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2))
        & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_listsp__inf__eq,axiom,
    ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)),
    file('theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_listsp__infI,axiom,
    ! [V_B_2,V_l_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
     => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
       => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ),
    file('theBenchmark.p',fact_listsp__infI) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_listsp__mono,axiom,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ),
    file('theBenchmark.p',fact_listsp__mono) ).

fof(fact_listsp__lists__eq,axiom,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ),
    file('theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_,axiom,
    ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2),
    file('theBenchmark.p',fact_) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)),
    file('theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_distinct__product,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ),
    file('theBenchmark.p',fact_distinct__product) ).

fof(fact_product__list__set,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))),
    file('theBenchmark.p',fact_product__list__set) ).

fof(fact_sublists__powset,axiom,
    ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)),
    file('theBenchmark.p',fact_sublists__powset) ).

fof(fact_length__sublists,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = 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_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
    file('theBenchmark.p',fact_length__sublists) ).

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(fact_sublists_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))),
    file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).

fof(fact_distinct__set__sublists,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ),
    file('theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_set__n__lists,axiom,
    ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))),
    file('theBenchmark.p',fact_set__n__lists) ).

fof(fact_enum__the__def,axiom,
    ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2),
    file('theBenchmark.p',fact_enum__the__def) ).

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_n__lists_Osimps_I1_J,axiom,
    ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = 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_n__lists_Osimps_I1_J) ).

fof(fact_n__lists__Nil,axiom,
    ! [T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(T_a,V_n,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_n__lists__Nil) ).

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_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ),
    file('theBenchmark.p',fact_length__n__lists__elem) ).

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_a,T_b] :
      ( ( class_Smallcheck_Osmall(T_a)
        & class_Smallcheck_Osmall(T_b) )
     => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,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_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ),
    file('theBenchmark.p',fact_small__prod__def) ).

fof(fact_small_H_Opinduct,axiom,
    ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
     => ( ! [B_f,B_d,B_i] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
               => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
                 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
             => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
       => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ),
    file('theBenchmark.p',fact_small_H_Opinduct) ).

fof(fact_map__of__zip__enum__inject,axiom,
    ! [V_ys_2,V_xs_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
       => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
         => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2)))
           => V_xs_2 = V_ys_2 ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__enum__inject) ).

fof(fact_enum__prod__def,axiom,
    ! [T_b,T_a] :
      ( ( class_Enum_Oenum(T_b)
        & class_Enum_Oenum(T_a) )
     => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ),
    file('theBenchmark.p',fact_enum__prod__def) ).

fof(fact_UNIV__enum,axiom,
    ! [T_a] :
      ( class_Enum_Oenum(T_a)
     => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ),
    file('theBenchmark.p',fact_UNIV__enum) ).

fof(fact_enum__UNIV,axiom,
    ! [T_a] :
      ( class_Enum_Oenum(T_a)
     => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_enum__UNIV) ).

fof(fact_in__enum,axiom,
    ! [V_x_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ),
    file('theBenchmark.p',fact_in__enum) ).

fof(fact_enum__option__def,axiom,
    ! [T_a] :
      ( class_Enum_Oenum(T_a)
     => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ),
    file('theBenchmark.p',fact_enum__option__def) ).

fof(fact_enum__distinct,axiom,
    ! [T_a] :
      ( class_Enum_Oenum(T_a)
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ),
    file('theBenchmark.p',fact_enum__distinct) ).

fof(fact_enum__fun__code,axiom,
    ! [T_b,T_a] :
      ( ( class_Enum_Oenum(T_b)
        & class_HOL_Oequal(T_a)
        & class_Enum_Oenum(T_a) )
     => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ),
    file('theBenchmark.p',fact_enum__fun__code) ).

fof(fact_enum__fun__def,axiom,
    ! [T_b,T_a] :
      ( ( class_Enum_Oenum(T_b)
        & class_Enum_Oenum(T_a) )
     => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ),
    file('theBenchmark.p',fact_enum__fun__def) ).

fof(fact_all__n__lists__def,axiom,
    ! [V_n_2,V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a)))))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_all__n__lists__def) ).

fof(fact_ex__n__lists__def,axiom,
    ! [V_n_2,V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
      <=> ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) ) ) ),
    file('theBenchmark.p',fact_ex__n__lists__def) ).

fof(fact_enum__all__fun__def,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
      <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ),
    file('theBenchmark.p',fact_enum__all__fun__def) ).

fof(fact_enum__ex__fun__def,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
      <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ),
    file('theBenchmark.p',fact_enum__ex__fun__def) ).

fof(fact_enum__all__prod__def,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ),
    file('theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ),
    file('theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_all__code,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ),
    file('theBenchmark.p',fact_all__code) ).

fof(fact_exists__code,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ),
    file('theBenchmark.p',fact_exists__code) ).

fof(fact_enum__all,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
      <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__all) ).

fof(fact_enum__ex,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
      <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__ex) ).

fof(fact_enum__all__option__def,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
      <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
          & hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) ) ) ),
    file('theBenchmark.p',fact_enum__all__option__def) ).

fof(fact_enum__ex__option__def,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
      <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
          | hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) ) ) ),
    file('theBenchmark.p',fact_enum__ex__option__def) ).

fof(fact_order__fun_I1_J,axiom,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Orderings_Oorder(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ),
    file('theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_order__fun_I2_J,axiom,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_Orderings_Oorder(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
      <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_order__fun_I2_J) ).

fof(fact_enum__ex__fun__code,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_HOL_Oequal(T_a)
        & class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
      <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ),
    file('theBenchmark.p',fact_enum__ex__fun__code) ).

fof(fact_enum__all__fun__code,axiom,
    ! [V_P_2,T_a,T_b] :
      ( ( class_HOL_Oequal(T_a)
        & class_Enum_Oenum(T_a)
        & class_Enum_Oenum(T_b) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
      <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ),
    file('theBenchmark.p',fact_enum__all__fun__code) ).

fof(fact_map__of__zip__enum__is__Some,axiom,
    ! [V_x,V_ys,T_b,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))
       => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ),
    file('theBenchmark.p',fact_map__of__zip__enum__is__Some) ).

fof(fact_list__all2__def,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__all2__def) ).

fof(fact_list__all2__lengthD,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_list__all2__dropI,axiom,
    ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
     => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ),
    file('theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__takeI,axiom,
    ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
     => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ),
    file('theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_list__all2__eq,axiom,
    ! [T_a,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__eq) ).

fof(fact_list__all2__appendI,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
     => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2)
       => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ),
    file('theBenchmark.p',fact_list__all2__appendI) ).

fof(fact_list__all2__Nil,axiom,
    ! [V_ys_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_list__all2__Nil2,axiom,
    ! [V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_list__all2__append,axiom,
    ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
     => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))
      <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2)
          & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ),
    file('theBenchmark.p',fact_list__all2__append) ).

fof(fact_list__all2__map2,axiom,
    ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2))
    <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map2) ).

fof(fact_list__all2__map1,axiom,
    ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2)
    <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map1) ).

fof(fact_list__all2__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
    <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
        & hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_list__all2__nthD2,axiom,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))
       => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_list__all2__nthD,axiom,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
       => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_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_a)),V_xs_2)))
           => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_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_ys_2)))
         => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,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_a)),V_xs_2)))
     => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
       => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
         => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_list__all2I,axiom,
    ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
       => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_list__all2I) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [V_x_2,V_P_2,V_xs_2,T_a] :
      ( ! [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_a)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ),
    file('theBenchmark.p',fact_map__removeAll__inj__on) ).

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_removeAll__id,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_removeAll__id) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [V_xs_2,T_a] :
      ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
    <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_distinct__removeAll,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ),
    file('theBenchmark.p',fact_distinct__removeAll) ).

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_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_length__remdups__eq,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
    <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_set__remdups,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    file('theBenchmark.p',fact_set__remdups) ).

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_removeAll__append,axiom,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
    file('theBenchmark.p',fact_removeAll__append) ).

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_a] :
      ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
    <=> V_x_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [V_x_2,T_a] :
      ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
    <=> V_x_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_remdups__map__remdups,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( V_x != V_y
       => hAPP(c_List_OremoveAll(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),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) )
      & ( V_x = V_y
       => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ),
    file('theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_distinct__remove1__removeAll,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ),
    file('theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) ),
    file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)),
    file('theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_map__removeAll__inj,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ),
    file('theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_set__removeAll,axiom,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_set__removeAll) ).

fof(fact_length__remdups__concat,axiom,
    ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))),
    file('theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

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_map__concat,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_map__concat) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [V_xss_2,T_a] :
      ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [V_xss_2,T_a] :
      ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_sort__key__simps_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_concat__conv__foldl,axiom,
    ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2),
    file('theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_foldl__conv__concat,axiom,
    ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)),
    file('theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_set__sort,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ),
    file('theBenchmark.p',fact_set__sort) ).

fof(fact_length__sort,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_length__sort) ).

fof(fact_distinct__sort,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
      <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__sort) ).

fof(fact_length__concat,axiom,
    ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)),
    file('theBenchmark.p',fact_length__concat) ).

fof(fact_set__concat,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)),
    file('theBenchmark.p',fact_set__concat) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ),
    file('theBenchmark.p',fact_sort__key__simps_I2_J) ).

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_sort__foldl__insort,axiom,
    ! [V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ),
    file('theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
       => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
        <=> V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_concat__injective,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
         => V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__injective) ).

fof(fact_concat__map__singleton,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2),
    file('theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))),
    file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))),
    file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_filter__concat,axiom,
    ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__concat) ).

fof(fact_filter__sort,axiom,
    ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ),
    file('theBenchmark.p',fact_filter__sort) ).

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_partition__filter2,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_partition__filter2) ).

fof(fact_distinct__filter,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__filter) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2),
    file('theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_length__filter__le,axiom,
    ! [V_xs_2,V_P_2,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)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    file('theBenchmark.p',fact_length__filter__le) ).

fof(fact_filter__is__subset,axiom,
    ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    file('theBenchmark.p',fact_filter__is__subset) ).

fof(fact_filter__id__conv,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__id__conv) ).

fof(fact_filter__insort__triv,axiom,
    ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_remove1__filter__not,axiom,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_filter__remove1,axiom,
    ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)),
    file('theBenchmark.p',fact_filter__remove1) ).

fof(fact_filter__filter,axiom,
    ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_filter__filter) ).

fof(fact_partition__filter1,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2),
    file('theBenchmark.p',fact_partition__filter1) ).

fof(fact_filter__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)),
    file('theBenchmark.p',fact_filter__append) ).

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_filter_Osimps_I1_J,axiom,
    ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_filter__empty__conv,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => ~ hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_filter__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__map) ).

fof(fact_removeAll__filter__not,axiom,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_remdups__filter,axiom,
    ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)),
    file('theBenchmark.p',fact_remdups__filter) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))),
    file('theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_nth__transpose,axiom,
    ! [V_xs_2,T_a,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_a))),c_List_Otranspose(T_a,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ),
    file('theBenchmark.p',fact_nth__transpose) ).

fof(fact_transpose__map__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)),
    file('theBenchmark.p',fact_transpose__map__map) ).

fof(fact_set__filter,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)),
    file('theBenchmark.p',fact_set__filter) ).

fof(fact_length__filter__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_length__filter__map) ).

fof(fact_length__filter__less,axiom,
    ! [V_P_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_length__filter__less) ).

fof(fact_partition__filter__conv,axiom,
    ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_set__minus__filter__out,axiom,
    ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    file('theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__in__sublist,axiom,
    ! [V_s_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ),
    file('theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_transpose__empty,axiom,
    ! [V_xs_2,T_a] :
      ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
         => B_x = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_transpose__empty) ).

fof(fact_length__filter__conv__card,axiom,
    ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))),
    file('theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)))
     => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_map__filter__def,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),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,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)),
    file('theBenchmark.p',fact_map__filter__def) ).

fof(fact_map__filter__simps_I2_J,axiom,
    ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_map__filter__simps_I2_J) ).

fof(fact_map__of__filter__in,axiom,
    ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2)
     => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
       => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),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_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_map__filter__simps_I1_J) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,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_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2),
    file('theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2),
    file('theBenchmark.p',fact_pick__drop__zero) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(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_Opsimps_I1_J) ).

fof(fact_map__filter__map__filter,axiom,
    ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2),
    file('theBenchmark.p',fact_map__filter__map__filter) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [V_xss_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)))
     => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_transpose__max__length,axiom,
    ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)),
    file('theBenchmark.p',fact_transpose__max__length) ).

fof(fact_transpose__aux__max,axiom,
    ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_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_a)),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)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_foldr__append,axiom,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)),
    file('theBenchmark.p',fact_foldr__append) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2,
    file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)),
    file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [V_a_2,V_xs_2,T_a] :
      ( class_Groups_Oab__semigroup__add(T_a)
     => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ),
    file('theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_foldr__map,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2),
    file('theBenchmark.p',fact_foldr__map) ).

fof(fact_foldl__foldr1,axiom,
    ! [V_xs_2,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [V_xs_2,V_a_2,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_length__transpose,axiom,
    ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__transpose) ).

fof(fact_sublist__def,axiom,
    ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__def) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__shift__lemma) ).

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_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_length__upt,axiom,
    ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
    file('theBenchmark.p',fact_length__upt) ).

fof(fact_upt__Suc__append,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_upt__Suc,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ),
    file('theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__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_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__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_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__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_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__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_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_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_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_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_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_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_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_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_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_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_map__nth,axiom,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2,
    file('theBenchmark.p',fact_map__nth) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_nth__map__upt,axiom,
    ! [V_f_2,T_a,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_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_transpose__rectangle,axiom,
    ! [V_n_2,T_a,V_xs_2] :
      ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
       => 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_a))),V_xs_2)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 )
       => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),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_insort__key__remove1,axiom,
    ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
         => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),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_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ),
    file('theBenchmark.p',fact_insort__key__remove1) ).

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__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__Cons,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
          & c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__Cons) ).

fof(fact_sorted__sort,axiom,
    ! [V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__sort) ).

fof(fact_sorted__insort,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))
      <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ),
    file('theBenchmark.p',fact_sorted__insort) ).

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_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__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__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_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__insert,axiom,
    ! [V_x_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert) ).

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_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__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_sorted__many__eq,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)))
      <=> ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_sorted__many__eq) ).

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_sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
       => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
         => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
           => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
             => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
               => V_xs_2 = V_ys_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_sorted__sort__key,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ),
    file('theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_sorted__map__remove1,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_sorted__insort__key,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)))
      <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_sorted__map__same,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ),
    file('theBenchmark.p',fact_sorted__map__same) ).

fof(fact_sorted__filter,axiom,
    ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__filter) ).

fof(fact_sorted__same,axiom,
    ! [V_xs_2,V_g_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__same) ).

fof(fact_sorted__append,axiom,
    ! [V_ys_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) )
          & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
          & c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__append) ).

fof(fact_filter__insort,axiom,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
       => ( hBOOL(hAPP(V_P_2,V_x_2))
         => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_filter__insort) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [V_a1_2,V_a2_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
      <=> ( c_List_Olinorder__class_Osorted(T_a,V_a1_2)
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) ) ) ),
    file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__list__of__set,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)))
          & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
          & hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_insort__remove1,axiom,
    ! [V_xs_2,V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_insort__remove1) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,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_a)),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_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__equals__nth__mono) ).

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_map__sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
       => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
         => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
           => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
             => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
               => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
                 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_transpose__column,axiom,
    ! [V_i_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),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_a))),V_xs_2)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ),
    file('theBenchmark.p',fact_transpose__column) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),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_a))),c_List_Otranspose(T_a,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_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2))))
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ),
    file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_inj__on__rev,axiom,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2),
    file('theBenchmark.p',fact_inj__on__rev) ).

fof(fact_distinct__rev,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rev) ).

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_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_Nil__is__rev__conv,axiom,
    ! [V_xs_2,T_a] :
      ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
    <=> V_xs_2 = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_singleton__rev__conv,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [V_x_2,V_xs_2,T_a] :
      ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_rev__singleton__conv) ).

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__eq__Cons__iff,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_a] :
      ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_rev__concat,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))),
    file('theBenchmark.p',fact_rev__concat) ).

fof(fact_rev__map,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    file('theBenchmark.p',fact_rev__map) ).

fof(fact_rev__filter,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)),
    file('theBenchmark.p',fact_rev__filter) ).

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_set__rev,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    file('theBenchmark.p',fact_set__rev) ).

fof(fact_list__all2__rev1,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
    <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ),
    file('theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_list__all2__rev,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2))
    <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__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_a] :
      ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),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_a] :
      ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
    <=> V_xs_2 = hAPP(c_List_Orev(T_a),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_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_foldl__foldr,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2),
    file('theBenchmark.p',fact_foldl__foldr) ).

fof(fact_foldr__foldl,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    file('theBenchmark.p',fact_foldr__foldl) ).

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_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))),
    file('theBenchmark.p',fact_sorted__transpose) ).

fof(fact_rev__foldl__cons,axiom,
    ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2),
    file('theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_rev__drop,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__take) ).

fof(fact_rotate__rev,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
    file('theBenchmark.p',fact_rotate__rev) ).

fof(fact_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_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_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_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
       => ( ( V_xs_2 != c_List_Olist_ONil(T_a)
           => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
          & ( V_xs_2 = c_List_Olist_ONil(T_a)
           => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_length__transpose__sorted,axiom,
    ! [V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
     => ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,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_a] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),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_a))),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_transpose__column__length) ).

fof(fact_transpose__transpose,axiom,
    ! [V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
     => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),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_sorted__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_length__takeWhile__le,axiom,
    ! [V_xs_2,V_P_2,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_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    file('theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_set__takeWhileD,axiom,
    ! [V_xs_2,V_P_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_takeWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_takeWhile__map) ).

fof(fact_takeWhile__tail,axiom,
    ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_distinct__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__takeWhile) ).

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_takeWhile__append1,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
     => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ),
    file('theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_takeWhile__nth,axiom,
    ! [V_xs_2,V_P_2,T_a,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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ),
    file('theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_takeWhile__not__last,axiom,
    ! [T_a,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
       => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,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_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
       => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),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_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_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_takeWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,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_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2,
    file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_dropWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_dropWhile__map) ).

fof(fact_sorted__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_length__dropWhile__le,axiom,
    ! [V_xs_2,V_P_2,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_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    file('theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_hd__dropWhile,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
     => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_distinct__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_dropWhile__append1,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_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_P_2,T_a] :
      ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
    <=> ( ~ hBOOL(hAPP(V_P_2,V_y_2))
        & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_dropWhile__nth,axiom,
    ! [V_xs_2,V_P_2,T_a,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_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_listsum__map__filter,axiom,
    ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
           => ( ~ hBOOL(hAPP(V_P_2,B_x))
             => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),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_takeWhile__eq__filter,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
         => ~ hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [V_P_2,V_xs_2,T_a,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(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
         => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
       => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [V_xs_2,T_a,V_P_2,V_j_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ),
    file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_sorted_Osimps,axiom,
    ! [V_a_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
      <=> ( ? [B_xs,B_x] :
              ( c_List_Olinorder__class_Osorted(T_a,B_xs)
              & ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
              & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) )
          | V_a_2 = c_List_Olist_ONil(T_a) ) ) ),
    file('theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_map__upds__def,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))),
    file('theBenchmark.p',fact_map__upds__def) ).

fof(fact_map__comp__def,axiom,
    ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)),
    file('theBenchmark.p',fact_map__comp__def) ).

fof(fact_map__of__append,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)),
    file('theBenchmark.p',fact_map__of__append) ).

fof(fact_map__comp__empty_I1_J,axiom,
    ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_map__comp__empty_I1_J) ).

fof(fact_map__comp__empty_I2_J,axiom,
    ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a),
    file('theBenchmark.p',fact_map__comp__empty_I2_J) ).

fof(fact_map__comp__simps_I2_J,axiom,
    ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
      ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
     => c_Map_Omap__comp(T_a,T_c,T_b,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__add__find__right,axiom,
    ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
      ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
     => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ),
    file('theBenchmark.p',fact_map__add__find__right) ).

fof(fact_map__comp__Some__iff,axiom,
    ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
      ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
    <=> ? [B_k_H] :
          ( hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
          & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) ) ),
    file('theBenchmark.p',fact_map__comp__Some__iff) ).

fof(fact_map__add__upd,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),
    file('theBenchmark.p',fact_map__add__upd) ).

fof(fact_map__add__SomeD,axiom,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
     => ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),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_a,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
    <=> ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ),
    file('theBenchmark.p',fact_map__add__Some__iff) ).

fof(fact_map__comp__simps_I1_J,axiom,
    ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
      ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
     => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ),
    file('theBenchmark.p',fact_map__comp__simps_I1_J) ).

fof(fact_map__add__None,axiom,
    ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
      ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
    <=> ( hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a)
        & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ),
    file('theBenchmark.p',fact_map__add__None) ).

fof(fact_map__add__empty,axiom,
    ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2,
    file('theBenchmark.p',fact_map__add__empty) ).

fof(fact_empty__map__add,axiom,
    ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2,
    file('theBenchmark.p',fact_empty__map__add) ).

fof(fact_map__add__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2),
    file('theBenchmark.p',fact_map__add__upds) ).

fof(fact_dom__map__add,axiom,
    ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)),
    file('theBenchmark.p',fact_dom__map__add) ).

fof(fact_map__add__dom__app__simps_I2_J,axiom,
    ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
     => hAPP(c_Map_Omap__add(T_a,T_b,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_b,V_m_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_a,T_b,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_b,V_m_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).

fof(fact_map__add__assoc,axiom,
    ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2),
    file('theBenchmark.p',fact_map__add__assoc) ).

fof(fact_inj__on__map__add__dom,axiom,
    ! [V_m_H_2,V_m_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2))
    <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ),
    file('theBenchmark.p',fact_inj__on__map__add__dom) ).

fof(fact_map__add__def,axiom,
    ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)),
    file('theBenchmark.p',fact_map__add__def) ).

fof(fact_map__add__comm,axiom,
    ! [V_m2_2,V_m1_2,T_b,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
     => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ),
    file('theBenchmark.p',fact_map__add__comm) ).

fof(fact_map__comp__None__iff,axiom,
    ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
      ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
    <=> ( ? [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) )
        | hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ),
    file('theBenchmark.p',fact_map__comp__None__iff) ).

fof(fact_map__add__map__of__foldr,axiom,
    ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2),
    file('theBenchmark.p',fact_map__add__map__of__foldr) ).

fof(fact_map__add__upd__left,axiom,
    ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
     => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ),
    file('theBenchmark.p',fact_map__add__upd__left) ).

fof(fact_finite__range__map__of__map__add,axiom,
    ! [V_l_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__map__of__map__add) ).

fof(fact_List_Oinsert__def,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
       => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_not__in__set__insert,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_distinct__insert,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_Oinsert(T_a,V_x,V_xs))) ),
    file('theBenchmark.p',fact_distinct__insert) ).

fof(fact_insert__remdups,axiom,
    ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
    file('theBenchmark.p',fact_insert__remdups) ).

fof(fact_in__set__insert,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
     => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_in__set__insert) ).

fof(fact_List_Oset__insert,axiom,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_insert__Nil,axiom,
    ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_insert__Nil) ).

fof(fact_concat__map__maps,axiom,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2),
    file('theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_maps__def) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)),
    file('theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_distinct__concat,axiom,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
     => ( ! [B_ys] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
           => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
       => ( ! [B_ys] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
             => ! [B_zs] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
                 => ( B_ys != B_zs
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__concat) ).

fof(fact_ran__restrictD,axiom,
    ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2))))
     => ? [B_x] :
          ( hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ran__restrictD) ).

fof(fact_measures__lesseq,axiom,
    ! [V_fs_2,T_a,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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
    file('theBenchmark.p',fact_measures__lesseq) ).

fof(fact_in__measures_I2_J,axiom,
    ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
          & 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))) ) ),
    file('theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_wf__measures,axiom,
    ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)),
    file('theBenchmark.p',fact_wf__measures) ).

fof(fact_in__measures_I1_J,axiom,
    ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))),
    file('theBenchmark.p',fact_in__measures_I1_J) ).

fof(fact_measures__def,axiom,
    ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)),
    file('theBenchmark.p',fact_measures__def) ).

fof(fact_measures__less,axiom,
    ! [V_fs_2,T_a,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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
    file('theBenchmark.p',fact_measures__less) ).

fof(fact_foldl__apply,axiom,
    ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) )
     => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ),
    file('theBenchmark.p',fact_foldl__apply) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2))
       => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) )
     => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ),
    file('theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_map__of__eqI,axiom,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))))
           => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) )
       => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ),
    file('theBenchmark.p',fact_map__of__eqI) ).

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_dropWhile__append2,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ),
    file('theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_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_a)),V_a_2)))
           => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) )
       => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_finite__map__freshness,axiom,
    ! [V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
       => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ),
    file('theBenchmark.p',fact_finite__map__freshness) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [V_A_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
       => ? [B_x] :
            ( ! [B_y] :
                ( ( hBOOL(hAPP(c_List_Odistinct(T_a),B_y))
                  & c_List_Olinorder__class_Osorted(T_a,B_y)
                  & hAPP(c_List_Oset(T_a),B_y) = V_A_2 )
               => B_y = B_x )
            & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
            & c_List_Olinorder__class_Osorted(T_a,B_x)
            & hAPP(c_List_Oset(T_a),B_x) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_takeWhile__append2,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ),
    file('theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_insort__is__Cons,axiom,
    ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
      ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
    <=> ? [B_us,B_vs] :
          ( V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
          & hBOOL(hAPP(V_P_2,V_x_2))
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
             => ~ hBOOL(hAPP(V_P_2,B_x)) )
          & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) ) ),
    file('theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)
    <=> ? [B_us,B_vs] :
          ( V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
          & hBOOL(hAPP(V_P_2,V_x_2))
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
             => ~ hBOOL(hAPP(V_P_2,B_x)) )
          & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) ) ),
    file('theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_list__ball__nth,axiom,
    ! [V_P_2,V_xs_2,T_a,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_a)),V_xs_2)))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
           => hBOOL(hAPP(V_P_2,B_x)) )
       => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ),
    file('theBenchmark.p',fact_list__ball__nth) ).

fof(fact_sorted_OCons,axiom,
    ! [V_x_2,V_xs_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
       => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
         => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_sorted_OCons) ).

fof(fact_list__ex__length,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
    <=> ? [B_n] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_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_a)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex__length) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
    <=> ? [B_ys] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys)))
          & ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ),
    file('theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_list__ex__simps_I2_J,axiom,
    ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_list__ex__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__ex(T_a,V_P_2,V_ys_2)
        | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_list__ex__append) ).

fof(fact_list__ex__iff,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex__iff) ).

fof(fact_list__ex__rev,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
    <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_list__ex__rev) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
    <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
    <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ),
    file('theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
    <=> ? [B_ys,B_zs] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs)))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ),
    file('theBenchmark.p',fact_in__set__conv__decomp__last) ).

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

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

fof(fact_list__all__length,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,V_xs_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_a)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ),
    file('theBenchmark.p',fact_list__all__length) ).

fof(fact_measure__function__int,axiom,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    file('theBenchmark.p',fact_measure__function__int) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
    <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        & hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_list__all__rev,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
    <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_list__all__rev) ).

fof(fact_Ball__set__list__all,axiom,
    ! [V_P_2,V_xs_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_measure__fst,axiom,
    ! [T_b,V_f_2,T_a] :
      ( c_FunDef_Ois__measure(T_a,V_f_2)
     => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ),
    file('theBenchmark.p',fact_measure__fst) ).

fof(fact_measure__snd,axiom,
    ! [T_b,V_f_2,T_a] :
      ( c_FunDef_Ois__measure(T_a,V_f_2)
     => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ),
    file('theBenchmark.p',fact_measure__snd) ).

fof(fact_list__all__iff,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_list__all__iff) ).

fof(fact_is__measure_Osimps,axiom,
    ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2),
    file('theBenchmark.p',fact_is__measure_Osimps) ).

fof(fact_is__measure_Oequations,axiom,
    ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2),
    file('theBenchmark.p',fact_is__measure_Oequations) ).

fof(fact_is__measure_Ointros,axiom,
    ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2),
    file('theBenchmark.p',fact_is__measure_Ointros) ).

fof(fact_measure__size,axiom,
    ! [T_a] :
      ( class_Nat_Osize(T_a)
     => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ),
    file('theBenchmark.p',fact_measure__size) ).

fof(fact_list__all__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__all(T_a,V_P_2,V_ys_2)
        & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_list__all__append) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_list__all__iff__raw,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
    <=> ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
         => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) )
        & ( hBOOL(hAPP(V_P_2,V_x_2))
         => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) ) ),
    file('theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_equal__fun__def,axiom,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( class_Enum_Oenum(T_a)
        & class_HOL_Oequal(T_b) )
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
           => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ),
    file('theBenchmark.p',fact_equal__fun__def) ).

fof(fact_list__ex1__simps_I1_J,axiom,
    ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_list__ex1__simps_I1_J) ).

fof(fact_equal,axiom,
    ! [T_a] :
      ( class_HOL_Oequal(T_a)
     => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ),
    file('theBenchmark.p',fact_equal) ).

fof(fact_equal__refl,axiom,
    ! [V_x,T_a] :
      ( class_HOL_Oequal(T_a)
     => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ),
    file('theBenchmark.p',fact_equal__refl) ).

fof(fact_equal__eq,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_HOL_Oequal(T_a)
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_equal__eq) ).

fof(fact_eq__equal,axiom,
    ! [T_a] :
      ( class_HOL_Oequal(T_a)
     => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ),
    file('theBenchmark.p',fact_eq__equal) ).

fof(fact_exists1__code,axiom,
    ! [V_P_2,T_a] :
      ( class_Enum_Oenum(T_a)
     => ( ? [B_x] :
            ( ! [B_y] :
                ( hBOOL(hAPP(V_P_2,B_y))
               => B_y = B_x )
            & hBOOL(hAPP(V_P_2,B_x)) )
      <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ),
    file('theBenchmark.p',fact_exists1__code) ).

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

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

fof(fact_list__ex1__iff,axiom,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( ! [B_y] :
              ( ( hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) )
             => B_y = B_x )
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_size__code,axiom,
    ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)),
    file('theBenchmark.p',fact_size__code) ).

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_eq__int__code_I7_J,axiom,
    ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))),
    file('theBenchmark.p',fact_eq__int__code_I7_J) ).

fof(fact_eq__int__code_I11_J,axiom,
    ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)),
    file('theBenchmark.p',fact_eq__int__code_I11_J) ).

fof(fact_eq__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_eq__int__code_I13_J) ).

fof(fact_eq__int__code_I1_J,axiom,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_eq__int__code_I1_J) ).

fof(fact_eq__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_eq__int__code_I16_J) ).

fof(fact_eq__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_eq__number__of__int__code) ).

fof(fact_eq__int__code_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('theBenchmark.p',fact_eq__int__code_I6_J) ).

fof(fact_eq__int__code_I4_J,axiom,
    ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))),
    file('theBenchmark.p',fact_eq__int__code_I4_J) ).

fof(fact_eq__int__code_I10_J,axiom,
    ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)),
    file('theBenchmark.p',fact_eq__int__code_I10_J) ).

fof(fact_equal__int__def,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
    <=> 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_equal__int__def) ).

fof(fact_eq__int__code_I14_J,axiom,
    ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))),
    file('theBenchmark.p',fact_eq__int__code_I14_J) ).

fof(fact_eq__int__code_I15_J,axiom,
    ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))),
    file('theBenchmark.p',fact_eq__int__code_I15_J) ).

fof(fact_eq__int__code_I3_J,axiom,
    ! [V_k2_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ),
    file('theBenchmark.p',fact_eq__int__code_I3_J) ).

fof(fact_eq__int__code_I9_J,axiom,
    ! [V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__int__code_I9_J) ).

fof(fact_eq__int__code_I8_J,axiom,
    ! [V_k2_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ),
    file('theBenchmark.p',fact_eq__int__code_I8_J) ).

fof(fact_eq__int__code_I12_J,axiom,
    ! [V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_eq__int__code_I12_J) ).

fof(fact_eq__int__code_I5_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('theBenchmark.p',fact_eq__int__code_I5_J) ).

fof(fact_eq__int__code_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('theBenchmark.p',fact_eq__int__code_I2_J) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)),
    file('theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_seq__case,axiom,
    ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    file('theBenchmark.p',fact_seq__case) ).

fof(fact_eq__int__refl,axiom,
    ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)),
    file('theBenchmark.p',fact_eq__int__refl) ).

fof(fact_yieldn__def,axiom,
    ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)),
    file('theBenchmark.p',fact_yieldn__def) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_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(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
    file('theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2)
    <=> ( V_lazy__sequence_2 = V_lazy__sequence_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact__01,axiom,
    ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)),
    file('theBenchmark.p',fact__01) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).

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

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,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_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),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_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) ),
    file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__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_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),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__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

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

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

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

fof(fact_neg__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_neg__bind__def) ).

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

fof(fact_neg__map__def,axiom,
    ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)),
    file('theBenchmark.p',fact_neg__map__def) ).

fof(fact_neg__single__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2),
    file('theBenchmark.p',fact_neg__single__def) ).

fof(fact_pos__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_pos__bind__def) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
    file('theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_pos__map__def,axiom,
    ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),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_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2),
    file('theBenchmark.p',fact_pos__single__def) ).

fof(fact_length__splice,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(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__splice) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
    file('theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_splice__Nil2,axiom,
    ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
    file('theBenchmark.p',fact_splice__Nil2) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
    file('theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
    file('theBenchmark.p',fact_splice_Osimps_I2_J) ).

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) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
    file('theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_acyclicP__converse,axiom,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2))))
    <=> c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_converse__meet,axiom,
    ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)),
    file('theBenchmark.p',fact_converse__meet) ).

fof(fact_conversep__eq,axiom,
    ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal,
    file('theBenchmark.p',fact_conversep__eq) ).

fof(fact_conversep__conversep,axiom,
    ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_conversep__conversep) ).

fof(fact_conversep__iff,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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_Oequations,axiom,
    ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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_Ointros,axiom,
    ! [T_b,T_a,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_a,T_b,V_r_2),V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_conversepD,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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__noteq,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2))
    <=> V_x_2 != V_y_2 ),
    file('theBenchmark.p',fact_conversep__noteq) ).

fof(fact_converse__pred__comp,axiom,
    ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)),
    file('theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_converse__join,axiom,
    ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)),
    file('theBenchmark.p',fact_converse__join) ).

fof(fact_conversep__converse__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ),
    file('theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact__02,axiom,
    ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),
    file('theBenchmark.p',fact__02) ).

fof(fact_tl__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ),
    file('theBenchmark.p',fact_tl__replicate) ).

fof(fact_zip__replicate,axiom,
    ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    file('theBenchmark.p',fact_zip__replicate) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),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_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
    file('theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_replicate__Suc,axiom,
    ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
    file('theBenchmark.p',fact_replicate__Suc) ).

fof(fact_rev__replicate,axiom,
    ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
    file('theBenchmark.p',fact_rev__replicate) ).

fof(fact_last__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
    file('theBenchmark.p',fact_last__replicate) ).

fof(fact_drop__replicate,axiom,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
    file('theBenchmark.p',fact_drop__replicate) ).

fof(fact_hd__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
    file('theBenchmark.p',fact_hd__replicate) ).

fof(fact_take__replicate,axiom,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
    file('theBenchmark.p',fact_take__replicate) ).

fof(fact_Ball__set__replicate,axiom,
    ! [V_P_2,V_a_2,V_n_2,T_a] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2))))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_Bex__set__replicate,axiom,
    ! [V_P_2,V_a_2,V_n_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) )
    <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_Bex__set__replicate) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] :
      ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2)
    <=> ( ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 = V_y_2 )
        & V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_nth__replicate,axiom,
    ! [V_x,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),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__replicate) ).

fof(fact_in__set__replicate,axiom,
    ! [V_y_2,V_n_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2))))
    <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_in__set__replicate) ).

fof(fact_replicate__add,axiom,
    ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)),
    file('theBenchmark.p',fact_replicate__add) ).

fof(fact_append__replicate__commute,axiom,
    ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)),
    file('theBenchmark.p',fact_append__replicate__commute) ).

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_fun__HOL_Oequal,axiom,
    ! [T_1,T_2] :
      ( ( class_HOL_Oequal(T_1)
        & class_Enum_Oenum(T_2) )
     => class_HOL_Oequal(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__HOL_Oequal) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(arity_Com__Ocom__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Com_Ocom),
    file('theBenchmark.p',arity_Com__Ocom__HOL_Oequal) ).

fof(arity_Com__Ocom__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ocom),
    file('theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).

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__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__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).

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__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__HOL_Oequal) ).

fof(arity_Nat__Onat__Nat_Osize,axiom,
    class_Nat_Osize(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).

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_HOL__Obool__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__HOL_Oequal) ).

fof(arity_HOL__Obool__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(arity_HOL__Obool__Nat_Osize,axiom,
    class_Nat_Osize(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).

fof(arity_Com__Ostate__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Com_Ostate),
    file('theBenchmark.p',arity_Com__Ostate__HOL_Oequal) ).

fof(arity_Com__Ostate__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ostate),
    file('theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).

fof(arity_List__Olist__HOL_Oequal,axiom,
    ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)),
    file('theBenchmark.p',arity_List__Olist__HOL_Oequal) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
    file('theBenchmark.p',arity_List__Olist__Nat_Osize) ).

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_sum__HOL_Oequal,axiom,
    ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)),
    file('theBenchmark.p',arity_sum__HOL_Oequal) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
    file('theBenchmark.p',arity_sum__Nat_Osize) ).

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_Option__Ooption__HOL_Oequal,axiom,
    ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)),
    file('theBenchmark.p',arity_Option__Ooption__HOL_Oequal) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [T_1] :
      ( class_Enum_Oenum(T_1)
     => class_Enum_Oenum(tc_Option_Ooption(T_1)) ),
    file('theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
    file('theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

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_prod__HOL_Oequal,axiom,
    ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)),
    file('theBenchmark.p',arity_prod__HOL_Oequal) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
    file('theBenchmark.p',arity_prod__Nat_Osize) ).

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_Product____Type__Ounit__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__HOL_Oequal) ).

fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).

fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
    class_Nat_Osize(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).

fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Code__Evaluation_Oterm),
    file('theBenchmark.p',arity_Code____Evaluation__Oterm__HOL_Oequal) ).

fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    file('theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).

fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
    ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)),
    file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__HOL_Oequal) ).

fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
    file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

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__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__HOL_Oequal) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).

fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
    ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(help_c__COMBI__1,axiom,
    ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
    file('theBenchmark.p',help_c__COMBI__1) ).

fof(help_c__COMBK__1,axiom,
    ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
    file('theBenchmark.p',help_c__COMBK__1) ).

fof(help_c__COMBB__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBB__1) ).

fof(help_c__COMBC__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    file('theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBS__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBS__1) ).

fof(help_c__fequal__1,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
    file('theBenchmark.p',help_c__fequal__1) ).

fof(help_c__fequal__2,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
      | V_x_2 != V_y_2 ),
    file('theBenchmark.p',help_c__fequal__2) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('theBenchmark.p',help_c__fFalse__1) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('theBenchmark.p',help_c__fTrue__1) ).

fof(help_c__fNot__1,axiom,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    file('theBenchmark.p',help_c__fNot__1) ).

fof(help_c__fNot__2,axiom,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | ~ ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fNot__2) ).

fof(help_c__fconj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fconj__1) ).

fof(help_c__fconj__2,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__3) ).

fof(help_c__fdisj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fdisj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fimplies__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fimplies__1) ).

fof(help_c__fimplies__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fimplies__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fimplies__3) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),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))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),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_Procs)),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    file('theBenchmark.p',conj_2) ).

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]) ).

cnf(f_1_4,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_3]) ).

fof(f_2_1,plain,
    ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_empty]) ).

fof(f_2_2,plain,
    ! [U_4,U_3] : c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(f_3_2,plain,
    ! [U_6,U_5] : c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_a),V_fun1_2),V_com_2),V_fun2_2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple_Oinject]) ).

fof(f_4_2,plain,
    ! [U_13,U_12,U_11,U_10,U_9,U_8,U_7] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_8),U_9),U_10) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_11),U_12),U_13)
        | U_10 != U_13
        | U_9 != U_12
        | U_8 != U_11 )
      & ( ( U_10 = U_13
          & U_9 = U_12
          & U_8 = U_11 )
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_8),U_9),U_10) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_11),U_12),U_13) ) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ( ! [U_27,U_25,U_23,U_21,U_19,U_17] :
        ( ! [U_15] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_17),U_19),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_23),U_25),U_27)
        | U_21 != U_27
        | U_19 != U_25
        | U_17 != U_23 )
    & ! [U_26,U_24,U_22,U_20,U_18,U_16] :
        ( ! [U_14] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26)
        | ( U_20 = U_26
          & U_18 = U_24
          & U_16 = U_22 ) ) ),
    inference(miniscope,[status(thm)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( U_16 = U_22
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_5,plain,
    ( U_18 = U_24
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_6,plain,
    ( U_20 = U_26
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_7,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_17),U_19),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_23),U_25),U_27)
    | U_21 != U_27
    | U_19 != U_25
    | U_17 != U_23 ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_1,plain,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_cut]) ).

fof(f_5_2,plain,
    ! [U_31,U_30,U_29,U_28] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert]) ).

fof(f_6_2,plain,
    ! [U_35,U_34,U_33,U_32] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
        & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ),
    inference(fof_nnf,[status(thm)],[fact_derivs__insertD]) ).

fof(f_7_2,plain,
    ! [U_39,U_38,U_37,U_36] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,U_39)
        & c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_36),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_36),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ),
    inference(clausify,[status(thm)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,U_39)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_weak__Body]) ).

fof(f_8_2,plain,
    ! [U_44,U_43,U_42,U_41,U_40] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_40,U_41,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_40)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_40),U_42),hAPP(c_Com_Ocom_OBODY,U_43)),U_44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_40),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_40,U_41,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_40)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_40),U_42),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_43))),U_44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_40),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_40,U_41,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_40)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_40),U_42),hAPP(c_Com_Ocom_OBODY,U_43)),U_44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_40),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_40,U_41,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_40)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_40),U_42),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_43))),U_44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_40),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OBody]) ).

fof(f_9_2,plain,
    ! [U_49,U_48,U_47,U_46,U_45] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_45,U_46,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),c_Com_Ocom_OBODY)),U_48)),U_49))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_45,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_45),tc_HOL_Obool)),U_46),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),c_Com_Ocom_OBODY)),U_48)),U_49)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),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_48)),U_49)) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

cnf(f_9_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_45,U_46,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),c_Com_Ocom_OBODY)),U_48)),U_49))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_45,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_45),tc_HOL_Obool)),U_46),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),c_Com_Ocom_OBODY)),U_48)),U_49)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_45),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),hAPP(hAPP(c_COMBB(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_45,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_45))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_45)),U_47)),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_48)),U_49)) ),
    inference(clausify,[status(thm)],[f_9_2]) ).

fof(f_10_1,plain,
    ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_BodyN]) ).

fof(f_10_2,plain,
    ! [U_54,U_53,U_52,U_51,U_50] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_50,U_54,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Com_Ocom_OBODY,U_52)),U_53)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_50),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_50,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Com_Ocom_OBODY,U_52)),U_53)),U_54),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_52))),U_53)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_50),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_50,U_54,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Com_Ocom_OBODY,U_52)),U_53)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_50),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_50,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Com_Ocom_OBODY,U_52)),U_53)),U_54),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_50)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_50),U_51),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_52))),U_53)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_50),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [V_s1,V_s,V_P] :
      ( hBOOL(hAPP(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(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_11_2,plain,
    ! [U_57,U_56,U_55] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_55))),U_56),U_57))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_55)),U_56),U_57)) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

cnf(f_11_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_55))),U_56),U_57))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_55)),U_56),U_57)) ),
    inference(clausify,[status(thm)],[f_11_2]) ).

fof(f_12_1,plain,
    ! [V_s1,V_s0,V_pn] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1))
      | ~ hBOOL(hAPP(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_12_2,plain,
    ! [U_60,U_59,U_58] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_58)),U_59),U_60))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_58))),U_59),U_60)) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

cnf(f_12_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_58)),U_59),U_60))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_58))),U_59),U_60)) ),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_1,plain,
    ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Body__sound__lemma]) ).

fof(f_13_2,plain,
    ! [U_65,U_64,U_63,U_62,U_61] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_61,U_62,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),c_Com_Ocom_OBODY)),U_64)),U_65))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_61),tc_HOL_Obool)),U_62),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),c_Com_Ocom_OBODY)),U_64)),U_65)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),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_64)),U_65)) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_61,U_62,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),c_Com_Ocom_OBODY)),U_64)),U_65))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_61),tc_HOL_Obool)),U_62),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),c_Com_Ocom_OBODY)),U_64)),U_65)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_61),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),hAPP(hAPP(c_COMBB(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_61,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_61))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_61)),U_63)),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_64)),U_65)) ),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
        | ~ hBOOL(hAPP(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(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(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_14_2,plain,
    ! [U_68,U_67,U_66] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_66)),U_67),U_68))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_66))),U_67),U_68)) )
      & ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_66))),U_67),U_68))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_66)),U_67),U_68)) ) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ( ! [U_74,U_72,U_70] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_70)),U_72),U_74))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_70))),U_72),U_74)) )
    & ! [U_73,U_71,U_69] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_69))),U_71),U_73))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_69)),U_71),U_73)) ) ),
    inference(miniscope,[status(thm)],[f_14_2]) ).

cnf(f_14_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_69))),U_71),U_73))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_69)),U_71),U_73)) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

cnf(f_14_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,U_70)),U_72),U_74))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_70))),U_72),U_74)) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [V_Ga_2,V_pn_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_MGT__BodyN]) ).

fof(f_15_2,plain,
    ! [U_76,U_75] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_76,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_75))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_75))),U_76),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

cnf(f_15_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_76,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_75))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_75))),U_76),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_75)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_15_2]) ).

fof(f_16_1,plain,
    ! [V_pn_2,V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Body1]) ).

fof(f_16_2,plain,
    ! [U_82,U_81,U_80,U_79,U_78,U_77] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_77,U_78,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_77),hAPP(U_79,U_82)),hAPP(c_Com_Ocom_OBODY,U_82)),hAPP(U_80,U_82))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_77),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_82),U_81))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_77,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_77),tc_HOL_Obool)),U_78),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_77),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),hAPP(hAPP(c_COMBB(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_77)),U_79)),c_Com_Ocom_OBODY)),U_80)),U_81)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_77),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),hAPP(hAPP(c_COMBB(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_77)),U_79)),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_80)),U_81)) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

cnf(f_16_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_77,U_78,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_77),hAPP(U_79,U_82)),hAPP(c_Com_Ocom_OBODY,U_82)),hAPP(U_80,U_82))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_77),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_82),U_81))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_77,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_77),tc_HOL_Obool)),U_78),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_77),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),hAPP(hAPP(c_COMBB(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_77)),U_79)),c_Com_Ocom_OBODY)),U_80)),U_81)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_77),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),hAPP(hAPP(c_COMBB(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_77,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_77))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_77)),U_79)),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_80)),U_81)) ),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_1,plain,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_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_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).

fof(f_17_2,plain,
    ! [U_86,U_85,U_84,U_83] :
      ( ( hAPP(c_Set_Oimage(U_84,U_85,hAPP(c_COMBK(U_85,U_84),U_86)),U_83) = hAPP(hAPP(c_Set_Oinsert(U_85),U_86),c_Orderings_Obot__class_Obot(tc_fun(U_85,tc_HOL_Obool)))
        | U_83 = c_Orderings_Obot__class_Obot(tc_fun(U_84,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_84,U_85,hAPP(c_COMBK(U_85,U_84),U_86)),U_83) = c_Orderings_Obot__class_Obot(tc_fun(U_85,tc_HOL_Obool))
        | U_83 != c_Orderings_Obot__class_Obot(tc_fun(U_84,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ( ! [U_94,U_92,U_90,U_88] :
        ( hAPP(c_Set_Oimage(U_90,U_92,hAPP(c_COMBK(U_92,U_90),U_94)),U_88) = hAPP(hAPP(c_Set_Oinsert(U_92),U_94),c_Orderings_Obot__class_Obot(tc_fun(U_92,tc_HOL_Obool)))
        | U_88 = c_Orderings_Obot__class_Obot(tc_fun(U_90,tc_HOL_Obool)) )
    & ! [U_93,U_91,U_89,U_87] :
        ( hAPP(c_Set_Oimage(U_89,U_91,hAPP(c_COMBK(U_91,U_89),U_93)),U_87) = c_Orderings_Obot__class_Obot(tc_fun(U_91,tc_HOL_Obool))
        | U_87 != c_Orderings_Obot__class_Obot(tc_fun(U_89,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_17_2]) ).

cnf(f_17_4,plain,
    ( hAPP(c_Set_Oimage(U_89,U_91,hAPP(c_COMBK(U_91,U_89),U_93)),U_87) = c_Orderings_Obot__class_Obot(tc_fun(U_91,tc_HOL_Obool))
    | U_87 != c_Orderings_Obot__class_Obot(tc_fun(U_89,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_17_3]) ).

cnf(f_17_5,plain,
    ( hAPP(c_Set_Oimage(U_90,U_92,hAPP(c_COMBK(U_92,U_90),U_94)),U_88) = hAPP(hAPP(c_Set_Oinsert(U_92),U_94),c_Orderings_Obot__class_Obot(tc_fun(U_92,tc_HOL_Obool)))
    | U_88 = c_Orderings_Obot__class_Obot(tc_fun(U_90,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_1,plain,
    ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).

fof(f_18_2,plain,
    ! [U_97,U_96,U_95] : hAPP(hAPP(c_Set_Oinsert(U_95),U_96),U_97) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_95,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_95),U_96),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool)))),U_97),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

cnf(f_18_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_95),U_96),U_97) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_95,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_95),U_96),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool)))),U_97),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( 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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1E]) ).

fof(f_19_2,plain,
    ! [U_101,U_100,U_99,U_98] :
      ( hBOOL(hAPP(U_100,U_101))
      | hBOOL(hAPP(U_99,U_101))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_98,tc_HOL_Obool)),U_99),U_100),U_101)) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_101,U_100,U_99] :
      ( ! [U_98] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_98,tc_HOL_Obool)),U_99),U_100),U_101))
      | hBOOL(hAPP(U_100,U_101))
      | hBOOL(hAPP(U_99,U_101)) ),
    inference(miniscope,[status(thm)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_98,tc_HOL_Obool)),U_99),U_100),U_101))
    | hBOOL(hAPP(U_100,U_101))
    | hBOOL(hAPP(U_99,U_101)) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_1,plain,
    ! [T_a,V_A_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_20_2,plain,
    ! [U_105,U_104,U_103,U_102] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_105,tc_HOL_Obool)),U_104),U_102),U_103))
      | ( ~ hBOOL(hAPP(U_104,U_103))
        & ~ hBOOL(hAPP(U_102,U_103)) ) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    ( ~ hBOOL(hAPP(U_102,U_103))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_105,tc_HOL_Obool)),U_104),U_102),U_103)) ),
    inference(clausify,[status(thm)],[f_20_2]) ).

cnf(f_20_4,plain,
    ( ~ hBOOL(hAPP(U_104,U_103))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_105,tc_HOL_Obool)),U_104),U_102),U_103)) ),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).

fof(f_21_2,plain,
    ! [U_110,U_109,U_108,U_107,U_106] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_107,U_106)),U_108),U_109),U_110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_106),hAPP(U_108,U_110)),hAPP(U_109,U_110))
      | ~ class_Lattices_Olattice(U_106) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_107,U_106)),U_108),U_109),U_110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_106),hAPP(U_108,U_110)),hAPP(U_109,U_110))
    | ~ class_Lattices_Olattice(U_106) ),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [V_x_2,T_b,T_a] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Orderings_Obot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).

fof(f_22_2,plain,
    ! [U_113,U_112,U_111] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_112,U_111)),U_113) = c_Orderings_Obot__class_Obot(U_111)
      | ~ class_Orderings_Obot(U_111) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_112,U_111)),U_113) = c_Orderings_Obot__class_Obot(U_111)
    | ~ class_Orderings_Obot(U_111) ),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,plain,
    ! [V_c_2,T_a,V_B_2,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      | ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).

fof(f_23_2,plain,
    ! [U_117,U_116,U_115,U_114] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
        & ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
        & hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114)) )
      | U_114 != U_115 ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

cnf(f_23_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114))
    | hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114))
    | U_114 != U_115 ),
    inference(clausify,[status(thm)],[f_23_2]) ).

cnf(f_23_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
    | hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114))
    | U_114 != U_115 ),
    inference(clausify,[status(thm)],[f_23_2]) ).

cnf(f_23_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_114))
    | hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
    | U_114 != U_115 ),
    inference(clausify,[status(thm)],[f_23_2]) ).

cnf(f_23_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
    | hBOOL(hAPP(hAPP(c_member(U_116),U_117),U_115))
    | U_114 != U_115 ),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_emptyE]) ).

fof(f_24_2,plain,
    ! [U_119,U_118] : ~ hBOOL(hAPP(hAPP(c_member(U_118),U_119),c_Orderings_Obot__class_Obot(tc_fun(U_118,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_118),U_119),c_Orderings_Obot__class_Obot(tc_fun(U_118,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2)))
      | ( V_a_2 != V_b_2
        & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insertCI]) ).

fof(f_25_2,plain,
    ! [U_123,U_122,U_121,U_120] :
      ( hBOOL(hAPP(hAPP(c_member(U_120),U_121),hAPP(hAPP(c_Set_Oinsert(U_120),U_123),U_122)))
      | ( U_121 != U_123
        & ~ hBOOL(hAPP(hAPP(c_member(U_120),U_121),U_122)) ) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_120),U_121),U_122))
    | hBOOL(hAPP(hAPP(c_member(U_120),U_121),hAPP(hAPP(c_Set_Oinsert(U_120),U_123),U_122))) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( U_121 != U_123
    | hBOOL(hAPP(hAPP(c_member(U_120),U_121),hAPP(hAPP(c_Set_Oinsert(U_120),U_123),U_122))) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_insertE]) ).

fof(f_26_2,plain,
    ! [U_127,U_126,U_125,U_124] :
      ( hBOOL(hAPP(hAPP(c_member(U_124),U_125),U_127))
      | U_125 = U_126
      | ~ hBOOL(hAPP(hAPP(c_member(U_124),U_125),hAPP(hAPP(c_Set_Oinsert(U_124),U_126),U_127))) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

cnf(f_26_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_124),U_125),U_127))
    | U_125 = U_126
    | ~ hBOOL(hAPP(hAPP(c_member(U_124),U_125),hAPP(hAPP(c_Set_Oinsert(U_124),U_126),U_127))) ),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),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_27_2,plain,
    ! [U_133,U_132,U_131,U_130,U_129,U_128] :
      ( hBOOL(hAPP(hAPP(c_member(U_133),U_128),hAPP(c_Set_Oimage(U_131,U_133,U_129),U_132)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
      | U_128 != hAPP(U_129,U_130) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_133),U_128),hAPP(c_Set_Oimage(U_131,U_133,U_129),U_132)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
    | U_128 != hAPP(U_129,U_130) ),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UnCI]) ).

fof(f_28_2,plain,
    ! [U_137,U_136,U_135,U_134] :
      ( hBOOL(hAPP(hAPP(c_member(U_134),U_135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_134,tc_HOL_Obool)),U_137),U_136)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_134),U_135),U_137))
        & ~ hBOOL(hAPP(hAPP(c_member(U_134),U_135),U_136)) ) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

cnf(f_28_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_134),U_135),U_136))
    | hBOOL(hAPP(hAPP(c_member(U_134),U_135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_134,tc_HOL_Obool)),U_137),U_136))) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_134),U_135),U_137))
    | hBOOL(hAPP(hAPP(c_member(U_134),U_135),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_134,tc_HOL_Obool)),U_137),U_136))) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

fof(f_29_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnE]) ).

fof(f_29_2,plain,
    ! [U_141,U_140,U_139,U_138] :
      ( hBOOL(hAPP(hAPP(c_member(U_138),U_139),U_141))
      | hBOOL(hAPP(hAPP(c_member(U_138),U_139),U_140))
      | ~ hBOOL(hAPP(hAPP(c_member(U_138),U_139),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_138,tc_HOL_Obool)),U_140),U_141))) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_138),U_139),U_141))
    | hBOOL(hAPP(hAPP(c_member(U_138),U_139),U_140))
    | ~ hBOOL(hAPP(hAPP(c_member(U_138),U_139),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_138,tc_HOL_Obool)),U_140),U_141))) ),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_1,plain,
    ! [V_A_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__def]) ).

fof(f_30_2,plain,
    ! [U_144,U_143,U_142] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_142),U_143),U_144))
        | ~ hBOOL(hAPP(U_144,U_143)) )
      & ( hBOOL(hAPP(U_144,U_143))
        | ~ hBOOL(hAPP(hAPP(c_member(U_142),U_143),U_144)) ) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ( ! [U_150,U_148] :
        ( ! [U_146] : hBOOL(hAPP(hAPP(c_member(U_146),U_148),U_150))
        | ~ hBOOL(hAPP(U_150,U_148)) )
    & ! [U_149,U_147] :
        ( ! [U_145] : ~ hBOOL(hAPP(hAPP(c_member(U_145),U_147),U_149))
        | hBOOL(hAPP(U_149,U_147)) ) ),
    inference(miniscope,[status(thm)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_145),U_147),U_149))
    | hBOOL(hAPP(U_149,U_147)) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

cnf(f_30_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_146),U_148),U_150))
    | ~ hBOOL(hAPP(U_150,U_148)) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).

fof(f_31_2,plain,
    ! [U_153,U_152,U_151] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_151),U_152),hAPP(c_fequal,U_153)))
        | U_152 != U_153 )
      & ( U_152 = U_153
        | ~ hBOOL(hAPP(hAPP(c_member(U_151),U_152),hAPP(c_fequal,U_153))) ) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ( ! [U_159,U_157] :
        ( ! [U_155] : hBOOL(hAPP(hAPP(c_member(U_155),U_157),hAPP(c_fequal,U_159)))
        | U_157 != U_159 )
    & ! [U_158,U_156] :
        ( ! [U_154] : ~ hBOOL(hAPP(hAPP(c_member(U_154),U_156),hAPP(c_fequal,U_158)))
        | U_156 = U_158 ) ),
    inference(miniscope,[status(thm)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_154),U_156),hAPP(c_fequal,U_158)))
    | U_156 = U_158 ),
    inference(clausify,[status(thm)],[f_31_3]) ).

cnf(f_31_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_155),U_157),hAPP(c_fequal,U_159)))
    | U_157 != U_159 ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) != hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).

fof(f_32_2,plain,
    ! [U_162,U_161,U_160] :
      ( ( hAPP(hAPP(c_COMBC(U_160,tc_fun(U_160,tc_HOL_Obool),tc_HOL_Obool),c_member(U_160)),U_161) = hAPP(hAPP(c_COMBC(U_160,tc_fun(U_160,tc_HOL_Obool),tc_HOL_Obool),c_member(U_160)),U_162)
        | U_161 != U_162 )
      & ( U_161 = U_162
        | hAPP(hAPP(c_COMBC(U_160,tc_fun(U_160,tc_HOL_Obool),tc_HOL_Obool),c_member(U_160)),U_161) != hAPP(hAPP(c_COMBC(U_160,tc_fun(U_160,tc_HOL_Obool),tc_HOL_Obool),c_member(U_160)),U_162) ) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ( ! [U_168,U_166] :
        ( ! [U_164] : hAPP(hAPP(c_COMBC(U_164,tc_fun(U_164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_164)),U_166) = hAPP(hAPP(c_COMBC(U_164,tc_fun(U_164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_164)),U_168)
        | U_166 != U_168 )
    & ! [U_167,U_165] :
        ( ! [U_163] : hAPP(hAPP(c_COMBC(U_163,tc_fun(U_163,tc_HOL_Obool),tc_HOL_Obool),c_member(U_163)),U_165) != hAPP(hAPP(c_COMBC(U_163,tc_fun(U_163,tc_HOL_Obool),tc_HOL_Obool),c_member(U_163)),U_167)
        | U_165 = U_167 ) ),
    inference(miniscope,[status(thm)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( hAPP(hAPP(c_COMBC(U_163,tc_fun(U_163,tc_HOL_Obool),tc_HOL_Obool),c_member(U_163)),U_165) != hAPP(hAPP(c_COMBC(U_163,tc_fun(U_163,tc_HOL_Obool),tc_HOL_Obool),c_member(U_163)),U_167)
    | U_165 = U_167 ),
    inference(clausify,[status(thm)],[f_32_3]) ).

cnf(f_32_5,plain,
    ( hAPP(hAPP(c_COMBC(U_164,tc_fun(U_164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_164)),U_166) = hAPP(hAPP(c_COMBC(U_164,tc_fun(U_164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_164)),U_168)
    | U_166 != U_168 ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [V_x_2,T_a,V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).

fof(f_33_2,plain,
    ! [U_172,U_171,U_170,U_169] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_169))
          | ~ hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_170)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_170))
          | ~ hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_169)) ) )
      | U_169 != U_170 ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_170))
    | ~ hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_169))
    | U_169 != U_170 ),
    inference(clausify,[status(thm)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_169))
    | ~ hBOOL(hAPP(hAPP(c_member(U_171),U_172),U_170))
    | U_169 != U_170 ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [V_A_2,T_a,V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).

fof(f_34_2,plain,
    ! [U_176,U_175,U_174,U_173] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_175),U_173),U_176))
          | ~ hBOOL(hAPP(hAPP(c_member(U_175),U_174),U_176)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_175),U_174),U_176))
          | ~ hBOOL(hAPP(hAPP(c_member(U_175),U_173),U_176)) ) )
      | U_173 != U_174 ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_175),U_174),U_176))
    | ~ hBOOL(hAPP(hAPP(c_member(U_175),U_173),U_176))
    | U_173 != U_174 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_175),U_173),U_176))
    | ~ hBOOL(hAPP(hAPP(c_member(U_175),U_174),U_176))
    | U_173 != U_174 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [V_A_2,T_a,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).

fof(f_35_2,plain,
    ! [U_180,U_179,U_178,U_177] :
      ( hBOOL(hAPP(hAPP(c_member(U_179),U_177),U_180))
      | ~ hBOOL(hAPP(hAPP(c_member(U_179),U_178),U_180))
      | U_177 != U_178 ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_179),U_177),U_180))
    | ~ hBOOL(hAPP(hAPP(c_member(U_179),U_178),U_180))
    | U_177 != U_178 ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [V_a_2,T_a,V_A_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_equals0D]) ).

fof(f_36_2,plain,
    ! [U_183,U_182,U_181] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_182),U_183),U_181))
      | U_181 != c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_182),U_183),U_181))
    | U_181 != c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).

fof(f_37_2,plain,
    ! [U_185,U_184] : ~ hBOOL(hAPP(hAPP(c_member(U_184),U_185),c_Orderings_Obot__class_Obot(tc_fun(U_184,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_184),U_185),c_Orderings_Obot__class_Obot(tc_fun(U_184,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [V_A_2,T_a] :
      ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).

fof(f_38_2,plain,
    ! [U_189,U_188] :
      ( ( ? [U_187] : hBOOL(hAPP(hAPP(c_member(U_188),U_187),U_189))
        | U_189 = c_Orderings_Obot__class_Obot(tc_fun(U_188,tc_HOL_Obool)) )
      & ( U_189 != c_Orderings_Obot__class_Obot(tc_fun(U_188,tc_HOL_Obool))
        | ! [U_186] : ~ hBOOL(hAPP(hAPP(c_member(U_188),U_186),U_189)) ) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ( ! [U_193,U_191] :
        ( ? [U_187] : hBOOL(hAPP(hAPP(c_member(U_191),U_187),U_193))
        | U_193 = c_Orderings_Obot__class_Obot(tc_fun(U_191,tc_HOL_Obool)) )
    & ! [U_192,U_190] :
        ( U_192 != c_Orderings_Obot__class_Obot(tc_fun(U_190,tc_HOL_Obool))
        | ! [U_186] : ~ hBOOL(hAPP(hAPP(c_member(U_190),U_186),U_192)) ) ),
    inference(miniscope,[status(thm)],[f_38_2]) ).

fof(f_38_4,plain,
    ( ! [U_193,U_191] :
        ( hBOOL(hAPP(hAPP(c_member(U_191),sK2(U_193,U_191)),U_193))
        | U_193 = c_Orderings_Obot__class_Obot(tc_fun(U_191,tc_HOL_Obool)) )
    & ! [U_192,U_190] :
        ( U_192 != c_Orderings_Obot__class_Obot(tc_fun(U_190,tc_HOL_Obool))
        | ! [U_186] : ~ hBOOL(hAPP(hAPP(c_member(U_190),U_186),U_192)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_187,sK2(U_193,U_191))],[f_38_3]) ).

cnf(f_38_5,plain,
    ( U_192 != c_Orderings_Obot__class_Obot(tc_fun(U_190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_190),U_186),U_192)) ),
    inference(clausify,[status(thm)],[f_38_4]) ).

cnf(f_38_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_191),sK2(U_193,U_191)),U_193))
    | U_193 = c_Orderings_Obot__class_Obot(tc_fun(U_191,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_38_4]) ).

fof(f_39_1,plain,
    ! [V_A_2,T_a] :
      ( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).

fof(f_39_2,plain,
    ! [U_197,U_196] :
      ( ( ! [U_195] : ~ hBOOL(hAPP(hAPP(c_member(U_196),U_195),U_197))
        | U_197 != c_Orderings_Obot__class_Obot(tc_fun(U_196,tc_HOL_Obool)) )
      & ( U_197 = c_Orderings_Obot__class_Obot(tc_fun(U_196,tc_HOL_Obool))
        | ? [U_194] : hBOOL(hAPP(hAPP(c_member(U_196),U_194),U_197)) ) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ( ! [U_201,U_199] :
        ( ! [U_195] : ~ hBOOL(hAPP(hAPP(c_member(U_199),U_195),U_201))
        | U_201 != c_Orderings_Obot__class_Obot(tc_fun(U_199,tc_HOL_Obool)) )
    & ! [U_200,U_198] :
        ( U_200 = c_Orderings_Obot__class_Obot(tc_fun(U_198,tc_HOL_Obool))
        | ? [U_194] : hBOOL(hAPP(hAPP(c_member(U_198),U_194),U_200)) ) ),
    inference(miniscope,[status(thm)],[f_39_2]) ).

fof(f_39_4,plain,
    ( ! [U_201,U_199] :
        ( ! [U_195] : ~ hBOOL(hAPP(hAPP(c_member(U_199),U_195),U_201))
        | U_201 != c_Orderings_Obot__class_Obot(tc_fun(U_199,tc_HOL_Obool)) )
    & ! [U_200,U_198] :
        ( U_200 = c_Orderings_Obot__class_Obot(tc_fun(U_198,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_198),sK3(U_200,U_198)),U_200)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_194,sK3(U_200,U_198))],[f_39_3]) ).

cnf(f_39_5,plain,
    ( U_200 = c_Orderings_Obot__class_Obot(tc_fun(U_198,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_198),sK3(U_200,U_198)),U_200)) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

cnf(f_39_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_199),U_195),U_201))
    | U_201 != c_Orderings_Obot__class_Obot(tc_fun(U_199,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_39_4]) ).

fof(f_40_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).

fof(f_40_2,plain,
    ! [U_204,U_203,U_202] :
      ( hAPP(hAPP(c_Set_Oinsert(U_202),U_203),U_204) = U_204
      | ~ hBOOL(hAPP(hAPP(c_member(U_202),U_203),U_204)) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_202),U_203),U_204) = U_204
    | ~ hBOOL(hAPP(hAPP(c_member(U_202),U_203),U_204)) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insertI2]) ).

fof(f_41_2,plain,
    ! [U_208,U_207,U_206,U_205] :
      ( hBOOL(hAPP(hAPP(c_member(U_205),U_206),hAPP(hAPP(c_Set_Oinsert(U_205),U_208),U_207)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_205),U_206),hAPP(hAPP(c_Set_Oinsert(U_205),U_208),U_207)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) != hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) ) )
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).

fof(f_42_2,plain,
    ! [U_212,U_211,U_210,U_209] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_211) = hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_212)
          | U_211 != U_212 )
        & ( U_211 = U_212
          | hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_211) != hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_212) ) )
      | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_212))
      | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_211)) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    ( U_211 = U_212
    | hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_211) != hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_212)
    | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_212))
    | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_211)) ),
    inference(clausify,[status(thm)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_211) = hAPP(hAPP(c_Set_Oinsert(U_209),U_210),U_212)
    | U_211 != U_212
    | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_212))
    | hBOOL(hAPP(hAPP(c_member(U_209),U_210),U_211)) ),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
          & V_a_2 != V_b_2 ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
        | V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).

fof(f_43_2,plain,
    ! [U_216,U_215,U_214,U_213] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_213),U_214),hAPP(hAPP(c_Set_Oinsert(U_213),U_215),U_216)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_213),U_214),U_216))
          & U_214 != U_215 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_213),U_214),U_216))
        | U_214 = U_215
        | ~ hBOOL(hAPP(hAPP(c_member(U_213),U_214),hAPP(hAPP(c_Set_Oinsert(U_213),U_215),U_216))) ) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ( ! [U_224,U_222,U_220,U_218] :
        ( hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(hAPP(c_Set_Oinsert(U_218),U_222),U_224)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_218),U_220),U_224))
          & U_220 != U_222 ) )
    & ! [U_223,U_221,U_219,U_217] :
        ( hBOOL(hAPP(hAPP(c_member(U_217),U_219),U_223))
        | U_219 = U_221
        | ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(hAPP(c_Set_Oinsert(U_217),U_221),U_223))) ) ),
    inference(miniscope,[status(thm)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_217),U_219),U_223))
    | U_219 = U_221
    | ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(hAPP(c_Set_Oinsert(U_217),U_221),U_223))) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

cnf(f_43_5,plain,
    ( U_220 != U_222
    | hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(hAPP(c_Set_Oinsert(U_218),U_222),U_224))) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

cnf(f_43_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_218),U_220),U_224))
    | hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(hAPP(c_Set_Oinsert(U_218),U_222),U_224))) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insertI1]) ).

fof(f_44_2,plain,
    ! [U_227,U_226,U_225] : hBOOL(hAPP(hAPP(c_member(U_225),U_226),hAPP(hAPP(c_Set_Oinsert(U_225),U_226),U_227))),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_225),U_226),hAPP(hAPP(c_Set_Oinsert(U_225),U_226),U_227))),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | V_b_2 != hAPP(V_f_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).

fof(f_45_2,plain,
    ! [U_233,U_232,U_231,U_230,U_229,U_228] :
      ( hBOOL(hAPP(hAPP(c_member(U_233),U_231),hAPP(c_Set_Oimage(U_228,U_233,U_232),U_230)))
      | U_231 != hAPP(U_232,U_229)
      | ~ hBOOL(hAPP(hAPP(c_member(U_228),U_229),U_230)) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_233),U_231),hAPP(c_Set_Oimage(U_228,U_233,U_232),U_230)))
    | U_231 != hAPP(U_232,U_229)
    | ~ hBOOL(hAPP(hAPP(c_member(U_228),U_229),U_230)) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_imageI]) ).

fof(f_46_2,plain,
    ! [U_238,U_237,U_236,U_235,U_234] :
      ( hBOOL(hAPP(hAPP(c_member(U_237),hAPP(U_238,U_235)),hAPP(c_Set_Oimage(U_234,U_237,U_238),U_236)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_234),U_235),U_236)) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_237),hAPP(U_238,U_235)),hAPP(c_Set_Oimage(U_234,U_237,U_238),U_236)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_234),U_235),U_236)) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
        | ! [B_x] :
            ( V_z_2 != hAPP(V_f_2,B_x)
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( V_z_2 = hAPP(V_f_2,B_x)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__iff]) ).

fof(f_47_2,plain,
    ! [U_245,U_244,U_243,U_242,U_241] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_241),U_242),hAPP(c_Set_Oimage(U_243,U_241,U_244),U_245)))
        | ! [U_240] :
            ( U_242 != hAPP(U_244,U_240)
            | ~ hBOOL(hAPP(hAPP(c_member(U_243),U_240),U_245)) ) )
      & ( ? [U_239] :
            ( U_242 = hAPP(U_244,U_239)
            & hBOOL(hAPP(hAPP(c_member(U_243),U_239),U_245)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_241),U_242),hAPP(c_Set_Oimage(U_243,U_241,U_244),U_245))) ) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ( ! [U_255,U_253,U_251,U_249] :
        ( ! [U_247] : hBOOL(hAPP(hAPP(c_member(U_247),U_249),hAPP(c_Set_Oimage(U_251,U_247,U_253),U_255)))
        | ! [U_240] :
            ( U_249 != hAPP(U_253,U_240)
            | ~ hBOOL(hAPP(hAPP(c_member(U_251),U_240),U_255)) ) )
    & ! [U_254,U_252,U_250,U_248] :
        ( ! [U_246] : ~ hBOOL(hAPP(hAPP(c_member(U_246),U_248),hAPP(c_Set_Oimage(U_250,U_246,U_252),U_254)))
        | ? [U_239] :
            ( U_248 = hAPP(U_252,U_239)
            & hBOOL(hAPP(hAPP(c_member(U_250),U_239),U_254)) ) ) ),
    inference(miniscope,[status(thm)],[f_47_2]) ).

fof(f_47_4,plain,
    ( ! [U_255,U_253,U_251,U_249] :
        ( ! [U_247] : hBOOL(hAPP(hAPP(c_member(U_247),U_249),hAPP(c_Set_Oimage(U_251,U_247,U_253),U_255)))
        | ! [U_240] :
            ( U_249 != hAPP(U_253,U_240)
            | ~ hBOOL(hAPP(hAPP(c_member(U_251),U_240),U_255)) ) )
    & ! [U_254,U_252,U_250,U_248] :
        ( ! [U_246] : ~ hBOOL(hAPP(hAPP(c_member(U_246),U_248),hAPP(c_Set_Oimage(U_250,U_246,U_252),U_254)))
        | ( U_248 = hAPP(U_252,sK4(U_254,U_252,U_250,U_248))
          & hBOOL(hAPP(hAPP(c_member(U_250),sK4(U_254,U_252,U_250,U_248)),U_254)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_239,sK4(U_254,U_252,U_250,U_248))],[f_47_3]) ).

cnf(f_47_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_250),sK4(U_254,U_252,U_250,U_248)),U_254))
    | ~ hBOOL(hAPP(hAPP(c_member(U_246),U_248),hAPP(c_Set_Oimage(U_250,U_246,U_252),U_254))) ),
    inference(clausify,[status(thm)],[f_47_4]) ).

cnf(f_47_6,plain,
    ( U_248 = hAPP(U_252,sK4(U_254,U_252,U_250,U_248))
    | ~ hBOOL(hAPP(hAPP(c_member(U_246),U_248),hAPP(c_Set_Oimage(U_250,U_246,U_252),U_254))) ),
    inference(clausify,[status(thm)],[f_47_4]) ).

cnf(f_47_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_247),U_249),hAPP(c_Set_Oimage(U_251,U_247,U_253),U_255)))
    | U_249 != hAPP(U_253,U_240)
    | ~ hBOOL(hAPP(hAPP(c_member(U_251),U_240),U_255)) ),
    inference(clausify,[status(thm)],[f_47_4]) ).

fof(f_48_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI2]) ).

fof(f_48_2,plain,
    ! [U_259,U_258,U_257,U_256] :
      ( hBOOL(hAPP(hAPP(c_member(U_256),U_257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_256,tc_HOL_Obool)),U_259),U_258)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_256),U_257),U_258)) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_256),U_257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_256,tc_HOL_Obool)),U_259),U_258)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_256),U_257),U_258)) ),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI1]) ).

fof(f_49_2,plain,
    ! [U_263,U_262,U_261,U_260] :
      ( hBOOL(hAPP(hAPP(c_member(U_260),U_261),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_260,tc_HOL_Obool)),U_262),U_263)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_260),U_261),U_262)) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_260),U_261),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_260,tc_HOL_Obool)),U_262),U_263)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_260),U_261),U_262)) ),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).

fof(f_50_2,plain,
    ! [U_267,U_266,U_265,U_264] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_264),U_265),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_264,tc_HOL_Obool)),U_266),U_267)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_264),U_265),U_267))
          & ~ hBOOL(hAPP(hAPP(c_member(U_264),U_265),U_266)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_264),U_265),U_267))
        | hBOOL(hAPP(hAPP(c_member(U_264),U_265),U_266))
        | ~ hBOOL(hAPP(hAPP(c_member(U_264),U_265),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_264,tc_HOL_Obool)),U_266),U_267))) ) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ( ! [U_275,U_273,U_271,U_269] :
        ( hBOOL(hAPP(hAPP(c_member(U_269),U_271),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_273),U_275)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_269),U_271),U_275))
          & ~ hBOOL(hAPP(hAPP(c_member(U_269),U_271),U_273)) ) )
    & ! [U_274,U_272,U_270,U_268] :
        ( hBOOL(hAPP(hAPP(c_member(U_268),U_270),U_274))
        | hBOOL(hAPP(hAPP(c_member(U_268),U_270),U_272))
        | ~ hBOOL(hAPP(hAPP(c_member(U_268),U_270),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_268,tc_HOL_Obool)),U_272),U_274))) ) ),
    inference(miniscope,[status(thm)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_268),U_270),U_274))
    | hBOOL(hAPP(hAPP(c_member(U_268),U_270),U_272))
    | ~ hBOOL(hAPP(hAPP(c_member(U_268),U_270),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_268,tc_HOL_Obool)),U_272),U_274))) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

cnf(f_50_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_269),U_271),U_273))
    | hBOOL(hAPP(hAPP(c_member(U_269),U_271),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_273),U_275))) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

cnf(f_50_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_269),U_271),U_275))
    | hBOOL(hAPP(hAPP(c_member(U_269),U_271),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_273),U_275))) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [V_x_2,T_a] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).

fof(f_51_2,plain,
    ! [U_277,U_276] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool)),U_277))
        | ~ hBOOL(hAPP(hAPP(c_member(U_276),U_277),c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_276),U_277),c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool)),U_277)) ) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ( ! [U_281,U_279] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_279,tc_HOL_Obool)),U_281))
        | ~ hBOOL(hAPP(hAPP(c_member(U_279),U_281),c_Orderings_Obot__class_Obot(tc_fun(U_279,tc_HOL_Obool)))) )
    & ! [U_280,U_278] :
        ( hBOOL(hAPP(hAPP(c_member(U_278),U_280),c_Orderings_Obot__class_Obot(tc_fun(U_278,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_278,tc_HOL_Obool)),U_280)) ) ),
    inference(miniscope,[status(thm)],[f_51_2]) ).

cnf(f_51_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_278),U_280),c_Orderings_Obot__class_Obot(tc_fun(U_278,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_278,tc_HOL_Obool)),U_280)) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_5,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_279,tc_HOL_Obool)),U_281))
    | ~ hBOOL(hAPP(hAPP(c_member(U_279),U_281),c_Orderings_Obot__class_Obot(tc_fun(U_279,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).

fof(f_52_2,plain,
    ! [U_285,U_284,U_283,U_282] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_282,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_282,tc_fun(U_282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_282)),U_283)),hAPP(hAPP(c_COMBC(U_282,tc_fun(U_282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_282)),U_284)),U_285))
        | ~ hBOOL(hAPP(hAPP(c_member(U_282),U_285),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_282,tc_HOL_Obool)),U_283),U_284))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_282),U_285),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_282,tc_HOL_Obool)),U_283),U_284)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_282,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_282,tc_fun(U_282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_282)),U_283)),hAPP(hAPP(c_COMBC(U_282,tc_fun(U_282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_282)),U_284)),U_285)) ) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ( ! [U_293,U_291,U_289,U_287] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_287,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_287,tc_fun(U_287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_287)),U_289)),hAPP(hAPP(c_COMBC(U_287,tc_fun(U_287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_287)),U_291)),U_293))
        | ~ hBOOL(hAPP(hAPP(c_member(U_287),U_293),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_287,tc_HOL_Obool)),U_289),U_291))) )
    & ! [U_292,U_290,U_288,U_286] :
        ( hBOOL(hAPP(hAPP(c_member(U_286),U_292),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_286,tc_HOL_Obool)),U_288),U_290)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_286,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_286,tc_fun(U_286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_286)),U_288)),hAPP(hAPP(c_COMBC(U_286,tc_fun(U_286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_286)),U_290)),U_292)) ) ),
    inference(miniscope,[status(thm)],[f_52_2]) ).

cnf(f_52_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_286),U_292),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_286,tc_HOL_Obool)),U_288),U_290)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_286,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_286,tc_fun(U_286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_286)),U_288)),hAPP(hAPP(c_COMBC(U_286,tc_fun(U_286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_286)),U_290)),U_292)) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

cnf(f_52_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_287,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_287,tc_fun(U_287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_287)),U_289)),hAPP(hAPP(c_COMBC(U_287,tc_fun(U_287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_287)),U_291)),U_293))
    | ~ hBOOL(hAPP(hAPP(c_member(U_287),U_293),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_287,tc_HOL_Obool)),U_289),U_291))) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( V_b_2 = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_singletonE]) ).

fof(f_53_2,plain,
    ! [U_296,U_295,U_294] :
      ( U_295 = U_296
      | ~ hBOOL(hAPP(hAPP(c_member(U_294),U_295),hAPP(hAPP(c_Set_Oinsert(U_294),U_296),c_Orderings_Obot__class_Obot(tc_fun(U_294,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_296,U_295] :
      ( ! [U_294] : ~ hBOOL(hAPP(hAPP(c_member(U_294),U_295),hAPP(hAPP(c_Set_Oinsert(U_294),U_296),c_Orderings_Obot__class_Obot(tc_fun(U_294,tc_HOL_Obool)))))
      | U_295 = U_296 ),
    inference(miniscope,[status(thm)],[f_53_2]) ).

cnf(f_53_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_294),U_295),hAPP(hAPP(c_Set_Oinsert(U_294),U_296),c_Orderings_Obot__class_Obot(tc_fun(U_294,tc_HOL_Obool)))))
    | U_295 = U_296 ),
    inference(clausify,[status(thm)],[f_53_3]) ).

fof(f_54_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
        | V_b_2 != V_a_2 )
      & ( V_b_2 = V_a_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).

fof(f_54_2,plain,
    ! [U_299,U_298,U_297] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_297),U_298),hAPP(hAPP(c_Set_Oinsert(U_297),U_299),c_Orderings_Obot__class_Obot(tc_fun(U_297,tc_HOL_Obool)))))
        | U_298 != U_299 )
      & ( U_298 = U_299
        | ~ hBOOL(hAPP(hAPP(c_member(U_297),U_298),hAPP(hAPP(c_Set_Oinsert(U_297),U_299),c_Orderings_Obot__class_Obot(tc_fun(U_297,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ( ! [U_305,U_303] :
        ( ! [U_301] : hBOOL(hAPP(hAPP(c_member(U_301),U_303),hAPP(hAPP(c_Set_Oinsert(U_301),U_305),c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)))))
        | U_303 != U_305 )
    & ! [U_304,U_302] :
        ( ! [U_300] : ~ hBOOL(hAPP(hAPP(c_member(U_300),U_302),hAPP(hAPP(c_Set_Oinsert(U_300),U_304),c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool)))))
        | U_302 = U_304 ) ),
    inference(miniscope,[status(thm)],[f_54_2]) ).

cnf(f_54_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_300),U_302),hAPP(hAPP(c_Set_Oinsert(U_300),U_304),c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool)))))
    | U_302 = U_304 ),
    inference(clausify,[status(thm)],[f_54_3]) ).

cnf(f_54_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_301),U_303),hAPP(hAPP(c_Set_Oinsert(U_301),U_305),c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)))))
    | U_303 != U_305 ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__image]) ).

fof(f_55_2,plain,
    ! [U_310,U_309,U_308,U_307,U_306] :
      ( hAPP(hAPP(c_Set_Oinsert(U_309),hAPP(U_310,U_307)),hAPP(c_Set_Oimage(U_306,U_309,U_310),U_308)) = hAPP(c_Set_Oimage(U_306,U_309,U_310),U_308)
      | ~ hBOOL(hAPP(hAPP(c_member(U_306),U_307),U_308)) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_309),hAPP(U_310,U_307)),hAPP(c_Set_Oimage(U_306,U_309,U_310),U_308)) = hAPP(c_Set_Oimage(U_306,U_309,U_310),U_308)
    | ~ hBOOL(hAPP(hAPP(c_member(U_306),U_307),U_308)) ),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [V_c_2,T_b,V_A_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant]) ).

fof(f_56_2,plain,
    ! [U_315,U_314,U_313,U_312,U_311] :
      ( hAPP(c_Set_Oimage(U_311,U_314,hAPP(c_COMBK(U_314,U_311),U_315)),U_313) = hAPP(hAPP(c_Set_Oinsert(U_314),U_315),c_Orderings_Obot__class_Obot(tc_fun(U_314,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_311),U_312),U_313)) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    ( hAPP(c_Set_Oimage(U_311,U_314,hAPP(c_COMBK(U_314,U_311),U_315)),U_313) = hAPP(hAPP(c_Set_Oinsert(U_314),U_315),c_Orderings_Obot__class_Obot(tc_fun(U_314,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_311),U_312),U_313)) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [V_ts_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__sound]) ).

fof(f_57_2,plain,
    ! [U_318,U_317,U_316] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_316,U_317,U_318)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_316,U_317,U_318) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_316,U_317,U_318)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_316,U_317,U_318) ),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [V_x_2,V_A_2,V_y_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),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_a),V_y_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__code]) ).

fof(f_58_2,plain,
    ! [U_322,U_321,U_320,U_319] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_319),U_320),U_321),U_322))
        | ( ~ hBOOL(hAPP(U_321,U_322))
          & U_320 != U_322 ) )
      & ( hBOOL(hAPP(U_321,U_322))
        | U_320 = U_322
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_319),U_320),U_321),U_322)) ) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ( ! [U_330,U_328,U_326] :
        ( ! [U_324] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_324),U_326),U_328),U_330))
        | ( ~ hBOOL(hAPP(U_328,U_330))
          & U_326 != U_330 ) )
    & ! [U_329,U_327,U_325] :
        ( ! [U_323] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_323),U_325),U_327),U_329))
        | hBOOL(hAPP(U_327,U_329))
        | U_325 = U_329 ) ),
    inference(miniscope,[status(thm)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_323),U_325),U_327),U_329))
    | hBOOL(hAPP(U_327,U_329))
    | U_325 = U_329 ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_5,plain,
    ( U_326 != U_330
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_324),U_326),U_328),U_330)) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_6,plain,
    ( ~ hBOOL(hAPP(U_328,U_330))
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_324),U_326),U_328),U_330)) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).

fof(f_59_2,plain,
    ! [U_334,U_333,U_332,U_331] : hAPP(hAPP(c_Set_Oinsert(U_331),U_332),hAPP(hAPP(c_Set_Oinsert(U_331),U_333),U_334)) = hAPP(hAPP(c_Set_Oinsert(U_331),U_333),hAPP(hAPP(c_Set_Oinsert(U_331),U_332),U_334)),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_331),U_332),hAPP(hAPP(c_Set_Oinsert(U_331),U_333),U_334)) = hAPP(hAPP(c_Set_Oinsert(U_331),U_333),hAPP(hAPP(c_Set_Oinsert(U_331),U_332),U_334)),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).

fof(f_60_2,plain,
    ! [U_337,U_336,U_335] : hAPP(hAPP(c_Set_Oinsert(U_335),U_336),hAPP(hAPP(c_Set_Oinsert(U_335),U_336),U_337)) = hAPP(hAPP(c_Set_Oinsert(U_335),U_336),U_337),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_335),U_336),hAPP(hAPP(c_Set_Oinsert(U_335),U_336),U_337)) = hAPP(hAPP(c_Set_Oinsert(U_335),U_336),U_337),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_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_61_2,plain,
    ! [U_341,U_340,U_339,U_338] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_339),U_340)),U_341) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_339),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_340),U_341))
      | ~ class_Lattices_Osemilattice__sup(U_338) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_339),U_340)),U_341) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_339),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_338),U_340),U_341))
    | ~ class_Lattices_Osemilattice__sup(U_338) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_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_62_2,plain,
    ! [U_345,U_344,U_343,U_342] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_343),U_344)),U_345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_343),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_344),U_345))
      | ~ class_Lattices_Olattice(U_342) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_343),U_344)),U_345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_343),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_342),U_344),U_345))
    | ~ class_Lattices_Olattice(U_342) ),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_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_63_2,plain,
    ! [U_349,U_348,U_347,U_346] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_347),U_348)),U_349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_348),U_349))
      | ~ class_Lattices_Osemilattice__sup(U_346) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_347),U_348)),U_349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_346),U_348),U_349))
    | ~ class_Lattices_Osemilattice__sup(U_346) ),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_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_64_2,plain,
    ! [U_353,U_352,U_351,U_350] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_351),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_352),U_353)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_351),U_353))
      | ~ class_Lattices_Osemilattice__sup(U_350) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

cnf(f_64_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_351),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_352),U_353)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_352),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_350),U_351),U_353))
    | ~ class_Lattices_Osemilattice__sup(U_350) ),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_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_65_2,plain,
    ! [U_357,U_356,U_355,U_354] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_356),U_357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_355),U_357))
      | ~ class_Lattices_Olattice(U_354) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_356),U_357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_354),U_355),U_357))
    | ~ class_Lattices_Olattice(U_354) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_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_66_2,plain,
    ! [U_361,U_360,U_359,U_358] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_359),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_360),U_361)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_360),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_359),U_361))
      | ~ class_Lattices_Osemilattice__sup(U_358) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_359),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_360),U_361)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_360),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_358),U_359),U_361))
    | ~ class_Lattices_Osemilattice__sup(U_358) ),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_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_67_2,plain,
    ! [U_364,U_363,U_362] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),U_364)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),U_364)
      | ~ class_Lattices_Osemilattice__sup(U_362) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),U_364)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_362),U_363),U_364)
    | ~ class_Lattices_Osemilattice__sup(U_362) ),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_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_68_2,plain,
    ! [U_367,U_366,U_365] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),U_367)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),U_367)
      | ~ class_Lattices_Olattice(U_365) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),U_367)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_365),U_366),U_367)
    | ~ class_Lattices_Olattice(U_365) ),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_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_69_2,plain,
    ! [U_370,U_369,U_368] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_370)
      | ~ class_Lattices_Osemilattice__sup(U_368) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_370)
    | ~ class_Lattices_Osemilattice__sup(U_368) ),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_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_70_2,plain,
    ! [U_373,U_372,U_371] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_371),U_372),U_373) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_371),U_373),U_372)
      | ~ class_Lattices_Osemilattice__sup(U_371) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_371),U_372),U_373) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_371),U_373),U_372)
    | ~ class_Lattices_Osemilattice__sup(U_371) ),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_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_71_2,plain,
    ! [U_376,U_375,U_374] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_374),U_375),U_376) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_374),U_376),U_375)
      | ~ class_Lattices_Olattice(U_374) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_374),U_375),U_376) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_374),U_376),U_375)
    | ~ class_Lattices_Olattice(U_374) ),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_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_72_2,plain,
    ! [U_379,U_378,U_377] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_377),U_378),U_379) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_377),U_379),U_378)
      | ~ class_Lattices_Osemilattice__sup(U_377) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_377),U_378),U_379) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_377),U_379),U_378)
    | ~ class_Lattices_Osemilattice__sup(U_377) ),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_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_73_2,plain,
    ! [U_381,U_380] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_380),U_381),U_381) = U_381
      | ~ class_Lattices_Osemilattice__sup(U_380) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_380),U_381),U_381) = U_381
    | ~ class_Lattices_Osemilattice__sup(U_380) ),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_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_74_2,plain,
    ! [U_383,U_382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_383) = U_383
      | ~ class_Lattices_Osemilattice__sup(U_382) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_383) = U_383
    | ~ class_Lattices_Osemilattice__sup(U_382) ),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [V_A_2,T_a,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_75_2,plain,
    ! [U_387,U_386,U_385,U_384] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_386,tc_HOL_Obool)),U_387),U_384),U_385))
      | ~ hBOOL(hAPP(U_384,U_385)) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_386,tc_HOL_Obool)),U_387),U_384),U_385))
    | ~ hBOOL(hAPP(U_384,U_385)) ),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [V_B_2,T_a,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_76_2,plain,
    ! [U_391,U_390,U_389,U_388] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_390,tc_HOL_Obool)),U_388),U_391),U_389))
      | ~ hBOOL(hAPP(U_388,U_389)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_390,tc_HOL_Obool)),U_388),U_391),U_389))
    | ~ hBOOL(hAPP(U_388,U_389)) ),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).

fof(f_77_2,plain,
    ! [U_401,U_400,U_399,U_398] :
      ( ( ! [U_397] :
            ( hBOOL(hAPP(U_401,U_397))
            | ~ hBOOL(hAPP(hAPP(c_member(U_398),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_398,tc_HOL_Obool)),U_399),U_400))) )
        | ? [U_396] :
            ( ~ hBOOL(hAPP(U_401,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_398),U_396),U_400)) )
        | ? [U_395] :
            ( ~ hBOOL(hAPP(U_401,U_395))
            & hBOOL(hAPP(hAPP(c_member(U_398),U_395),U_399)) ) )
      & ( ( ! [U_394] :
              ( hBOOL(hAPP(U_401,U_394))
              | ~ hBOOL(hAPP(hAPP(c_member(U_398),U_394),U_400)) )
          & ! [U_393] :
              ( hBOOL(hAPP(U_401,U_393))
              | ~ hBOOL(hAPP(hAPP(c_member(U_398),U_393),U_399)) ) )
        | ? [U_392] :
            ( ~ hBOOL(hAPP(U_401,U_392))
            & hBOOL(hAPP(hAPP(c_member(U_398),U_392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_398,tc_HOL_Obool)),U_399),U_400))) ) ) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ( ! [U_409,U_407,U_405,U_403] :
        ( ! [U_397] :
            ( hBOOL(hAPP(U_409,U_397))
            | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) )
        | ? [U_396] :
            ( ~ hBOOL(hAPP(U_409,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_403),U_396),U_407)) )
        | ? [U_395] :
            ( ~ hBOOL(hAPP(U_409,U_395))
            & hBOOL(hAPP(hAPP(c_member(U_403),U_395),U_405)) ) )
    & ! [U_408,U_406,U_404,U_402] :
        ( ( ! [U_394] :
              ( hBOOL(hAPP(U_408,U_394))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406)) )
          & ! [U_393] :
              ( hBOOL(hAPP(U_408,U_393))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404)) ) )
        | ? [U_392] :
            ( ~ hBOOL(hAPP(U_408,U_392))
            & hBOOL(hAPP(hAPP(c_member(U_402),U_392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ) ) ),
    inference(miniscope,[status(thm)],[f_77_2]) ).

fof(f_77_4,plain,
    ( ! [U_409,U_407,U_405,U_403] :
        ( ! [U_397] :
            ( hBOOL(hAPP(U_409,U_397))
            | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) )
        | ? [U_396] :
            ( ~ hBOOL(hAPP(U_409,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_403),U_396),U_407)) )
        | ? [U_395] :
            ( ~ hBOOL(hAPP(U_409,U_395))
            & hBOOL(hAPP(hAPP(c_member(U_403),U_395),U_405)) ) )
    & ! [U_408,U_406,U_404,U_402] :
        ( ( ! [U_394] :
              ( hBOOL(hAPP(U_408,U_394))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406)) )
          & ! [U_393] :
              ( hBOOL(hAPP(U_408,U_393))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404)) ) )
        | ( ~ hBOOL(hAPP(U_408,sK5(U_408,U_406,U_404,U_402)))
          & hBOOL(hAPP(hAPP(c_member(U_402),sK5(U_408,U_406,U_404,U_402)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_392,sK5(U_408,U_406,U_404,U_402))],[f_77_3]) ).

fof(f_77_5,plain,
    ( ! [U_409,U_407,U_405,U_403] :
        ( ! [U_397] :
            ( hBOOL(hAPP(U_409,U_397))
            | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) )
        | ? [U_396] :
            ( ~ hBOOL(hAPP(U_409,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_403),U_396),U_407)) )
        | ( ~ hBOOL(hAPP(U_409,sK6(U_409,U_407,U_405,U_403)))
          & hBOOL(hAPP(hAPP(c_member(U_403),sK6(U_409,U_407,U_405,U_403)),U_405)) ) )
    & ! [U_408,U_406,U_404,U_402] :
        ( ( ! [U_394] :
              ( hBOOL(hAPP(U_408,U_394))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406)) )
          & ! [U_393] :
              ( hBOOL(hAPP(U_408,U_393))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404)) ) )
        | ( ~ hBOOL(hAPP(U_408,sK5(U_408,U_406,U_404,U_402)))
          & hBOOL(hAPP(hAPP(c_member(U_402),sK5(U_408,U_406,U_404,U_402)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_395,sK6(U_409,U_407,U_405,U_403))],[f_77_4]) ).

fof(f_77_6,plain,
    ( ! [U_409,U_407,U_405,U_403] :
        ( ! [U_397] :
            ( hBOOL(hAPP(U_409,U_397))
            | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) )
        | ( ~ hBOOL(hAPP(U_409,sK7(U_409,U_407,U_405,U_403)))
          & hBOOL(hAPP(hAPP(c_member(U_403),sK7(U_409,U_407,U_405,U_403)),U_407)) )
        | ( ~ hBOOL(hAPP(U_409,sK6(U_409,U_407,U_405,U_403)))
          & hBOOL(hAPP(hAPP(c_member(U_403),sK6(U_409,U_407,U_405,U_403)),U_405)) ) )
    & ! [U_408,U_406,U_404,U_402] :
        ( ( ! [U_394] :
              ( hBOOL(hAPP(U_408,U_394))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406)) )
          & ! [U_393] :
              ( hBOOL(hAPP(U_408,U_393))
              | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404)) ) )
        | ( ~ hBOOL(hAPP(U_408,sK5(U_408,U_406,U_404,U_402)))
          & hBOOL(hAPP(hAPP(c_member(U_402),sK5(U_408,U_406,U_404,U_402)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_396,sK7(U_409,U_407,U_405,U_403))],[f_77_5]) ).

cnf(f_77_7,plain,
    ( hBOOL(hAPP(U_408,U_393))
    | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404))
    | hBOOL(hAPP(hAPP(c_member(U_402),sK5(U_408,U_406,U_404,U_402)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_8,plain,
    ( hBOOL(hAPP(U_408,U_394))
    | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406))
    | hBOOL(hAPP(hAPP(c_member(U_402),sK5(U_408,U_406,U_404,U_402)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_402,tc_HOL_Obool)),U_404),U_406))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_9,plain,
    ( hBOOL(hAPP(U_408,U_393))
    | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_393),U_404))
    | ~ hBOOL(hAPP(U_408,sK5(U_408,U_406,U_404,U_402))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_10,plain,
    ( hBOOL(hAPP(U_408,U_394))
    | ~ hBOOL(hAPP(hAPP(c_member(U_402),U_394),U_406))
    | ~ hBOOL(hAPP(U_408,sK5(U_408,U_406,U_404,U_402))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_403),sK7(U_409,U_407,U_405,U_403)),U_407))
    | hBOOL(hAPP(hAPP(c_member(U_403),sK6(U_409,U_407,U_405,U_403)),U_405))
    | hBOOL(hAPP(U_409,U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_12,plain,
    ( ~ hBOOL(hAPP(U_409,sK7(U_409,U_407,U_405,U_403)))
    | hBOOL(hAPP(hAPP(c_member(U_403),sK6(U_409,U_407,U_405,U_403)),U_405))
    | hBOOL(hAPP(U_409,U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_403),sK7(U_409,U_407,U_405,U_403)),U_407))
    | ~ hBOOL(hAPP(U_409,sK6(U_409,U_407,U_405,U_403)))
    | hBOOL(hAPP(U_409,U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

cnf(f_77_14,plain,
    ( ~ hBOOL(hAPP(U_409,sK7(U_409,U_407,U_405,U_403)))
    | ~ hBOOL(hAPP(U_409,sK6(U_409,U_407,U_405,U_403)))
    | hBOOL(hAPP(U_409,U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_403),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_403,tc_HOL_Obool)),U_405),U_407))) ),
    inference(clausify,[status(thm)],[f_77_6]) ).

fof(f_78_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_a] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ( ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
          & ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).

fof(f_78_2,plain,
    ! [U_419,U_418,U_417,U_416] :
      ( ( ? [U_415] :
            ( hBOOL(hAPP(U_419,U_415))
            & hBOOL(hAPP(hAPP(c_member(U_416),U_415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_416,tc_HOL_Obool)),U_417),U_418))) )
        | ( ! [U_414] :
              ( ~ hBOOL(hAPP(U_419,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_416),U_414),U_418)) )
          & ! [U_413] :
              ( ~ hBOOL(hAPP(U_419,U_413))
              | ~ hBOOL(hAPP(hAPP(c_member(U_416),U_413),U_417)) ) ) )
      & ( ? [U_412] :
            ( hBOOL(hAPP(U_419,U_412))
            & hBOOL(hAPP(hAPP(c_member(U_416),U_412),U_418)) )
        | ? [U_411] :
            ( hBOOL(hAPP(U_419,U_411))
            & hBOOL(hAPP(hAPP(c_member(U_416),U_411),U_417)) )
        | ! [U_410] :
            ( ~ hBOOL(hAPP(U_419,U_410))
            | ~ hBOOL(hAPP(hAPP(c_member(U_416),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_416,tc_HOL_Obool)),U_417),U_418))) ) ) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ( ! [U_427,U_425,U_423,U_421] :
        ( ? [U_415] :
            ( hBOOL(hAPP(U_427,U_415))
            & hBOOL(hAPP(hAPP(c_member(U_421),U_415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425))) )
        | ( ! [U_414] :
              ( ~ hBOOL(hAPP(U_427,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) )
          & ! [U_413] :
              ( ~ hBOOL(hAPP(U_427,U_413))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ) ) )
    & ! [U_426,U_424,U_422,U_420] :
        ( ? [U_412] :
            ( hBOOL(hAPP(U_426,U_412))
            & hBOOL(hAPP(hAPP(c_member(U_420),U_412),U_424)) )
        | ? [U_411] :
            ( hBOOL(hAPP(U_426,U_411))
            & hBOOL(hAPP(hAPP(c_member(U_420),U_411),U_422)) )
        | ! [U_410] :
            ( ~ hBOOL(hAPP(U_426,U_410))
            | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ) ) ),
    inference(miniscope,[status(thm)],[f_78_2]) ).

fof(f_78_4,plain,
    ( ! [U_427,U_425,U_423,U_421] :
        ( ? [U_415] :
            ( hBOOL(hAPP(U_427,U_415))
            & hBOOL(hAPP(hAPP(c_member(U_421),U_415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425))) )
        | ( ! [U_414] :
              ( ~ hBOOL(hAPP(U_427,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) )
          & ! [U_413] :
              ( ~ hBOOL(hAPP(U_427,U_413))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ) ) )
    & ! [U_426,U_424,U_422,U_420] :
        ( ? [U_412] :
            ( hBOOL(hAPP(U_426,U_412))
            & hBOOL(hAPP(hAPP(c_member(U_420),U_412),U_424)) )
        | ( hBOOL(hAPP(U_426,sK8(U_426,U_424,U_422,U_420)))
          & hBOOL(hAPP(hAPP(c_member(U_420),sK8(U_426,U_424,U_422,U_420)),U_422)) )
        | ! [U_410] :
            ( ~ hBOOL(hAPP(U_426,U_410))
            | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_411,sK8(U_426,U_424,U_422,U_420))],[f_78_3]) ).

fof(f_78_5,plain,
    ( ! [U_427,U_425,U_423,U_421] :
        ( ? [U_415] :
            ( hBOOL(hAPP(U_427,U_415))
            & hBOOL(hAPP(hAPP(c_member(U_421),U_415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425))) )
        | ( ! [U_414] :
              ( ~ hBOOL(hAPP(U_427,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) )
          & ! [U_413] :
              ( ~ hBOOL(hAPP(U_427,U_413))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ) ) )
    & ! [U_426,U_424,U_422,U_420] :
        ( ( hBOOL(hAPP(U_426,sK9(U_426,U_424,U_422,U_420)))
          & hBOOL(hAPP(hAPP(c_member(U_420),sK9(U_426,U_424,U_422,U_420)),U_424)) )
        | ( hBOOL(hAPP(U_426,sK8(U_426,U_424,U_422,U_420)))
          & hBOOL(hAPP(hAPP(c_member(U_420),sK8(U_426,U_424,U_422,U_420)),U_422)) )
        | ! [U_410] :
            ( ~ hBOOL(hAPP(U_426,U_410))
            | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_412,sK9(U_426,U_424,U_422,U_420))],[f_78_4]) ).

fof(f_78_6,plain,
    ( ! [U_427,U_425,U_423,U_421] :
        ( ( hBOOL(hAPP(U_427,sK10(U_427,U_425,U_423,U_421)))
          & hBOOL(hAPP(hAPP(c_member(U_421),sK10(U_427,U_425,U_423,U_421)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425))) )
        | ( ! [U_414] :
              ( ~ hBOOL(hAPP(U_427,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) )
          & ! [U_413] :
              ( ~ hBOOL(hAPP(U_427,U_413))
              | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ) ) )
    & ! [U_426,U_424,U_422,U_420] :
        ( ( hBOOL(hAPP(U_426,sK9(U_426,U_424,U_422,U_420)))
          & hBOOL(hAPP(hAPP(c_member(U_420),sK9(U_426,U_424,U_422,U_420)),U_424)) )
        | ( hBOOL(hAPP(U_426,sK8(U_426,U_424,U_422,U_420)))
          & hBOOL(hAPP(hAPP(c_member(U_420),sK8(U_426,U_424,U_422,U_420)),U_422)) )
        | ! [U_410] :
            ( ~ hBOOL(hAPP(U_426,U_410))
            | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_415,sK10(U_427,U_425,U_423,U_421))],[f_78_5]) ).

cnf(f_78_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_420),sK9(U_426,U_424,U_422,U_420)),U_424))
    | hBOOL(hAPP(hAPP(c_member(U_420),sK8(U_426,U_424,U_422,U_420)),U_422))
    | ~ hBOOL(hAPP(U_426,U_410))
    | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_8,plain,
    ( hBOOL(hAPP(U_426,sK9(U_426,U_424,U_422,U_420)))
    | hBOOL(hAPP(hAPP(c_member(U_420),sK8(U_426,U_424,U_422,U_420)),U_422))
    | ~ hBOOL(hAPP(U_426,U_410))
    | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_420),sK9(U_426,U_424,U_422,U_420)),U_424))
    | hBOOL(hAPP(U_426,sK8(U_426,U_424,U_422,U_420)))
    | ~ hBOOL(hAPP(U_426,U_410))
    | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_10,plain,
    ( hBOOL(hAPP(U_426,sK9(U_426,U_424,U_422,U_420)))
    | hBOOL(hAPP(U_426,sK8(U_426,U_424,U_422,U_420)))
    | ~ hBOOL(hAPP(U_426,U_410))
    | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_420,tc_HOL_Obool)),U_422),U_424))) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_421),sK10(U_427,U_425,U_423,U_421)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425)))
    | ~ hBOOL(hAPP(U_427,U_413))
    | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_12,plain,
    ( hBOOL(hAPP(U_427,sK10(U_427,U_425,U_423,U_421)))
    | ~ hBOOL(hAPP(U_427,U_413))
    | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_413),U_423)) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_421),sK10(U_427,U_425,U_423,U_421)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_421,tc_HOL_Obool)),U_423),U_425)))
    | ~ hBOOL(hAPP(U_427,U_414))
    | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

cnf(f_78_14,plain,
    ( hBOOL(hAPP(U_427,sK10(U_427,U_425,U_423,U_421)))
    | ~ hBOOL(hAPP(U_427,U_414))
    | ~ hBOOL(hAPP(hAPP(c_member(U_421),U_414),U_425)) ),
    inference(clausify,[status(thm)],[f_78_6]) ).

fof(f_79_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).

fof(f_79_2,plain,
    ! [U_431,U_430,U_429,U_428] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_429),U_430)),U_431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_429),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_430),U_431)),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_429),U_430)),U_431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_429),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_428,tc_HOL_Obool)),U_430),U_431)),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).

fof(f_80_2,plain,
    ! [U_435,U_434,U_433,U_432] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_434),U_435)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_434),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_433),U_435)),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

cnf(f_80_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_434),U_435)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_434),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_432,tc_HOL_Obool)),U_433),U_435)),
    inference(clausify,[status(thm)],[f_80_2]) ).

fof(f_81_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).

fof(f_81_2,plain,
    ! [U_438,U_437,U_436] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).

fof(f_82_2,plain,
    ! [U_441,U_440,U_439] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_439,tc_HOL_Obool)),U_440),U_441) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_439,tc_HOL_Obool)),U_441),U_440),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_439,tc_HOL_Obool)),U_440),U_441) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_439,tc_HOL_Obool)),U_441),U_440),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).

fof(f_83_2,plain,
    ! [U_443,U_442] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_442,tc_HOL_Obool)),U_443),U_443) = U_443,
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_442,tc_HOL_Obool)),U_443),U_443) = U_443,
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_1,plain,
    ! [V_u,V_t,V_s,V_c] :
      ( V_u = V_t
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_u))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_com__det]) ).

fof(f_84_2,plain,
    ! [U_447,U_446,U_445,U_444] :
      ( U_447 = U_446
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_444),U_445),U_447))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_444),U_445),U_446)) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( U_447 = U_446
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_444),U_445),U_447))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_444),U_445),U_446)) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_image__image]) ).

fof(f_85_2,plain,
    ! [U_453,U_452,U_451,U_450,U_449,U_448] : hAPP(c_Set_Oimage(U_448,U_449,U_450),hAPP(c_Set_Oimage(U_451,U_448,U_452),U_453)) = hAPP(c_Set_Oimage(U_451,U_449,hAPP(hAPP(c_COMBB(U_448,U_449,U_451),U_450),U_452)),U_453),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    hAPP(c_Set_Oimage(U_448,U_449,U_450),hAPP(c_Set_Oimage(U_451,U_448,U_452),U_453)) = hAPP(c_Set_Oimage(U_451,U_449,hAPP(hAPP(c_COMBB(U_448,U_449,U_451),U_450),U_452)),U_453),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [V_Q_2,V_P_2,V_c_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_MGF__complete]) ).

fof(f_86_2,plain,
    ! [U_456,U_455,U_454] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),U_455),U_454),U_456)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),U_455),U_454),U_456)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_454)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

cnf(f_86_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),U_455),U_454),U_456)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),U_455),U_454),U_456)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_454)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_86_2]) ).

fof(f_87_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),hAPP(c_Natural_Oevalc,V_c_2)),
    inference(fof_nnf,[status(thm)],[fact_MGT__def]) ).

fof(f_87_2,plain,
    ! [U_457] : c_Hoare__Mirabelle_OMGT(U_457) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_457),hAPP(c_Natural_Oevalc,U_457)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    c_Hoare__Mirabelle_OMGT(U_457) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_457),hAPP(c_Natural_Oevalc,U_457)),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [V_x_2,T_b,T_a] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Orderings_Obot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).

fof(f_88_2,plain,
    ! [U_460,U_459,U_458] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_459,U_458)),U_460) = c_Orderings_Obot__class_Obot(U_458)
      | ~ class_Orderings_Obot(U_458) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_459,U_458)),U_460) = c_Orderings_Obot__class_Obot(U_458)
    | ~ class_Orderings_Obot(U_458) ),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( V_a_2 = V_b_2
      | hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).

fof(f_89_2,plain,
    ! [U_463,U_462,U_461] :
      ( U_462 = U_463
      | hAPP(hAPP(c_Set_Oinsert(U_461),U_462),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_461),U_463),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_463,U_462] :
      ( ! [U_461] : hAPP(hAPP(c_Set_Oinsert(U_461),U_462),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_461),U_463),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool)))
      | U_462 = U_463 ),
    inference(miniscope,[status(thm)],[f_89_2]) ).

cnf(f_89_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_461),U_462),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_461),U_463),c_Orderings_Obot__class_Obot(tc_fun(U_461,tc_HOL_Obool)))
    | U_462 = U_463 ),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).

fof(f_90_2,plain,
    ! [U_468,U_467,U_466,U_465,U_464] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_464),U_465),hAPP(hAPP(c_Set_Oinsert(U_464),U_466),c_Orderings_Obot__class_Obot(tc_fun(U_464,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_464),U_467),hAPP(hAPP(c_Set_Oinsert(U_464),U_468),c_Orderings_Obot__class_Obot(tc_fun(U_464,tc_HOL_Obool))))
        | ( ( U_466 != U_467
            | U_465 != U_468 )
          & ( U_466 != U_468
            | U_465 != U_467 ) ) )
      & ( ( U_466 = U_467
          & U_465 = U_468 )
        | ( U_466 = U_468
          & U_465 = U_467 )
        | hAPP(hAPP(c_Set_Oinsert(U_464),U_465),hAPP(hAPP(c_Set_Oinsert(U_464),U_466),c_Orderings_Obot__class_Obot(tc_fun(U_464,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_464),U_467),hAPP(hAPP(c_Set_Oinsert(U_464),U_468),c_Orderings_Obot__class_Obot(tc_fun(U_464,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ( ! [U_478,U_476,U_474,U_472] :
        ( ! [U_470] : hAPP(hAPP(c_Set_Oinsert(U_470),U_472),hAPP(hAPP(c_Set_Oinsert(U_470),U_474),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_470),U_476),hAPP(hAPP(c_Set_Oinsert(U_470),U_478),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool))))
        | ( ( U_474 != U_476
            | U_472 != U_478 )
          & ( U_474 != U_478
            | U_472 != U_476 ) ) )
    & ! [U_477,U_475,U_473,U_471] :
        ( ! [U_469] : hAPP(hAPP(c_Set_Oinsert(U_469),U_471),hAPP(hAPP(c_Set_Oinsert(U_469),U_473),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_469),U_475),hAPP(hAPP(c_Set_Oinsert(U_469),U_477),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool))))
        | ( U_473 = U_475
          & U_471 = U_477 )
        | ( U_473 = U_477
          & U_471 = U_475 ) ) ),
    inference(miniscope,[status(thm)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( U_471 = U_477
    | U_471 = U_475
    | hAPP(hAPP(c_Set_Oinsert(U_469),U_471),hAPP(hAPP(c_Set_Oinsert(U_469),U_473),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_469),U_475),hAPP(hAPP(c_Set_Oinsert(U_469),U_477),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_5,plain,
    ( U_473 = U_475
    | U_471 = U_475
    | hAPP(hAPP(c_Set_Oinsert(U_469),U_471),hAPP(hAPP(c_Set_Oinsert(U_469),U_473),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_469),U_475),hAPP(hAPP(c_Set_Oinsert(U_469),U_477),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_6,plain,
    ( U_471 = U_477
    | U_473 = U_477
    | hAPP(hAPP(c_Set_Oinsert(U_469),U_471),hAPP(hAPP(c_Set_Oinsert(U_469),U_473),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_469),U_475),hAPP(hAPP(c_Set_Oinsert(U_469),U_477),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_7,plain,
    ( U_473 = U_475
    | U_473 = U_477
    | hAPP(hAPP(c_Set_Oinsert(U_469),U_471),hAPP(hAPP(c_Set_Oinsert(U_469),U_473),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_469),U_475),hAPP(hAPP(c_Set_Oinsert(U_469),U_477),c_Orderings_Obot__class_Obot(tc_fun(U_469,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_8,plain,
    ( U_474 != U_478
    | U_472 != U_476
    | hAPP(hAPP(c_Set_Oinsert(U_470),U_472),hAPP(hAPP(c_Set_Oinsert(U_470),U_474),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_470),U_476),hAPP(hAPP(c_Set_Oinsert(U_470),U_478),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

cnf(f_90_9,plain,
    ( U_474 != U_476
    | U_472 != U_478
    | hAPP(hAPP(c_Set_Oinsert(U_470),U_472),hAPP(hAPP(c_Set_Oinsert(U_470),U_474),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_470),U_476),hAPP(hAPP(c_Set_Oinsert(U_470),U_478),c_Orderings_Obot__class_Obot(tc_fun(U_470,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).

fof(f_91_2,plain,
    ! [U_481,U_480,U_479] : hAPP(hAPP(c_Set_Oinsert(U_479),U_480),U_481) != c_Orderings_Obot__class_Obot(tc_fun(U_479,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_479),U_480),U_481) != c_Orderings_Obot__class_Obot(tc_fun(U_479,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_1,plain,
    ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).

fof(f_92_2,plain,
    ! [U_484,U_483,U_482] : c_Orderings_Obot__class_Obot(tc_fun(U_482,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_482),U_483),U_484),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_482,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_482),U_483),U_484),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
          | V_y_2 != c_Orderings_Obot__class_Obot(T_a)
          | V_x_2 != c_Orderings_Obot__class_Obot(T_a) )
        & ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_a)
            & V_x_2 = c_Orderings_Obot__class_Obot(T_a) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_a) ) )
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).

fof(f_93_2,plain,
    ! [U_487,U_486,U_485] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_485),U_486),U_487) = c_Orderings_Obot__class_Obot(U_485)
          | U_487 != c_Orderings_Obot__class_Obot(U_485)
          | U_486 != c_Orderings_Obot__class_Obot(U_485) )
        & ( ( U_487 = c_Orderings_Obot__class_Obot(U_485)
            & U_486 = c_Orderings_Obot__class_Obot(U_485) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_485),U_486),U_487) != c_Orderings_Obot__class_Obot(U_485) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_485) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    ( U_486 = c_Orderings_Obot__class_Obot(U_485)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_485),U_486),U_487) != c_Orderings_Obot__class_Obot(U_485)
    | ~ class_Lattices_Obounded__lattice__bot(U_485) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( U_487 = c_Orderings_Obot__class_Obot(U_485)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_485),U_486),U_487) != c_Orderings_Obot__class_Obot(U_485)
    | ~ class_Lattices_Obounded__lattice__bot(U_485) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

cnf(f_93_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_485),U_486),U_487) = c_Orderings_Obot__class_Obot(U_485)
    | U_487 != c_Orderings_Obot__class_Obot(U_485)
    | U_486 != c_Orderings_Obot__class_Obot(U_485)
    | ~ class_Lattices_Obounded__lattice__bot(U_485) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_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_94_2,plain,
    ! [U_489,U_488] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_488),U_489),c_Orderings_Obot__class_Obot(U_488)) = U_489
      | ~ class_Lattices_Obounded__lattice__bot(U_488) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_488),U_489),c_Orderings_Obot__class_Obot(U_488)) = U_489
    | ~ class_Lattices_Obounded__lattice__bot(U_488) ),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_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_95_2,plain,
    ! [U_491,U_490] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_490),c_Orderings_Obot__class_Obot(U_490)),U_491) = U_491
      | ~ class_Lattices_Obounded__lattice__bot(U_490) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_490),c_Orderings_Obot__class_Obot(U_490)),U_491) = U_491
    | ~ class_Lattices_Obounded__lattice__bot(U_490) ),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_1,plain,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,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(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).

fof(f_96_2,plain,
    ! [U_495,U_494,U_493,U_492] :
      ( ( hAPP(c_Set_Oimage(U_492,U_493,U_494),U_495) = c_Orderings_Obot__class_Obot(tc_fun(U_493,tc_HOL_Obool))
        | U_495 != c_Orderings_Obot__class_Obot(tc_fun(U_492,tc_HOL_Obool)) )
      & ( U_495 = c_Orderings_Obot__class_Obot(tc_fun(U_492,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_492,U_493,U_494),U_495) != c_Orderings_Obot__class_Obot(tc_fun(U_493,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ( ! [U_503,U_501,U_499,U_497] :
        ( hAPP(c_Set_Oimage(U_497,U_499,U_501),U_503) = c_Orderings_Obot__class_Obot(tc_fun(U_499,tc_HOL_Obool))
        | U_503 != c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool)) )
    & ! [U_502,U_500,U_498,U_496] :
        ( U_502 = c_Orderings_Obot__class_Obot(tc_fun(U_496,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_496,U_498,U_500),U_502) != c_Orderings_Obot__class_Obot(tc_fun(U_498,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( U_502 = c_Orderings_Obot__class_Obot(tc_fun(U_496,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_496,U_498,U_500),U_502) != c_Orderings_Obot__class_Obot(tc_fun(U_498,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

cnf(f_96_5,plain,
    ( hAPP(c_Set_Oimage(U_497,U_499,U_501),U_503) = c_Orderings_Obot__class_Obot(tc_fun(U_499,tc_HOL_Obool))
    | U_503 != c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_image__empty]) ).

fof(f_97_2,plain,
    ! [U_506,U_505,U_504] : hAPP(c_Set_Oimage(U_504,U_505,U_506),c_Orderings_Obot__class_Obot(tc_fun(U_504,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_505,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    hAPP(c_Set_Oimage(U_504,U_505,U_506),c_Orderings_Obot__class_Obot(tc_fun(U_504,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_505,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),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))
        | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).

fof(f_98_2,plain,
    ! [U_510,U_509,U_508,U_507] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_507,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_508,U_507,U_509),U_510)
        | U_510 != c_Orderings_Obot__class_Obot(tc_fun(U_508,tc_HOL_Obool)) )
      & ( U_510 = c_Orderings_Obot__class_Obot(tc_fun(U_508,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_507,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_508,U_507,U_509),U_510) ) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ( ! [U_518,U_516,U_514] :
        ( ! [U_512] : c_Orderings_Obot__class_Obot(tc_fun(U_512,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_514,U_512,U_516),U_518)
        | U_518 != c_Orderings_Obot__class_Obot(tc_fun(U_514,tc_HOL_Obool)) )
    & ! [U_517,U_515,U_513] :
        ( ! [U_511] : c_Orderings_Obot__class_Obot(tc_fun(U_511,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_513,U_511,U_515),U_517)
        | U_517 = c_Orderings_Obot__class_Obot(tc_fun(U_513,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_98_2]) ).

cnf(f_98_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_511,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_513,U_511,U_515),U_517)
    | U_517 = c_Orderings_Obot__class_Obot(tc_fun(U_513,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_98_3]) ).

cnf(f_98_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_512,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_514,U_512,U_516),U_518)
    | U_518 != c_Orderings_Obot__class_Obot(tc_fun(U_514,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_98_3]) ).

fof(f_99_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).

fof(f_99_2,plain,
    ! [U_521,U_520,U_519] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_519,tc_HOL_Obool)),U_520),U_521) = c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool))
        | U_521 != c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool))
        | U_520 != c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool)) )
      & ( ( U_521 = c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool))
          & U_520 = c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_519,tc_HOL_Obool)),U_520),U_521) != c_Orderings_Obot__class_Obot(tc_fun(U_519,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ( ! [U_527,U_525,U_523] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_523,tc_HOL_Obool)),U_525),U_527) = c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))
        | U_527 != c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))
        | U_525 != c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool)) )
    & ! [U_526,U_524,U_522] :
        ( ( U_526 = c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool))
          & U_524 = c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_522,tc_HOL_Obool)),U_524),U_526) != c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( U_524 = c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_522,tc_HOL_Obool)),U_524),U_526) != c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

cnf(f_99_5,plain,
    ( U_526 = c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_522,tc_HOL_Obool)),U_524),U_526) != c_Orderings_Obot__class_Obot(tc_fun(U_522,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

cnf(f_99_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_523,tc_HOL_Obool)),U_525),U_527) = c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))
    | U_527 != c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))
    | U_525 != c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).

fof(f_100_2,plain,
    ! [U_529,U_528] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_528,tc_HOL_Obool)),U_529),c_Orderings_Obot__class_Obot(tc_fun(U_528,tc_HOL_Obool))) = U_529,
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_528,tc_HOL_Obool)),U_529),c_Orderings_Obot__class_Obot(tc_fun(U_528,tc_HOL_Obool))) = U_529,
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).

fof(f_101_2,plain,
    ! [U_531,U_530] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_530,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_530,tc_HOL_Obool))),U_531) = U_531,
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_530,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_530,tc_HOL_Obool))),U_531) = U_531,
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__insert]) ).

fof(f_102_2,plain,
    ! [U_536,U_535,U_534,U_533,U_532] : hAPP(c_Set_Oimage(U_532,U_533,U_534),hAPP(hAPP(c_Set_Oinsert(U_532),U_535),U_536)) = hAPP(hAPP(c_Set_Oinsert(U_533),hAPP(U_534,U_535)),hAPP(c_Set_Oimage(U_532,U_533,U_534),U_536)),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    hAPP(c_Set_Oimage(U_532,U_533,U_534),hAPP(hAPP(c_Set_Oinsert(U_532),U_535),U_536)) = hAPP(hAPP(c_Set_Oinsert(U_533),hAPP(U_534,U_535)),hAPP(c_Set_Oimage(U_532,U_533,U_534),U_536)),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).

fof(f_103_2,plain,
    ! [U_540,U_539,U_538,U_537] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_537),U_538),U_539)),U_540) = hAPP(hAPP(c_Set_Oinsert(U_537),U_538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),U_539),U_540)),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_537),U_538),U_539)),U_540) = hAPP(hAPP(c_Set_Oinsert(U_537),U_538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),U_539),U_540)),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).

fof(f_104_2,plain,
    ! [U_544,U_543,U_542,U_541] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_542),hAPP(hAPP(c_Set_Oinsert(U_541),U_543),U_544)) = hAPP(hAPP(c_Set_Oinsert(U_541),U_543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_542),U_544)),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_542),hAPP(hAPP(c_Set_Oinsert(U_541),U_543),U_544)) = hAPP(hAPP(c_Set_Oinsert(U_541),U_543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_542),U_544)),
    inference(clausify,[status(thm)],[f_104_2]) ).

fof(f_105_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).

fof(f_105_2,plain,
    ! [U_549,U_548,U_547,U_546,U_545] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_546,U_545)),U_547),U_548),U_549) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_545),hAPP(U_547,U_549)),hAPP(U_548,U_549))
      | ~ class_Lattices_Olattice(U_545) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_546,U_545)),U_547),U_548),U_549) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_545),hAPP(U_547,U_549)),hAPP(U_548,U_549))
    | ~ class_Lattices_Olattice(U_545) ),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,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__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Un]) ).

fof(f_106_2,plain,
    ! [U_554,U_553,U_552,U_551,U_550] : hAPP(c_Set_Oimage(U_550,U_551,U_552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_550,tc_HOL_Obool)),U_553),U_554)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_551,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_550,U_551,U_552),U_553)),hAPP(c_Set_Oimage(U_550,U_551,U_552),U_554)),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

cnf(f_106_3,plain,
    hAPP(c_Set_Oimage(U_550,U_551,U_552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_550,tc_HOL_Obool)),U_553),U_554)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_551,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_550,U_551,U_552),U_553)),hAPP(c_Set_Oimage(U_550,U_551,U_552),U_554)),
    inference(clausify,[status(thm)],[f_106_2]) ).

fof(f_107_1,plain,
    ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).

fof(f_107_2,plain,
    ! [U_556,U_555] : c_Set_Othe__elem(U_555,hAPP(hAPP(c_Set_Oinsert(U_555),U_556),c_Orderings_Obot__class_Obot(tc_fun(U_555,tc_HOL_Obool)))) = U_556,
    inference(variable_rename,[status(thm)],[f_107_1]) ).

cnf(f_107_3,plain,
    c_Set_Othe__elem(U_555,hAPP(hAPP(c_Set_Oinsert(U_555),U_556),c_Orderings_Obot__class_Obot(tc_fun(U_555,tc_HOL_Obool)))) = U_556,
    inference(clausify,[status(thm)],[f_107_2]) ).

fof(f_108_1,plain,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_MGT__alternI]) ).

fof(f_108_2,plain,
    ! [U_558,U_557] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_557,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,U_558))))),c_fequal))),U_558),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_557,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_558)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_557,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,U_558))))),c_fequal))),U_558),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_557,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_558)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_109_2,plain,
    ! [U_564,U_563,U_562,U_561,U_560,U_559] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_559,U_560,U_561,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_559),U_562),U_563),U_564)) = hAPP(hAPP(hAPP(U_561,U_562),U_563),U_564),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(U_559,U_560,U_561,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_559),U_562),U_563),U_564)) = hAPP(hAPP(hAPP(U_561,U_562),U_563),U_564),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_110_2,plain,
    ! [U_570,U_569,U_568,U_567,U_566,U_565] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_565,U_566,U_567,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_565),U_568),U_569),U_570)) = hAPP(hAPP(hAPP(U_567,U_568),U_569),U_570),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(U_565,U_566,U_567,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_565),U_568),U_569),U_570)) = hAPP(hAPP(hAPP(U_567,U_568),U_569),U_570),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),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_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) ) ),
    inference(fof_nnf,[status(thm)],[fact_escape]) ).

fof(f_111_2,plain,
    ! [U_577,U_576,U_575,U_574,U_573] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),U_573),U_576),U_577)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
      | ? [U_572,U_571] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_571))),U_576),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(U_577,U_572)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_573,U_572),U_571)) ) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_577,U_576,U_575,U_574,U_573] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),U_573),U_576),U_577)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
      | ? [U_571] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_571))),U_576),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(U_577,sK11(U_577,U_576,U_575,U_574,U_573))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_573,sK11(U_577,U_576,U_575,U_574,U_573)),U_571)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_572,sK11(U_577,U_576,U_575,U_574,U_573))],[f_111_2]) ).

fof(f_111_4,plain,
    ! [U_577,U_576,U_575,U_574,U_573] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),U_573),U_576),U_577)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK12(U_577,U_576,U_575,U_574,U_573)))),U_576),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(U_577,sK11(U_577,U_576,U_575,U_574,U_573))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
        & hBOOL(hAPP(hAPP(U_573,sK11(U_577,U_576,U_575,U_574,U_573)),sK12(U_577,U_576,U_575,U_574,U_573))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_571,sK12(U_577,U_576,U_575,U_574,U_573))],[f_111_3]) ).

cnf(f_111_5,plain,
    ( hBOOL(hAPP(hAPP(U_573,sK11(U_577,U_576,U_575,U_574,U_573)),sK12(U_577,U_576,U_575,U_574,U_573)))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),U_573),U_576),U_577)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_111_4]) ).

cnf(f_111_6,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK12(U_577,U_576,U_575,U_574,U_573)))),U_576),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_574),hAPP(U_577,sK11(U_577,U_576,U_575,U_574,U_573))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool))))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_574,U_575,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_574)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_574),U_573),U_576),U_577)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_574),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_111_4]) ).

fof(f_112_1,plain,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(fof_nnf,[status(thm)],[fact_MGT__alternD]) ).

fof(f_112_2,plain,
    ! [U_579,U_578] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_579)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,U_579))))),c_fequal))),U_579),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ( ! [U_579,U_578] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_579)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,U_579))))),c_fequal))),U_579),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) )
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(miniscope,[status(thm)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_579)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_578,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,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)),tc_Com_Ostate),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)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,U_579))))),c_fequal))),U_579),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).

fof(f_113_2,plain,
    ! [U_582,U_581,U_580] : c_Hoare__Mirabelle_Ohoare__derivs(U_580,U_581,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_580)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_580),U_582),c_Com_Ocom_OSKIP),U_582)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_580),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_580,U_581,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_580)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_580),U_582),c_Com_Ocom_OSKIP),U_582)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_580),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OSkip]) ).

fof(f_114_2,plain,
    ! [U_585,U_584,U_583] : c_Hoare__Mirabelle_Ohoare__derivs(U_583,U_584,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_583)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_583),U_585),c_Com_Ocom_OSKIP),U_585)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_583),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_583,U_584,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_583)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_583),U_585),c_Com_Ocom_OSKIP),U_585)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_583),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_1,plain,
    ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s))
          & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_conseq1]) ).

fof(f_115_2,plain,
    ! [U_593,U_592,U_591,U_590,U_589,U_588] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_593),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool))))
      | ? [U_587,U_586] :
          ( ~ hBOOL(hAPP(hAPP(U_590,U_587),U_586))
          & hBOOL(hAPP(hAPP(U_593,U_587),U_586)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_590),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_593,U_592,U_591,U_590,U_589,U_588] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_593),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool))))
      | ? [U_586] :
          ( ~ hBOOL(hAPP(hAPP(U_590,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),U_586))
          & hBOOL(hAPP(hAPP(U_593,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),U_586)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_590),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_587,sK13(U_593,U_592,U_591,U_590,U_589,U_588))],[f_115_2]) ).

fof(f_115_4,plain,
    ! [U_593,U_592,U_591,U_590,U_589,U_588] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_593),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_590,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),sK14(U_593,U_592,U_591,U_590,U_589,U_588)))
        & hBOOL(hAPP(hAPP(U_593,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),sK14(U_593,U_592,U_591,U_590,U_589,U_588))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_590),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_586,sK14(U_593,U_592,U_591,U_590,U_589,U_588))],[f_115_3]) ).

cnf(f_115_5,plain,
    ( hBOOL(hAPP(hAPP(U_593,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),sK14(U_593,U_592,U_591,U_590,U_589,U_588)))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_593),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_590),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

cnf(f_115_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_590,sK13(U_593,U_592,U_591,U_590,U_589,U_588)),sK14(U_593,U_592,U_591,U_590,U_589,U_588)))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_593),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_588,U_589,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_588)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_588),U_590),U_591),U_592)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_588),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

fof(f_116_1,plain,
    ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ? [B_Z,B_s] :
          ( ~ hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s))
          & hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_conseq2]) ).

fof(f_116_2,plain,
    ! [U_601,U_600,U_599,U_598,U_597,U_596] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_601)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool))))
      | ? [U_595,U_594] :
          ( ~ hBOOL(hAPP(hAPP(U_601,U_595),U_594))
          & hBOOL(hAPP(hAPP(U_600,U_595),U_594)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_600)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_601,U_600,U_599,U_598,U_597,U_596] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_601)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool))))
      | ? [U_594] :
          ( ~ hBOOL(hAPP(hAPP(U_601,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),U_594))
          & hBOOL(hAPP(hAPP(U_600,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),U_594)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_600)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_595,sK15(U_601,U_600,U_599,U_598,U_597,U_596))],[f_116_2]) ).

fof(f_116_4,plain,
    ! [U_601,U_600,U_599,U_598,U_597,U_596] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_601)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_601,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),sK16(U_601,U_600,U_599,U_598,U_597,U_596)))
        & hBOOL(hAPP(hAPP(U_600,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),sK16(U_601,U_600,U_599,U_598,U_597,U_596))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_600)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_594,sK16(U_601,U_600,U_599,U_598,U_597,U_596))],[f_116_3]) ).

cnf(f_116_5,plain,
    ( hBOOL(hAPP(hAPP(U_600,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),sK16(U_601,U_600,U_599,U_598,U_597,U_596)))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_601)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_600)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

cnf(f_116_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_601,sK15(U_601,U_600,U_599,U_598,U_597,U_596)),sK16(U_601,U_600,U_599,U_598,U_597,U_596)))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_601)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_596,U_597,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_596)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_596),U_598),U_599),U_600)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_596),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

fof(f_117_1,plain,
    ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Comp]) ).

fof(f_117_2,plain,
    ! [U_608,U_607,U_606,U_605,U_604,U_603,U_602] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_604),c_Com_Ocom_OSemi(U_605,U_607)),U_608)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_606),U_607),U_608)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_604),U_605),U_606)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_604),c_Com_Ocom_OSemi(U_605,U_607)),U_608)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_606),U_607),U_608)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_602,U_603,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_602)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_602),U_604),U_605),U_606)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_602),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_LoopF]) ).

fof(f_118_2,plain,
    ! [U_613,U_612,U_611,U_610,U_609] : c_Hoare__Mirabelle_Ohoare__derivs(U_609,U_610,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_609)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_609),hAPP(hAPP(c_COMBC(U_609,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_609),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_609),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_611))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_612))),c_Com_Ocom_OWhile(U_612,U_613)),U_611)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_609),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_609,U_610,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_609)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_609),hAPP(hAPP(c_COMBC(U_609,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_609),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_609),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_611))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_612))),c_Com_Ocom_OWhile(U_612,U_613)),U_611)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_609),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [V_c_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(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_119_2,plain,
    ! [U_616,U_615,U_614] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_614,U_616)),U_615),U_615))
      | hBOOL(hAPP(U_614,U_615)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_614,U_616)),U_615),U_615))
    | hBOOL(hAPP(U_614,U_615)) ),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
      | ~ hBOOL(hAPP(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_120_2,plain,
    ! [U_621,U_620,U_619,U_618,U_617] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_617,U_619)),U_618),U_621))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_617,U_619)),U_620),U_621))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_619),U_618),U_620))
      | ~ hBOOL(hAPP(U_617,U_618)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_617,U_619)),U_618),U_621))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_617,U_619)),U_620),U_621))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_619),U_618),U_620))
    | ~ hBOOL(hAPP(U_617,U_618)) ),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s1),V_s2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0),V_s0),V_s1)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc_OSemi]) ).

fof(f_121_2,plain,
    ! [U_626,U_625,U_624,U_623,U_622] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_622,U_625)),U_623),U_626))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_625),U_624),U_626))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_622),U_623),U_624)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_622,U_625)),U_623),U_626))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_625),U_624),U_626))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_622),U_623),U_624)) ),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_1,plain,
    ! [V_s] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_s)),
    inference(fof_nnf,[status(thm)],[fact_evalc_OSkip]) ).

fof(f_122_2,plain,
    ! [U_627] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_627),U_627)),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

cnf(f_122_3,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_627),U_627)),
    inference(clausify,[status(thm)],[f_122_2]) ).

fof(f_123_1,plain,
    ! [V_t,V_s] :
      ( V_t = V_s
      | ~ hBOOL(hAPP(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_123_2,plain,
    ! [U_629,U_628] :
      ( U_629 = U_628
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_628),U_629)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

cnf(f_123_3,plain,
    ( U_629 = U_628
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_628),U_629)) ),
    inference(clausify,[status(thm)],[f_123_2]) ).

fof(f_124_1,plain,
    ! [V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
              | ~ hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) )
        | ~ hBOOL(hAPP(V_a1_2,V_a2_2))
        | ~ hBOOL(hAPP(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_124_2,plain,
    ! [U_634,U_633,U_632] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_632,U_633)),U_634),U_634))
        | ( ! [U_631] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_632,U_633)),U_631),U_634))
              | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_633),U_634),U_631)) )
          & hBOOL(hAPP(U_632,U_634)) ) )
      & ( ? [U_630] :
            ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_632,U_633)),U_630),U_634))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_633),U_634),U_630)) )
        | ~ hBOOL(hAPP(U_632,U_634))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_632,U_633)),U_634),U_634)) ) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ( ! [U_640,U_638,U_636] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_640),U_640))
        | ( ! [U_631] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_631),U_640))
              | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_638),U_640),U_631)) )
          & hBOOL(hAPP(U_636,U_640)) ) )
    & ! [U_639,U_637,U_635] :
        ( ? [U_630] :
            ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),U_630),U_639))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_637),U_639),U_630)) )
        | ~ hBOOL(hAPP(U_635,U_639))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),U_639),U_639)) ) ),
    inference(miniscope,[status(thm)],[f_124_2]) ).

fof(f_124_4,plain,
    ( ! [U_640,U_638,U_636] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_640),U_640))
        | ( ! [U_631] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_631),U_640))
              | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_638),U_640),U_631)) )
          & hBOOL(hAPP(U_636,U_640)) ) )
    & ! [U_639,U_637,U_635] :
        ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),sK17(U_639,U_637,U_635)),U_639))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_637),U_639),sK17(U_639,U_637,U_635))) )
        | ~ hBOOL(hAPP(U_635,U_639))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),U_639),U_639)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_630,sK17(U_639,U_637,U_635))],[f_124_3]) ).

cnf(f_124_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_637),U_639),sK17(U_639,U_637,U_635)))
    | ~ hBOOL(hAPP(U_635,U_639))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),U_639),U_639)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),sK17(U_639,U_637,U_635)),U_639))
    | ~ hBOOL(hAPP(U_635,U_639))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_635,U_637)),U_639),U_639)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_7,plain,
    ( hBOOL(hAPP(U_636,U_640))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_640),U_640)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_631),U_640))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_638),U_640),U_631))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_636,U_638)),U_640),U_640)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

fof(f_125_1,plain,
    ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
                | ~ hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2))
              & hBOOL(hAPP(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(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_125_2,plain,
    ! [U_646,U_645,U_644,U_643] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_643,U_644)),U_645),U_646))
        | ( ( ! [U_642] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_643,U_644)),U_642),U_646))
                | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_644),U_645),U_642)) )
            | ~ hBOOL(hAPP(U_643,U_645)) )
          & ( hBOOL(hAPP(U_643,U_645))
            | U_646 != U_645 ) ) )
      & ( ( ? [U_641] :
              ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_643,U_644)),U_641),U_646))
              & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_644),U_645),U_641)) )
          & hBOOL(hAPP(U_643,U_645)) )
        | ( ~ hBOOL(hAPP(U_643,U_645))
          & U_646 = U_645 )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_643,U_644)),U_645),U_646)) ) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ( ! [U_654,U_652,U_650,U_648] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_652),U_654))
        | ( ( ! [U_642] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_642),U_654))
                | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_650),U_652),U_642)) )
            | ~ hBOOL(hAPP(U_648,U_652)) )
          & ( hBOOL(hAPP(U_648,U_652))
            | U_654 != U_652 ) ) )
    & ! [U_653,U_651,U_649,U_647] :
        ( ( ? [U_641] :
              ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_641),U_653))
              & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_649),U_651),U_641)) )
          & hBOOL(hAPP(U_647,U_651)) )
        | ( ~ hBOOL(hAPP(U_647,U_651))
          & U_653 = U_651 )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ) ),
    inference(miniscope,[status(thm)],[f_125_2]) ).

fof(f_125_4,plain,
    ( ! [U_654,U_652,U_650,U_648] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_652),U_654))
        | ( ( ! [U_642] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_642),U_654))
                | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_650),U_652),U_642)) )
            | ~ hBOOL(hAPP(U_648,U_652)) )
          & ( hBOOL(hAPP(U_648,U_652))
            | U_654 != U_652 ) ) )
    & ! [U_653,U_651,U_649,U_647] :
        ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),sK18(U_653,U_651,U_649,U_647)),U_653))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_649),U_651),sK18(U_653,U_651,U_649,U_647)))
          & hBOOL(hAPP(U_647,U_651)) )
        | ( ~ hBOOL(hAPP(U_647,U_651))
          & U_653 = U_651 )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_641,sK18(U_653,U_651,U_649,U_647))],[f_125_3]) ).

cnf(f_125_5,plain,
    ( hBOOL(hAPP(U_647,U_651))
    | U_653 = U_651
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_649),U_651),sK18(U_653,U_651,U_649,U_647)))
    | U_653 = U_651
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),sK18(U_653,U_651,U_649,U_647)),U_653))
    | U_653 = U_651
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_8,plain,
    ( hBOOL(hAPP(U_647,U_651))
    | ~ hBOOL(hAPP(U_647,U_651))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_649),U_651),sK18(U_653,U_651,U_649,U_647)))
    | ~ hBOOL(hAPP(U_647,U_651))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_10,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),sK18(U_653,U_651,U_649,U_647)),U_653))
    | ~ hBOOL(hAPP(U_647,U_651))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_647,U_649)),U_651),U_653)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_11,plain,
    ( hBOOL(hAPP(U_648,U_652))
    | U_654 != U_652
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_652),U_654)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_12,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_642),U_654))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_650),U_652),U_642))
    | ~ hBOOL(hAPP(U_648,U_652))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(U_648,U_650)),U_652),U_654)) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

fof(f_126_1,plain,
    ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2))
            | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1)) )
        | ~ hBOOL(hAPP(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_126_2,plain,
    ! [U_660,U_659,U_658,U_657] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_657,U_658)),U_659),U_660))
        | ! [U_656] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_658),U_656),U_660))
            | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_657),U_659),U_656)) ) )
      & ( ? [U_655] :
            ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_658),U_655),U_660))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_657),U_659),U_655)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_657,U_658)),U_659),U_660)) ) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ( ! [U_668,U_666,U_664,U_662] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_662,U_664)),U_666),U_668))
        | ! [U_656] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_664),U_656),U_668))
            | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_662),U_666),U_656)) ) )
    & ! [U_667,U_665,U_663,U_661] :
        ( ? [U_655] :
            ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_663),U_655),U_667))
            & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_661),U_665),U_655)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_661,U_663)),U_665),U_667)) ) ),
    inference(miniscope,[status(thm)],[f_126_2]) ).

fof(f_126_4,plain,
    ( ! [U_668,U_666,U_664,U_662] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_662,U_664)),U_666),U_668))
        | ! [U_656] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_664),U_656),U_668))
            | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_662),U_666),U_656)) ) )
    & ! [U_667,U_665,U_663,U_661] :
        ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_663),sK19(U_667,U_665,U_663,U_661)),U_667))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_661),U_665),sK19(U_667,U_665,U_663,U_661))) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_661,U_663)),U_665),U_667)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_655,sK19(U_667,U_665,U_663,U_661))],[f_126_3]) ).

cnf(f_126_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_661),U_665),sK19(U_667,U_665,U_663,U_661)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_661,U_663)),U_665),U_667)) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

cnf(f_126_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_663),sK19(U_667,U_665,U_663,U_661)),U_667))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_661,U_663)),U_665),U_667)) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

cnf(f_126_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_662,U_664)),U_666),U_668))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_664),U_656),U_668))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_662),U_666),U_656)) ),
    inference(clausify,[status(thm)],[f_126_4]) ).

fof(f_127_1,plain,
    ! [V_a] : hBOOL(hAPP(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_127_2,plain,
    ! [U_669] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_669),U_669)),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),U_669),U_669)),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_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_128_2,plain,
    ! [U_671,U_670] : c_Com_Ocom_OSemi(U_670,U_671) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_128_1]) ).

cnf(f_128_3,plain,
    c_Com_Ocom_OSemi(U_670,U_671) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_128_2]) ).

fof(f_129_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_129_2,plain,
    ! [U_673,U_672] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_672,U_673),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

cnf(f_129_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_672,U_673),
    inference(clausify,[status(thm)],[f_129_2]) ).

fof(f_130_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_130_2,plain,
    ! [U_675,U_674] : c_Com_Ocom_OWhile(U_674,U_675) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_130_1]) ).

cnf(f_130_3,plain,
    c_Com_Ocom_OWhile(U_674,U_675) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_130_2]) ).

fof(f_131_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_131_2,plain,
    ! [U_677,U_676] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_676,U_677),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

cnf(f_131_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_676,U_677),
    inference(clausify,[status(thm)],[f_131_2]) ).

fof(f_132_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_132_2,plain,
    ! [U_681,U_680,U_679,U_678] : c_Com_Ocom_OWhile(U_678,U_679) != c_Com_Ocom_OSemi(U_680,U_681),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    c_Com_Ocom_OWhile(U_678,U_679) != c_Com_Ocom_OSemi(U_680,U_681),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_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_133_2,plain,
    ! [U_685,U_684,U_683,U_682] : c_Com_Ocom_OSemi(U_682,U_683) != c_Com_Ocom_OWhile(U_684,U_685),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

cnf(f_133_3,plain,
    c_Com_Ocom_OSemi(U_682,U_683) != c_Com_Ocom_OWhile(U_684,U_685),
    inference(clausify,[status(thm)],[f_133_2]) ).

fof(f_134_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_134_2,plain,
    ! [U_686] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_686),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

cnf(f_134_3,plain,
    c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_686),
    inference(clausify,[status(thm)],[f_134_2]) ).

fof(f_135_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_135_2,plain,
    ! [U_687] : hAPP(c_Com_Ocom_OBODY,U_687) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_135_1]) ).

cnf(f_135_3,plain,
    hAPP(c_Com_Ocom_OBODY,U_687) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_135_2]) ).

fof(f_136_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_136_2,plain,
    ! [U_690,U_689,U_688] : hAPP(c_Com_Ocom_OBODY,U_688) != c_Com_Ocom_OSemi(U_689,U_690),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

cnf(f_136_3,plain,
    hAPP(c_Com_Ocom_OBODY,U_688) != c_Com_Ocom_OSemi(U_689,U_690),
    inference(clausify,[status(thm)],[f_136_2]) ).

fof(f_137_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_137_2,plain,
    ! [U_693,U_692,U_691] : c_Com_Ocom_OSemi(U_691,U_692) != hAPP(c_Com_Ocom_OBODY,U_693),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    c_Com_Ocom_OSemi(U_691,U_692) != hAPP(c_Com_Ocom_OBODY,U_693),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_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_138_2,plain,
    ! [U_696,U_695,U_694] : hAPP(c_Com_Ocom_OBODY,U_694) != c_Com_Ocom_OWhile(U_695,U_696),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

cnf(f_138_3,plain,
    hAPP(c_Com_Ocom_OBODY,U_694) != c_Com_Ocom_OWhile(U_695,U_696),
    inference(clausify,[status(thm)],[f_138_2]) ).

fof(f_139_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_139_2,plain,
    ! [U_698,U_697] :
      ( ( hAPP(c_Com_Ocom_OBODY,U_697) = hAPP(c_Com_Ocom_OBODY,U_698)
        | U_697 != U_698 )
      & ( U_697 = U_698
        | hAPP(c_Com_Ocom_OBODY,U_697) != hAPP(c_Com_Ocom_OBODY,U_698) ) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ( ! [U_702,U_700] :
        ( hAPP(c_Com_Ocom_OBODY,U_700) = hAPP(c_Com_Ocom_OBODY,U_702)
        | U_700 != U_702 )
    & ! [U_701,U_699] :
        ( U_699 = U_701
        | hAPP(c_Com_Ocom_OBODY,U_699) != hAPP(c_Com_Ocom_OBODY,U_701) ) ),
    inference(miniscope,[status(thm)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( U_699 = U_701
    | hAPP(c_Com_Ocom_OBODY,U_699) != hAPP(c_Com_Ocom_OBODY,U_701) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_5,plain,
    ( hAPP(c_Com_Ocom_OBODY,U_700) = hAPP(c_Com_Ocom_OBODY,U_702)
    | U_700 != U_702 ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_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_140_2,plain,
    ! [U_706,U_705,U_704,U_703] :
      ( ( c_Com_Ocom_OWhile(U_703,U_704) = c_Com_Ocom_OWhile(U_705,U_706)
        | U_704 != U_706
        | U_703 != U_705 )
      & ( ( U_704 = U_706
          & U_703 = U_705 )
        | c_Com_Ocom_OWhile(U_703,U_704) != c_Com_Ocom_OWhile(U_705,U_706) ) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ( ! [U_714,U_712,U_710,U_708] :
        ( c_Com_Ocom_OWhile(U_708,U_710) = c_Com_Ocom_OWhile(U_712,U_714)
        | U_710 != U_714
        | U_708 != U_712 )
    & ! [U_713,U_711,U_709,U_707] :
        ( ( U_709 = U_713
          & U_707 = U_711 )
        | c_Com_Ocom_OWhile(U_707,U_709) != c_Com_Ocom_OWhile(U_711,U_713) ) ),
    inference(miniscope,[status(thm)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( U_707 = U_711
    | c_Com_Ocom_OWhile(U_707,U_709) != c_Com_Ocom_OWhile(U_711,U_713) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_5,plain,
    ( U_709 = U_713
    | c_Com_Ocom_OWhile(U_707,U_709) != c_Com_Ocom_OWhile(U_711,U_713) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_6,plain,
    ( c_Com_Ocom_OWhile(U_708,U_710) = c_Com_Ocom_OWhile(U_712,U_714)
    | U_710 != U_714
    | U_708 != U_712 ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_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_141_2,plain,
    ! [U_718,U_717,U_716,U_715] :
      ( ( c_Com_Ocom_OSemi(U_715,U_716) = c_Com_Ocom_OSemi(U_717,U_718)
        | U_716 != U_718
        | U_715 != U_717 )
      & ( ( U_716 = U_718
          & U_715 = U_717 )
        | c_Com_Ocom_OSemi(U_715,U_716) != c_Com_Ocom_OSemi(U_717,U_718) ) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ( ! [U_726,U_724,U_722,U_720] :
        ( c_Com_Ocom_OSemi(U_720,U_722) = c_Com_Ocom_OSemi(U_724,U_726)
        | U_722 != U_726
        | U_720 != U_724 )
    & ! [U_725,U_723,U_721,U_719] :
        ( ( U_721 = U_725
          & U_719 = U_723 )
        | c_Com_Ocom_OSemi(U_719,U_721) != c_Com_Ocom_OSemi(U_723,U_725) ) ),
    inference(miniscope,[status(thm)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( U_719 = U_723
    | c_Com_Ocom_OSemi(U_719,U_721) != c_Com_Ocom_OSemi(U_723,U_725) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

cnf(f_141_5,plain,
    ( U_721 = U_725
    | c_Com_Ocom_OSemi(U_719,U_721) != c_Com_Ocom_OSemi(U_723,U_725) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

cnf(f_141_6,plain,
    ( c_Com_Ocom_OSemi(U_720,U_722) = c_Com_Ocom_OSemi(U_724,U_726)
    | U_722 != U_726
    | U_720 != U_724 ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_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_142_2,plain,
    ! [U_729,U_728,U_727] : c_Com_Ocom_OWhile(U_727,U_728) != hAPP(c_Com_Ocom_OBODY,U_729),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    c_Com_Ocom_OWhile(U_727,U_728) != hAPP(c_Com_Ocom_OBODY,U_729),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_1,plain,
    ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_the__elem__def]) ).

fof(f_143_2,plain,
    ! [U_731,U_730] : c_Set_Othe__elem(U_730,U_731) = c_HOL_OThe(U_730,hAPP(hAPP(c_COMBB(tc_fun(U_730,tc_HOL_Obool),tc_HOL_Obool,U_730),hAPP(c_fequal,U_731)),hAPP(hAPP(c_COMBC(U_730,tc_fun(U_730,tc_HOL_Obool),tc_fun(U_730,tc_HOL_Obool)),c_Set_Oinsert(U_730)),c_Orderings_Obot__class_Obot(tc_fun(U_730,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    c_Set_Othe__elem(U_730,U_731) = c_HOL_OThe(U_730,hAPP(hAPP(c_COMBB(tc_fun(U_730,tc_HOL_Obool),tc_HOL_Obool,U_730),hAPP(c_fequal,U_731)),hAPP(hAPP(c_COMBC(U_730,tc_fun(U_730,tc_HOL_Obool),tc_fun(U_730,tc_HOL_Obool)),c_Set_Oinsert(U_730)),c_Orderings_Obot__class_Obot(tc_fun(U_730,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_1,plain,
    ! [V_c_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c_2))
      | ~ c_Com_OWT__bodies
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(fof_nnf,[status(thm)],[fact_MGF]) ).

fof(f_144_2,plain,
    ! [U_732] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_732)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Com_OWT,U_732))
      | ~ c_Com_OWT__bodies
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ( ! [U_732] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_732)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Com_OWT,U_732)) )
    | ~ c_Com_OWT__bodies
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(miniscope,[status(thm)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_732)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Com_OWT,U_732))
    | ~ c_Com_OWT__bodies
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__ident]) ).

fof(f_145_2,plain,
    ! [U_734,U_733] : hAPP(c_Set_Oimage(U_733,U_733,c_COMBI(U_733)),U_734) = U_734,
    inference(variable_rename,[status(thm)],[f_145_1]) ).

cnf(f_145_3,plain,
    hAPP(c_Set_Oimage(U_733,U_733,c_COMBI(U_733)),U_734) = U_734,
    inference(clausify,[status(thm)],[f_145_2]) ).

fof(f_146_1,plain,
    ! [V_A_2,V_f_2,T_b,V_b_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
          & V_b_2 = hAPP(V_f_2,B_x) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_imageE]) ).

fof(f_146_2,plain,
    ! [U_740,U_739,U_738,U_737,U_736] :
      ( ? [U_735] :
          ( hBOOL(hAPP(hAPP(c_member(U_738),U_735),U_740))
          & U_737 = hAPP(U_739,U_735) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_736),U_737),hAPP(c_Set_Oimage(U_738,U_736,U_739),U_740))) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_740,U_739,U_738,U_737] :
      ( ! [U_736] : ~ hBOOL(hAPP(hAPP(c_member(U_736),U_737),hAPP(c_Set_Oimage(U_738,U_736,U_739),U_740)))
      | ? [U_735] :
          ( hBOOL(hAPP(hAPP(c_member(U_738),U_735),U_740))
          & U_737 = hAPP(U_739,U_735) ) ),
    inference(miniscope,[status(thm)],[f_146_2]) ).

fof(f_146_4,plain,
    ! [U_740,U_739,U_738,U_737] :
      ( ! [U_736] : ~ hBOOL(hAPP(hAPP(c_member(U_736),U_737),hAPP(c_Set_Oimage(U_738,U_736,U_739),U_740)))
      | ( hBOOL(hAPP(hAPP(c_member(U_738),sK20(U_740,U_739,U_738,U_737)),U_740))
        & U_737 = hAPP(U_739,sK20(U_740,U_739,U_738,U_737)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_735,sK20(U_740,U_739,U_738,U_737))],[f_146_3]) ).

cnf(f_146_5,plain,
    ( U_737 = hAPP(U_739,sK20(U_740,U_739,U_738,U_737))
    | ~ hBOOL(hAPP(hAPP(c_member(U_736),U_737),hAPP(c_Set_Oimage(U_738,U_736,U_739),U_740))) ),
    inference(clausify,[status(thm)],[f_146_4]) ).

cnf(f_146_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_738),sK20(U_740,U_739,U_738,U_737)),U_740))
    | ~ hBOOL(hAPP(hAPP(c_member(U_736),U_737),hAPP(c_Set_Oimage(U_738,U_736,U_739),U_740))) ),
    inference(clausify,[status(thm)],[f_146_4]) ).

fof(f_147_1,plain,
    ! [V_t,V_s,V_c2,V_c1] :
      ( ? [B_s1] :
          ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2),B_s1),V_t))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s),B_s1)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I4_J]) ).

fof(f_147_2,plain,
    ! [U_745,U_744,U_743,U_742] :
      ( ? [U_741] :
          ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_743),U_741),U_745))
          & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_742),U_744),U_741)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_742,U_743)),U_744),U_745)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_745,U_744,U_743,U_742] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_743),sK21(U_745,U_744,U_743,U_742)),U_745))
        & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_742),U_744),sK21(U_745,U_744,U_743,U_742))) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_742,U_743)),U_744),U_745)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_741,sK21(U_745,U_744,U_743,U_742))],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_742),U_744),sK21(U_745,U_744,U_743,U_742)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_742,U_743)),U_744),U_745)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_743),sK21(U_745,U_744,U_743,U_742)),U_745))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(U_742,U_743)),U_744),U_745)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Loop__sound__lemma]) ).

fof(f_148_2,plain,
    ! [U_750,U_749,U_748,U_747,U_746] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_746,U_747,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_746)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_746),U_748),c_Com_Ocom_OWhile(U_749,U_750)),c_Hoare__Mirabelle_Opeek__and(U_746,U_748,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_749)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_746),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_746,U_747,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_746)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_746),c_Hoare__Mirabelle_Opeek__and(U_746,U_748,U_749)),U_750),U_748)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_746),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_746,U_747,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_746)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_746),U_748),c_Com_Ocom_OWhile(U_749,U_750)),c_Hoare__Mirabelle_Opeek__and(U_746,U_748,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_749)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_746),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_746,U_747,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_746)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_746),c_Hoare__Mirabelle_Opeek__and(U_746,U_748,U_749)),U_750),U_748)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_746),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_1,plain,
    ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Loop]) ).

fof(f_149_2,plain,
    ! [U_755,U_754,U_753,U_752,U_751] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_751,U_752,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_751)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_751),U_753),c_Com_Ocom_OWhile(U_754,U_755)),c_Hoare__Mirabelle_Opeek__and(U_751,U_753,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_754)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_751),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_751,U_752,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_751)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_751),c_Hoare__Mirabelle_Opeek__and(U_751,U_753,U_754)),U_755),U_753)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_751),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

cnf(f_149_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_751,U_752,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_751)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_751),U_753),c_Com_Ocom_OWhile(U_754,U_755)),c_Hoare__Mirabelle_Opeek__and(U_751,U_753,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_754)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_751),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_751,U_752,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_751)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_751),c_Hoare__Mirabelle_Opeek__and(U_751,U_753,U_754)),U_755),U_753)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_751),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

fof(f_150_1,plain,
    ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,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))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,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))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
      | ? [B_p] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(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_b),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__pointwise]) ).

fof(f_150_2,plain,
    ! [U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_764)),U_762)),U_765)),U_758))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_761)),U_762)),U_763)),U_758))
      | ? [U_756] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_764,U_756)),hAPP(U_762,U_756)),hAPP(U_765,U_756))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_761,U_756)),hAPP(U_762,U_756)),hAPP(U_763,U_756))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_757),U_758)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_764)),U_762)),U_765)),U_758))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_761)),U_762)),U_763)),U_758))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_764,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_762,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_765,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_761,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_762,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_763,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_757),U_758)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_756,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))],[f_150_2]) ).

cnf(f_150_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_761,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_762,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_763,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool))))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_764)),U_762)),U_765)),U_758))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_761)),U_762)),U_763)),U_758))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_757),U_758)) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

cnf(f_150_5,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_759),hAPP(U_764,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_762,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757))),hAPP(U_765,sK22(U_765,U_764,U_763,U_762,U_761,U_760,U_759,U_758,U_757)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_759),tc_HOL_Obool))))
    | c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_764)),U_762)),U_765)),U_758))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_759,U_760,hAPP(c_Set_Oimage(U_757,tc_Hoare__Mirabelle_Otriple(U_759),hAPP(hAPP(c_COMBS(U_757,tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759)),hAPP(hAPP(c_COMBS(U_757,tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),hAPP(hAPP(c_COMBB(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_759,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_759))),U_757),c_Hoare__Mirabelle_Otriple_Otriple(U_759)),U_761)),U_762)),U_763)),U_758))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_757),U_758)) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_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_151_2,plain,
    ! [U_767,U_766] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_766),U_767),U_767) = U_767
      | ~ class_Lattices_Olattice(U_766) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_766),U_767),U_767) = U_767
    | ~ class_Lattices_Olattice(U_766) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_1,plain,
    ! [V_c_2,V_Ga_2] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Com_OWT,V_c_2))
      | ? [B_x] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) )
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(fof_nnf,[status(thm)],[fact_MGF__lemma1]) ).

fof(f_152_2,plain,
    ! [U_770,U_769] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_770)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Com_OWT,U_770))
      | ? [U_768] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_768))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_768),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) )
      | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ( ! [U_770,U_769] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_770)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Com_OWT,U_770))
        | ? [U_768] :
            ( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,U_768))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
            & hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_768),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ) )
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(miniscope,[status(thm)],[f_152_2]) ).

fof(f_152_4,plain,
    ( ! [U_770,U_769] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_770)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Com_OWT,U_770))
        | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,sK23(U_770,U_769)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK23(U_770,U_769)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ) )
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_768,sK23(U_770,U_769))],[f_152_3]) ).

cnf(f_152_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK23(U_770,U_769)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
    | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_770)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Com_OWT,U_770))
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(clausify,[status(thm)],[f_152_4]) ).

cnf(f_152_6,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,sK23(U_770,U_769)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,U_769,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(U_770)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Com_OWT,U_770))
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    inference(clausify,[status(thm)],[f_152_4]) ).

fof(f_153_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__insert]) ).

fof(f_153_2,plain,
    ! [U_775,U_774,U_773,U_772,U_771] : hAPP(c_Set_Ovimage(U_771,U_772,U_773),hAPP(hAPP(c_Set_Oinsert(U_772),U_774),U_775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_771,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_771,U_772,U_773),hAPP(hAPP(c_Set_Oinsert(U_772),U_774),c_Orderings_Obot__class_Obot(tc_fun(U_772,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_771,U_772,U_773),U_775)),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    hAPP(c_Set_Ovimage(U_771,U_772,U_773),hAPP(hAPP(c_Set_Oinsert(U_772),U_774),U_775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_771,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_771,U_772,U_773),hAPP(hAPP(c_Set_Oinsert(U_772),U_774),c_Orderings_Obot__class_Obot(tc_fun(U_772,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_771,U_772,U_773),U_775)),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_1,plain,
    ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),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_154_2,plain,
    ! [U_781,U_780,U_779,U_778,U_777,U_776] :
      ( hBOOL(hAPP(hAPP(c_member(U_781),U_777),hAPP(c_Set_Ovimage(U_781,U_779,U_776),U_780)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_779),U_778),U_780))
      | hAPP(U_776,U_777) != U_778 ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_781),U_777),hAPP(c_Set_Ovimage(U_781,U_779,U_776),U_780)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_779),U_778),U_780))
    | hAPP(U_776,U_777) != U_778 ),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_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_155_2,plain,
    ! [U_783,U_782] :
      ( hBOOL(hAPP(c_Com_OWT,U_783))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_782,U_783))) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_783] :
      ( ! [U_782] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_782,U_783)))
      | hBOOL(hAPP(c_Com_OWT,U_783)) ),
    inference(miniscope,[status(thm)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_782,U_783)))
    | hBOOL(hAPP(c_Com_OWT,U_783)) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_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_156_2,plain,
    ! [U_785,U_784] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_785))
        & hBOOL(hAPP(c_Com_OWT,U_784)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_784,U_785))) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_784))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_784,U_785))) ),
    inference(clausify,[status(thm)],[f_156_2]) ).

cnf(f_156_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_785))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_784,U_785))) ),
    inference(clausify,[status(thm)],[f_156_2]) ).

fof(f_157_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,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_a,T_b,V_f_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__code]) ).

fof(f_157_2,plain,
    ! [U_790,U_789,U_788,U_787,U_786] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_786,U_787,U_788),U_789),U_790))
        | ~ hBOOL(hAPP(U_789,hAPP(U_788,U_790))) )
      & ( hBOOL(hAPP(U_789,hAPP(U_788,U_790)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_786,U_787,U_788),U_789),U_790)) ) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ( ! [U_800,U_798,U_796] :
        ( ! [U_794,U_792] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_792,U_794,U_796),U_798),U_800))
        | ~ hBOOL(hAPP(U_798,hAPP(U_796,U_800))) )
    & ! [U_799,U_797,U_795] :
        ( ! [U_793,U_791] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_791,U_793,U_795),U_797),U_799))
        | hBOOL(hAPP(U_797,hAPP(U_795,U_799))) ) ),
    inference(miniscope,[status(thm)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_791,U_793,U_795),U_797),U_799))
    | hBOOL(hAPP(U_797,hAPP(U_795,U_799))) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

cnf(f_157_5,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_792,U_794,U_796),U_798),U_800))
    | ~ hBOOL(hAPP(U_798,hAPP(U_796,U_800))) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( ! [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_c,T_b,T_a,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).

fof(f_158_2,plain,
    ! [U_809,U_808,U_807,U_806,U_805,U_804,U_803,U_802] :
      ( ! [U_801] : hAPP(U_805,hAPP(U_806,U_801)) = hAPP(U_808,hAPP(U_809,U_801))
      | hAPP(c_Fun_Ocomp(U_802,U_803,U_804,U_805),U_806) != hAPP(c_Fun_Ocomp(U_807,U_803,U_804,U_808),U_809) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_809,U_808,U_807,U_806,U_805] :
      ( ! [U_804,U_803,U_802] : hAPP(c_Fun_Ocomp(U_802,U_803,U_804,U_805),U_806) != hAPP(c_Fun_Ocomp(U_807,U_803,U_804,U_808),U_809)
      | ! [U_801] : hAPP(U_805,hAPP(U_806,U_801)) = hAPP(U_808,hAPP(U_809,U_801)) ),
    inference(miniscope,[status(thm)],[f_158_2]) ).

cnf(f_158_4,plain,
    ( hAPP(c_Fun_Ocomp(U_802,U_803,U_804,U_805),U_806) != hAPP(c_Fun_Ocomp(U_807,U_803,U_804,U_808),U_809)
    | hAPP(U_805,hAPP(U_806,U_801)) = hAPP(U_808,hAPP(U_809,U_801)) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( 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_c,T_b,T_a,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).

fof(f_159_2,plain,
    ! [U_818,U_817,U_816,U_815,U_814,U_813,U_812,U_811,U_810] :
      ( hAPP(U_813,hAPP(U_814,U_818)) = hAPP(U_816,hAPP(U_817,U_818))
      | hAPP(c_Fun_Ocomp(U_810,U_811,U_812,U_813),U_814) != hAPP(c_Fun_Ocomp(U_815,U_811,U_812,U_816),U_817) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_818,U_817,U_816,U_815,U_814,U_813] :
      ( ! [U_812,U_811,U_810] : hAPP(c_Fun_Ocomp(U_810,U_811,U_812,U_813),U_814) != hAPP(c_Fun_Ocomp(U_815,U_811,U_812,U_816),U_817)
      | hAPP(U_813,hAPP(U_814,U_818)) = hAPP(U_816,hAPP(U_817,U_818)) ),
    inference(miniscope,[status(thm)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( hAPP(c_Fun_Ocomp(U_810,U_811,U_812,U_813),U_814) != hAPP(c_Fun_Ocomp(U_815,U_811,U_812,U_816),U_817)
    | hAPP(U_813,hAPP(U_814,U_818)) = hAPP(U_816,hAPP(U_817,U_818)) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,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_160_2,plain,
    ! [U_824,U_823,U_822,U_821,U_820,U_819] : hAPP(hAPP(c_Fun_Ocomp(U_819,U_820,U_821,U_822),U_823),U_824) = hAPP(U_822,hAPP(U_823,U_824)),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_819,U_820,U_821,U_822),U_823),U_824) = hAPP(U_822,hAPP(U_823,U_824)),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_1,plain,
    ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__compose]) ).

fof(f_161_2,plain,
    ! [U_830,U_829,U_828,U_827,U_826,U_825] : hAPP(c_Set_Ovimage(U_825,U_826,hAPP(c_Fun_Ocomp(U_827,U_826,U_825,U_828),U_829)),U_830) = hAPP(c_Set_Ovimage(U_825,U_827,U_829),hAPP(c_Set_Ovimage(U_827,U_826,U_828),U_830)),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    hAPP(c_Set_Ovimage(U_825,U_826,hAPP(c_Fun_Ocomp(U_827,U_826,U_825,U_828),U_829)),U_830) = hAPP(c_Set_Ovimage(U_825,U_827,U_829),hAPP(c_Set_Ovimage(U_827,U_826,U_828),U_830)),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_1,plain,
    ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__ident]) ).

fof(f_162_2,plain,
    ! [U_832,U_831] : hAPP(c_Set_Ovimage(U_831,U_831,c_COMBI(U_831)),U_832) = U_832,
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    hAPP(c_Set_Ovimage(U_831,U_831,c_COMBI(U_831)),U_832) = U_832,
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_1,plain,
    ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2),
    inference(fof_nnf,[status(thm)],[fact_o__assoc]) ).

fof(f_163_2,plain,
    ! [U_839,U_838,U_837,U_836,U_835,U_834,U_833] : hAPP(c_Fun_Ocomp(U_833,U_834,U_835,U_836),hAPP(c_Fun_Ocomp(U_837,U_833,U_835,U_838),U_839)) = hAPP(c_Fun_Ocomp(U_837,U_834,U_835,hAPP(c_Fun_Ocomp(U_833,U_834,U_837,U_836),U_838)),U_839),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    hAPP(c_Fun_Ocomp(U_833,U_834,U_835,U_836),hAPP(c_Fun_Ocomp(U_837,U_833,U_835,U_838),U_839)) = hAPP(c_Fun_Ocomp(U_837,U_834,U_835,hAPP(c_Fun_Ocomp(U_833,U_834,U_837,U_836),U_838)),U_839),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,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_164_2,plain,
    ! [U_845,U_844,U_843,U_842,U_841,U_840] : hAPP(hAPP(c_Fun_Ocomp(U_840,U_841,U_842,U_843),U_844),U_845) = hAPP(U_843,hAPP(U_844,U_845)),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_840,U_841,U_842,U_843),U_844),U_845) = hAPP(U_843,hAPP(U_844,U_845)),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_image__compose]) ).

fof(f_165_2,plain,
    ! [U_851,U_850,U_849,U_848,U_847,U_846] : hAPP(c_Set_Oimage(U_846,U_847,hAPP(c_Fun_Ocomp(U_848,U_847,U_846,U_849),U_850)),U_851) = hAPP(c_Set_Oimage(U_848,U_847,U_849),hAPP(c_Set_Oimage(U_846,U_848,U_850),U_851)),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

cnf(f_165_3,plain,
    hAPP(c_Set_Oimage(U_846,U_847,hAPP(c_Fun_Ocomp(U_848,U_847,U_846,U_849),U_850)),U_851) = hAPP(c_Set_Oimage(U_848,U_847,U_849),hAPP(c_Set_Oimage(U_846,U_848,U_850),U_851)),
    inference(clausify,[status(thm)],[f_165_2]) ).

fof(f_166_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]) ).

cnf(f_166_2,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_166_1]) ).

fof(f_167_1,plain,
    ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimageI2]) ).

fof(f_167_2,plain,
    ! [U_856,U_855,U_854,U_853,U_852] :
      ( hBOOL(hAPP(hAPP(c_member(U_856),U_854),hAPP(c_Set_Ovimage(U_856,U_852,U_853),U_855)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_852),hAPP(U_853,U_854)),U_855)) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_856),U_854),hAPP(c_Set_Ovimage(U_856,U_852,U_853),U_855)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_852),hAPP(U_853,U_854)),U_855)) ),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_vimageD]) ).

fof(f_168_2,plain,
    ! [U_861,U_860,U_859,U_858,U_857] :
      ( hBOOL(hAPP(hAPP(c_member(U_859),hAPP(U_860,U_858)),U_861))
      | ~ hBOOL(hAPP(hAPP(c_member(U_857),U_858),hAPP(c_Set_Ovimage(U_857,U_859,U_860),U_861))) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_861,U_860,U_859,U_858] :
      ( ! [U_857] : ~ hBOOL(hAPP(hAPP(c_member(U_857),U_858),hAPP(c_Set_Ovimage(U_857,U_859,U_860),U_861)))
      | hBOOL(hAPP(hAPP(c_member(U_859),hAPP(U_860,U_858)),U_861)) ),
    inference(miniscope,[status(thm)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_857),U_858),hAPP(c_Set_Ovimage(U_857,U_859,U_860),U_861)))
    | hBOOL(hAPP(hAPP(c_member(U_859),hAPP(U_860,U_858)),U_861)) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq]) ).

fof(f_169_2,plain,
    ! [U_866,U_865,U_864,U_863,U_862] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_862),U_863),hAPP(c_Set_Ovimage(U_862,U_864,U_865),U_866)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_864),hAPP(U_865,U_863)),U_866)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_864),hAPP(U_865,U_863)),U_866))
        | ~ hBOOL(hAPP(hAPP(c_member(U_862),U_863),hAPP(c_Set_Ovimage(U_862,U_864,U_865),U_866))) ) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ( ! [U_876,U_874,U_872,U_870] :
        ( ! [U_868] : hBOOL(hAPP(hAPP(c_member(U_868),U_870),hAPP(c_Set_Ovimage(U_868,U_872,U_874),U_876)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_872),hAPP(U_874,U_870)),U_876)) )
    & ! [U_875,U_873,U_871,U_869] :
        ( ! [U_867] : ~ hBOOL(hAPP(hAPP(c_member(U_867),U_869),hAPP(c_Set_Ovimage(U_867,U_871,U_873),U_875)))
        | hBOOL(hAPP(hAPP(c_member(U_871),hAPP(U_873,U_869)),U_875)) ) ),
    inference(miniscope,[status(thm)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_867),U_869),hAPP(c_Set_Ovimage(U_867,U_871,U_873),U_875)))
    | hBOOL(hAPP(hAPP(c_member(U_871),hAPP(U_873,U_869)),U_875)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_868),U_870),hAPP(c_Set_Ovimage(U_868,U_872,U_874),U_876)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_872),hAPP(U_874,U_870)),U_876)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__empty]) ).

fof(f_170_2,plain,
    ! [U_879,U_878,U_877] : hAPP(c_Set_Ovimage(U_877,U_878,U_879),c_Orderings_Obot__class_Obot(tc_fun(U_878,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_877,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    hAPP(c_Set_Ovimage(U_877,U_878,U_879),c_Orderings_Obot__class_Obot(tc_fun(U_878,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_877,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Un]) ).

fof(f_171_2,plain,
    ! [U_884,U_883,U_882,U_881,U_880] : hAPP(c_Set_Ovimage(U_880,U_881,U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_881,tc_HOL_Obool)),U_883),U_884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_880,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_880,U_881,U_882),U_883)),hAPP(c_Set_Ovimage(U_880,U_881,U_882),U_884)),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    hAPP(c_Set_Ovimage(U_880,U_881,U_882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_881,tc_HOL_Obool)),U_883),U_884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_880,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_880,U_881,U_882),U_883)),hAPP(c_Set_Ovimage(U_880,U_881,U_882),U_884)),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_1,plain,
    ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
        | ~ hBOOL(hAPP(V_p_2,V_s_2))
        | ~ hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) )
      & ( ( hBOOL(hAPP(V_p_2,V_s_2))
          & hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_peek__and__def]) ).

fof(f_172_2,plain,
    ! [U_889,U_888,U_887,U_886,U_885] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_885,U_886,U_887),U_888),U_889))
        | ~ hBOOL(hAPP(U_887,U_889))
        | ~ hBOOL(hAPP(hAPP(U_886,U_888),U_889)) )
      & ( ( hBOOL(hAPP(U_887,U_889))
          & hBOOL(hAPP(hAPP(U_886,U_888),U_889)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_885,U_886,U_887),U_888),U_889)) ) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ( ! [U_899,U_897,U_895,U_893] :
        ( ! [U_891] : hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_891,U_893,U_895),U_897),U_899))
        | ~ hBOOL(hAPP(U_895,U_899))
        | ~ hBOOL(hAPP(hAPP(U_893,U_897),U_899)) )
    & ! [U_898,U_896,U_894,U_892] :
        ( ! [U_890] : ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_890,U_892,U_894),U_896),U_898))
        | ( hBOOL(hAPP(U_894,U_898))
          & hBOOL(hAPP(hAPP(U_892,U_896),U_898)) ) ) ),
    inference(miniscope,[status(thm)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hBOOL(hAPP(hAPP(U_892,U_896),U_898))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_890,U_892,U_894),U_896),U_898)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

cnf(f_172_5,plain,
    ( hBOOL(hAPP(U_894,U_898))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_890,U_892,U_894),U_896),U_898)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

cnf(f_172_6,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_891,U_893,U_895),U_897),U_899))
    | ~ hBOOL(hAPP(U_895,U_899))
    | ~ hBOOL(hAPP(hAPP(U_893,U_897),U_899)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_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_173_2,plain,
    ! [U_901,U_900] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_901,U_900)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_900)) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_901,U_900)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_900)) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_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_174_2,plain,
    ! [U_903,U_902] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_902,U_903)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_903)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_903))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_902,U_903))) ) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ( ! [U_907] :
        ( ! [U_905] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_905,U_907)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_907)) )
    & ! [U_906] :
        ( ! [U_904] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_904,U_906)))
        | hBOOL(hAPP(c_Com_OWT,U_906)) ) ),
    inference(miniscope,[status(thm)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_904,U_906)))
    | hBOOL(hAPP(c_Com_OWT,U_906)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_905,U_907)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_907)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_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_175_2,plain,
    ! [U_909,U_908] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_908,U_909)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_909))
      | ~ hBOOL(hAPP(c_Com_OWT,U_908)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_908,U_909)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_909))
    | ~ hBOOL(hAPP(c_Com_OWT,U_908)) ),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_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_176_2,plain,
    ! [U_911,U_910] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_910,U_911)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_911))
        | ~ hBOOL(hAPP(c_Com_OWT,U_910)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_911))
          & hBOOL(hAPP(c_Com_OWT,U_910)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_910,U_911))) ) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ( ! [U_915,U_913] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_913,U_915)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_915))
        | ~ hBOOL(hAPP(c_Com_OWT,U_913)) )
    & ! [U_914,U_912] :
        ( ( hBOOL(hAPP(c_Com_OWT,U_914))
          & hBOOL(hAPP(c_Com_OWT,U_912)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_912,U_914))) ) ),
    inference(miniscope,[status(thm)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_912))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_912,U_914))) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

cnf(f_176_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_914))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_912,U_914))) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

cnf(f_176_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_913,U_915)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_915))
    | ~ hBOOL(hAPP(c_Com_OWT,U_913)) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I1_J]) ).

cnf(f_177_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_177_1]) ).

fof(f_178_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_OSkip]) ).

cnf(f_178_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_178_1]) ).

fof(f_179_1,plain,
    ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,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_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_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_vimage__singleton__eq]) ).

fof(f_179_2,plain,
    ! [U_920,U_919,U_918,U_917,U_916] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_916),U_917),hAPP(c_Set_Ovimage(U_916,U_918,U_919),hAPP(hAPP(c_Set_Oinsert(U_918),U_920),c_Orderings_Obot__class_Obot(tc_fun(U_918,tc_HOL_Obool))))))
        | hAPP(U_919,U_917) != U_920 )
      & ( hAPP(U_919,U_917) = U_920
        | ~ hBOOL(hAPP(hAPP(c_member(U_916),U_917),hAPP(c_Set_Ovimage(U_916,U_918,U_919),hAPP(hAPP(c_Set_Oinsert(U_918),U_920),c_Orderings_Obot__class_Obot(tc_fun(U_918,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ( ! [U_930,U_928,U_926,U_924] :
        ( ! [U_922] : hBOOL(hAPP(hAPP(c_member(U_922),U_924),hAPP(c_Set_Ovimage(U_922,U_926,U_928),hAPP(hAPP(c_Set_Oinsert(U_926),U_930),c_Orderings_Obot__class_Obot(tc_fun(U_926,tc_HOL_Obool))))))
        | hAPP(U_928,U_924) != U_930 )
    & ! [U_929,U_927,U_925,U_923] :
        ( ! [U_921] : ~ hBOOL(hAPP(hAPP(c_member(U_921),U_923),hAPP(c_Set_Ovimage(U_921,U_925,U_927),hAPP(hAPP(c_Set_Oinsert(U_925),U_929),c_Orderings_Obot__class_Obot(tc_fun(U_925,tc_HOL_Obool))))))
        | hAPP(U_927,U_923) = U_929 ) ),
    inference(miniscope,[status(thm)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_921),U_923),hAPP(c_Set_Ovimage(U_921,U_925,U_927),hAPP(hAPP(c_Set_Oinsert(U_925),U_929),c_Orderings_Obot__class_Obot(tc_fun(U_925,tc_HOL_Obool))))))
    | hAPP(U_927,U_923) = U_929 ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_922),U_924),hAPP(c_Set_Ovimage(U_922,U_926,U_928),hAPP(hAPP(c_Set_Oinsert(U_926),U_930),c_Orderings_Obot__class_Obot(tc_fun(U_926,tc_HOL_Obool))))))
    | hAPP(U_928,U_924) != U_930 ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [V_h_2,T_b,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).

fof(f_180_2,plain,
    ! [U_934,U_933,U_932,U_931] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_933),hAPP(c_Set_Oimage(U_931,U_933,U_934),U_932)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_931),U_932)) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

cnf(f_180_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_933),hAPP(c_Set_Oimage(U_931,U_933,U_934),U_932)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_931),U_932)) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

fof(f_181_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).

fof(f_181_2,plain,
    ! [U_937,U_936,U_935] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_935),hAPP(hAPP(c_Set_Oinsert(U_935),U_937),U_936)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_935),U_936)) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_935),hAPP(hAPP(c_Set_Oinsert(U_935),U_937),U_936)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_935),U_936)) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).

fof(f_182_2,plain,
    ! [U_938] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_938),c_Orderings_Obot__class_Obot(tc_fun(U_938,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_938),c_Orderings_Obot__class_Obot(tc_fun(U_938,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf]) ).

fof(f_183_2,plain,
    ! [U_945,U_944,U_943,U_942,U_941,U_940,U_939] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),U_941),c_Com_Ocom_OCond(U_942,U_943,U_945)),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),c_Hoare__Mirabelle_Opeek__and(U_939,U_941,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_942))),U_945),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),c_Hoare__Mirabelle_Opeek__and(U_939,U_941,U_942)),U_943),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),U_941),c_Com_Ocom_OCond(U_942,U_943,U_945)),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),c_Hoare__Mirabelle_Opeek__and(U_939,U_941,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_942))),U_945),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_939,U_940,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_939)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_939),c_Hoare__Mirabelle_Opeek__and(U_939,U_941,U_942)),U_943),U_944)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_939),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_1,plain,
    ! [V_Ga_2,V_F_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).

fof(f_184_2,plain,
    ! [U_948,U_947,U_946] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),U_948))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),U_947)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),U_948))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),U_947)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_946),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948))) ) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ( ! [U_954,U_952,U_950] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_950,tc_HOL_Obool)),U_952),U_954)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),U_954))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),U_952)) )
    & ! [U_953,U_951,U_949] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),U_953))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),U_951)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_949,tc_HOL_Obool)),U_951),U_953))) ) ),
    inference(miniscope,[status(thm)],[f_184_2]) ).

cnf(f_184_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),U_951))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_949,tc_HOL_Obool)),U_951),U_953))) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),U_953))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_949),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_949,tc_HOL_Obool)),U_951),U_953))) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_950,tc_HOL_Obool)),U_952),U_954)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),U_954))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_950),U_952)) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [V_Ga_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).

fof(f_185_2,plain,
    ! [U_957,U_956,U_955] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_955,tc_HOL_Obool)),U_956),U_957)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),U_957))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),U_956)) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

cnf(f_185_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_955,tc_HOL_Obool)),U_956),U_957)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),U_957))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_955),U_956)) ),
    inference(clausify,[status(thm)],[f_185_2]) ).

fof(f_186_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).

fof(f_186_2,plain,
    ! [U_960,U_959,U_958] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_958),hAPP(hAPP(c_Set_Oinsert(U_958),U_959),U_960)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_958),U_960)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_958),U_960))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_958),hAPP(hAPP(c_Set_Oinsert(U_958),U_959),U_960))) ) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ( ! [U_966,U_964,U_962] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_962),hAPP(hAPP(c_Set_Oinsert(U_962),U_964),U_966)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_962),U_966)) )
    & ! [U_965,U_963,U_961] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_961),U_965))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_961),hAPP(hAPP(c_Set_Oinsert(U_961),U_963),U_965))) ) ),
    inference(miniscope,[status(thm)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_961),U_965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_961),hAPP(hAPP(c_Set_Oinsert(U_961),U_963),U_965))) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

cnf(f_186_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_962),hAPP(hAPP(c_Set_Oinsert(U_962),U_964),U_966)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_962),U_966)) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(f_187_2,plain,
    ! [U_967] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_967),c_Orderings_Obot__class_Obot(tc_fun(U_967,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_967),c_Orderings_Obot__class_Obot(tc_fun(U_967,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_1,plain,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,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_a),c_Set_Oinsert(T_b)),V_f_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))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).

fof(f_188_2,plain,
    ! [U_971,U_970,U_969,U_968] :
      ( hAPP(c_Set_Oimage(U_968,U_970,U_971),U_969) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_970,tc_HOL_Obool),U_968,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_970,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_968,tc_fun(U_970,tc_HOL_Obool),tc_fun(U_970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_970,tc_fun(tc_fun(U_970,tc_HOL_Obool),tc_fun(U_970,tc_HOL_Obool)),U_968),c_Set_Oinsert(U_970)),U_971)),c_Orderings_Obot__class_Obot(tc_fun(U_970,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_970,tc_HOL_Obool))),U_969)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_968),U_969)) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    ( hAPP(c_Set_Oimage(U_968,U_970,U_971),U_969) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_970,tc_HOL_Obool),U_968,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_970,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_968,tc_fun(U_970,tc_HOL_Obool),tc_fun(U_970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_970,tc_fun(tc_fun(U_970,tc_HOL_Obool),tc_fun(U_970,tc_HOL_Obool)),U_968),c_Set_Oinsert(U_970)),U_971)),c_Orderings_Obot__class_Obot(tc_fun(U_970,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_970,tc_HOL_Obool))),U_969)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_968),U_969)) ),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(f_189_2,plain,
    ! [U_974,U_973,U_972] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_972,hAPP(hAPP(c_Set_Oinsert(U_972),U_974),U_973)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_972),U_974),c_Big__Operators_Olattice__class_OSup__fin(U_972,U_973))
      | U_973 = c_Orderings_Obot__class_Obot(tc_fun(U_972,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_972),U_974),U_973))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_972),U_973))
      | ~ class_Lattices_Olattice(U_972) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_972,hAPP(hAPP(c_Set_Oinsert(U_972),U_974),U_973)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_972),U_974),c_Big__Operators_Olattice__class_OSup__fin(U_972,U_973))
    | U_973 = c_Orderings_Obot__class_Obot(tc_fun(U_972,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_972),U_974),U_973))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_972),U_973))
    | ~ class_Lattices_Olattice(U_972) ),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_1,plain,
    ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).

fof(f_190_2,plain,
    ! [U_976,U_975] : c_HOL_OThe(U_975,hAPP(hAPP(c_COMBC(U_975,U_975,tc_HOL_Obool),c_fequal),U_976)) = U_976,
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    c_HOL_OThe(U_975,hAPP(hAPP(c_COMBC(U_975,U_975,tc_HOL_Obool),c_fequal),U_976)) = U_976,
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_1,plain,
    ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_t_2))
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ~ hBOOL(hAPP(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_191_2,plain,
    ! [U_981,U_980,U_979,U_978,U_977] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_979),U_980),U_981))
        & ~ hBOOL(hAPP(U_977,U_980)) )
      | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_978),U_980),U_981))
        & hBOOL(hAPP(U_977,U_980)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_977,U_978,U_979)),U_980),U_981)) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( ~ hBOOL(hAPP(U_977,U_980))
    | hBOOL(hAPP(U_977,U_980))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_977,U_978,U_979)),U_980),U_981)) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_979),U_980),U_981))
    | hBOOL(hAPP(U_977,U_980))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_977,U_978,U_979)),U_980),U_981)) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

cnf(f_191_5,plain,
    ( ~ hBOOL(hAPP(U_977,U_980))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_978),U_980),U_981))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_977,U_978,U_979)),U_980),U_981)) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

cnf(f_191_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_979),U_980),U_981))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_978),U_980),U_981))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_977,U_978,U_979)),U_980),U_981)) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_1,plain,
    ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(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(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_192_2,plain,
    ! [U_986,U_985,U_984,U_983,U_982] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_982,U_984,U_986)),U_983),U_985))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_984),U_983),U_985))
      | ~ hBOOL(hAPP(U_982,U_983)) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_982,U_984,U_986)),U_983),U_985))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_984),U_983),U_985))
    | ~ hBOOL(hAPP(U_982,U_983)) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(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(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_193_2,plain,
    ! [U_991,U_990,U_989,U_988,U_987] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_987,U_991,U_989)),U_988),U_990))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_989),U_988),U_990))
      | hBOOL(hAPP(U_987,U_988)) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_987,U_991,U_989)),U_988),U_990))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_989),U_988),U_990))
    | hBOOL(hAPP(U_987,U_988)) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_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_194_2,plain,
    ! [U_994,U_993,U_992] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_994))
        & hBOOL(hAPP(c_Com_OWT,U_993)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_992,U_993,U_994))) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_994,U_993] :
      ( ! [U_992] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_992,U_993,U_994)))
      | ( hBOOL(hAPP(c_Com_OWT,U_994))
        & hBOOL(hAPP(c_Com_OWT,U_993)) ) ),
    inference(miniscope,[status(thm)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_993))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_992,U_993,U_994))) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_994))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_992,U_993,U_994))) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_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_195_2,plain,
    ! [U_1000,U_999,U_998,U_997,U_996,U_995] :
      ( ( c_Com_Ocom_OCond(U_995,U_996,U_997) = c_Com_Ocom_OCond(U_998,U_999,U_1000)
        | U_997 != U_1000
        | U_996 != U_999
        | U_995 != U_998 )
      & ( ( U_997 = U_1000
          & U_996 = U_999
          & U_995 = U_998 )
        | c_Com_Ocom_OCond(U_995,U_996,U_997) != c_Com_Ocom_OCond(U_998,U_999,U_1000) ) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ( ! [U_1012,U_1010,U_1008,U_1006,U_1004,U_1002] :
        ( c_Com_Ocom_OCond(U_1002,U_1004,U_1006) = c_Com_Ocom_OCond(U_1008,U_1010,U_1012)
        | U_1006 != U_1012
        | U_1004 != U_1010
        | U_1002 != U_1008 )
    & ! [U_1011,U_1009,U_1007,U_1005,U_1003,U_1001] :
        ( ( U_1005 = U_1011
          & U_1003 = U_1009
          & U_1001 = U_1007 )
        | c_Com_Ocom_OCond(U_1001,U_1003,U_1005) != c_Com_Ocom_OCond(U_1007,U_1009,U_1011) ) ),
    inference(miniscope,[status(thm)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( U_1001 = U_1007
    | c_Com_Ocom_OCond(U_1001,U_1003,U_1005) != c_Com_Ocom_OCond(U_1007,U_1009,U_1011) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

cnf(f_195_5,plain,
    ( U_1003 = U_1009
    | c_Com_Ocom_OCond(U_1001,U_1003,U_1005) != c_Com_Ocom_OCond(U_1007,U_1009,U_1011) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

cnf(f_195_6,plain,
    ( U_1005 = U_1011
    | c_Com_Ocom_OCond(U_1001,U_1003,U_1005) != c_Com_Ocom_OCond(U_1007,U_1009,U_1011) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

cnf(f_195_7,plain,
    ( c_Com_Ocom_OCond(U_1002,U_1004,U_1006) = c_Com_Ocom_OCond(U_1008,U_1010,U_1012)
    | U_1006 != U_1012
    | U_1004 != U_1010
    | U_1002 != U_1008 ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_1,plain,
    ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_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__image__empty]) ).

fof(f_196_2,plain,
    ! [U_1017,U_1016,U_1015,U_1014,U_1013] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1013,U_1014,U_1015),U_1016),U_1017),c_Orderings_Obot__class_Obot(tc_fun(U_1014,tc_HOL_Obool))) = U_1017,
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1013,U_1014,U_1015),U_1016),U_1017),c_Orderings_Obot__class_Obot(tc_fun(U_1014,tc_HOL_Obool))) = U_1017,
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(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(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_197_2,plain,
    ! [U_1022,U_1021,U_1020,U_1019,U_1018] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1018,U_1019,U_1020)),U_1021),U_1022))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1020),U_1021),U_1022))
            | hBOOL(hAPP(U_1018,U_1021)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1019),U_1021),U_1022))
            | ~ hBOOL(hAPP(U_1018,U_1021)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1020),U_1021),U_1022))
          & ~ hBOOL(hAPP(U_1018,U_1021)) )
        | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1019),U_1021),U_1022))
          & hBOOL(hAPP(U_1018,U_1021)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1018,U_1019,U_1020)),U_1021),U_1022)) ) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ( ! [U_1032,U_1030,U_1028,U_1026,U_1024] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1024,U_1026,U_1028)),U_1030),U_1032))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1028),U_1030),U_1032))
            | hBOOL(hAPP(U_1024,U_1030)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1026),U_1030),U_1032))
            | ~ hBOOL(hAPP(U_1024,U_1030)) ) ) )
    & ! [U_1031,U_1029,U_1027,U_1025,U_1023] :
        ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1027),U_1029),U_1031))
          & ~ hBOOL(hAPP(U_1023,U_1029)) )
        | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1025),U_1029),U_1031))
          & hBOOL(hAPP(U_1023,U_1029)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1023,U_1025,U_1027)),U_1029),U_1031)) ) ),
    inference(miniscope,[status(thm)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( ~ hBOOL(hAPP(U_1023,U_1029))
    | hBOOL(hAPP(U_1023,U_1029))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1023,U_1025,U_1027)),U_1029),U_1031)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1027),U_1029),U_1031))
    | hBOOL(hAPP(U_1023,U_1029))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1023,U_1025,U_1027)),U_1029),U_1031)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_6,plain,
    ( ~ hBOOL(hAPP(U_1023,U_1029))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1025),U_1029),U_1031))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1023,U_1025,U_1027)),U_1029),U_1031)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1027),U_1029),U_1031))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1025),U_1029),U_1031))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1023,U_1025,U_1027)),U_1029),U_1031)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1026),U_1030),U_1032))
    | ~ hBOOL(hAPP(U_1024,U_1030))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1024,U_1026,U_1028)),U_1030),U_1032)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1028),U_1030),U_1032))
    | hBOOL(hAPP(U_1024,U_1030))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1024,U_1026,U_1028)),U_1030),U_1032)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_1,plain,
    ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(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(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(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(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_198_2,plain,
    ! [U_1037,U_1036,U_1035,U_1034,U_1033] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1033,U_1034,U_1035)),U_1036),U_1037))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1035),U_1036),U_1037))
            | hBOOL(hAPP(U_1033,U_1036)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1034),U_1036),U_1037))
            | ~ hBOOL(hAPP(U_1033,U_1036)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1035),U_1036),U_1037))
          & ~ hBOOL(hAPP(U_1033,U_1036)) )
        | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1034),U_1036),U_1037))
          & hBOOL(hAPP(U_1033,U_1036)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1033,U_1034,U_1035)),U_1036),U_1037)) ) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ( ! [U_1047,U_1045,U_1043,U_1041,U_1039] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1039,U_1041,U_1043)),U_1045),U_1047))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1043),U_1045),U_1047))
            | hBOOL(hAPP(U_1039,U_1045)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1041),U_1045),U_1047))
            | ~ hBOOL(hAPP(U_1039,U_1045)) ) ) )
    & ! [U_1046,U_1044,U_1042,U_1040,U_1038] :
        ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1042),U_1044),U_1046))
          & ~ hBOOL(hAPP(U_1038,U_1044)) )
        | ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1040),U_1044),U_1046))
          & hBOOL(hAPP(U_1038,U_1044)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1038,U_1040,U_1042)),U_1044),U_1046)) ) ),
    inference(miniscope,[status(thm)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( ~ hBOOL(hAPP(U_1038,U_1044))
    | hBOOL(hAPP(U_1038,U_1044))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1038,U_1040,U_1042)),U_1044),U_1046)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1042),U_1044),U_1046))
    | hBOOL(hAPP(U_1038,U_1044))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1038,U_1040,U_1042)),U_1044),U_1046)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_6,plain,
    ( ~ hBOOL(hAPP(U_1038,U_1044))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1040),U_1044),U_1046))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1038,U_1040,U_1042)),U_1044),U_1046)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1042),U_1044),U_1046))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1040),U_1044),U_1046))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1038,U_1040,U_1042)),U_1044),U_1046)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1041),U_1045),U_1047))
    | ~ hBOOL(hAPP(U_1039,U_1045))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1039,U_1041,U_1043)),U_1045),U_1047)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_1043),U_1045),U_1047))
    | hBOOL(hAPP(U_1039,U_1045))
    | hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(U_1039,U_1041,U_1043)),U_1045),U_1047)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_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_199_2,plain,
    ! [U_1050,U_1049,U_1048] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1050,U_1048,U_1049)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1049))
      | ~ hBOOL(hAPP(c_Com_OWT,U_1048)) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1050,U_1048,U_1049)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1049))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1048)) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_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_200_2,plain,
    ! [U_1053,U_1052,U_1051] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1051,U_1052,U_1053)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1053))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1052)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_1053))
          & hBOOL(hAPP(c_Com_OWT,U_1052)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1051,U_1052,U_1053))) ) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ( ! [U_1059,U_1057] :
        ( ! [U_1055] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1055,U_1057,U_1059)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1059))
        | ~ hBOOL(hAPP(c_Com_OWT,U_1057)) )
    & ! [U_1058,U_1056] :
        ( ! [U_1054] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1054,U_1056,U_1058)))
        | ( hBOOL(hAPP(c_Com_OWT,U_1058))
          & hBOOL(hAPP(c_Com_OWT,U_1056)) ) ) ),
    inference(miniscope,[status(thm)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1056))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1054,U_1056,U_1058))) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

cnf(f_200_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_1058))
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1054,U_1056,U_1058))) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

cnf(f_200_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_1055,U_1057,U_1059)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1059))
    | ~ hBOOL(hAPP(c_Com_OWT,U_1057)) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_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_201_2,plain,
    ! [U_1063,U_1062,U_1061,U_1060] : c_Com_Ocom_OCond(U_1060,U_1061,U_1062) != hAPP(c_Com_Ocom_OBODY,U_1063),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

cnf(f_201_3,plain,
    c_Com_Ocom_OCond(U_1060,U_1061,U_1062) != hAPP(c_Com_Ocom_OBODY,U_1063),
    inference(clausify,[status(thm)],[f_201_2]) ).

fof(f_202_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_202_2,plain,
    ! [U_1067,U_1066,U_1065,U_1064] : hAPP(c_Com_Ocom_OBODY,U_1064) != c_Com_Ocom_OCond(U_1065,U_1066,U_1067),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

cnf(f_202_3,plain,
    hAPP(c_Com_Ocom_OBODY,U_1064) != c_Com_Ocom_OCond(U_1065,U_1066,U_1067),
    inference(clausify,[status(thm)],[f_202_2]) ).

fof(f_203_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_203_2,plain,
    ! [U_1072,U_1071,U_1070,U_1069,U_1068] : c_Com_Ocom_OWhile(U_1068,U_1069) != c_Com_Ocom_OCond(U_1070,U_1071,U_1072),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

cnf(f_203_3,plain,
    c_Com_Ocom_OWhile(U_1068,U_1069) != c_Com_Ocom_OCond(U_1070,U_1071,U_1072),
    inference(clausify,[status(thm)],[f_203_2]) ).

fof(f_204_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_204_2,plain,
    ! [U_1077,U_1076,U_1075,U_1074,U_1073] : c_Com_Ocom_OCond(U_1073,U_1074,U_1075) != c_Com_Ocom_OWhile(U_1076,U_1077),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

cnf(f_204_3,plain,
    c_Com_Ocom_OCond(U_1073,U_1074,U_1075) != c_Com_Ocom_OWhile(U_1076,U_1077),
    inference(clausify,[status(thm)],[f_204_2]) ).

fof(f_205_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_205_2,plain,
    ! [U_1082,U_1081,U_1080,U_1079,U_1078] : c_Com_Ocom_OSemi(U_1078,U_1079) != c_Com_Ocom_OCond(U_1080,U_1081,U_1082),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

cnf(f_205_3,plain,
    c_Com_Ocom_OSemi(U_1078,U_1079) != c_Com_Ocom_OCond(U_1080,U_1081,U_1082),
    inference(clausify,[status(thm)],[f_205_2]) ).

fof(f_206_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_206_2,plain,
    ! [U_1087,U_1086,U_1085,U_1084,U_1083] : c_Com_Ocom_OCond(U_1083,U_1084,U_1085) != c_Com_Ocom_OSemi(U_1086,U_1087),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

cnf(f_206_3,plain,
    c_Com_Ocom_OCond(U_1083,U_1084,U_1085) != c_Com_Ocom_OSemi(U_1086,U_1087),
    inference(clausify,[status(thm)],[f_206_2]) ).

fof(f_207_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_207_2,plain,
    ! [U_1090,U_1089,U_1088] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_1088,U_1089,U_1090),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_1088,U_1089,U_1090),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_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_208_2,plain,
    ! [U_1093,U_1092,U_1091] : c_Com_Ocom_OCond(U_1091,U_1092,U_1093) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    c_Com_Ocom_OCond(U_1091,U_1092,U_1093) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).

fof(f_209_2,plain,
    ! [U_1095,U_1094] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1094,hAPP(hAPP(c_Set_Oinsert(U_1094),U_1095),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool)))) = U_1095
      | ~ class_Lattices_Olattice(U_1094) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1094,hAPP(hAPP(c_Set_Oinsert(U_1094),U_1095),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool)))) = U_1095
    | ~ class_Lattices_Olattice(U_1094) ),
    inference(clausify,[status(thm)],[f_209_2]) ).

fof(f_210_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_finite]) ).

fof(f_210_2,plain,
    ! [U_1097,U_1096] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1097))
      | ~ class_Finite__Set_Ofinite(U_1096) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

cnf(f_210_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1097))
    | ~ class_Finite__Set_Ofinite(U_1096) ),
    inference(clausify,[status(thm)],[f_210_2]) ).

fof(f_211_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_finite__code]) ).

fof(f_211_2,plain,
    ! [U_1099,U_1098] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1098),U_1099))
      | ~ class_Finite__Set_Ofinite(U_1098) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

cnf(f_211_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1098),U_1099))
    | ~ class_Finite__Set_Ofinite(U_1098) ),
    inference(clausify,[status(thm)],[f_211_2]) ).

fof(f_212_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).

fof(f_212_2,plain,
    ! [U_1102,U_1101,U_1100] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1100),U_1102),c_Big__Operators_Olattice__class_OSup__fin(U_1100,U_1101)) = c_Big__Operators_Olattice__class_OSup__fin(U_1100,U_1101)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1100),U_1102),U_1101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1100),U_1101))
      | ~ class_Lattices_Olattice(U_1100) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

cnf(f_212_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1100),U_1102),c_Big__Operators_Olattice__class_OSup__fin(U_1100,U_1101)) = c_Big__Operators_Olattice__class_OSup__fin(U_1100,U_1101)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1100),U_1102),U_1101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1100),U_1101))
    | ~ class_Lattices_Olattice(U_1100) ),
    inference(clausify,[status(thm)],[f_212_2]) ).

fof(f_213_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).

fof(f_213_2,plain,
    ! [U_1105,U_1104,U_1103] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1103,hAPP(hAPP(c_Set_Oinsert(U_1103),U_1105),U_1104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1103),U_1105),c_Big__Operators_Olattice__class_OSup__fin(U_1103,U_1104))
      | U_1104 = c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1104))
      | ~ class_Lattices_Olattice(U_1103) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

cnf(f_213_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1103,hAPP(hAPP(c_Set_Oinsert(U_1103),U_1105),U_1104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1103),U_1105),c_Big__Operators_Olattice__class_OSup__fin(U_1103,U_1104))
    | U_1104 = c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1104))
    | ~ class_Lattices_Olattice(U_1103) ),
    inference(clausify,[status(thm)],[f_213_2]) ).

fof(f_214_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).

fof(f_214_2,plain,
    ! [U_1108,U_1107,U_1106] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1106,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1106,tc_HOL_Obool)),U_1107),U_1108)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1106),c_Big__Operators_Olattice__class_OSup__fin(U_1106,U_1107)),c_Big__Operators_Olattice__class_OSup__fin(U_1106,U_1108))
      | U_1108 = c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1106),U_1108))
      | U_1107 = c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1106),U_1107))
      | ~ class_Lattices_Olattice(U_1106) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

cnf(f_214_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1106,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1106,tc_HOL_Obool)),U_1107),U_1108)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1106),c_Big__Operators_Olattice__class_OSup__fin(U_1106,U_1107)),c_Big__Operators_Olattice__class_OSup__fin(U_1106,U_1108))
    | U_1108 = c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1106),U_1108))
    | U_1107 = c_Orderings_Obot__class_Obot(tc_fun(U_1106,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1106),U_1107))
    | ~ class_Lattices_Olattice(U_1106) ),
    inference(clausify,[status(thm)],[f_214_2]) ).

fof(f_215_1,plain,
    ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(f_215_2,plain,
    ! [U_1110,U_1109] : c_HOL_OThe(U_1109,hAPP(c_fequal,U_1110)) = U_1110,
    inference(variable_rename,[status(thm)],[f_215_1]) ).

cnf(f_215_3,plain,
    c_HOL_OThe(U_1109,hAPP(c_fequal,U_1110)) = U_1110,
    inference(clausify,[status(thm)],[f_215_2]) ).

fof(f_216_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(f_216_2,plain,
    ! [U_1117,U_1116,U_1115,U_1114,U_1113,U_1112,U_1111] :
      ( ( ( hAPP(hAPP(U_1115,U_1117),U_1116) = U_1114
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1112),U_1116)) )
        & ( hAPP(hAPP(U_1115,U_1117),U_1116) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1111,U_1112,U_1113),U_1117),U_1114),U_1116)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1112),U_1116)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_1111,U_1112,U_1113,U_1114,U_1115) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

cnf(f_216_3,plain,
    ( hAPP(hAPP(U_1115,U_1117),U_1116) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1111,U_1112,U_1113),U_1117),U_1114),U_1116)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1112),U_1116))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_1111,U_1112,U_1113,U_1114,U_1115) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hAPP(hAPP(U_1115,U_1117),U_1116) = U_1114
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1112),U_1116))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_1111,U_1112,U_1113,U_1114,U_1115) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

fof(f_217_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).

fof(f_217_2,plain,
    ! [U_1121,U_1120] :
      ( hBOOL(hAPP(hAPP(c_member(U_1120),c_Big__Operators_Olattice__class_OSup__fin(U_1120,U_1121)),U_1121))
      | ? [U_1119,U_1118] : ~ hBOOL(hAPP(hAPP(c_member(U_1120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1120),U_1119),U_1118)),hAPP(hAPP(c_Set_Oinsert(U_1120),U_1119),hAPP(hAPP(c_Set_Oinsert(U_1120),U_1118),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))))))
      | U_1121 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1120),U_1121))
      | ~ class_Lattices_Olattice(U_1120) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_1121,U_1120] :
      ( hBOOL(hAPP(hAPP(c_member(U_1120),c_Big__Operators_Olattice__class_OSup__fin(U_1120,U_1121)),U_1121))
      | ? [U_1118] : ~ hBOOL(hAPP(hAPP(c_member(U_1120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1120),sK24(U_1121,U_1120)),U_1118)),hAPP(hAPP(c_Set_Oinsert(U_1120),sK24(U_1121,U_1120)),hAPP(hAPP(c_Set_Oinsert(U_1120),U_1118),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))))))
      | U_1121 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1120),U_1121))
      | ~ class_Lattices_Olattice(U_1120) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1119,sK24(U_1121,U_1120))],[f_217_2]) ).

fof(f_217_4,plain,
    ! [U_1121,U_1120] :
      ( hBOOL(hAPP(hAPP(c_member(U_1120),c_Big__Operators_Olattice__class_OSup__fin(U_1120,U_1121)),U_1121))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1120),sK24(U_1121,U_1120)),sK25(U_1121,U_1120))),hAPP(hAPP(c_Set_Oinsert(U_1120),sK24(U_1121,U_1120)),hAPP(hAPP(c_Set_Oinsert(U_1120),sK25(U_1121,U_1120)),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))))))
      | U_1121 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1120),U_1121))
      | ~ class_Lattices_Olattice(U_1120) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1118,sK25(U_1121,U_1120))],[f_217_3]) ).

cnf(f_217_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1120),c_Big__Operators_Olattice__class_OSup__fin(U_1120,U_1121)),U_1121))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1120),sK24(U_1121,U_1120)),sK25(U_1121,U_1120))),hAPP(hAPP(c_Set_Oinsert(U_1120),sK24(U_1121,U_1120)),hAPP(hAPP(c_Set_Oinsert(U_1120),sK25(U_1121,U_1120)),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))))))
    | U_1121 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1120),U_1121))
    | ~ class_Lattices_Olattice(U_1120) ),
    inference(clausify,[status(thm)],[f_217_4]) ).

fof(f_218_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(f_218_2,plain,
    ! [U_1126,U_1125,U_1124,U_1123,U_1122] :
      ( hAPP(U_1124,hAPP(hAPP(c_Set_Oinsert(U_1122),U_1126),U_1125)) = hAPP(hAPP(U_1123,U_1126),hAPP(U_1124,U_1125))
      | U_1125 = c_Orderings_Obot__class_Obot(tc_fun(U_1122,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_1122),U_1126),U_1125))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1122),U_1125))
      | ~ c_Finite__Set_Ofolding__one(U_1122,U_1123,U_1124) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    ( hAPP(U_1124,hAPP(hAPP(c_Set_Oinsert(U_1122),U_1126),U_1125)) = hAPP(hAPP(U_1123,U_1126),hAPP(U_1124,U_1125))
    | U_1125 = c_Orderings_Obot__class_Obot(tc_fun(U_1122,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_1122),U_1126),U_1125))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1122),U_1125))
    | ~ c_Finite__Set_Ofolding__one(U_1122,U_1123,U_1124) ),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem]) ).

fof(f_219_2,plain,
    ! [U_1132,U_1131,U_1130,U_1129,U_1128,U_1127] :
      ( hAPP(U_1130,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1127,tc_HOL_Obool)),U_1131),U_1132)) = hAPP(c_Fun_Ocomp(U_1128,U_1128,U_1128,hAPP(U_1130,U_1131)),hAPP(U_1130,U_1132))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1127),U_1132))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1127),U_1131))
      | ~ c_Finite__Set_Ofolding__idem(U_1127,U_1128,U_1129,U_1130) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

cnf(f_219_3,plain,
    ( hAPP(U_1130,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1127,tc_HOL_Obool)),U_1131),U_1132)) = hAPP(c_Fun_Ocomp(U_1128,U_1128,U_1128,hAPP(U_1130,U_1131)),hAPP(U_1130,U_1132))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1127),U_1132))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1127),U_1131))
    | ~ c_Finite__Set_Ofolding__idem(U_1127,U_1128,U_1129,U_1130) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem]) ).

fof(f_220_2,plain,
    ! [U_1138,U_1137,U_1136,U_1135,U_1134,U_1133] :
      ( hAPP(U_1136,hAPP(hAPP(c_Set_Oinsert(U_1133),U_1138),U_1137)) = hAPP(c_Fun_Ocomp(U_1134,U_1134,U_1134,hAPP(U_1136,U_1137)),hAPP(U_1135,U_1138))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1133),U_1137))
      | ~ c_Finite__Set_Ofolding__idem(U_1133,U_1134,U_1135,U_1136) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

cnf(f_220_3,plain,
    ( hAPP(U_1136,hAPP(hAPP(c_Set_Oinsert(U_1133),U_1138),U_1137)) = hAPP(c_Fun_Ocomp(U_1134,U_1134,U_1134,hAPP(U_1136,U_1137)),hAPP(U_1135,U_1138))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1133),U_1137))
    | ~ c_Finite__Set_Ofolding__idem(U_1133,U_1134,U_1135,U_1136) ),
    inference(clausify,[status(thm)],[f_220_2]) ).

fof(f_221_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem]) ).

fof(f_221_2,plain,
    ! [U_1144,U_1143,U_1142,U_1141,U_1140,U_1139] :
      ( hAPP(c_Fun_Ocomp(U_1140,U_1140,U_1140,hAPP(U_1142,U_1143)),hAPP(U_1141,U_1144)) = hAPP(U_1142,U_1143)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1139),U_1144),U_1143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1139),U_1143))
      | ~ c_Finite__Set_Ofolding__idem(U_1139,U_1140,U_1141,U_1142) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

cnf(f_221_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1140,U_1140,U_1140,hAPP(U_1142,U_1143)),hAPP(U_1141,U_1144)) = hAPP(U_1142,U_1143)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1139),U_1144),U_1143))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1139),U_1143))
    | ~ c_Finite__Set_Ofolding__idem(U_1139,U_1140,U_1141,U_1142) ),
    inference(clausify,[status(thm)],[f_221_2]) ).

fof(f_222_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).

fof(f_222_2,plain,
    ! [U_1149,U_1148,U_1147] :
      ( hAPP(U_1148,c_Big__Operators_Olattice__class_OSup__fin(U_1147,U_1149)) = c_Big__Operators_Olattice__class_OSup__fin(U_1147,hAPP(c_Set_Oimage(U_1147,U_1147,U_1148),U_1149))
      | U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1147),U_1149))
      | ? [U_1146,U_1145] : hAPP(U_1148,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),U_1146),U_1145)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),hAPP(U_1148,U_1146)),hAPP(U_1148,U_1145))
      | ~ class_Lattices_Olattice(U_1147) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_1149,U_1148,U_1147] :
      ( hAPP(U_1148,c_Big__Operators_Olattice__class_OSup__fin(U_1147,U_1149)) = c_Big__Operators_Olattice__class_OSup__fin(U_1147,hAPP(c_Set_Oimage(U_1147,U_1147,U_1148),U_1149))
      | U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1147),U_1149))
      | ? [U_1145] : hAPP(U_1148,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),sK26(U_1149,U_1148,U_1147)),U_1145)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),hAPP(U_1148,sK26(U_1149,U_1148,U_1147))),hAPP(U_1148,U_1145))
      | ~ class_Lattices_Olattice(U_1147) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1146,sK26(U_1149,U_1148,U_1147))],[f_222_2]) ).

fof(f_222_4,plain,
    ! [U_1149,U_1148,U_1147] :
      ( hAPP(U_1148,c_Big__Operators_Olattice__class_OSup__fin(U_1147,U_1149)) = c_Big__Operators_Olattice__class_OSup__fin(U_1147,hAPP(c_Set_Oimage(U_1147,U_1147,U_1148),U_1149))
      | U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1147),U_1149))
      | hAPP(U_1148,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),sK26(U_1149,U_1148,U_1147)),sK27(U_1149,U_1148,U_1147))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),hAPP(U_1148,sK26(U_1149,U_1148,U_1147))),hAPP(U_1148,sK27(U_1149,U_1148,U_1147)))
      | ~ class_Lattices_Olattice(U_1147) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1145,sK27(U_1149,U_1148,U_1147))],[f_222_3]) ).

cnf(f_222_5,plain,
    ( hAPP(U_1148,c_Big__Operators_Olattice__class_OSup__fin(U_1147,U_1149)) = c_Big__Operators_Olattice__class_OSup__fin(U_1147,hAPP(c_Set_Oimage(U_1147,U_1147,U_1148),U_1149))
    | U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1147),U_1149))
    | hAPP(U_1148,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),sK26(U_1149,U_1148,U_1147)),sK27(U_1149,U_1148,U_1147))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1147),hAPP(U_1148,sK26(U_1149,U_1148,U_1147))),hAPP(U_1148,sK27(U_1149,U_1148,U_1147)))
    | ~ class_Lattices_Olattice(U_1147) ),
    inference(clausify,[status(thm)],[f_222_4]) ).

fof(f_223_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).

fof(f_223_2,plain,
    ! [U_1154,U_1153,U_1152,U_1151,U_1150] :
      ( hAPP(U_1152,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1150,tc_HOL_Obool)),U_1153),U_1154)) = hAPP(hAPP(U_1151,hAPP(U_1152,U_1153)),hAPP(U_1152,U_1154))
      | U_1154 = c_Orderings_Obot__class_Obot(tc_fun(U_1150,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1150),U_1154))
      | U_1153 = c_Orderings_Obot__class_Obot(tc_fun(U_1150,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1150),U_1153))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1150,U_1151,U_1152) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

cnf(f_223_3,plain,
    ( hAPP(U_1152,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1150,tc_HOL_Obool)),U_1153),U_1154)) = hAPP(hAPP(U_1151,hAPP(U_1152,U_1153)),hAPP(U_1152,U_1154))
    | U_1154 = c_Orderings_Obot__class_Obot(tc_fun(U_1150,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1150),U_1154))
    | U_1153 = c_Orderings_Obot__class_Obot(tc_fun(U_1150,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1150),U_1153))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1150,U_1151,U_1152) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

fof(f_224_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).

fof(f_224_2,plain,
    ! [U_1159,U_1158,U_1157,U_1156,U_1155] :
      ( hAPP(U_1157,hAPP(hAPP(c_Set_Oinsert(U_1155),U_1159),U_1158)) = hAPP(hAPP(U_1156,U_1159),hAPP(U_1157,U_1158))
      | U_1158 = c_Orderings_Obot__class_Obot(tc_fun(U_1155,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1155),U_1158))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1155,U_1156,U_1157) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( hAPP(U_1157,hAPP(hAPP(c_Set_Oinsert(U_1155),U_1159),U_1158)) = hAPP(hAPP(U_1156,U_1159),hAPP(U_1157,U_1158))
    | U_1158 = c_Orderings_Obot__class_Obot(tc_fun(U_1155,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1155),U_1158))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1155,U_1156,U_1157) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert]) ).

fof(f_225_2,plain,
    ! [U_1165,U_1164,U_1163,U_1162,U_1161,U_1160] :
      ( hAPP(U_1163,hAPP(hAPP(c_Set_Oinsert(U_1160),U_1165),U_1164)) = hAPP(c_Fun_Ocomp(U_1161,U_1161,U_1161,hAPP(U_1163,U_1164)),hAPP(U_1162,U_1165))
      | hBOOL(hAPP(hAPP(c_member(U_1160),U_1165),U_1164))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1160),U_1164))
      | ~ c_Finite__Set_Ofolding(U_1160,U_1161,U_1162,U_1163) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( hAPP(U_1163,hAPP(hAPP(c_Set_Oinsert(U_1160),U_1165),U_1164)) = hAPP(c_Fun_Ocomp(U_1161,U_1161,U_1161,hAPP(U_1163,U_1164)),hAPP(U_1162,U_1165))
    | hBOOL(hAPP(hAPP(c_member(U_1160),U_1165),U_1164))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1160),U_1164))
    | ~ c_Finite__Set_Ofolding(U_1160,U_1161,U_1162,U_1163) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).

fof(f_226_2,plain,
    ! [U_1168,U_1167,U_1166] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_1166,U_1167) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1166),U_1168),c_Big__Operators_Olattice__class_OSup__fin(U_1166,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_1166,U_1167) = U_1168
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1166),U_1168),U_1167))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1166),U_1167))
      | ~ class_Lattices_Olattice(U_1166) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1166,U_1167) = U_1168
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1166),U_1168),U_1167))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1166),U_1167))
    | ~ class_Lattices_Olattice(U_1166) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1166,U_1167) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1166),U_1168),c_Big__Operators_Olattice__class_OSup__fin(U_1166,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1166,tc_HOL_Obool)),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1166),U_1168),U_1167))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1166),U_1167))
    | ~ class_Lattices_Olattice(U_1166) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffE]) ).

fof(f_227_2,plain,
    ! [U_1172,U_1171,U_1170,U_1169] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),U_1172))
        & hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),U_1171)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1172))) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),U_1171))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1172))) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

cnf(f_227_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),U_1172))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1169),U_1170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1172))) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DiffI]) ).

fof(f_228_2,plain,
    ! [U_1176,U_1175,U_1174,U_1173] :
      ( hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1173,tc_HOL_Obool)),U_1175),U_1176)))
      | hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),U_1176))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),U_1175)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1173,tc_HOL_Obool)),U_1175),U_1176)))
    | hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),U_1176))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1173),U_1174),U_1175)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).

fof(f_229_2,plain,
    ! [U_1179,U_1178,U_1177] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1177),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1177,tc_HOL_Obool)),U_1178),U_1179)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1177),U_1178)) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1177),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1177,tc_HOL_Obool)),U_1178),U_1179)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1177),U_1178)) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).

fof(f_230_2,plain,
    ! [U_1184,U_1183,U_1182,U_1181,U_1180] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1181,U_1180)),U_1182),U_1183),U_1184) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1180),hAPP(U_1182,U_1184)),hAPP(U_1183,U_1184))
      | ~ class_Groups_Ominus(U_1180) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1181,U_1180)),U_1182),U_1183),U_1184) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1180),hAPP(U_1182,U_1184)),hAPP(U_1183,U_1184))
    | ~ class_Groups_Ominus(U_1180) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__idemp]) ).

fof(f_231_2,plain,
    ! [U_1187,U_1186,U_1185] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),U_1186),U_1187)),U_1187) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),U_1186),U_1187),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),U_1186),U_1187)),U_1187) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1185,tc_HOL_Obool)),U_1186),U_1187),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).

fof(f_232_2,plain,
    ! [U_1192,U_1191,U_1190,U_1189,U_1188] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1189,U_1188)),U_1190),U_1191),U_1192) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1188),hAPP(U_1190,U_1192)),hAPP(U_1191,U_1192))
      | ~ class_Groups_Ominus(U_1188) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1189,U_1188)),U_1190),U_1191),U_1192) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1188),hAPP(U_1190,U_1192)),hAPP(U_1191,U_1192))
    | ~ class_Groups_Ominus(U_1188) ),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_a] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).

fof(f_233_2,plain,
    ! [U_1196,U_1195,U_1194,U_1193] :
      ( hAPP(hAPP(U_1194,U_1196),U_1196) = U_1196
      | ~ c_Finite__Set_Ofolding__one__idem(U_1193,U_1194,U_1195) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_1196,U_1195,U_1194] :
      ( ! [U_1193] : ~ c_Finite__Set_Ofolding__one__idem(U_1193,U_1194,U_1195)
      | hAPP(hAPP(U_1194,U_1196),U_1196) = U_1196 ),
    inference(miniscope,[status(thm)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_1193,U_1194,U_1195)
    | hAPP(hAPP(U_1194,U_1196),U_1196) = U_1196 ),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).

fof(f_234_2,plain,
    ! [U_1200,U_1199,U_1198,U_1197] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_1197),U_1198),U_1200))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1197),U_1198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1197,tc_HOL_Obool)),U_1199),U_1200))) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1197),U_1198),U_1200))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1197),U_1198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1197,tc_HOL_Obool)),U_1199),U_1200))) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).

fof(f_235_2,plain,
    ! [U_1204,U_1203,U_1202,U_1201] :
      ( hBOOL(hAPP(hAPP(c_member(U_1201),U_1202),U_1203))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1201),U_1202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1201,tc_HOL_Obool)),U_1203),U_1204))) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1201),U_1202),U_1203))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1201),U_1202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1201,tc_HOL_Obool)),U_1203),U_1204))) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).

fof(f_236_2,plain,
    ! [U_1208,U_1207,U_1206,U_1205] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1205,tc_HOL_Obool)),U_1207),U_1208)))
        | hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),U_1208))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),U_1207)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),U_1208))
          & hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),U_1207)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1205),U_1206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1205,tc_HOL_Obool)),U_1207),U_1208))) ) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ( ! [U_1216,U_1214,U_1212,U_1210] :
        ( hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1210,tc_HOL_Obool)),U_1214),U_1216)))
        | hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),U_1216))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),U_1214)) )
    & ! [U_1215,U_1213,U_1211,U_1209] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),U_1215))
          & hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),U_1213)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1209,tc_HOL_Obool)),U_1213),U_1215))) ) ),
    inference(miniscope,[status(thm)],[f_236_2]) ).

cnf(f_236_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),U_1213))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1209,tc_HOL_Obool)),U_1213),U_1215))) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),U_1215))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1209),U_1211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1209,tc_HOL_Obool)),U_1213),U_1215))) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1210,tc_HOL_Obool)),U_1214),U_1216)))
    | hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),U_1216))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1210),U_1212),U_1214)) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).

fof(f_237_2,plain,
    ! [U_1218,U_1217] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1217,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1217,tc_HOL_Obool))),U_1218) = c_Orderings_Obot__class_Obot(tc_fun(U_1217,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1217,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1217,tc_HOL_Obool))),U_1218) = c_Orderings_Obot__class_Obot(tc_fun(U_1217,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).

fof(f_238_2,plain,
    ! [U_1220,U_1219] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1220),c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))) = U_1220,
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1220),c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))) = U_1220,
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).

fof(f_239_2,plain,
    ! [U_1222,U_1221] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1221,tc_HOL_Obool)),U_1222),U_1222) = c_Orderings_Obot__class_Obot(tc_fun(U_1221,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

cnf(f_239_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1221,tc_HOL_Obool)),U_1222),U_1222) = c_Orderings_Obot__class_Obot(tc_fun(U_1221,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_239_2]) ).

fof(f_240_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).

fof(f_240_2,plain,
    ! [U_1225,U_1224,U_1223] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1223,tc_HOL_Obool)),U_1225),U_1224)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1225)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1225))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1223,tc_HOL_Obool)),U_1225),U_1224))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1224)) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

cnf(f_240_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1225))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1223,tc_HOL_Obool)),U_1225),U_1224)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1224)) ),
    inference(clausify,[status(thm)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1223,tc_HOL_Obool)),U_1225),U_1224)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1225))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1223),U_1224)) ),
    inference(clausify,[status(thm)],[f_240_2]) ).

fof(f_241_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(f_241_2,plain,
    ! [U_1228,U_1227,U_1226] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1226,tc_HOL_Obool)),U_1227),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1226,tc_HOL_Obool)),U_1228),U_1227)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1226,tc_HOL_Obool)),U_1227),U_1228),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1226,tc_HOL_Obool)),U_1227),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1226,tc_HOL_Obool)),U_1228),U_1227)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1226,tc_HOL_Obool)),U_1227),U_1228),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_1,plain,
    ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(f_242_2,plain,
    ! [U_1231,U_1230,U_1229] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1229,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1229,tc_HOL_Obool)),U_1230),U_1231)),U_1231) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1229,tc_HOL_Obool)),U_1230),U_1231),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1229,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1229,tc_HOL_Obool)),U_1230),U_1231)),U_1231) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1229,tc_HOL_Obool)),U_1230),U_1231),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).

fof(f_243_2,plain,
    ! [U_1235,U_1234,U_1233,U_1232] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1232,tc_HOL_Obool)),U_1233),U_1234)),U_1235) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1232,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),U_1233),U_1235)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),U_1234),U_1235)),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1232,tc_HOL_Obool)),U_1233),U_1234)),U_1235) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1232,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),U_1233),U_1235)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1232,tc_HOL_Obool)),U_1234),U_1235)),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Diff]) ).

fof(f_244_2,plain,
    ! [U_1240,U_1239,U_1238,U_1237,U_1236] : hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1237,tc_HOL_Obool)),U_1239),U_1240)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1236,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),U_1239)),hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),U_1240)),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1237,tc_HOL_Obool)),U_1239),U_1240)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1236,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),U_1239)),hAPP(c_Set_Ovimage(U_1236,U_1237,U_1238),U_1240)),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_1,plain,
    ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp]) ).

fof(f_245_2,plain,
    ! [U_1248,U_1247,U_1246,U_1245,U_1244,U_1243,U_1242,U_1241] :
      ( hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),U_1248)) = hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),U_1248))
      | ~ c_Finite__Set_Ofolding(U_1241,U_1242,U_1243,U_1244) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_1248,U_1247,U_1246,U_1245,U_1244,U_1243,U_1242] :
      ( ! [U_1241] : ~ c_Finite__Set_Ofolding(U_1241,U_1242,U_1243,U_1244)
      | hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),U_1248)) = hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),U_1248)) ),
    inference(miniscope,[status(thm)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_1241,U_1242,U_1243,U_1244)
    | hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),U_1248)) = hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1247)),hAPP(c_Fun_Ocomp(U_1242,U_1242,U_1245,hAPP(U_1243,U_1246)),U_1248)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp]) ).

fof(f_246_2,plain,
    ! [U_1254,U_1253,U_1252,U_1251,U_1250,U_1249] :
      ( hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1253)),hAPP(U_1251,U_1254)) = hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1254)),hAPP(U_1251,U_1253))
      | ~ c_Finite__Set_Ofolding(U_1249,U_1250,U_1251,U_1252) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_1254,U_1253,U_1252,U_1251,U_1250] :
      ( ! [U_1249] : ~ c_Finite__Set_Ofolding(U_1249,U_1250,U_1251,U_1252)
      | hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1253)),hAPP(U_1251,U_1254)) = hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1254)),hAPP(U_1251,U_1253)) ),
    inference(miniscope,[status(thm)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_1249,U_1250,U_1251,U_1252)
    | hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1253)),hAPP(U_1251,U_1254)) = hAPP(c_Fun_Ocomp(U_1250,U_1250,U_1250,hAPP(U_1251,U_1254)),hAPP(U_1251,U_1253)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_1,plain,
    ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2)
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J]) ).

fof(f_247_2,plain,
    ! [U_1265,U_1264,U_1263,U_1262,U_1261,U_1260,U_1259,U_1258,U_1257,U_1256,U_1255] :
      ( hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1261,U_1262),hAPP(c_Fun_Ocomp(U_1263,U_1259,U_1261,U_1264),U_1265)) = hAPP(c_Fun_Ocomp(U_1263,U_1260,U_1261,hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1263,U_1262),U_1264)),U_1265)
      | ~ c_Finite__Set_Ofolding(U_1255,U_1256,U_1257,U_1258) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ( ! [U_1265,U_1264,U_1263,U_1262,U_1261,U_1260,U_1259] : hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1261,U_1262),hAPP(c_Fun_Ocomp(U_1263,U_1259,U_1261,U_1264),U_1265)) = hAPP(c_Fun_Ocomp(U_1263,U_1260,U_1261,hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1263,U_1262),U_1264)),U_1265)
    | ! [U_1258,U_1257,U_1256,U_1255] : ~ c_Finite__Set_Ofolding(U_1255,U_1256,U_1257,U_1258) ),
    inference(miniscope,[status(thm)],[f_247_2]) ).

cnf(f_247_4,plain,
    ( hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1261,U_1262),hAPP(c_Fun_Ocomp(U_1263,U_1259,U_1261,U_1264),U_1265)) = hAPP(c_Fun_Ocomp(U_1263,U_1260,U_1261,hAPP(c_Fun_Ocomp(U_1259,U_1260,U_1263,U_1262),U_1264)),U_1265)
    | ~ c_Finite__Set_Ofolding(U_1255,U_1256,U_1257,U_1258) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( ( ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).

fof(f_248_2,plain,
    ! [U_1270,U_1269,U_1268,U_1267,U_1266] :
      ( ( ( hAPP(U_1268,hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),U_1269)) = hAPP(hAPP(U_1267,U_1270),hAPP(U_1268,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)) )
        & ( hAPP(U_1268,hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),U_1269)) = U_1270
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1266),U_1269))
      | ~ c_Finite__Set_Ofolding__one(U_1266,U_1267,U_1268) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    ( hAPP(U_1268,hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),U_1269)) = U_1270
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1266),U_1269))
    | ~ c_Finite__Set_Ofolding__one(U_1266,U_1267,U_1268) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( hAPP(U_1268,hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),U_1269)) = hAPP(hAPP(U_1267,U_1270),hAPP(U_1268,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1266,tc_HOL_Obool)),U_1269),hAPP(hAPP(c_Set_Oinsert(U_1266),U_1270),c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1266,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1266),U_1269))
    | ~ c_Finite__Set_Ofolding__one(U_1266,U_1267,U_1268) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).

fof(f_249_2,plain,
    ! [U_1274,U_1273,U_1272,U_1271] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1271,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1271),U_1272),U_1274)),U_1273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1271,tc_HOL_Obool)),U_1274),U_1273)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1271),U_1272),U_1273)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1271,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1271),U_1272),U_1274)),U_1273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1271,tc_HOL_Obool)),U_1274),U_1273)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1271),U_1272),U_1273)) ),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).

fof(f_250_2,plain,
    ! [U_1278,U_1277,U_1276,U_1275] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1275,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1275),U_1276),U_1278)),U_1277) = hAPP(hAPP(c_Set_Oinsert(U_1275),U_1276),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1275,tc_HOL_Obool)),U_1278),U_1277))
        | hBOOL(hAPP(hAPP(c_member(U_1275),U_1276),U_1277)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1275,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1275),U_1276),U_1278)),U_1277) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1275,tc_HOL_Obool)),U_1278),U_1277)
        | ~ hBOOL(hAPP(hAPP(c_member(U_1275),U_1276),U_1277)) ) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ( ! [U_1286,U_1284,U_1282,U_1280] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1280,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1280),U_1282),U_1286)),U_1284) = hAPP(hAPP(c_Set_Oinsert(U_1280),U_1282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1280,tc_HOL_Obool)),U_1286),U_1284))
        | hBOOL(hAPP(hAPP(c_member(U_1280),U_1282),U_1284)) )
    & ! [U_1285,U_1283,U_1281,U_1279] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1279,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1279),U_1281),U_1285)),U_1283) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1279,tc_HOL_Obool)),U_1285),U_1283)
        | ~ hBOOL(hAPP(hAPP(c_member(U_1279),U_1281),U_1283)) ) ),
    inference(miniscope,[status(thm)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1279,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1279),U_1281),U_1285)),U_1283) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1279,tc_HOL_Obool)),U_1285),U_1283)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1279),U_1281),U_1283)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

cnf(f_250_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1280,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1280),U_1282),U_1286)),U_1284) = hAPP(hAPP(c_Set_Oinsert(U_1280),U_1282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1280,tc_HOL_Obool)),U_1286),U_1284))
    | hBOOL(hAPP(hAPP(c_member(U_1280),U_1282),U_1284)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).

fof(f_251_2,plain,
    ! [U_1290,U_1289,U_1288,U_1287] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1288),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1289),U_1290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1288),U_1290)),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1289),c_Orderings_Obot__class_Obot(tc_fun(U_1287,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

cnf(f_251_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1288),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1289),U_1290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1288),U_1290)),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1289),c_Orderings_Obot__class_Obot(tc_fun(U_1287,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).

fof(f_252_2,plain,
    ! [U_1294,U_1293,U_1292,U_1291] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),U_1292),hAPP(hAPP(c_Set_Oinsert(U_1291),U_1293),U_1294)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),U_1292),hAPP(hAPP(c_Set_Oinsert(U_1291),U_1293),c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool))))),U_1294),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),U_1292),hAPP(hAPP(c_Set_Oinsert(U_1291),U_1293),U_1294)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1291,tc_HOL_Obool)),U_1292),hAPP(hAPP(c_Set_Oinsert(U_1291),U_1293),c_Orderings_Obot__class_Obot(tc_fun(U_1291,tc_HOL_Obool))))),U_1294),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_1,plain,
    ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).

fof(f_253_2,plain,
    ! [U_1297,U_1296,U_1295] : hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1295,tc_HOL_Obool)),U_1297),hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),U_1297),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

cnf(f_253_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1295,tc_HOL_Obool)),U_1297),hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1295),U_1296),U_1297),
    inference(clausify,[status(thm)],[f_253_2]) ).

fof(f_254_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).

fof(f_254_2,plain,
    ! [U_1301,U_1300,U_1299,U_1298] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),U_1301))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),U_1301))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),U_1301)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),U_1301)))) ) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ( ! [U_1309,U_1307,U_1305,U_1303] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1305),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1307),U_1309))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1305),U_1309))) )
    & ! [U_1308,U_1306,U_1304,U_1302] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),U_1308)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),U_1308)))) ) ),
    inference(miniscope,[status(thm)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),U_1308)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),U_1308)))) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

cnf(f_254_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1305),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1307),U_1309))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1305),U_1309))) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove]) ).

fof(f_255_2,plain,
    ! [U_1315,U_1314,U_1313,U_1312,U_1311,U_1310] :
      ( hAPP(U_1313,hAPP(hAPP(c_Set_Oinsert(U_1310),U_1315),U_1314)) = hAPP(c_Fun_Ocomp(U_1311,U_1311,U_1311,hAPP(U_1313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1310,tc_HOL_Obool)),U_1314),hAPP(hAPP(c_Set_Oinsert(U_1310),U_1315),c_Orderings_Obot__class_Obot(tc_fun(U_1310,tc_HOL_Obool)))))),hAPP(U_1312,U_1315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1310),U_1314))
      | ~ c_Finite__Set_Ofolding(U_1310,U_1311,U_1312,U_1313) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

cnf(f_255_3,plain,
    ( hAPP(U_1313,hAPP(hAPP(c_Set_Oinsert(U_1310),U_1315),U_1314)) = hAPP(c_Fun_Ocomp(U_1311,U_1311,U_1311,hAPP(U_1313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1310,tc_HOL_Obool)),U_1314),hAPP(hAPP(c_Set_Oinsert(U_1310),U_1315),c_Orderings_Obot__class_Obot(tc_fun(U_1310,tc_HOL_Obool)))))),hAPP(U_1312,U_1315))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1310),U_1314))
    | ~ c_Finite__Set_Ofolding(U_1310,U_1311,U_1312,U_1313) ),
    inference(clausify,[status(thm)],[f_255_2]) ).

fof(f_256_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( ( ( 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_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).

fof(f_256_2,plain,
    ! [U_1320,U_1319,U_1318,U_1317,U_1316] :
      ( ( ( hAPP(U_1318,U_1319) = hAPP(hAPP(U_1317,U_1320),hAPP(U_1318,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)) )
        & ( hAPP(U_1318,U_1319) = U_1320
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1316),U_1320),U_1319))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1316),U_1319))
      | ~ c_Finite__Set_Ofolding__one(U_1316,U_1317,U_1318) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( hAPP(U_1318,U_1319) = U_1320
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1316),U_1320),U_1319))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1316),U_1319))
    | ~ c_Finite__Set_Ofolding__one(U_1316,U_1317,U_1318) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hAPP(U_1318,U_1319) = hAPP(hAPP(U_1317,U_1320),hAPP(U_1318,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1316,tc_HOL_Obool)),U_1319),hAPP(hAPP(c_Set_Oinsert(U_1316),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1316,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1316),U_1320),U_1319))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1316),U_1319))
    | ~ c_Finite__Set_Ofolding__one(U_1316,U_1317,U_1318) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_1,plain,
    ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)
      | ~ c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp]) ).

fof(f_257_2,plain,
    ! [U_1327,U_1326,U_1325,U_1324,U_1323,U_1322,U_1321] :
      ( hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327)) = hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327)
      | ~ c_Finite__Set_Ofolding__idem(U_1321,U_1322,U_1323,U_1324) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_1327,U_1326,U_1325,U_1324,U_1323,U_1322] :
      ( ! [U_1321] : ~ c_Finite__Set_Ofolding__idem(U_1321,U_1322,U_1323,U_1324)
      | hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327)) = hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327) ),
    inference(miniscope,[status(thm)],[f_257_2]) ).

cnf(f_257_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_1321,U_1322,U_1323,U_1324)
    | hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327)) = hAPP(c_Fun_Ocomp(U_1322,U_1322,U_1325,hAPP(U_1323,U_1326)),U_1327) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp]) ).

fof(f_258_2,plain,
    ! [U_1332,U_1331,U_1330,U_1329,U_1328] :
      ( hAPP(c_Fun_Ocomp(U_1329,U_1329,U_1329,hAPP(U_1330,U_1332)),hAPP(U_1330,U_1332)) = hAPP(U_1330,U_1332)
      | ~ c_Finite__Set_Ofolding__idem(U_1328,U_1329,U_1330,U_1331) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_1332,U_1331,U_1330,U_1329] :
      ( ! [U_1328] : ~ c_Finite__Set_Ofolding__idem(U_1328,U_1329,U_1330,U_1331)
      | hAPP(c_Fun_Ocomp(U_1329,U_1329,U_1329,hAPP(U_1330,U_1332)),hAPP(U_1330,U_1332)) = hAPP(U_1330,U_1332) ),
    inference(miniscope,[status(thm)],[f_258_2]) ).

cnf(f_258_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_1328,U_1329,U_1330,U_1331)
    | hAPP(c_Fun_Ocomp(U_1329,U_1329,U_1329,hAPP(U_1330,U_1332)),hAPP(U_1330,U_1332)) = hAPP(U_1330,U_1332) ),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oremove]) ).

fof(f_259_2,plain,
    ! [U_1338,U_1337,U_1336,U_1335,U_1334,U_1333] :
      ( hAPP(U_1336,U_1337) = hAPP(c_Fun_Ocomp(U_1334,U_1334,U_1334,hAPP(U_1336,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1333,tc_HOL_Obool)),U_1337),hAPP(hAPP(c_Set_Oinsert(U_1333),U_1338),c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool)))))),hAPP(U_1335,U_1338))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1333),U_1338),U_1337))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1333),U_1337))
      | ~ c_Finite__Set_Ofolding(U_1333,U_1334,U_1335,U_1336) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

cnf(f_259_3,plain,
    ( hAPP(U_1336,U_1337) = hAPP(c_Fun_Ocomp(U_1334,U_1334,U_1334,hAPP(U_1336,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1333,tc_HOL_Obool)),U_1337),hAPP(hAPP(c_Set_Oinsert(U_1333),U_1338),c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool)))))),hAPP(U_1335,U_1338))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1333),U_1338),U_1337))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1333),U_1337))
    | ~ c_Finite__Set_Ofolding(U_1333,U_1334,U_1335,U_1336) ),
    inference(clausify,[status(thm)],[f_259_2]) ).

fof(f_260_1,plain,
    ! [V_A_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(f_260_2,plain,
    ! [U_1341,U_1340,U_1339] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1339,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1339),U_1340),U_1341)),hAPP(hAPP(c_Set_Oinsert(U_1339),U_1340),c_Orderings_Obot__class_Obot(tc_fun(U_1339,tc_HOL_Obool)))) = U_1341
      | hBOOL(hAPP(hAPP(c_member(U_1339),U_1340),U_1341)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1339,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1339),U_1340),U_1341)),hAPP(hAPP(c_Set_Oinsert(U_1339),U_1340),c_Orderings_Obot__class_Obot(tc_fun(U_1339,tc_HOL_Obool)))) = U_1341
    | hBOOL(hAPP(hAPP(c_member(U_1339),U_1340),U_1341)) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).

fof(f_261_2,plain,
    ! [U_1344,U_1343,U_1342] :
      ( hAPP(hAPP(c_Set_Oinsert(U_1342),U_1343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1342,tc_HOL_Obool)),U_1344),hAPP(hAPP(c_Set_Oinsert(U_1342),U_1343),c_Orderings_Obot__class_Obot(tc_fun(U_1342,tc_HOL_Obool))))) = U_1344
      | ~ hBOOL(hAPP(hAPP(c_member(U_1342),U_1343),U_1344)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_1342),U_1343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1342,tc_HOL_Obool)),U_1344),hAPP(hAPP(c_Set_Oinsert(U_1342),U_1343),c_Orderings_Obot__class_Obot(tc_fun(U_1342,tc_HOL_Obool))))) = U_1344
    | ~ hBOOL(hAPP(hAPP(c_member(U_1342),U_1343),U_1344)) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_1,plain,
    ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H]) ).

fof(f_262_2,plain,
    ! [U_1352,U_1351,U_1350,U_1349,U_1348,U_1347,U_1346,U_1345] :
      ( hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1350)),hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1349)),U_1352)) = hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1349)),hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1350)),U_1352))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1345),U_1350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1345),U_1349))
      | ~ c_Finite__Set_Ofolding(U_1345,U_1346,U_1347,U_1348) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1350)),hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1349)),U_1352)) = hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1349)),hAPP(c_Fun_Ocomp(U_1346,U_1346,U_1351,hAPP(U_1348,U_1350)),U_1352))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1345),U_1350))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1345),U_1349))
    | ~ c_Finite__Set_Ofolding(U_1345,U_1346,U_1347,U_1348) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H]) ).

fof(f_263_2,plain,
    ! [U_1358,U_1357,U_1356,U_1355,U_1354,U_1353] :
      ( hAPP(c_Fun_Ocomp(U_1354,U_1354,U_1354,hAPP(U_1356,U_1358)),hAPP(U_1356,U_1357)) = hAPP(c_Fun_Ocomp(U_1354,U_1354,U_1354,hAPP(U_1356,U_1357)),hAPP(U_1356,U_1358))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1358))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1357))
      | ~ c_Finite__Set_Ofolding(U_1353,U_1354,U_1355,U_1356) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1354,U_1354,U_1354,hAPP(U_1356,U_1358)),hAPP(U_1356,U_1357)) = hAPP(c_Fun_Ocomp(U_1354,U_1354,U_1354,hAPP(U_1356,U_1357)),hAPP(U_1356,U_1358))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1358))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1357))
    | ~ c_Finite__Set_Ofolding(U_1353,U_1354,U_1355,U_1356) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H]) ).

fof(f_264_2,plain,
    ! [U_1366,U_1365,U_1364,U_1363,U_1362,U_1361,U_1360,U_1359] :
      ( hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1361,U_1365)),hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1362,U_1363)),U_1366)) = hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1362,U_1363)),hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1361,U_1365)),U_1366))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1359),U_1363))
      | ~ c_Finite__Set_Ofolding(U_1359,U_1360,U_1361,U_1362) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1361,U_1365)),hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1362,U_1363)),U_1366)) = hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1362,U_1363)),hAPP(c_Fun_Ocomp(U_1360,U_1360,U_1364,hAPP(U_1361,U_1365)),U_1366))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1359),U_1363))
    | ~ c_Finite__Set_Ofolding(U_1359,U_1360,U_1361,U_1362) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H]) ).

fof(f_265_2,plain,
    ! [U_1372,U_1371,U_1370,U_1369,U_1368,U_1367] :
      ( hAPP(c_Fun_Ocomp(U_1368,U_1368,U_1368,hAPP(U_1369,U_1372)),hAPP(U_1370,U_1371)) = hAPP(c_Fun_Ocomp(U_1368,U_1368,U_1368,hAPP(U_1370,U_1371)),hAPP(U_1369,U_1372))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1367),U_1371))
      | ~ c_Finite__Set_Ofolding(U_1367,U_1368,U_1369,U_1370) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1368,U_1368,U_1368,hAPP(U_1369,U_1372)),hAPP(U_1370,U_1371)) = hAPP(c_Fun_Ocomp(U_1368,U_1368,U_1368,hAPP(U_1370,U_1371)),hAPP(U_1369,U_1372))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1367),U_1371))
    | ~ c_Finite__Set_Ofolding(U_1367,U_1368,U_1369,U_1370) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).

fof(f_266_2,plain,
    ! [U_1376,U_1375,U_1374,U_1373] :
      ( hAPP(U_1375,hAPP(hAPP(c_Set_Oinsert(U_1373),U_1376),c_Orderings_Obot__class_Obot(tc_fun(U_1373,tc_HOL_Obool)))) = U_1376
      | ~ c_Finite__Set_Ofolding__one(U_1373,U_1374,U_1375) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( hAPP(U_1375,hAPP(hAPP(c_Set_Oinsert(U_1373),U_1376),c_Orderings_Obot__class_Obot(tc_fun(U_1373,tc_HOL_Obool)))) = U_1376
    | ~ c_Finite__Set_Ofolding__one(U_1373,U_1374,U_1375) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( 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_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).

fof(f_267_2,plain,
    ! [U_1381,U_1380,U_1379,U_1378,U_1377] :
      ( hAPP(hAPP(U_1378,U_1381),hAPP(U_1379,U_1380)) = hAPP(U_1379,U_1380)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1377),U_1381),U_1380))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1377),U_1380))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1377,U_1378,U_1379) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

cnf(f_267_3,plain,
    ( hAPP(hAPP(U_1378,U_1381),hAPP(U_1379,U_1380)) = hAPP(U_1379,U_1380)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1377),U_1381),U_1380))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1377),U_1380))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1377,U_1378,U_1379) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

fof(f_268_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(f_268_2,plain,
    ! [U_1388,U_1387,U_1386,U_1385,U_1384,U_1383,U_1382] :
      ( hAPP(hAPP(U_1386,U_1388),U_1387) = U_1385
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1383),U_1387))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_1382,U_1383,U_1384,U_1385,U_1386) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_1388,U_1387,U_1386,U_1385,U_1384,U_1383] :
      ( ! [U_1382] : ~ c_Big__Operators_Ocomm__monoid__big(U_1382,U_1383,U_1384,U_1385,U_1386)
      | hAPP(hAPP(U_1386,U_1388),U_1387) = U_1385
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1383),U_1387)) ),
    inference(miniscope,[status(thm)],[f_268_2]) ).

cnf(f_268_4,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_1382,U_1383,U_1384,U_1385,U_1386)
    | hAPP(hAPP(U_1386,U_1388),U_1387) = U_1385
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1383),U_1387)) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).

fof(f_269_2,plain,
    ! [U_1391,U_1390,U_1389] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),U_1390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1389),U_1391),c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),U_1390)) = U_1391
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1389),U_1390))
      | ~ class_Lattices_Olattice(U_1389) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),U_1390)) = U_1391
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1389),U_1390))
    | ~ class_Lattices_Olattice(U_1389) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

cnf(f_269_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),U_1390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1389),U_1391),c_Big__Operators_Olattice__class_OSup__fin(U_1389,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1389,tc_HOL_Obool)),U_1390),hAPP(hAPP(c_Set_Oinsert(U_1389),U_1391),c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1389),U_1390))
    | ~ class_Lattices_Olattice(U_1389) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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_b,tc_HOL_Obool)),V_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_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).

fof(f_270_2,plain,
    ! [U_1399,U_1398,U_1397,U_1396,U_1395,U_1394,U_1393,U_1392] :
      ( hAPP(U_1397,U_1398) = hAPP(hAPP(U_1394,hAPP(U_1396,U_1399)),hAPP(U_1397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1393,tc_HOL_Obool)),U_1398),hAPP(hAPP(c_Set_Oinsert(U_1393),U_1399),c_Orderings_Obot__class_Obot(tc_fun(U_1393,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1393),U_1399),U_1398))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1393),U_1398))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1392,U_1393,U_1394,U_1395,U_1396,U_1397) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_1399,U_1398,U_1397,U_1396,U_1395,U_1394,U_1393] :
      ( ! [U_1392] : ~ c_Finite__Set_Ofolding__image__simple(U_1392,U_1393,U_1394,U_1395,U_1396,U_1397)
      | hAPP(U_1397,U_1398) = hAPP(hAPP(U_1394,hAPP(U_1396,U_1399)),hAPP(U_1397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1393,tc_HOL_Obool)),U_1398),hAPP(hAPP(c_Set_Oinsert(U_1393),U_1399),c_Orderings_Obot__class_Obot(tc_fun(U_1393,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1393),U_1399),U_1398))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1393),U_1398)) ),
    inference(miniscope,[status(thm)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1392,U_1393,U_1394,U_1395,U_1396,U_1397)
    | hAPP(U_1397,U_1398) = hAPP(hAPP(U_1394,hAPP(U_1396,U_1399)),hAPP(U_1397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1393,tc_HOL_Obool)),U_1398),hAPP(hAPP(c_Set_Oinsert(U_1393),U_1399),c_Orderings_Obot__class_Obot(tc_fun(U_1393,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1393),U_1399),U_1398))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1393),U_1398)) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_b,tc_HOL_Obool)),V_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_Ofolding__image__simple(T_a,T_b,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_271_2,plain,
    ! [U_1407,U_1406,U_1405,U_1404,U_1403,U_1402,U_1401,U_1400] :
      ( hAPP(U_1405,hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),U_1406)) = hAPP(hAPP(U_1402,hAPP(U_1404,U_1407)),hAPP(U_1405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1401,tc_HOL_Obool)),U_1406),hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),c_Orderings_Obot__class_Obot(tc_fun(U_1401,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1401),U_1406))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1400,U_1401,U_1402,U_1403,U_1404,U_1405) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_1407,U_1406,U_1405,U_1404,U_1403,U_1402,U_1401] :
      ( ! [U_1400] : ~ c_Finite__Set_Ofolding__image__simple(U_1400,U_1401,U_1402,U_1403,U_1404,U_1405)
      | hAPP(U_1405,hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),U_1406)) = hAPP(hAPP(U_1402,hAPP(U_1404,U_1407)),hAPP(U_1405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1401,tc_HOL_Obool)),U_1406),hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),c_Orderings_Obot__class_Obot(tc_fun(U_1401,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1401),U_1406)) ),
    inference(miniscope,[status(thm)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1400,U_1401,U_1402,U_1403,U_1404,U_1405)
    | hAPP(U_1405,hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),U_1406)) = hAPP(hAPP(U_1402,hAPP(U_1404,U_1407)),hAPP(U_1405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1401,tc_HOL_Obool)),U_1406),hAPP(hAPP(c_Set_Oinsert(U_1401),U_1407),c_Orderings_Obot__class_Obot(tc_fun(U_1401,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1401),U_1406)) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).

fof(f_272_2,plain,
    ! [U_1413,U_1412,U_1411,U_1410] :
      ( hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(U_1412,U_1413)),U_1413))
      | ? [U_1409,U_1408] : ~ hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(hAPP(U_1411,U_1409),U_1408)),hAPP(hAPP(c_Set_Oinsert(U_1410),U_1409),hAPP(hAPP(c_Set_Oinsert(U_1410),U_1408),c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))))))
      | U_1413 = c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1410),U_1413))
      | ~ c_Finite__Set_Ofolding__one(U_1410,U_1411,U_1412) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_1413,U_1412,U_1411,U_1410] :
      ( hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(U_1412,U_1413)),U_1413))
      | ? [U_1408] : ~ hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(hAPP(U_1411,sK28(U_1413,U_1412,U_1411,U_1410)),U_1408)),hAPP(hAPP(c_Set_Oinsert(U_1410),sK28(U_1413,U_1412,U_1411,U_1410)),hAPP(hAPP(c_Set_Oinsert(U_1410),U_1408),c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))))))
      | U_1413 = c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1410),U_1413))
      | ~ c_Finite__Set_Ofolding__one(U_1410,U_1411,U_1412) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1409,sK28(U_1413,U_1412,U_1411,U_1410))],[f_272_2]) ).

fof(f_272_4,plain,
    ! [U_1413,U_1412,U_1411,U_1410] :
      ( hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(U_1412,U_1413)),U_1413))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(hAPP(U_1411,sK28(U_1413,U_1412,U_1411,U_1410)),sK29(U_1413,U_1412,U_1411,U_1410))),hAPP(hAPP(c_Set_Oinsert(U_1410),sK28(U_1413,U_1412,U_1411,U_1410)),hAPP(hAPP(c_Set_Oinsert(U_1410),sK29(U_1413,U_1412,U_1411,U_1410)),c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))))))
      | U_1413 = c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1410),U_1413))
      | ~ c_Finite__Set_Ofolding__one(U_1410,U_1411,U_1412) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1408,sK29(U_1413,U_1412,U_1411,U_1410))],[f_272_3]) ).

cnf(f_272_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(U_1412,U_1413)),U_1413))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1410),hAPP(hAPP(U_1411,sK28(U_1413,U_1412,U_1411,U_1410)),sK29(U_1413,U_1412,U_1411,U_1410))),hAPP(hAPP(c_Set_Oinsert(U_1410),sK28(U_1413,U_1412,U_1411,U_1410)),hAPP(hAPP(c_Set_Oinsert(U_1410),sK29(U_1413,U_1412,U_1411,U_1410)),c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))))))
    | U_1413 = c_Orderings_Obot__class_Obot(tc_fun(U_1410,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1410),U_1413))
    | ~ c_Finite__Set_Ofolding__one(U_1410,U_1411,U_1412) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

fof(f_273_1,plain,
    ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( ( hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
      & ( hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).

fof(f_273_2,plain,
    ! [U_1419,U_1418,U_1417,U_1416,U_1415,U_1414] :
      ( ( hAPP(c_Set_Oimage(U_1414,U_1417,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1414,U_1417),U_1418),U_1415),U_1419)),U_1416) = hAPP(c_Set_Oimage(U_1414,U_1417,U_1418),U_1416)
        | hBOOL(hAPP(hAPP(c_member(U_1414),U_1415),U_1416)) )
      & ( hAPP(c_Set_Oimage(U_1414,U_1417,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1414,U_1417),U_1418),U_1415),U_1419)),U_1416) = hAPP(hAPP(c_Set_Oinsert(U_1417),U_1419),hAPP(c_Set_Oimage(U_1414,U_1417,U_1418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1414,tc_HOL_Obool)),U_1416),hAPP(hAPP(c_Set_Oinsert(U_1414),U_1415),c_Orderings_Obot__class_Obot(tc_fun(U_1414,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1414),U_1415),U_1416)) ) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ( ! [U_1431,U_1429,U_1427,U_1425,U_1423,U_1421] :
        ( hAPP(c_Set_Oimage(U_1421,U_1427,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1421,U_1427),U_1429),U_1423),U_1431)),U_1425) = hAPP(c_Set_Oimage(U_1421,U_1427,U_1429),U_1425)
        | hBOOL(hAPP(hAPP(c_member(U_1421),U_1423),U_1425)) )
    & ! [U_1430,U_1428,U_1426,U_1424,U_1422,U_1420] :
        ( hAPP(c_Set_Oimage(U_1420,U_1426,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1420,U_1426),U_1428),U_1422),U_1430)),U_1424) = hAPP(hAPP(c_Set_Oinsert(U_1426),U_1430),hAPP(c_Set_Oimage(U_1420,U_1426,U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1420,tc_HOL_Obool)),U_1424),hAPP(hAPP(c_Set_Oinsert(U_1420),U_1422),c_Orderings_Obot__class_Obot(tc_fun(U_1420,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1420),U_1422),U_1424)) ) ),
    inference(miniscope,[status(thm)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( hAPP(c_Set_Oimage(U_1420,U_1426,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1420,U_1426),U_1428),U_1422),U_1430)),U_1424) = hAPP(hAPP(c_Set_Oinsert(U_1426),U_1430),hAPP(c_Set_Oimage(U_1420,U_1426,U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1420,tc_HOL_Obool)),U_1424),hAPP(hAPP(c_Set_Oinsert(U_1420),U_1422),c_Orderings_Obot__class_Obot(tc_fun(U_1420,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1420),U_1422),U_1424)) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

cnf(f_273_5,plain,
    ( hAPP(c_Set_Oimage(U_1421,U_1427,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1421,U_1427),U_1429),U_1423),U_1431)),U_1425) = hAPP(c_Set_Oimage(U_1421,U_1427,U_1429),U_1425)
    | hBOOL(hAPP(hAPP(c_member(U_1421),U_1423),U_1425)) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_1,plain,
    ! [V_P_2,V_A_2,T_a] :
      ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
      | ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          & hBOOL(hAPP(V_P_2,B_A))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) )
      | ~ hBOOL(hAPP(V_P_2,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).

fof(f_274_2,plain,
    ! [U_1436,U_1435,U_1434] :
      ( hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
      | ? [U_1433,U_1432] :
          ( ~ hBOOL(hAPP(U_1436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1434,tc_HOL_Obool)),U_1432),hAPP(hAPP(c_Set_Oinsert(U_1434),U_1433),c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_1436,U_1432))
          & hBOOL(hAPP(hAPP(c_member(U_1434),U_1433),U_1432))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1432)) )
      | ~ hBOOL(hAPP(U_1436,U_1435))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_1436,U_1435,U_1434] :
      ( hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
      | ? [U_1432] :
          ( ~ hBOOL(hAPP(U_1436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1434,tc_HOL_Obool)),U_1432),hAPP(hAPP(c_Set_Oinsert(U_1434),sK30(U_1436,U_1435,U_1434)),c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_1436,U_1432))
          & hBOOL(hAPP(hAPP(c_member(U_1434),sK30(U_1436,U_1435,U_1434)),U_1432))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1432)) )
      | ~ hBOOL(hAPP(U_1436,U_1435))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1433,sK30(U_1436,U_1435,U_1434))],[f_274_2]) ).

fof(f_274_4,plain,
    ! [U_1436,U_1435,U_1434] :
      ( hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_1436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1434,tc_HOL_Obool)),sK31(U_1436,U_1435,U_1434)),hAPP(hAPP(c_Set_Oinsert(U_1434),sK30(U_1436,U_1435,U_1434)),c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_1436,sK31(U_1436,U_1435,U_1434)))
        & hBOOL(hAPP(hAPP(c_member(U_1434),sK30(U_1436,U_1435,U_1434)),sK31(U_1436,U_1435,U_1434)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),sK31(U_1436,U_1435,U_1434))) )
      | ~ hBOOL(hAPP(U_1436,U_1435))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1432,sK31(U_1436,U_1435,U_1434))],[f_274_3]) ).

cnf(f_274_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),sK31(U_1436,U_1435,U_1434)))
    | hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1436,U_1435))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1434),sK30(U_1436,U_1435,U_1434)),sK31(U_1436,U_1435,U_1434)))
    | hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1436,U_1435))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_7,plain,
    ( hBOOL(hAPP(U_1436,sK31(U_1436,U_1435,U_1434)))
    | hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1436,U_1435))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_8,plain,
    ( ~ hBOOL(hAPP(U_1436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1434,tc_HOL_Obool)),sK31(U_1436,U_1435,U_1434)),hAPP(hAPP(c_Set_Oinsert(U_1434),sK30(U_1436,U_1435,U_1434)),c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))))
    | hBOOL(hAPP(U_1436,c_Orderings_Obot__class_Obot(tc_fun(U_1434,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1436,U_1435))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1434),U_1435)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

fof(f_275_1,plain,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).

fof(f_275_2,plain,
    ! [U_1443,U_1442,U_1441,U_1440,U_1439] :
      ( hAPP(U_1442,hAPP(U_1441,U_1443)) = hAPP(U_1441,hAPP(c_Set_Oimage(U_1439,U_1439,U_1442),U_1443))
      | U_1443 = c_Orderings_Obot__class_Obot(tc_fun(U_1439,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1439),U_1443))
      | ? [U_1438,U_1437] : hAPP(U_1442,hAPP(hAPP(U_1440,U_1438),U_1437)) != hAPP(hAPP(U_1440,hAPP(U_1442,U_1438)),hAPP(U_1442,U_1437))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1439,U_1440,U_1441) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_1443,U_1442,U_1441,U_1440,U_1439] :
      ( hAPP(U_1442,hAPP(U_1441,U_1443)) = hAPP(U_1441,hAPP(c_Set_Oimage(U_1439,U_1439,U_1442),U_1443))
      | U_1443 = c_Orderings_Obot__class_Obot(tc_fun(U_1439,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1439),U_1443))
      | ? [U_1437] : hAPP(U_1442,hAPP(hAPP(U_1440,sK32(U_1443,U_1442,U_1441,U_1440,U_1439)),U_1437)) != hAPP(hAPP(U_1440,hAPP(U_1442,sK32(U_1443,U_1442,U_1441,U_1440,U_1439))),hAPP(U_1442,U_1437))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1439,U_1440,U_1441) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1438,sK32(U_1443,U_1442,U_1441,U_1440,U_1439))],[f_275_2]) ).

fof(f_275_4,plain,
    ! [U_1443,U_1442,U_1441,U_1440,U_1439] :
      ( hAPP(U_1442,hAPP(U_1441,U_1443)) = hAPP(U_1441,hAPP(c_Set_Oimage(U_1439,U_1439,U_1442),U_1443))
      | U_1443 = c_Orderings_Obot__class_Obot(tc_fun(U_1439,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1439),U_1443))
      | hAPP(U_1442,hAPP(hAPP(U_1440,sK32(U_1443,U_1442,U_1441,U_1440,U_1439)),sK33(U_1443,U_1442,U_1441,U_1440,U_1439))) != hAPP(hAPP(U_1440,hAPP(U_1442,sK32(U_1443,U_1442,U_1441,U_1440,U_1439))),hAPP(U_1442,sK33(U_1443,U_1442,U_1441,U_1440,U_1439)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1439,U_1440,U_1441) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1437,sK33(U_1443,U_1442,U_1441,U_1440,U_1439))],[f_275_3]) ).

cnf(f_275_5,plain,
    ( hAPP(U_1442,hAPP(U_1441,U_1443)) = hAPP(U_1441,hAPP(c_Set_Oimage(U_1439,U_1439,U_1442),U_1443))
    | U_1443 = c_Orderings_Obot__class_Obot(tc_fun(U_1439,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1439),U_1443))
    | hAPP(U_1442,hAPP(hAPP(U_1440,sK32(U_1443,U_1442,U_1441,U_1440,U_1439)),sK33(U_1443,U_1442,U_1441,U_1440,U_1439))) != hAPP(hAPP(U_1440,hAPP(U_1442,sK32(U_1443,U_1442,U_1441,U_1440,U_1439))),hAPP(U_1442,sK33(U_1443,U_1442,U_1441,U_1440,U_1439)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1439,U_1440,U_1441) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

fof(f_276_1,plain,
    ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

fof(f_276_2,plain,
    ! [U_1444] : c_Finite__Set_Ofun__left__comm__idem(U_1444,tc_fun(U_1444,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_1444,tc_HOL_Obool),tc_fun(tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),U_1444),hAPP(c_COMBC(tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_1444,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_1444,tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),c_Set_Oinsert(U_1444)),c_Orderings_Obot__class_Obot(tc_fun(U_1444,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_1444,tc_fun(U_1444,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_1444,tc_HOL_Obool),tc_fun(tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),U_1444),hAPP(c_COMBC(tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_1444,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_1444,tc_fun(U_1444,tc_HOL_Obool),tc_fun(U_1444,tc_HOL_Obool)),c_Set_Oinsert(U_1444)),c_Orderings_Obot__class_Obot(tc_fun(U_1444,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(f_277_2,plain,
    ! [U_1452,U_1451,U_1450,U_1449,U_1448,U_1447,U_1446,U_1445] :
      ( hAPP(U_1450,hAPP(hAPP(c_Set_Oinsert(U_1446),U_1452),U_1451)) = hAPP(hAPP(U_1447,hAPP(U_1449,U_1452)),hAPP(U_1450,U_1451))
      | hBOOL(hAPP(hAPP(c_member(U_1446),U_1452),U_1451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1446),U_1451))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1445,U_1446,U_1447,U_1448,U_1449,U_1450) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_1452,U_1451,U_1450,U_1449,U_1448,U_1447,U_1446] :
      ( ! [U_1445] : ~ c_Finite__Set_Ofolding__image__simple(U_1445,U_1446,U_1447,U_1448,U_1449,U_1450)
      | hAPP(U_1450,hAPP(hAPP(c_Set_Oinsert(U_1446),U_1452),U_1451)) = hAPP(hAPP(U_1447,hAPP(U_1449,U_1452)),hAPP(U_1450,U_1451))
      | hBOOL(hAPP(hAPP(c_member(U_1446),U_1452),U_1451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1446),U_1451)) ),
    inference(miniscope,[status(thm)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1445,U_1446,U_1447,U_1448,U_1449,U_1450)
    | hAPP(U_1450,hAPP(hAPP(c_Set_Oinsert(U_1446),U_1452),U_1451)) = hAPP(hAPP(U_1447,hAPP(U_1449,U_1452)),hAPP(U_1450,U_1451))
    | hBOOL(hAPP(hAPP(c_member(U_1446),U_1452),U_1451))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1446),U_1451)) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Rings_Oring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).

fof(f_278_2,plain,
    ! [U_1457,U_1456,U_1455,U_1454,U_1453] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1454,U_1453),U_1457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1454,tc_HOL_Obool)),U_1455),hAPP(hAPP(c_Set_Oinsert(U_1454),U_1456),c_Orderings_Obot__class_Obot(tc_fun(U_1454,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1453),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1454,U_1453),U_1457),U_1455)),hAPP(U_1457,U_1456))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1454),U_1456),U_1455))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1454),U_1455))
      | ~ class_Rings_Oring(U_1453) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1454,U_1453),U_1457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1454,tc_HOL_Obool)),U_1455),hAPP(hAPP(c_Set_Oinsert(U_1454),U_1456),c_Orderings_Obot__class_Obot(tc_fun(U_1454,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1453),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1454,U_1453),U_1457),U_1455)),hAPP(U_1457,U_1456))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1454),U_1456),U_1455))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1454),U_1455))
    | ~ class_Rings_Oring(U_1453) ),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).

fof(f_279_2,plain,
    ! [U_1462,U_1461,U_1460,U_1459,U_1458] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Set_Oinsert(U_1459),U_1461),c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),U_1460)
          | hBOOL(hAPP(hAPP(c_member(U_1459),U_1461),U_1460)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Set_Oinsert(U_1459),U_1461),c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),U_1460)),hAPP(U_1462,U_1461))
          | ~ hBOOL(hAPP(hAPP(c_member(U_1459),U_1461),U_1460)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1459),U_1460))
      | ~ class_Groups_Oab__group__add(U_1458) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Set_Oinsert(U_1459),U_1461),c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),U_1460)),hAPP(U_1462,U_1461))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1459),U_1461),U_1460))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1459),U_1460))
    | ~ class_Groups_Oab__group__add(U_1458) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

cnf(f_279_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Set_Oinsert(U_1459),U_1461),c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1459,U_1458),U_1462),U_1460)
    | hBOOL(hAPP(hAPP(c_member(U_1459),U_1461),U_1460))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1459),U_1460))
    | ~ class_Groups_Oab__group__add(U_1458) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion]) ).

fof(f_280_2,plain,
    ! [U_1468,U_1467,U_1466,U_1465,U_1464,U_1463] :
      ( hAPP(U_1466,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1463,tc_HOL_Obool)),U_1467),U_1468)) = hAPP(c_Fun_Ocomp(U_1464,U_1464,U_1464,hAPP(U_1466,U_1467)),hAPP(U_1466,U_1468))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1467),U_1468) != c_Orderings_Obot__class_Obot(tc_fun(U_1463,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1463),U_1468))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1463),U_1467))
      | ~ c_Finite__Set_Ofolding(U_1463,U_1464,U_1465,U_1466) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    ( hAPP(U_1466,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1463,tc_HOL_Obool)),U_1467),U_1468)) = hAPP(c_Fun_Ocomp(U_1464,U_1464,U_1464,hAPP(U_1466,U_1467)),hAPP(U_1466,U_1468))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1467),U_1468) != c_Orderings_Obot__class_Obot(tc_fun(U_1463,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1463),U_1468))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1463),U_1467))
    | ~ c_Finite__Set_Ofolding(U_1463,U_1464,U_1465,U_1466) ),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( ( 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_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1E]) ).

fof(f_281_2,plain,
    ! [U_1472,U_1471,U_1470,U_1469] :
      ( ( hBOOL(hAPP(U_1471,U_1472))
        & hBOOL(hAPP(U_1470,U_1472)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1469,tc_HOL_Obool)),U_1470),U_1471),U_1472)) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_1472,U_1471,U_1470] :
      ( ! [U_1469] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1469,tc_HOL_Obool)),U_1470),U_1471),U_1472))
      | ( hBOOL(hAPP(U_1471,U_1472))
        & hBOOL(hAPP(U_1470,U_1472)) ) ),
    inference(miniscope,[status(thm)],[f_281_2]) ).

cnf(f_281_4,plain,
    ( hBOOL(hAPP(U_1470,U_1472))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1469,tc_HOL_Obool)),U_1470),U_1471),U_1472)) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

cnf(f_281_5,plain,
    ( hBOOL(hAPP(U_1471,U_1472))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1469,tc_HOL_Obool)),U_1470),U_1471),U_1472)) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_1,plain,
    ! [T_a,V_B_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_282_2,plain,
    ! [U_1476,U_1475,U_1474,U_1473] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1476,tc_HOL_Obool)),U_1473),U_1475),U_1474))
      | ~ hBOOL(hAPP(U_1475,U_1474))
      | ~ hBOOL(hAPP(U_1473,U_1474)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

cnf(f_282_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1476,tc_HOL_Obool)),U_1473),U_1475),U_1474))
    | ~ hBOOL(hAPP(U_1475,U_1474))
    | ~ hBOOL(hAPP(U_1473,U_1474)) ),
    inference(clausify,[status(thm)],[f_282_2]) ).

fof(f_283_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_283_2,plain,
    ! [U_1480,U_1479,U_1478,U_1477] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1477,U_1478),U_1479),U_1480),hAPP(U_1479,U_1480)) = U_1479,
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1477,U_1478),U_1479),U_1480),hAPP(U_1479,U_1480)) = U_1479,
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_IntI]) ).

fof(f_284_2,plain,
    ! [U_1484,U_1483,U_1482,U_1481] :
      ( hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1481,tc_HOL_Obool)),U_1483),U_1484)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),U_1484))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),U_1483)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

cnf(f_284_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1481,tc_HOL_Obool)),U_1483),U_1484)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),U_1484))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1481),U_1482),U_1483)) ),
    inference(clausify,[status(thm)],[f_284_2]) ).

fof(f_285_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntE]) ).

fof(f_285_2,plain,
    ! [U_1488,U_1487,U_1486,U_1485] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),U_1488))
        & hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),U_1487)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1485,tc_HOL_Obool)),U_1487),U_1488))) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),U_1487))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1485,tc_HOL_Obool)),U_1487),U_1488))) ),
    inference(clausify,[status(thm)],[f_285_2]) ).

cnf(f_285_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),U_1488))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1485),U_1486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1485,tc_HOL_Obool)),U_1487),U_1488))) ),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_1,plain,
    ! [V_Ga_2,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).

fof(f_286_2,plain,
    ! [U_1491,U_1490,U_1489] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1489,tc_HOL_Obool)),U_1490),U_1491)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),U_1491))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),U_1490)) ) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

cnf(f_286_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),U_1490))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1489,tc_HOL_Obool)),U_1490),U_1491))) ),
    inference(clausify,[status(thm)],[f_286_2]) ).

cnf(f_286_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),U_1491))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1489,tc_HOL_Obool)),U_1490),U_1491))) ),
    inference(clausify,[status(thm)],[f_286_2]) ).

fof(f_287_1,plain,
    ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),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_287_2,plain,
    ! [U_1496,U_1495,U_1494,U_1493,U_1492] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1495,U_1496),U_1492),U_1493),U_1494) = U_1492
      | hAPP(U_1492,U_1493) != U_1494 ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1495,U_1496),U_1492),U_1493),U_1494) = U_1492
    | hAPP(U_1492,U_1493) != U_1494 ),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_1,plain,
    ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_288_2,plain,
    ! [U_1502,U_1501,U_1500,U_1499,U_1498,U_1497] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1499,U_1500),U_1501),U_1498),U_1502),U_1497) = hAPP(U_1501,U_1497)
      | U_1497 = U_1498 ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1499,U_1500),U_1501),U_1498),U_1502),U_1497) = hAPP(U_1501,U_1497)
    | U_1497 = U_1498 ),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_1,plain,
    ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_289_2,plain,
    ! [U_1509,U_1508,U_1507,U_1506,U_1505,U_1504,U_1503] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),U_1507),U_1503),U_1508)),U_1504),U_1509) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),U_1507),U_1504),U_1509)),U_1503),U_1508)
      | U_1503 = U_1504 ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),U_1507),U_1503),U_1508)),U_1504),U_1509) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1505,U_1506),U_1507),U_1504),U_1509)),U_1503),U_1508)
    | U_1503 = U_1504 ),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_1,plain,
    ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_a,T_b),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_290_2,plain,
    ! [U_1515,U_1514,U_1513,U_1512,U_1511,U_1510] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1512,U_1513),U_1514),U_1511),U_1515),U_1510) = hAPP(U_1514,U_1510)
        | U_1510 = U_1511 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1512,U_1513),U_1514),U_1511),U_1515),U_1510) = U_1515
        | U_1510 != U_1511 ) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ( ! [U_1527,U_1525,U_1523,U_1521,U_1519,U_1517] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1521,U_1523),U_1525),U_1519),U_1527),U_1517) = hAPP(U_1525,U_1517)
        | U_1517 = U_1519 )
    & ! [U_1526,U_1524,U_1522,U_1520,U_1518,U_1516] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1520,U_1522),U_1524),U_1518),U_1526),U_1516) = U_1526
        | U_1516 != U_1518 ) ),
    inference(miniscope,[status(thm)],[f_290_2]) ).

cnf(f_290_4,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1520,U_1522),U_1524),U_1518),U_1526),U_1516) = U_1526
    | U_1516 != U_1518 ),
    inference(clausify,[status(thm)],[f_290_3]) ).

cnf(f_290_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1521,U_1523),U_1525),U_1519),U_1527),U_1517) = hAPP(U_1525,U_1517)
    | U_1517 = U_1519 ),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),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_291_2,plain,
    ! [U_1532,U_1531,U_1530,U_1529,U_1528] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1528,U_1529),U_1530),U_1531),U_1532),U_1531) = U_1532,
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1528,U_1529),U_1530),U_1531),U_1532),U_1531) = U_1532,
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).

fof(f_292_2,plain,
    ! [U_1538,U_1537,U_1536,U_1535,U_1534,U_1533] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),U_1535),U_1536),U_1537)),U_1536),U_1538) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),U_1535),U_1536),U_1538),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

cnf(f_292_3,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),U_1535),U_1536),U_1537)),U_1536),U_1538) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1533,U_1534),U_1535),U_1536),U_1538),
    inference(clausify,[status(thm)],[f_292_2]) ).

fof(f_293_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_a,T_b),V_f_2),V_x_2),V_y_2) != V_f_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).

fof(f_293_2,plain,
    ! [U_1543,U_1542,U_1541,U_1540,U_1539] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1539,U_1540),U_1541),U_1542),U_1543) = U_1541
        | hAPP(U_1541,U_1542) != U_1543 )
      & ( hAPP(U_1541,U_1542) = U_1543
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1539,U_1540),U_1541),U_1542),U_1543) != U_1541 ) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_1553,U_1551,U_1549] :
        ( ! [U_1547,U_1545] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1545,U_1547),U_1549),U_1551),U_1553) = U_1549
        | hAPP(U_1549,U_1551) != U_1553 )
    & ! [U_1552,U_1550,U_1548] :
        ( ! [U_1546,U_1544] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1544,U_1546),U_1548),U_1550),U_1552) != U_1548
        | hAPP(U_1548,U_1550) = U_1552 ) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1544,U_1546),U_1548),U_1550),U_1552) != U_1548
    | hAPP(U_1548,U_1550) = U_1552 ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1545,U_1547),U_1549),U_1551),U_1553) = U_1549
    | hAPP(U_1549,U_1551) != U_1553 ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_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_294_2,plain,
    ! [U_1555,U_1554] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1554),U_1555),U_1555) = U_1555
      | ~ class_Lattices_Olattice(U_1554) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

cnf(f_294_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1554),U_1555),U_1555) = U_1555
    | ~ class_Lattices_Olattice(U_1554) ),
    inference(clausify,[status(thm)],[f_294_2]) ).

fof(f_295_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).

fof(f_295_2,plain,
    ! [U_1559,U_1558,U_1557,U_1556] :
      ( hBOOL(hAPP(U_1558,U_1559))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1556,tc_HOL_Obool)),U_1557),U_1558),U_1559)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_1559,U_1558] :
      ( ! [U_1557,U_1556] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1556,tc_HOL_Obool)),U_1557),U_1558),U_1559))
      | hBOOL(hAPP(U_1558,U_1559)) ),
    inference(miniscope,[status(thm)],[f_295_2]) ).

cnf(f_295_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1556,tc_HOL_Obool)),U_1557),U_1558),U_1559))
    | hBOOL(hAPP(U_1558,U_1559)) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).

fof(f_296_2,plain,
    ! [U_1563,U_1562,U_1561,U_1560] :
      ( hBOOL(hAPP(U_1561,U_1563))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1560,tc_HOL_Obool)),U_1561),U_1562),U_1563)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1563,U_1562,U_1561] :
      ( ! [U_1560] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1560,tc_HOL_Obool)),U_1561),U_1562),U_1563))
      | hBOOL(hAPP(U_1561,U_1563)) ),
    inference(miniscope,[status(thm)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1560,tc_HOL_Obool)),U_1561),U_1562),U_1563))
    | hBOOL(hAPP(U_1561,U_1563)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).

fof(f_297_2,plain,
    ! [U_1568,U_1567,U_1566,U_1565,U_1564] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1565,U_1564)),U_1566),U_1567),U_1568) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1564),hAPP(U_1566,U_1568)),hAPP(U_1567,U_1568))
      | ~ class_Lattices_Olattice(U_1564) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1565,U_1564)),U_1566),U_1567),U_1568) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1564),hAPP(U_1566,U_1568)),hAPP(U_1567,U_1568))
    | ~ class_Lattices_Olattice(U_1564) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_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_298_2,plain,
    ! [U_1572,U_1571,U_1570,U_1569] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1570),U_1571)),U_1572) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1570),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1571),U_1572))
      | ~ class_Lattices_Osemilattice__inf(U_1569) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1570),U_1571)),U_1572) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1570),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1569),U_1571),U_1572))
    | ~ class_Lattices_Osemilattice__inf(U_1569) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_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_299_2,plain,
    ! [U_1576,U_1575,U_1574,U_1573] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1574),U_1575)),U_1576) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1574),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1575),U_1576))
      | ~ class_Lattices_Olattice(U_1573) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

cnf(f_299_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1574),U_1575)),U_1576) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1574),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1573),U_1575),U_1576))
    | ~ class_Lattices_Olattice(U_1573) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

fof(f_300_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_300_2,plain,
    ! [U_1580,U_1579,U_1578,U_1577] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),U_1579)),U_1580) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1579),U_1580))
      | ~ class_Lattices_Osemilattice__inf(U_1577) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

cnf(f_300_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),U_1579)),U_1580) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1577),U_1579),U_1580))
    | ~ class_Lattices_Osemilattice__inf(U_1577) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

fof(f_301_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).

fof(f_301_2,plain,
    ! [U_1584,U_1583,U_1582,U_1581] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1582),U_1583)),U_1584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1582),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1583),U_1584)),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

cnf(f_301_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1582),U_1583)),U_1584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1582),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1581,tc_HOL_Obool)),U_1583),U_1584)),
    inference(clausify,[status(thm)],[f_301_2]) ).

fof(f_302_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_302_2,plain,
    ! [U_1588,U_1587,U_1586,U_1585] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),U_1588)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),U_1588))
      | ~ class_Lattices_Osemilattice__inf(U_1585) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

cnf(f_302_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),U_1588)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1587),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1585),U_1586),U_1588))
    | ~ class_Lattices_Osemilattice__inf(U_1585) ),
    inference(clausify,[status(thm)],[f_302_2]) ).

fof(f_303_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_303_2,plain,
    ! [U_1592,U_1591,U_1590,U_1589] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),U_1592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1590),U_1592))
      | ~ class_Lattices_Olattice(U_1589) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

cnf(f_303_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),U_1592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1591),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1589),U_1590),U_1592))
    | ~ class_Lattices_Olattice(U_1589) ),
    inference(clausify,[status(thm)],[f_303_2]) ).

fof(f_304_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_304_2,plain,
    ! [U_1596,U_1595,U_1594,U_1593] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1595),U_1596)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1595),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1596))
      | ~ class_Lattices_Osemilattice__inf(U_1593) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

cnf(f_304_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1595),U_1596)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1595),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1593),U_1594),U_1596))
    | ~ class_Lattices_Osemilattice__inf(U_1593) ),
    inference(clausify,[status(thm)],[f_304_2]) ).

fof(f_305_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).

fof(f_305_2,plain,
    ! [U_1600,U_1599,U_1598,U_1597] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1598),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1599),U_1600)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1599),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1598),U_1600)),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1598),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1599),U_1600)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1599),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1597,tc_HOL_Obool)),U_1598),U_1600)),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_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_306_2,plain,
    ! [U_1603,U_1602,U_1601] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),U_1603)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),U_1603)
      | ~ class_Lattices_Osemilattice__inf(U_1601) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

cnf(f_306_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),U_1603)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1601),U_1602),U_1603)
    | ~ class_Lattices_Osemilattice__inf(U_1601) ),
    inference(clausify,[status(thm)],[f_306_2]) ).

fof(f_307_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_307_2,plain,
    ! [U_1606,U_1605,U_1604] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),U_1606)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),U_1606)
      | ~ class_Lattices_Olattice(U_1604) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),U_1606)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1604),U_1605),U_1606)
    | ~ class_Lattices_Olattice(U_1604) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_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_308_2,plain,
    ! [U_1609,U_1608,U_1607] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),U_1609)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),U_1609)
      | ~ class_Lattices_Osemilattice__inf(U_1607) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),U_1609)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1607),U_1608),U_1609)
    | ~ class_Lattices_Osemilattice__inf(U_1607) ),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).

fof(f_309_2,plain,
    ! [U_1612,U_1611,U_1610] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),U_1612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),U_1612),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),U_1612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1610,tc_HOL_Obool)),U_1611),U_1612),
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_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_310_2,plain,
    ! [U_1615,U_1614,U_1613] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1613),U_1614),U_1615) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1613),U_1615),U_1614)
      | ~ class_Lattices_Osemilattice__inf(U_1613) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

cnf(f_310_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1613),U_1614),U_1615) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1613),U_1615),U_1614)
    | ~ class_Lattices_Osemilattice__inf(U_1613) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

fof(f_311_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_311_2,plain,
    ! [U_1618,U_1617,U_1616] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1616),U_1617),U_1618) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1616),U_1618),U_1617)
      | ~ class_Lattices_Olattice(U_1616) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

cnf(f_311_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1616),U_1617),U_1618) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1616),U_1618),U_1617)
    | ~ class_Lattices_Olattice(U_1616) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

fof(f_312_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_312_2,plain,
    ! [U_1621,U_1620,U_1619] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1619),U_1620),U_1621) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1619),U_1621),U_1620)
      | ~ class_Lattices_Osemilattice__inf(U_1619) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

cnf(f_312_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1619),U_1620),U_1621) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1619),U_1621),U_1620)
    | ~ class_Lattices_Osemilattice__inf(U_1619) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

fof(f_313_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).

fof(f_313_2,plain,
    ! [U_1624,U_1623,U_1622] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1622,tc_HOL_Obool)),U_1623),U_1624) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1622,tc_HOL_Obool)),U_1624),U_1623),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1622,tc_HOL_Obool)),U_1623),U_1624) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1622,tc_HOL_Obool)),U_1624),U_1623),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).

fof(f_314_2,plain,
    ! [U_1629,U_1628,U_1627,U_1626,U_1625] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1626,U_1625)),U_1627),U_1628),U_1629) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1625),hAPP(U_1627,U_1629)),hAPP(U_1628,U_1629))
      | ~ class_Lattices_Olattice(U_1625) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

cnf(f_314_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1626,U_1625)),U_1627),U_1628),U_1629) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1625),hAPP(U_1627,U_1629)),hAPP(U_1628,U_1629))
    | ~ class_Lattices_Olattice(U_1625) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_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_315_2,plain,
    ! [U_1631,U_1630] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1630),U_1631),U_1631) = U_1631
      | ~ class_Lattices_Osemilattice__inf(U_1630) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

cnf(f_315_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1630),U_1631),U_1631) = U_1631
    | ~ class_Lattices_Osemilattice__inf(U_1630) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_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_316_2,plain,
    ! [U_1633,U_1632] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1632),U_1633),U_1633) = U_1633
      | ~ class_Lattices_Osemilattice__inf(U_1632) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

cnf(f_316_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1632),U_1633),U_1633) = U_1633
    | ~ class_Lattices_Osemilattice__inf(U_1632) ),
    inference(clausify,[status(thm)],[f_316_2]) ).

fof(f_317_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).

fof(f_317_2,plain,
    ! [U_1635,U_1634] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1634,tc_HOL_Obool)),U_1635),U_1635) = U_1635,
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1634,tc_HOL_Obool)),U_1635),U_1635) = U_1635,
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
      ( 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_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).

fof(f_318_2,plain,
    ! [U_1640,U_1639,U_1638,U_1637,U_1636] :
      ( hAPP(hAPP(U_1638,U_1639),hAPP(hAPP(U_1638,U_1639),U_1640)) = hAPP(hAPP(U_1638,U_1639),U_1640)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_1636,U_1637,U_1638) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_1640,U_1639,U_1638] :
      ( ! [U_1637,U_1636] : ~ c_Finite__Set_Ofun__left__comm__idem(U_1636,U_1637,U_1638)
      | hAPP(hAPP(U_1638,U_1639),hAPP(hAPP(U_1638,U_1639),U_1640)) = hAPP(hAPP(U_1638,U_1639),U_1640) ),
    inference(miniscope,[status(thm)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_1636,U_1637,U_1638)
    | hAPP(hAPP(U_1638,U_1639),hAPP(hAPP(U_1638,U_1639),U_1640)) = hAPP(hAPP(U_1638,U_1639),U_1640) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).

fof(f_319_2,plain,
    ! [U_1641] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_1641,U_1641,c_Lattices_Osemilattice__inf__class_Oinf(U_1641))
      | ~ class_Lattices_Osemilattice__inf(U_1641) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

cnf(f_319_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_1641,U_1641,c_Lattices_Osemilattice__inf__class_Oinf(U_1641))
    | ~ class_Lattices_Osemilattice__inf(U_1641) ),
    inference(clausify,[status(thm)],[f_319_2]) ).

fof(f_320_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).

fof(f_320_2,plain,
    ! [U_1647,U_1646,U_1645,U_1644,U_1643,U_1642] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1643,U_1642),hAPP(hAPP(c_COMBC(U_1643,tc_fun(U_1644,tc_HOL_Obool),U_1642),hAPP(hAPP(c_COMBB(tc_fun(U_1644,U_1642),tc_fun(tc_fun(U_1644,tc_HOL_Obool),U_1642),U_1643),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1644,U_1642)),U_1645)),U_1646)),U_1647) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1644,U_1642),hAPP(hAPP(c_COMBC(U_1644,tc_fun(U_1643,tc_HOL_Obool),U_1642),hAPP(hAPP(c_COMBB(tc_fun(U_1643,U_1642),tc_fun(tc_fun(U_1643,tc_HOL_Obool),U_1642),U_1644),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1643,U_1642)),hAPP(c_COMBC(U_1643,U_1644,U_1642),U_1645))),U_1647)),U_1646)
      | ~ class_Groups_Ocomm__monoid__add(U_1642) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1643,U_1642),hAPP(hAPP(c_COMBC(U_1643,tc_fun(U_1644,tc_HOL_Obool),U_1642),hAPP(hAPP(c_COMBB(tc_fun(U_1644,U_1642),tc_fun(tc_fun(U_1644,tc_HOL_Obool),U_1642),U_1643),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1644,U_1642)),U_1645)),U_1646)),U_1647) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1644,U_1642),hAPP(hAPP(c_COMBC(U_1644,tc_fun(U_1643,tc_HOL_Obool),U_1642),hAPP(hAPP(c_COMBB(tc_fun(U_1643,U_1642),tc_fun(tc_fun(U_1643,tc_HOL_Obool),U_1642),U_1644),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1643,U_1642)),hAPP(c_COMBC(U_1643,U_1644,U_1642),U_1645))),U_1647)),U_1646)
    | ~ class_Groups_Ocomm__monoid__add(U_1642) ),
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_1,plain,
    ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),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_a,T_b),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_321_2,plain,
    ! [U_1653,U_1652,U_1651,U_1650,U_1649,U_1648] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1650,U_1651),U_1652),U_1649),U_1653),U_1648) = hAPP(U_1652,U_1648)
        | U_1648 = U_1649 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1650,U_1651),U_1652),U_1649),U_1653),U_1648) = U_1653
        | U_1648 != U_1649 ) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ( ! [U_1665,U_1663,U_1661,U_1659,U_1657,U_1655] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1659,U_1661),U_1663),U_1657),U_1665),U_1655) = hAPP(U_1663,U_1655)
        | U_1655 = U_1657 )
    & ! [U_1664,U_1662,U_1660,U_1658,U_1656,U_1654] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1658,U_1660),U_1662),U_1656),U_1664),U_1654) = U_1664
        | U_1654 != U_1656 ) ),
    inference(miniscope,[status(thm)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1658,U_1660),U_1662),U_1656),U_1664),U_1654) = U_1664
    | U_1654 != U_1656 ),
    inference(clausify,[status(thm)],[f_321_3]) ).

cnf(f_321_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1659,U_1661),U_1663),U_1657),U_1665),U_1655) = hAPP(U_1663,U_1655)
    | U_1655 = U_1657 ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).

fof(f_322_2,plain,
    ! [U_1670,U_1669,U_1668,U_1667,U_1666] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_1669,U_1667,hAPP(hAPP(c_COMBB(U_1666,tc_fun(U_1667,U_1667),U_1669),U_1668),U_1670))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_1666,U_1667,U_1668) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_1669,U_1667,hAPP(hAPP(c_COMBB(U_1666,tc_fun(U_1667,U_1667),U_1669),U_1668),U_1670))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_1666,U_1667,U_1668) ),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_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_323_2,plain,
    ! [U_1672,U_1671] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1671),U_1672),c_Orderings_Obot__class_Obot(U_1671)) = c_Orderings_Obot__class_Obot(U_1671)
      | ~ class_Lattices_Obounded__lattice__bot(U_1671) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1671),U_1672),c_Orderings_Obot__class_Obot(U_1671)) = c_Orderings_Obot__class_Obot(U_1671)
    | ~ class_Lattices_Obounded__lattice__bot(U_1671) ),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_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_324_2,plain,
    ! [U_1674,U_1673] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1673),c_Orderings_Obot__class_Obot(U_1673)),U_1674) = c_Orderings_Obot__class_Obot(U_1673)
      | ~ class_Lattices_Obounded__lattice__bot(U_1673) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1673),c_Orderings_Obot__class_Obot(U_1673)),U_1674) = c_Orderings_Obot__class_Obot(U_1673)
    | ~ class_Lattices_Obounded__lattice__bot(U_1673) ),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_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_325_2,plain,
    ! [U_1678,U_1677,U_1676,U_1675] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1675),U_1676),U_1677)),U_1678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1675),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),U_1676),U_1678)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),U_1677),U_1678))
      | ~ class_Lattices_Odistrib__lattice(U_1675) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

cnf(f_325_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1675),U_1676),U_1677)),U_1678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1675),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),U_1676),U_1678)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1675),U_1677),U_1678))
    | ~ class_Lattices_Odistrib__lattice(U_1675) ),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_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_326_2,plain,
    ! [U_1682,U_1681,U_1680,U_1679] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1679),U_1680),U_1681)),U_1682) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),U_1680),U_1682)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),U_1681),U_1682))
      | ~ class_Lattices_Odistrib__lattice(U_1679) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1679),U_1680),U_1681)),U_1682) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),U_1680),U_1682)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1679),U_1681),U_1682))
    | ~ class_Lattices_Odistrib__lattice(U_1679) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_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_327_2,plain,
    ! [U_1686,U_1685,U_1684,U_1683] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1683),U_1685),U_1686)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1683),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),U_1685)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),U_1686))
      | ~ class_Lattices_Odistrib__lattice(U_1683) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1683),U_1685),U_1686)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1683),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),U_1685)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1683),U_1684),U_1686))
    | ~ class_Lattices_Odistrib__lattice(U_1683) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_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_328_2,plain,
    ! [U_1690,U_1689,U_1688,U_1687] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1687),U_1689),U_1690)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),U_1689)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),U_1690))
      | ~ class_Lattices_Odistrib__lattice(U_1687) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1687),U_1689),U_1690)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),U_1689)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1687),U_1688),U_1690))
    | ~ class_Lattices_Odistrib__lattice(U_1687) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_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_329_2,plain,
    ! [U_1693,U_1692,U_1691] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1691),U_1692),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1691),U_1692),U_1693)) = U_1692
      | ~ class_Lattices_Olattice(U_1691) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1691),U_1692),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1691),U_1692),U_1693)) = U_1692
    | ~ class_Lattices_Olattice(U_1691) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_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_330_2,plain,
    ! [U_1696,U_1695,U_1694] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1694),U_1695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1694),U_1695),U_1696)) = U_1695
      | ~ class_Lattices_Olattice(U_1694) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1694),U_1695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1694),U_1695),U_1696)) = U_1695
    | ~ class_Lattices_Olattice(U_1694) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).

fof(f_331_2,plain,
    ! [U_1700,U_1699,U_1698,U_1697] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1697,tc_HOL_Obool)),U_1699),U_1700)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),U_1700))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),U_1699)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),U_1700))
          & hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),U_1699)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1697),U_1698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1697,tc_HOL_Obool)),U_1699),U_1700))) ) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ( ! [U_1708,U_1706,U_1704,U_1702] :
        ( hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1702,tc_HOL_Obool)),U_1706),U_1708)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),U_1708))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),U_1706)) )
    & ! [U_1707,U_1705,U_1703,U_1701] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),U_1707))
          & hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),U_1705)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1701,tc_HOL_Obool)),U_1705),U_1707))) ) ),
    inference(miniscope,[status(thm)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),U_1705))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1701,tc_HOL_Obool)),U_1705),U_1707))) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

cnf(f_331_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),U_1707))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1701),U_1703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1701,tc_HOL_Obool)),U_1705),U_1707))) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

cnf(f_331_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1702,tc_HOL_Obool)),U_1706),U_1708)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),U_1708))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1702),U_1704),U_1706)) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD1]) ).

fof(f_332_2,plain,
    ! [U_1712,U_1711,U_1710,U_1709] :
      ( hBOOL(hAPP(hAPP(c_member(U_1709),U_1710),U_1711))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1709),U_1710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1709,tc_HOL_Obool)),U_1711),U_1712))) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1709),U_1710),U_1711))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1709),U_1710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1709,tc_HOL_Obool)),U_1711),U_1712))) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD2]) ).

fof(f_333_2,plain,
    ! [U_1716,U_1715,U_1714,U_1713] :
      ( hBOOL(hAPP(hAPP(c_member(U_1713),U_1714),U_1716))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1713),U_1714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1713,tc_HOL_Obool)),U_1715),U_1716))) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1713),U_1714),U_1716))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1713),U_1714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1713,tc_HOL_Obool)),U_1715),U_1716))) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] :
            ( ? [B_xa] :
                ( B_x = B_xa
                & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( B_x != B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).

fof(f_334_2,plain,
    ! [U_1723,U_1722,U_1721] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1721,tc_HOL_Obool)),U_1722),U_1723) = c_Orderings_Obot__class_Obot(tc_fun(U_1721,tc_HOL_Obool))
        | ? [U_1720] :
            ( ? [U_1719] :
                ( U_1720 = U_1719
                & hBOOL(hAPP(hAPP(c_member(U_1721),U_1719),U_1723)) )
            & hBOOL(hAPP(hAPP(c_member(U_1721),U_1720),U_1722)) ) )
      & ( ! [U_1718] :
            ( ! [U_1717] :
                ( U_1718 != U_1717
                | ~ hBOOL(hAPP(hAPP(c_member(U_1721),U_1717),U_1723)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1721),U_1718),U_1722)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1721,tc_HOL_Obool)),U_1722),U_1723) != c_Orderings_Obot__class_Obot(tc_fun(U_1721,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ( ! [U_1729,U_1727,U_1725] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool))
        | ? [U_1720] :
            ( ? [U_1719] :
                ( U_1720 = U_1719
                & hBOOL(hAPP(hAPP(c_member(U_1725),U_1719),U_1729)) )
            & hBOOL(hAPP(hAPP(c_member(U_1725),U_1720),U_1727)) ) )
    & ! [U_1728,U_1726,U_1724] :
        ( ! [U_1718] :
            ( ! [U_1717] :
                ( U_1718 != U_1717
                | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1717),U_1728)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1718),U_1726)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1724,tc_HOL_Obool)),U_1726),U_1728) != c_Orderings_Obot__class_Obot(tc_fun(U_1724,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_334_2]) ).

fof(f_334_4,plain,
    ( ! [U_1729,U_1727,U_1725] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool))
        | ( ? [U_1719] :
              ( sK34(U_1729,U_1727,U_1725) = U_1719
              & hBOOL(hAPP(hAPP(c_member(U_1725),U_1719),U_1729)) )
          & hBOOL(hAPP(hAPP(c_member(U_1725),sK34(U_1729,U_1727,U_1725)),U_1727)) ) )
    & ! [U_1728,U_1726,U_1724] :
        ( ! [U_1718] :
            ( ! [U_1717] :
                ( U_1718 != U_1717
                | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1717),U_1728)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1718),U_1726)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1724,tc_HOL_Obool)),U_1726),U_1728) != c_Orderings_Obot__class_Obot(tc_fun(U_1724,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1720,sK34(U_1729,U_1727,U_1725))],[f_334_3]) ).

fof(f_334_5,plain,
    ( ! [U_1729,U_1727,U_1725] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool))
        | ( sK34(U_1729,U_1727,U_1725) = sK35(U_1729,U_1727,U_1725)
          & hBOOL(hAPP(hAPP(c_member(U_1725),sK35(U_1729,U_1727,U_1725)),U_1729))
          & hBOOL(hAPP(hAPP(c_member(U_1725),sK34(U_1729,U_1727,U_1725)),U_1727)) ) )
    & ! [U_1728,U_1726,U_1724] :
        ( ! [U_1718] :
            ( ! [U_1717] :
                ( U_1718 != U_1717
                | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1717),U_1728)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1718),U_1726)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1724,tc_HOL_Obool)),U_1726),U_1728) != c_Orderings_Obot__class_Obot(tc_fun(U_1724,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1719,sK35(U_1729,U_1727,U_1725))],[f_334_4]) ).

cnf(f_334_6,plain,
    ( U_1718 != U_1717
    | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1717),U_1728))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1724),U_1718),U_1726))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1724,tc_HOL_Obool)),U_1726),U_1728) != c_Orderings_Obot__class_Obot(tc_fun(U_1724,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_334_5]) ).

cnf(f_334_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1725),sK34(U_1729,U_1727,U_1725)),U_1727))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_334_5]) ).

cnf(f_334_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1725),sK35(U_1729,U_1727,U_1725)),U_1729))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_334_5]) ).

cnf(f_334_9,plain,
    ( sK34(U_1729,U_1727,U_1725) = sK35(U_1729,U_1727,U_1725)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1725,tc_HOL_Obool)),U_1727),U_1729) = c_Orderings_Obot__class_Obot(tc_fun(U_1725,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_334_5]) ).

fof(f_335_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).

fof(f_335_2,plain,
    ! [U_1731,U_1730] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1730,tc_HOL_Obool)),U_1731),c_Orderings_Obot__class_Obot(tc_fun(U_1730,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1730,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1730,tc_HOL_Obool)),U_1731),c_Orderings_Obot__class_Obot(tc_fun(U_1730,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1730,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_1,plain,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).

fof(f_336_2,plain,
    ! [U_1733,U_1732] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1732,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1732,tc_HOL_Obool))),U_1733) = c_Orderings_Obot__class_Obot(tc_fun(U_1732,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1732,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1732,tc_HOL_Obool))),U_1733) = c_Orderings_Obot__class_Obot(tc_fun(U_1732,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).

fof(f_337_2,plain,
    ! [U_1737,U_1736,U_1735,U_1734] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),U_1736)),hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),U_1737)) = hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1734,tc_HOL_Obool)),U_1736),U_1737)),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),U_1736)),hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),U_1737)) = hAPP(hAPP(c_Set_Oinsert(U_1734),U_1735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1734,tc_HOL_Obool)),U_1736),U_1737)),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).

fof(f_338_2,plain,
    ! [U_1741,U_1740,U_1739,U_1738] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1739),U_1740)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1740),U_1741))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1741),U_1739)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1739),U_1740)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1740),U_1741))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1741),U_1739)),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1739),U_1740)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1740),U_1741))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),U_1741),U_1739)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1738,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1739),U_1740)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1740),U_1741))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1738,tc_HOL_Obool)),U_1741),U_1739)),
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(f_339_2,plain,
    ! [U_1745,U_1744,U_1743,U_1742] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1742,tc_HOL_Obool)),U_1743),U_1744)),U_1745) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1742,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),U_1743),U_1745)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),U_1744),U_1745)),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1742,tc_HOL_Obool)),U_1743),U_1744)),U_1745) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1742,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),U_1743),U_1745)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1742,tc_HOL_Obool)),U_1744),U_1745)),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(f_340_2,plain,
    ! [U_1749,U_1748,U_1747,U_1746] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1746,tc_HOL_Obool)),U_1747),U_1748)),U_1749) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1746,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),U_1747),U_1749)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),U_1748),U_1749)),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1746,tc_HOL_Obool)),U_1747),U_1748)),U_1749) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1746,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),U_1747),U_1749)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1746,tc_HOL_Obool)),U_1748),U_1749)),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).

fof(f_341_2,plain,
    ! [U_1753,U_1752,U_1751,U_1750] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1750,tc_HOL_Obool)),U_1752),U_1753)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1750,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),U_1752)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),U_1753)),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1750,tc_HOL_Obool)),U_1752),U_1753)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1750,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),U_1752)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1750,tc_HOL_Obool)),U_1751),U_1753)),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).

fof(f_342_2,plain,
    ! [U_1757,U_1756,U_1755,U_1754] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1754,tc_HOL_Obool)),U_1756),U_1757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1754,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),U_1756)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),U_1757)),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1754,tc_HOL_Obool)),U_1756),U_1757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1754,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),U_1756)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1754,tc_HOL_Obool)),U_1755),U_1757)),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).

fof(f_343_2,plain,
    ! [U_1761,U_1760,U_1759,U_1758] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1759),U_1760)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1761),U_1760)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1759),U_1760)),U_1761),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1759),U_1760)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1761),U_1760)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1759),U_1760)),U_1761),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(f_344_2,plain,
    ! [U_1765,U_1764,U_1763,U_1762] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1762,tc_HOL_Obool)),U_1763),U_1764)),U_1765) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1762,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),U_1763),U_1765)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),U_1764),U_1765)),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1762,tc_HOL_Obool)),U_1763),U_1764)),U_1765) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1762,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),U_1763),U_1765)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1762,tc_HOL_Obool)),U_1764),U_1765)),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).

fof(f_345_2,plain,
    ! [U_1769,U_1768,U_1767,U_1766] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1766,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1766,tc_HOL_Obool)),U_1767),U_1768)),U_1769) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1766,tc_HOL_Obool)),U_1767),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1766,tc_HOL_Obool)),U_1768),U_1769)),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1766,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1766,tc_HOL_Obool)),U_1767),U_1768)),U_1769) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1766,tc_HOL_Obool)),U_1767),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1766,tc_HOL_Obool)),U_1768),U_1769)),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(f_346_2,plain,
    ! [U_1773,U_1772,U_1771,U_1770] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1770,tc_HOL_Obool)),U_1772),U_1773)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1770,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),U_1772)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),U_1773)),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1770,tc_HOL_Obool)),U_1772),U_1773)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1770,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),U_1772)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1770,tc_HOL_Obool)),U_1771),U_1773)),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Int]) ).

fof(f_347_2,plain,
    ! [U_1778,U_1777,U_1776,U_1775,U_1774] : hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1775,tc_HOL_Obool)),U_1777),U_1778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1774,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),U_1777)),hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),U_1778)),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1775,tc_HOL_Obool)),U_1777),U_1778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1774,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),U_1777)),hAPP(c_Set_Ovimage(U_1774,U_1775,U_1776),U_1778)),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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))
      | ~ 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__image__simple(T_a,T_b,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_348_2,plain,
    ! [U_1786,U_1785,U_1784,U_1783,U_1782,U_1781,U_1780,U_1779] :
      ( hAPP(hAPP(U_1781,hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))),hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))) = hAPP(hAPP(U_1781,hAPP(U_1784,U_1785)),hAPP(U_1784,U_1786))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1786))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1785))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1779,U_1780,U_1781,U_1782,U_1783,U_1784) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1786,U_1785,U_1784,U_1783,U_1782,U_1781,U_1780] :
      ( ! [U_1779] : ~ c_Finite__Set_Ofolding__image__simple(U_1779,U_1780,U_1781,U_1782,U_1783,U_1784)
      | hAPP(hAPP(U_1781,hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))),hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))) = hAPP(hAPP(U_1781,hAPP(U_1784,U_1785)),hAPP(U_1784,U_1786))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1786))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1785)) ),
    inference(miniscope,[status(thm)],[f_348_2]) ).

cnf(f_348_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1779,U_1780,U_1781,U_1782,U_1783,U_1784)
    | hAPP(hAPP(U_1781,hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))),hAPP(U_1784,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1780,tc_HOL_Obool)),U_1785),U_1786))) = hAPP(hAPP(U_1781,hAPP(U_1784,U_1785)),hAPP(U_1784,U_1786))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1786))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1780),U_1785)) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).

fof(f_349_2,plain,
    ! [U_1791,U_1790,U_1789,U_1788,U_1787] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),hAPP(hAPP(c_COMBS(U_1788,U_1787,U_1787),hAPP(hAPP(c_COMBB(U_1787,tc_fun(U_1787,U_1787),U_1788),c_Groups_Ominus__class_Ominus(U_1787)),U_1789)),U_1790)),U_1791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1787),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),U_1789),U_1791)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),U_1790),U_1791))
      | ~ class_Groups_Oab__group__add(U_1787) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),hAPP(hAPP(c_COMBS(U_1788,U_1787,U_1787),hAPP(hAPP(c_COMBB(U_1787,tc_fun(U_1787,U_1787),U_1788),c_Groups_Ominus__class_Ominus(U_1787)),U_1789)),U_1790)),U_1791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1787),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),U_1789),U_1791)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1788,U_1787),U_1790),U_1791))
    | ~ class_Groups_Oab__group__add(U_1787) ),
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).

fof(f_350_2,plain,
    ! [U_1795,U_1794,U_1793,U_1792] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1792,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1793)),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1794)),U_1795))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1792),U_1795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1792,tc_HOL_Obool)),U_1793),U_1794))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_1792),U_1795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1792,tc_HOL_Obool)),U_1793),U_1794)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1792,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1793)),hAPP(hAPP(c_COMBC(U_1792,tc_fun(U_1792,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1792)),U_1794)),U_1795)) ) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ( ! [U_1803,U_1801,U_1799,U_1797] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1797,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1797,tc_fun(U_1797,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1797)),U_1799)),hAPP(hAPP(c_COMBC(U_1797,tc_fun(U_1797,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1797)),U_1801)),U_1803))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1797),U_1803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1797,tc_HOL_Obool)),U_1799),U_1801))) )
    & ! [U_1802,U_1800,U_1798,U_1796] :
        ( hBOOL(hAPP(hAPP(c_member(U_1796),U_1802),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),U_1798),U_1800)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1796,tc_fun(U_1796,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1796)),U_1798)),hAPP(hAPP(c_COMBC(U_1796,tc_fun(U_1796,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1796)),U_1800)),U_1802)) ) ),
    inference(miniscope,[status(thm)],[f_350_2]) ).

cnf(f_350_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1796),U_1802),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),U_1798),U_1800)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1796,tc_fun(U_1796,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1796)),U_1798)),hAPP(hAPP(c_COMBC(U_1796,tc_fun(U_1796,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1796)),U_1800)),U_1802)) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

cnf(f_350_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1797,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1797,tc_fun(U_1797,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1797)),U_1799)),hAPP(hAPP(c_COMBC(U_1797,tc_fun(U_1797,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1797)),U_1801)),U_1803))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1797),U_1803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1797,tc_HOL_Obool)),U_1799),U_1801))) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,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_351_2,plain,
    ! [U_1810,U_1809,U_1808,U_1807,U_1806,U_1805,U_1804] : hAPP(c_Fun_Ocomp(U_1804,U_1805,U_1806,U_1807),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1806,U_1804),U_1808),U_1809),U_1810)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1806,U_1805),hAPP(c_Fun_Ocomp(U_1804,U_1805,U_1806,U_1807),U_1808)),U_1809),hAPP(U_1807,U_1810)),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    hAPP(c_Fun_Ocomp(U_1804,U_1805,U_1806,U_1807),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1806,U_1804),U_1808),U_1809),U_1810)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_1806,U_1805),hAPP(c_Fun_Ocomp(U_1804,U_1805,U_1806,U_1807),U_1808)),U_1809),hAPP(U_1807,U_1810)),
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_1,plain,
    ! [V_f_2,V_A_2,V_a_2,T_a] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(f_352_2,plain,
    ! [U_1814,U_1813,U_1812,U_1811] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1811,tc_Nat_Onat),U_1814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1811,tc_HOL_Obool)),U_1813),hAPP(hAPP(c_Set_Oinsert(U_1811),U_1812),c_Orderings_Obot__class_Obot(tc_fun(U_1811,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1811,tc_Nat_Onat),U_1814),U_1813)
        | hBOOL(hAPP(hAPP(c_member(U_1811),U_1812),U_1813)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1811,tc_Nat_Onat),U_1814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1811,tc_HOL_Obool)),U_1813),hAPP(hAPP(c_Set_Oinsert(U_1811),U_1812),c_Orderings_Obot__class_Obot(tc_fun(U_1811,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1811,tc_Nat_Onat),U_1814),U_1813)),hAPP(U_1814,U_1812))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1811),U_1812),U_1813)) ) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ( ! [U_1822,U_1820,U_1818,U_1816] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1816,tc_Nat_Onat),U_1822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1816,tc_HOL_Obool)),U_1820),hAPP(hAPP(c_Set_Oinsert(U_1816),U_1818),c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1816,tc_Nat_Onat),U_1822),U_1820)
        | hBOOL(hAPP(hAPP(c_member(U_1816),U_1818),U_1820)) )
    & ! [U_1821,U_1819,U_1817,U_1815] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1815,tc_Nat_Onat),U_1821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1815,tc_HOL_Obool)),U_1819),hAPP(hAPP(c_Set_Oinsert(U_1815),U_1817),c_Orderings_Obot__class_Obot(tc_fun(U_1815,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1815,tc_Nat_Onat),U_1821),U_1819)),hAPP(U_1821,U_1817))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1815),U_1817),U_1819)) ) ),
    inference(miniscope,[status(thm)],[f_352_2]) ).

cnf(f_352_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1815,tc_Nat_Onat),U_1821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1815,tc_HOL_Obool)),U_1819),hAPP(hAPP(c_Set_Oinsert(U_1815),U_1817),c_Orderings_Obot__class_Obot(tc_fun(U_1815,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1815,tc_Nat_Onat),U_1821),U_1819)),hAPP(U_1821,U_1817))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1815),U_1817),U_1819)) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

cnf(f_352_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1816,tc_Nat_Onat),U_1822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1816,tc_HOL_Obool)),U_1820),hAPP(hAPP(c_Set_Oinsert(U_1816),U_1818),c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1816,tc_Nat_Onat),U_1822),U_1820)
    | hBOOL(hAPP(hAPP(c_member(U_1816),U_1818),U_1820)) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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))
      | ~ 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__image__simple(T_a,T_b,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_353_2,plain,
    ! [U_1830,U_1829,U_1828,U_1827,U_1826,U_1825,U_1824,U_1823] :
      ( hAPP(U_1828,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830)) = hAPP(hAPP(U_1825,hAPP(U_1828,U_1829)),hAPP(U_1828,U_1830))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830) != c_Orderings_Obot__class_Obot(tc_fun(U_1824,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1829))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1823,U_1824,U_1825,U_1826,U_1827,U_1828) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1830,U_1829,U_1828,U_1827,U_1826,U_1825,U_1824] :
      ( ! [U_1823] : ~ c_Finite__Set_Ofolding__image__simple(U_1823,U_1824,U_1825,U_1826,U_1827,U_1828)
      | hAPP(U_1828,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830)) = hAPP(hAPP(U_1825,hAPP(U_1828,U_1829)),hAPP(U_1828,U_1830))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830) != c_Orderings_Obot__class_Obot(tc_fun(U_1824,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1829)) ),
    inference(miniscope,[status(thm)],[f_353_2]) ).

cnf(f_353_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1823,U_1824,U_1825,U_1826,U_1827,U_1828)
    | hAPP(U_1828,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830)) = hAPP(hAPP(U_1825,hAPP(U_1828,U_1829)),hAPP(U_1828,U_1830))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1824,tc_HOL_Obool)),U_1829),U_1830) != c_Orderings_Obot__class_Obot(tc_fun(U_1824,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1824),U_1829)) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(f_354_2,plain,
    ! [U_1831] : c_Finite__Set_Ofun__left__comm__idem(U_1831,tc_fun(U_1831,tc_HOL_Obool),c_Set_Oinsert(U_1831)),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_1831,tc_fun(U_1831,tc_HOL_Obool),c_Set_Oinsert(U_1831)),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).

fof(f_355_2,plain,
    ! [U_1832] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_1832,U_1832,c_Lattices_Osemilattice__sup__class_Osup(U_1832))
      | ~ class_Lattices_Osemilattice__sup(U_1832) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

cnf(f_355_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_1832,U_1832,c_Lattices_Osemilattice__sup__class_Osup(U_1832))
    | ~ class_Lattices_Osemilattice__sup(U_1832) ),
    inference(clausify,[status(thm)],[f_355_2]) ).

fof(f_356_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem]) ).

fof(f_356_2,plain,
    ! [U_1836,U_1835,U_1834,U_1833] :
      ( hAPP(c_Fun_Ocomp(U_1834,U_1834,U_1834,hAPP(U_1835,U_1836)),hAPP(U_1835,U_1836)) = hAPP(U_1835,U_1836)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_1833,U_1834,U_1835) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1836,U_1835,U_1834] :
      ( ! [U_1833] : ~ c_Finite__Set_Ofun__left__comm__idem(U_1833,U_1834,U_1835)
      | hAPP(c_Fun_Ocomp(U_1834,U_1834,U_1834,hAPP(U_1835,U_1836)),hAPP(U_1835,U_1836)) = hAPP(U_1835,U_1836) ),
    inference(miniscope,[status(thm)],[f_356_2]) ).

cnf(f_356_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_1833,U_1834,U_1835)
    | hAPP(c_Fun_Ocomp(U_1834,U_1834,U_1834,hAPP(U_1835,U_1836)),hAPP(U_1835,U_1836)) = hAPP(U_1835,U_1836) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).

fof(f_357_2,plain,
    ! [U_1840,U_1839,U_1838,U_1837] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1837,tc_HOL_Obool)),U_1839),hAPP(hAPP(c_Set_Oinsert(U_1837),U_1838),U_1840)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1837,tc_HOL_Obool)),U_1839),U_1840)
        | hBOOL(hAPP(hAPP(c_member(U_1837),U_1838),U_1839)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1837,tc_HOL_Obool)),U_1839),hAPP(hAPP(c_Set_Oinsert(U_1837),U_1838),U_1840)) = hAPP(hAPP(c_Set_Oinsert(U_1837),U_1838),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1837,tc_HOL_Obool)),U_1839),U_1840))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1837),U_1838),U_1839)) ) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ( ! [U_1848,U_1846,U_1844,U_1842] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1842,tc_HOL_Obool)),U_1846),hAPP(hAPP(c_Set_Oinsert(U_1842),U_1844),U_1848)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1842,tc_HOL_Obool)),U_1846),U_1848)
        | hBOOL(hAPP(hAPP(c_member(U_1842),U_1844),U_1846)) )
    & ! [U_1847,U_1845,U_1843,U_1841] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1841,tc_HOL_Obool)),U_1845),hAPP(hAPP(c_Set_Oinsert(U_1841),U_1843),U_1847)) = hAPP(hAPP(c_Set_Oinsert(U_1841),U_1843),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1841,tc_HOL_Obool)),U_1845),U_1847))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1841),U_1843),U_1845)) ) ),
    inference(miniscope,[status(thm)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1841,tc_HOL_Obool)),U_1845),hAPP(hAPP(c_Set_Oinsert(U_1841),U_1843),U_1847)) = hAPP(hAPP(c_Set_Oinsert(U_1841),U_1843),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1841,tc_HOL_Obool)),U_1845),U_1847))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1841),U_1843),U_1845)) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

cnf(f_357_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1842,tc_HOL_Obool)),U_1846),hAPP(hAPP(c_Set_Oinsert(U_1842),U_1844),U_1848)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1842,tc_HOL_Obool)),U_1846),U_1848)
    | hBOOL(hAPP(hAPP(c_member(U_1842),U_1844),U_1846)) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).

fof(f_358_2,plain,
    ! [U_1852,U_1851,U_1850,U_1849] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1849,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1849),U_1850),U_1852)),U_1851) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1849,tc_HOL_Obool)),U_1852),U_1851)
        | hBOOL(hAPP(hAPP(c_member(U_1849),U_1850),U_1851)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1849,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1849),U_1850),U_1852)),U_1851) = hAPP(hAPP(c_Set_Oinsert(U_1849),U_1850),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1849,tc_HOL_Obool)),U_1852),U_1851))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1849),U_1850),U_1851)) ) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ( ! [U_1860,U_1858,U_1856,U_1854] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1854,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1854),U_1856),U_1860)),U_1858) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1854,tc_HOL_Obool)),U_1860),U_1858)
        | hBOOL(hAPP(hAPP(c_member(U_1854),U_1856),U_1858)) )
    & ! [U_1859,U_1857,U_1855,U_1853] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1853,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1853),U_1855),U_1859)),U_1857) = hAPP(hAPP(c_Set_Oinsert(U_1853),U_1855),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1853,tc_HOL_Obool)),U_1859),U_1857))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1853),U_1855),U_1857)) ) ),
    inference(miniscope,[status(thm)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1853,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1853),U_1855),U_1859)),U_1857) = hAPP(hAPP(c_Set_Oinsert(U_1853),U_1855),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1853,tc_HOL_Obool)),U_1859),U_1857))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1853),U_1855),U_1857)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1854,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1854),U_1856),U_1860)),U_1858) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1854,tc_HOL_Obool)),U_1860),U_1858)
    | hBOOL(hAPP(hAPP(c_member(U_1854),U_1856),U_1858)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(f_359_2,plain,
    ! [U_1864,U_1863,U_1862,U_1861] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1861,tc_HOL_Obool)),U_1863),hAPP(hAPP(c_Set_Oinsert(U_1861),U_1862),U_1864)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1861,tc_HOL_Obool)),U_1863),U_1864)
      | hBOOL(hAPP(hAPP(c_member(U_1861),U_1862),U_1863)) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

cnf(f_359_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1861,tc_HOL_Obool)),U_1863),hAPP(hAPP(c_Set_Oinsert(U_1861),U_1862),U_1864)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1861,tc_HOL_Obool)),U_1863),U_1864)
    | hBOOL(hAPP(hAPP(c_member(U_1861),U_1862),U_1863)) ),
    inference(clausify,[status(thm)],[f_359_2]) ).

fof(f_360_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(f_360_2,plain,
    ! [U_1868,U_1867,U_1866,U_1865] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1865,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1865),U_1866),U_1868)),U_1867) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1865,tc_HOL_Obool)),U_1868),U_1867)
      | hBOOL(hAPP(hAPP(c_member(U_1865),U_1866),U_1867)) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1865,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1865),U_1866),U_1868)),U_1867) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1865,tc_HOL_Obool)),U_1868),U_1867)
    | hBOOL(hAPP(hAPP(c_member(U_1865),U_1866),U_1867)) ),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).

fof(f_361_2,plain,
    ! [U_1872,U_1871,U_1870,U_1869] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1869,tc_HOL_Obool)),U_1871),hAPP(hAPP(c_Set_Oinsert(U_1869),U_1870),U_1872)) = hAPP(hAPP(c_Set_Oinsert(U_1869),U_1870),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1869,tc_HOL_Obool)),U_1871),U_1872))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1869),U_1870),U_1871)) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1869,tc_HOL_Obool)),U_1871),hAPP(hAPP(c_Set_Oinsert(U_1869),U_1870),U_1872)) = hAPP(hAPP(c_Set_Oinsert(U_1869),U_1870),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1869,tc_HOL_Obool)),U_1871),U_1872))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1869),U_1870),U_1871)) ),
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).

fof(f_362_2,plain,
    ! [U_1876,U_1875,U_1874,U_1873] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1873),U_1874),U_1876)),U_1875) = hAPP(hAPP(c_Set_Oinsert(U_1873),U_1874),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1873,tc_HOL_Obool)),U_1876),U_1875))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1873),U_1874),U_1875)) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1873),U_1874),U_1876)),U_1875) = hAPP(hAPP(c_Set_Oinsert(U_1873),U_1874),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1873,tc_HOL_Obool)),U_1876),U_1875))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1873),U_1874),U_1875)) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).

fof(f_363_2,plain,
    ! [U_1879,U_1878,U_1877] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1877,tc_HOL_Obool)),U_1878),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1877,tc_HOL_Obool)),U_1879),U_1878)) = c_Orderings_Obot__class_Obot(tc_fun(U_1877,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

cnf(f_363_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1877,tc_HOL_Obool)),U_1878),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1877,tc_HOL_Obool)),U_1879),U_1878)) = c_Orderings_Obot__class_Obot(tc_fun(U_1877,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_363_2]) ).

fof(f_364_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).

fof(f_364_2,plain,
    ! [U_1882,U_1881,U_1880] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1880,tc_HOL_Obool)),U_1881),U_1882) = U_1881
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1880,tc_HOL_Obool)),U_1881),U_1882) != c_Orderings_Obot__class_Obot(tc_fun(U_1880,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1880,tc_HOL_Obool)),U_1881),U_1882) = U_1881
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1880,tc_HOL_Obool)),U_1881),U_1882) != c_Orderings_Obot__class_Obot(tc_fun(U_1880,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_1,plain,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2
      | ~ c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).

fof(f_365_2,plain,
    ! [U_1888,U_1887,U_1886,U_1885,U_1884,U_1883] :
      ( hAPP(U_1888,c_Orderings_Obot__class_Obot(tc_fun(U_1884,tc_HOL_Obool))) = U_1886
      | ~ c_Finite__Set_Ofolding__image__simple(U_1883,U_1884,U_1885,U_1886,U_1887,U_1888) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1888,U_1887,U_1886,U_1885,U_1884] :
      ( ! [U_1883] : ~ c_Finite__Set_Ofolding__image__simple(U_1883,U_1884,U_1885,U_1886,U_1887,U_1888)
      | hAPP(U_1888,c_Orderings_Obot__class_Obot(tc_fun(U_1884,tc_HOL_Obool))) = U_1886 ),
    inference(miniscope,[status(thm)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1883,U_1884,U_1885,U_1886,U_1887,U_1888)
    | hAPP(U_1888,c_Orderings_Obot__class_Obot(tc_fun(U_1884,tc_HOL_Obool))) = U_1886 ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).

fof(f_366_2,plain,
    ! [U_1892,U_1891,U_1890,U_1889] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1889,tc_HOL_Obool)),U_1891),U_1892)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1889,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),U_1891)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),U_1892)),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1889,tc_HOL_Obool)),U_1891),U_1892)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1889,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),U_1891)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1889,tc_HOL_Obool)),U_1890),U_1892)),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).

fof(f_367_2,plain,
    ! [U_1896,U_1895,U_1894,U_1893] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1893,tc_HOL_Obool)),U_1895),U_1896)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1893,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),U_1895)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),U_1896)),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1893,tc_HOL_Obool)),U_1895),U_1896)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1893,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),U_1895)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1893,tc_HOL_Obool)),U_1894),U_1896)),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).

fof(f_368_2,plain,
    ! [U_1899,U_1898,U_1897] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1897,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1897,tc_HOL_Obool)),U_1898),U_1899)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1897,tc_HOL_Obool)),U_1898),U_1899)) = U_1898,
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1897,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1897,tc_HOL_Obool)),U_1898),U_1899)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1897,tc_HOL_Obool)),U_1898),U_1899)) = U_1898,
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).

fof(f_369_2,plain,
    ! [U_1902,U_1901,U_1900] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1900),U_1902),c_Big__Operators_Olattice__class_OSup__fin(U_1900,U_1901)) = U_1902
      | ~ hBOOL(hAPP(hAPP(c_member(U_1900),U_1902),U_1901))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1900),U_1901))
      | ~ class_Lattices_Olattice(U_1900) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1900),U_1902),c_Big__Operators_Olattice__class_OSup__fin(U_1900,U_1901)) = U_1902
    | ~ hBOOL(hAPP(hAPP(c_member(U_1900),U_1902),U_1901))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1900),U_1901))
    | ~ class_Lattices_Olattice(U_1900) ),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_a,T_b,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_370_2,plain,
    ! [U_1909,U_1908,U_1907,U_1906,U_1905,U_1904,U_1903] :
      ( hAPP(U_1908,U_1909) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1903,U_1904,U_1905),U_1907),U_1906),U_1909)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1904),U_1909))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1903,U_1904,U_1905,U_1906,U_1907,U_1908) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    ( hAPP(U_1908,U_1909) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_1903,U_1904,U_1905),U_1907),U_1906),U_1909)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1904),U_1909))
    | ~ c_Finite__Set_Ofolding__image__simple(U_1903,U_1904,U_1905,U_1906,U_1907,U_1908) ),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter]) ).

fof(f_371_2,plain,
    ! [U_1915,U_1914,U_1913,U_1912,U_1911,U_1910] :
      ( hAPP(c_Fun_Ocomp(U_1911,U_1911,U_1911,hAPP(U_1913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1910,tc_HOL_Obool)),U_1914),U_1915))),hAPP(U_1913,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1910,tc_HOL_Obool)),U_1914),U_1915))) = hAPP(c_Fun_Ocomp(U_1911,U_1911,U_1911,hAPP(U_1913,U_1914)),hAPP(U_1913,U_1915))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1910),U_1915))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1910),U_1914))
      | ~ c_Finite__Set_Ofolding(U_1910,U_1911,U_1912,U_1913) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    ( hAPP(c_Fun_Ocomp(U_1911,U_1911,U_1911,hAPP(U_1913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1910,tc_HOL_Obool)),U_1914),U_1915))),hAPP(U_1913,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1910,tc_HOL_Obool)),U_1914),U_1915))) = hAPP(c_Fun_Ocomp(U_1911,U_1911,U_1911,hAPP(U_1913,U_1914)),hAPP(U_1913,U_1915))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1910),U_1915))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1910),U_1914))
    | ~ c_Finite__Set_Ofolding(U_1910,U_1911,U_1912,U_1913) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).

fof(f_372_2,plain,
    ! [U_1920,U_1919,U_1918,U_1917,U_1916] :
      ( hAPP(U_1918,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1916,tc_HOL_Obool)),U_1919),U_1920)) = hAPP(hAPP(U_1917,hAPP(U_1918,U_1919)),hAPP(U_1918,U_1920))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1916,tc_HOL_Obool)),U_1919),U_1920) != c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
      | U_1920 = c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1916),U_1920))
      | U_1919 = c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1916),U_1919))
      | ~ c_Finite__Set_Ofolding__one(U_1916,U_1917,U_1918) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    ( hAPP(U_1918,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1916,tc_HOL_Obool)),U_1919),U_1920)) = hAPP(hAPP(U_1917,hAPP(U_1918,U_1919)),hAPP(U_1918,U_1920))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1916,tc_HOL_Obool)),U_1919),U_1920) != c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
    | U_1920 = c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1916),U_1920))
    | U_1919 = c_Orderings_Obot__class_Obot(tc_fun(U_1916,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1916),U_1919))
    | ~ c_Finite__Set_Ofolding__one(U_1916,U_1917,U_1918) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).

fof(f_373_2,plain,
    ! [U_1925,U_1924,U_1923,U_1922,U_1921] :
      ( hAPP(hAPP(U_1922,hAPP(U_1923,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925))),hAPP(U_1923,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925))) = hAPP(hAPP(U_1922,hAPP(U_1923,U_1924)),hAPP(U_1923,U_1925))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925) = c_Orderings_Obot__class_Obot(tc_fun(U_1921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1921),U_1925))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1921),U_1924))
      | ~ c_Finite__Set_Ofolding__one(U_1921,U_1922,U_1923) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

cnf(f_373_3,plain,
    ( hAPP(hAPP(U_1922,hAPP(U_1923,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925))),hAPP(U_1923,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925))) = hAPP(hAPP(U_1922,hAPP(U_1923,U_1924)),hAPP(U_1923,U_1925))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1921,tc_HOL_Obool)),U_1924),U_1925) = c_Orderings_Obot__class_Obot(tc_fun(U_1921,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1921),U_1925))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1921),U_1924))
    | ~ c_Finite__Set_Ofolding__one(U_1921,U_1922,U_1923) ),
    inference(clausify,[status(thm)],[f_373_2]) ).

fof(f_374_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).

fof(f_374_2,plain,
    ! [U_1928,U_1927,U_1926] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1926,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1926,tc_HOL_Obool)),U_1927),U_1928)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1926),c_Big__Operators_Olattice__class_OSup__fin(U_1926,U_1927)),c_Big__Operators_Olattice__class_OSup__fin(U_1926,U_1928))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1926,tc_HOL_Obool)),U_1927),U_1928) != c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
      | U_1928 = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1926),U_1928))
      | U_1927 = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1926),U_1927))
      | ~ class_Lattices_Olattice(U_1926) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

cnf(f_374_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1926,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1926,tc_HOL_Obool)),U_1927),U_1928)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1926),c_Big__Operators_Olattice__class_OSup__fin(U_1926,U_1927)),c_Big__Operators_Olattice__class_OSup__fin(U_1926,U_1928))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1926,tc_HOL_Obool)),U_1927),U_1928) != c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
    | U_1928 = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1926),U_1928))
    | U_1927 = c_Orderings_Obot__class_Obot(tc_fun(U_1926,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1926),U_1927))
    | ~ class_Lattices_Olattice(U_1926) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

fof(f_375_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).

fof(f_375_2,plain,
    ! [U_1931,U_1930,U_1929] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1929),c_Big__Operators_Olattice__class_OSup__fin(U_1929,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931))),c_Big__Operators_Olattice__class_OSup__fin(U_1929,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1929),c_Big__Operators_Olattice__class_OSup__fin(U_1929,U_1930)),c_Big__Operators_Olattice__class_OSup__fin(U_1929,U_1931))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931) = c_Orderings_Obot__class_Obot(tc_fun(U_1929,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1929),U_1931))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1929),U_1930))
      | ~ class_Lattices_Olattice(U_1929) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

cnf(f_375_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1929),c_Big__Operators_Olattice__class_OSup__fin(U_1929,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931))),c_Big__Operators_Olattice__class_OSup__fin(U_1929,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1929),c_Big__Operators_Olattice__class_OSup__fin(U_1929,U_1930)),c_Big__Operators_Olattice__class_OSup__fin(U_1929,U_1931))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931) = c_Orderings_Obot__class_Obot(tc_fun(U_1929,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1929),U_1931))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1929),U_1930))
    | ~ class_Lattices_Olattice(U_1929) ),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).

fof(f_376_2,plain,
    ! [U_1934,U_1933,U_1932] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_1932,U_1933) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1932),U_1934),c_Big__Operators_Olattice__class_OInf__fin(U_1932,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_1932,U_1933) = U_1934
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1932),U_1934),U_1933))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1932),U_1933))
      | ~ class_Lattices_Olattice(U_1932) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

cnf(f_376_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1932,U_1933) = U_1934
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1932),U_1934),U_1933))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1932),U_1933))
    | ~ class_Lattices_Olattice(U_1932) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

cnf(f_376_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1932,U_1933) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1932),U_1934),c_Big__Operators_Olattice__class_OInf__fin(U_1932,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1932,tc_HOL_Obool)),U_1933),hAPP(hAPP(c_Set_Oinsert(U_1932),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1932,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1932),U_1934),U_1933))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1932),U_1933))
    | ~ class_Lattices_Olattice(U_1932) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

fof(f_377_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).

fof(f_377_2,plain,
    ! [U_1939,U_1938,U_1937,U_1936,U_1935] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1936,U_1935),U_1939),U_1937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1935),hAPP(U_1939,U_1938)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1936,U_1935),U_1939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1936,tc_HOL_Obool)),U_1937),hAPP(hAPP(c_Set_Oinsert(U_1936),U_1938),c_Orderings_Obot__class_Obot(tc_fun(U_1936,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1936),U_1938),U_1937))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1936),U_1937))
      | ~ class_Groups_Ocomm__monoid__add(U_1935) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1936,U_1935),U_1939),U_1937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1935),hAPP(U_1939,U_1938)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1936,U_1935),U_1939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1936,tc_HOL_Obool)),U_1937),hAPP(hAPP(c_Set_Oinsert(U_1936),U_1938),c_Orderings_Obot__class_Obot(tc_fun(U_1936,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1936),U_1938),U_1937))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1936),U_1937))
    | ~ class_Groups_Ocomm__monoid__add(U_1935) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).

fof(f_378_2,plain,
    ! [U_1944,U_1943,U_1942,U_1941,U_1940] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1941,U_1940),U_1944),U_1942) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),hAPP(U_1944,U_1943)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1941,U_1940),U_1944),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1941,tc_HOL_Obool)),U_1942),hAPP(hAPP(c_Set_Oinsert(U_1941),U_1943),c_Orderings_Obot__class_Obot(tc_fun(U_1941,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1941),U_1943),U_1942))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1941),U_1942))
      | ~ class_Groups_Ocomm__monoid__add(U_1940) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1941,U_1940),U_1944),U_1942) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),hAPP(U_1944,U_1943)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1941,U_1940),U_1944),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1941,tc_HOL_Obool)),U_1942),hAPP(hAPP(c_Set_Oinsert(U_1941),U_1943),c_Orderings_Obot__class_Obot(tc_fun(U_1941,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1941),U_1943),U_1942))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1941),U_1942))
    | ~ class_Groups_Ocomm__monoid__add(U_1940) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).

fof(f_379_2,plain,
    ! [U_1947,U_1946,U_1945] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_1945,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1945),c_Big__Operators_Olattice__class_OInf__fin(U_1945,U_1946)),c_Big__Operators_Olattice__class_OInf__fin(U_1945,U_1947))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947) != c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
      | U_1947 = c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1945),U_1947))
      | U_1946 = c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1945),U_1946))
      | ~ class_Lattices_Olattice(U_1945) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1945,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1945),c_Big__Operators_Olattice__class_OInf__fin(U_1945,U_1946)),c_Big__Operators_Olattice__class_OInf__fin(U_1945,U_1947))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947) != c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
    | U_1947 = c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1945),U_1947))
    | U_1946 = c_Orderings_Obot__class_Obot(tc_fun(U_1945,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1945),U_1946))
    | ~ class_Lattices_Olattice(U_1945) ),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).

fof(f_380_2,plain,
    ! [U_1950,U_1949,U_1948] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1948),c_Big__Operators_Olattice__class_OInf__fin(U_1948,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950))),c_Big__Operators_Olattice__class_OInf__fin(U_1948,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1948),c_Big__Operators_Olattice__class_OInf__fin(U_1948,U_1949)),c_Big__Operators_Olattice__class_OInf__fin(U_1948,U_1950))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950) = c_Orderings_Obot__class_Obot(tc_fun(U_1948,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1948),U_1950))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1948),U_1949))
      | ~ class_Lattices_Olattice(U_1948) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1948),c_Big__Operators_Olattice__class_OInf__fin(U_1948,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950))),c_Big__Operators_Olattice__class_OInf__fin(U_1948,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1948),c_Big__Operators_Olattice__class_OInf__fin(U_1948,U_1949)),c_Big__Operators_Olattice__class_OInf__fin(U_1948,U_1950))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1948,tc_HOL_Obool)),U_1949),U_1950) = c_Orderings_Obot__class_Obot(tc_fun(U_1948,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1948),U_1950))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1948),U_1949))
    | ~ class_Lattices_Olattice(U_1948) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).

fof(f_381_2,plain,
    ! [U_1953,U_1952,U_1951] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),U_1952)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1951),U_1953),c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),U_1952)) = U_1953
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1951),U_1952))
      | ~ class_Lattices_Olattice(U_1951) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),U_1952)) = U_1953
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1951),U_1952))
    | ~ class_Lattices_Olattice(U_1951) ),
    inference(clausify,[status(thm)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),U_1952)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1951),U_1953),c_Big__Operators_Olattice__class_OInf__fin(U_1951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1951,tc_HOL_Obool)),U_1952),hAPP(hAPP(c_Set_Oinsert(U_1951),U_1953),c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1951,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1951),U_1952))
    | ~ class_Lattices_Olattice(U_1951) ),
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(f_382_2,plain,
    ! [U_1956,U_1955,U_1954] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_1954,hAPP(hAPP(c_Set_Oinsert(U_1954),U_1956),U_1955)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1954),U_1956),c_Big__Operators_Olattice__class_OInf__fin(U_1954,U_1955))
      | U_1955 = c_Orderings_Obot__class_Obot(tc_fun(U_1954,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_1954),U_1956),U_1955))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1954),U_1955))
      | ~ class_Lattices_Olattice(U_1954) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1954,hAPP(hAPP(c_Set_Oinsert(U_1954),U_1956),U_1955)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1954),U_1956),c_Big__Operators_Olattice__class_OInf__fin(U_1954,U_1955))
    | U_1955 = c_Orderings_Obot__class_Obot(tc_fun(U_1954,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_1954),U_1956),U_1955))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1954),U_1955))
    | ~ class_Lattices_Olattice(U_1954) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != V_z_2
          & 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))
      | ~ c_Finite__Set_Ofolding__image__simple(T_a,T_b,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_383_2,plain,
    ! [U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959,U_1958] :
      ( hAPP(U_1963,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)) = hAPP(hAPP(U_1960,hAPP(U_1963,U_1964)),hAPP(U_1963,U_1965))
      | ? [U_1957] :
          ( hAPP(U_1962,U_1957) != U_1961
          & hBOOL(hAPP(hAPP(c_member(U_1959),U_1957),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1964))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1958,U_1959,U_1960,U_1961,U_1962,U_1963) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959] :
      ( ! [U_1958] : ~ c_Finite__Set_Ofolding__image__simple(U_1958,U_1959,U_1960,U_1961,U_1962,U_1963)
      | hAPP(U_1963,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)) = hAPP(hAPP(U_1960,hAPP(U_1963,U_1964)),hAPP(U_1963,U_1965))
      | ? [U_1957] :
          ( hAPP(U_1962,U_1957) != U_1961
          & hBOOL(hAPP(hAPP(c_member(U_1959),U_1957),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1964)) ),
    inference(miniscope,[status(thm)],[f_383_2]) ).

fof(f_383_4,plain,
    ! [U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959] :
      ( ! [U_1958] : ~ c_Finite__Set_Ofolding__image__simple(U_1958,U_1959,U_1960,U_1961,U_1962,U_1963)
      | hAPP(U_1963,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)) = hAPP(hAPP(U_1960,hAPP(U_1963,U_1964)),hAPP(U_1963,U_1965))
      | ( hAPP(U_1962,sK36(U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)) != U_1961
        & hBOOL(hAPP(hAPP(c_member(U_1959),sK36(U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1964)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1957,sK36(U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959))],[f_383_3]) ).

cnf(f_383_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1959),sK36(U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)))
    | hAPP(U_1963,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)) = hAPP(hAPP(U_1960,hAPP(U_1963,U_1964)),hAPP(U_1963,U_1965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1964))
    | ~ c_Finite__Set_Ofolding__image__simple(U_1958,U_1959,U_1960,U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_383_4]) ).

cnf(f_383_6,plain,
    ( hAPP(U_1962,sK36(U_1965,U_1964,U_1963,U_1962,U_1961,U_1960,U_1959)) != U_1961
    | hAPP(U_1963,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1959,tc_HOL_Obool)),U_1964),U_1965)) = hAPP(hAPP(U_1960,hAPP(U_1963,U_1964)),hAPP(U_1963,U_1965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1959),U_1964))
    | ~ c_Finite__Set_Ofolding__image__simple(U_1958,U_1959,U_1960,U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_383_4]) ).

fof(f_384_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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))
      | ~ 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__image__simple__idem(T_a,T_b,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_384_2,plain,
    ! [U_1973,U_1972,U_1971,U_1970,U_1969,U_1968,U_1967,U_1966] :
      ( hAPP(U_1971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1967,tc_HOL_Obool)),U_1972),U_1973)) = hAPP(hAPP(U_1968,hAPP(U_1971,U_1972)),hAPP(U_1971,U_1973))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1973))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1972))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1966,U_1967,U_1968,U_1969,U_1970,U_1971) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1973,U_1972,U_1971,U_1970,U_1969,U_1968,U_1967] :
      ( ! [U_1966] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1966,U_1967,U_1968,U_1969,U_1970,U_1971)
      | hAPP(U_1971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1967,tc_HOL_Obool)),U_1972),U_1973)) = hAPP(hAPP(U_1968,hAPP(U_1971,U_1972)),hAPP(U_1971,U_1973))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1973))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1972)) ),
    inference(miniscope,[status(thm)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1966,U_1967,U_1968,U_1969,U_1970,U_1971)
    | hAPP(U_1971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1967,tc_HOL_Obool)),U_1972),U_1973)) = hAPP(hAPP(U_1968,hAPP(U_1971,U_1972)),hAPP(U_1971,U_1973))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1973))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1967),U_1972)) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(f_385_2,plain,
    ! [U_1976,U_1975,U_1974] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1974,hAPP(hAPP(c_Set_Oinsert(U_1974),U_1976),U_1975)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1974,U_1974,c_Lattices_Osemilattice__sup__class_Osup(U_1974)),U_1976),U_1975)
      | hBOOL(hAPP(hAPP(c_member(U_1974),U_1976),U_1975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1974),U_1975))
      | ~ class_Lattices_Olattice(U_1974) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

cnf(f_385_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1974,hAPP(hAPP(c_Set_Oinsert(U_1974),U_1976),U_1975)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1974,U_1974,c_Lattices_Osemilattice__sup__class_Osup(U_1974)),U_1976),U_1975)
    | hBOOL(hAPP(hAPP(c_member(U_1974),U_1976),U_1975))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1974),U_1975))
    | ~ class_Lattices_Olattice(U_1974) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

fof(f_386_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).

fof(f_386_2,plain,
    ! [U_1981,U_1980,U_1979,U_1978,U_1977] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1978,tc_HOL_Obool)),U_1979),U_1980)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1977),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),U_1979)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),U_1980))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1978,tc_HOL_Obool)),U_1979),U_1980)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1978),U_1980))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1978),U_1979))
      | ~ class_Groups_Oab__group__add(U_1977) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1978,tc_HOL_Obool)),U_1979),U_1980)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1977),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),U_1979)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),U_1980))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1978,U_1977),U_1981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1978,tc_HOL_Obool)),U_1979),U_1980)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1978),U_1980))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1978),U_1979))
    | ~ class_Groups_Oab__group__add(U_1977) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,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_387_2,plain,
    ! [U_1988,U_1987,U_1986,U_1985,U_1984,U_1983,U_1982] :
      ( hAPP(hAPP(U_1984,U_1988),U_1988) = U_1988
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1982,U_1983,U_1984,U_1985,U_1986,U_1987) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1988,U_1987,U_1986,U_1985,U_1984] :
      ( ! [U_1983,U_1982] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1982,U_1983,U_1984,U_1985,U_1986,U_1987)
      | hAPP(hAPP(U_1984,U_1988),U_1988) = U_1988 ),
    inference(miniscope,[status(thm)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1982,U_1983,U_1984,U_1985,U_1986,U_1987)
    | hAPP(hAPP(U_1984,U_1988),U_1988) = U_1988 ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,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__empty]) ).

fof(f_388_2,plain,
    ! [U_1992,U_1991,U_1990,U_1989] : hAPP(hAPP(c_Finite__Set_Ofold(U_1989,U_1990,U_1991),U_1992),c_Orderings_Obot__class_Obot(tc_fun(U_1989,tc_HOL_Obool))) = U_1992,
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_1989,U_1990,U_1991),U_1992),c_Orderings_Obot__class_Obot(tc_fun(U_1989,tc_HOL_Obool))) = U_1992,
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).

fof(f_389_2,plain,
    ! [U_1997,U_1996,U_1995,U_1994,U_1993] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),hAPP(hAPP(c_COMBS(U_1994,U_1993,U_1993),hAPP(hAPP(c_COMBB(U_1993,tc_fun(U_1993,U_1993),U_1994),c_Groups_Oplus__class_Oplus(U_1993)),U_1995)),U_1996)),U_1997) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),U_1995),U_1997)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),U_1996),U_1997))
      | ~ class_Groups_Ocomm__monoid__add(U_1993) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

cnf(f_389_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),hAPP(hAPP(c_COMBS(U_1994,U_1993,U_1993),hAPP(hAPP(c_COMBB(U_1993,tc_fun(U_1993,U_1993),U_1994),c_Groups_Oplus__class_Oplus(U_1993)),U_1995)),U_1996)),U_1997) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),U_1995),U_1997)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1994,U_1993),U_1996),U_1997))
    | ~ class_Groups_Ocomm__monoid__add(U_1993) ),
    inference(clausify,[status(thm)],[f_389_2]) ).

fof(f_390_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).

fof(f_390_2,plain,
    ! [U_2000,U_1999,U_1998] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_1998,hAPP(hAPP(c_Set_Oinsert(U_1998),U_2000),U_1999)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1998,U_1998,c_Lattices_Osemilattice__inf__class_Oinf(U_1998)),U_2000),U_1999)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1998),U_1999))
      | ~ class_Lattices_Olattice(U_1998) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1998,hAPP(hAPP(c_Set_Oinsert(U_1998),U_2000),U_1999)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1998,U_1998,c_Lattices_Osemilattice__inf__class_Oinf(U_1998)),U_2000),U_1999)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1998),U_1999))
    | ~ class_Lattices_Olattice(U_1998) ),
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_1,plain,
    ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).

fof(f_391_2,plain,
    ! [U_2004,U_2003,U_2002,U_2001] : hAPP(c_Finite__Set_Ofold__image(U_2001,U_2002,U_2003),U_2004) = c_Finite__Set_Ofold(U_2002,U_2001,hAPP(hAPP(c_COMBB(U_2001,tc_fun(U_2001,U_2001),U_2002),U_2003),U_2004)),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    hAPP(c_Finite__Set_Ofold__image(U_2001,U_2002,U_2003),U_2004) = c_Finite__Set_Ofold(U_2002,U_2001,hAPP(hAPP(c_COMBB(U_2001,tc_fun(U_2001,U_2001),U_2002),U_2003),U_2004)),
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(f_392_2,plain,
    ! [U_2007,U_2006,U_2005] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2005,hAPP(hAPP(c_Set_Oinsert(U_2005),U_2007),U_2006)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2005,U_2005,c_Lattices_Osemilattice__inf__class_Oinf(U_2005)),U_2007),U_2006)
      | hBOOL(hAPP(hAPP(c_member(U_2005),U_2007),U_2006))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
      | ~ class_Lattices_Olattice(U_2005) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

cnf(f_392_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2005,hAPP(hAPP(c_Set_Oinsert(U_2005),U_2007),U_2006)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2005,U_2005,c_Lattices_Osemilattice__inf__class_Oinf(U_2005)),U_2007),U_2006)
    | hBOOL(hAPP(hAPP(c_member(U_2005),U_2007),U_2006))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
    | ~ class_Lattices_Olattice(U_2005) ),
    inference(clausify,[status(thm)],[f_392_2]) ).

fof(f_393_1,plain,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold]) ).

fof(f_393_2,plain,
    ! [U_2013,U_2012,U_2011,U_2010,U_2009,U_2008] :
      ( hAPP(hAPP(U_2011,U_2012),U_2013) = hAPP(hAPP(c_Finite__Set_Ofold(U_2008,U_2009,U_2010),U_2013),U_2012)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2008),U_2012))
      | ~ c_Finite__Set_Ofolding(U_2008,U_2009,U_2010,U_2011) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( hAPP(hAPP(U_2011,U_2012),U_2013) = hAPP(hAPP(c_Finite__Set_Ofold(U_2008,U_2009,U_2010),U_2013),U_2012)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2008),U_2012))
    | ~ c_Finite__Set_Ofolding(U_2008,U_2009,U_2010,U_2011) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).

fof(f_394_2,plain,
    ! [U_2015,U_2014] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2014,hAPP(hAPP(c_Set_Oinsert(U_2014),U_2015),c_Orderings_Obot__class_Obot(tc_fun(U_2014,tc_HOL_Obool)))) = U_2015
      | ~ class_Lattices_Olattice(U_2014) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

cnf(f_394_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2014,hAPP(hAPP(c_Set_Oinsert(U_2014),U_2015),c_Orderings_Obot__class_Obot(tc_fun(U_2014,tc_HOL_Obool)))) = U_2015
    | ~ class_Lattices_Olattice(U_2014) ),
    inference(clausify,[status(thm)],[f_394_2]) ).

fof(f_395_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).

fof(f_395_2,plain,
    ! [U_2020,U_2019,U_2018,U_2017,U_2016] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),hAPP(hAPP(c_COMBS(U_2017,U_2016,U_2016),hAPP(hAPP(c_COMBB(U_2016,tc_fun(U_2016,U_2016),U_2017),c_Groups_Oplus__class_Oplus(U_2016)),U_2019)),U_2020)),U_2018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),U_2019),U_2018)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),U_2020),U_2018))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2017),U_2018))
      | ~ class_Groups_Ocomm__monoid__add(U_2016) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),hAPP(hAPP(c_COMBS(U_2017,U_2016,U_2016),hAPP(hAPP(c_COMBB(U_2016,tc_fun(U_2016,U_2016),U_2017),c_Groups_Oplus__class_Oplus(U_2016)),U_2019)),U_2020)),U_2018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),U_2019),U_2018)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2017,U_2016),U_2020),U_2018))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2017),U_2018))
    | ~ class_Groups_Ocomm__monoid__add(U_2016) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).

fof(f_396_2,plain,
    ! [U_2023,U_2022,U_2021] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2021,tc_HOL_Obool)),U_2022),U_2023) = hAPP(hAPP(c_Finite__Set_Ofold(U_2021,tc_fun(U_2021,tc_HOL_Obool),c_Set_Oinsert(U_2021)),U_2023),U_2022)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2021),U_2022)) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2021,tc_HOL_Obool)),U_2022),U_2023) = hAPP(hAPP(c_Finite__Set_Ofold(U_2021,tc_fun(U_2021,tc_HOL_Obool),c_Set_Oinsert(U_2021)),U_2023),U_2022)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2021),U_2022)) ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).

fof(f_397_2,plain,
    ! [U_2027,U_2026,U_2025,U_2024] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2024,U_2024,c_Lattices_Osemilattice__sup__class_Osup(U_2024)),U_2026),hAPP(hAPP(c_Set_Oinsert(U_2024),U_2027),U_2025)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2024),U_2027),hAPP(hAPP(c_Finite__Set_Ofold(U_2024,U_2024,c_Lattices_Osemilattice__sup__class_Osup(U_2024)),U_2026),U_2025))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2024),U_2025))
      | ~ class_Lattices_Osemilattice__sup(U_2024) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

cnf(f_397_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2024,U_2024,c_Lattices_Osemilattice__sup__class_Osup(U_2024)),U_2026),hAPP(hAPP(c_Set_Oinsert(U_2024),U_2027),U_2025)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2024),U_2027),hAPP(hAPP(c_Finite__Set_Ofold(U_2024,U_2024,c_Lattices_Osemilattice__sup__class_Osup(U_2024)),U_2026),U_2025))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2024),U_2025))
    | ~ class_Lattices_Osemilattice__sup(U_2024) ),
    inference(clausify,[status(thm)],[f_397_2]) ).

fof(f_398_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).

fof(f_398_2,plain,
    ! [U_2031,U_2030,U_2029,U_2028] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),hAPP(hAPP(c_Set_Oinsert(U_2028),U_2031),U_2029)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2028),U_2031),hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),U_2029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2028),U_2029))
      | ~ class_Lattices_Osemilattice__inf(U_2028) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),hAPP(hAPP(c_Set_Oinsert(U_2028),U_2031),U_2029)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2028),U_2031),hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),U_2029))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2028),U_2029))
    | ~ class_Lattices_Osemilattice__inf(U_2028) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).

fof(f_399_2,plain,
    ! [U_2035,U_2034,U_2033,U_2032] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2032,tc_HOL_Obool)),U_2033),U_2034)) = 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_2032,tc_Nat_Onat),U_2035),U_2033)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),U_2034))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2032,tc_HOL_Obool)),U_2033),U_2034)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2034))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033)) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2032,tc_HOL_Obool)),U_2033),U_2034)) = 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_2032,tc_Nat_Onat),U_2035),U_2033)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),U_2034))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,tc_Nat_Onat),U_2035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2032,tc_HOL_Obool)),U_2033),U_2034)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2034))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033)) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).

fof(f_400_2,plain,
    ! [U_2041,U_2040,U_2039,U_2038,U_2037,U_2036] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2036,U_2037,U_2038),U_2040),hAPP(hAPP(c_Set_Oinsert(U_2036),U_2041),U_2039)) = hAPP(hAPP(U_2038,U_2041),hAPP(hAPP(c_Finite__Set_Ofold(U_2036,U_2037,U_2038),U_2040),U_2039))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2036),U_2039))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_2036,U_2037,U_2038) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2036,U_2037,U_2038),U_2040),hAPP(hAPP(c_Set_Oinsert(U_2036),U_2041),U_2039)) = hAPP(hAPP(U_2038,U_2041),hAPP(hAPP(c_Finite__Set_Ofold(U_2036,U_2037,U_2038),U_2040),U_2039))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2036),U_2039))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_2036,U_2037,U_2038) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).

fof(f_401_2,plain,
    ! [U_2047,U_2046,U_2045,U_2044,U_2043,U_2042] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2042,U_2043,U_2044),U_2046),hAPP(hAPP(c_Set_Oinsert(U_2042),U_2047),U_2045)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2042,U_2043,U_2044),hAPP(hAPP(U_2044,U_2047),U_2046)),U_2045)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2045))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_2042,U_2043,U_2044) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

cnf(f_401_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2042,U_2043,U_2044),U_2046),hAPP(hAPP(c_Set_Oinsert(U_2042),U_2047),U_2045)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2042,U_2043,U_2044),hAPP(hAPP(U_2044,U_2047),U_2046)),U_2045)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2045))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_2042,U_2043,U_2044) ),
    inference(clausify,[status(thm)],[f_401_2]) ).

fof(f_402_1,plain,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).

fof(f_402_2,plain,
    ! [U_2052,U_2051,U_2050,U_2049,U_2048] :
      ( hAPP(U_2050,hAPP(hAPP(c_Set_Oinsert(U_2048),U_2052),U_2051)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2048,U_2048,U_2049),U_2052),U_2051)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2048),U_2051))
      | ~ c_Finite__Set_Ofolding__one__idem(U_2048,U_2049,U_2050) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

cnf(f_402_3,plain,
    ( hAPP(U_2050,hAPP(hAPP(c_Set_Oinsert(U_2048),U_2052),U_2051)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2048,U_2048,U_2049),U_2052),U_2051)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2048),U_2051))
    | ~ c_Finite__Set_Ofolding__one__idem(U_2048,U_2049,U_2050) ),
    inference(clausify,[status(thm)],[f_402_2]) ).

fof(f_403_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).

fof(f_403_2,plain,
    ! [U_2055,U_2054,U_2053] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2053),U_2055),c_Big__Operators_Olattice__class_OInf__fin(U_2053,U_2054)) = U_2055
      | ~ hBOOL(hAPP(hAPP(c_member(U_2053),U_2055),U_2054))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2053),U_2054))
      | ~ class_Lattices_Olattice(U_2053) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

cnf(f_403_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2053),U_2055),c_Big__Operators_Olattice__class_OInf__fin(U_2053,U_2054)) = U_2055
    | ~ hBOOL(hAPP(hAPP(c_member(U_2053),U_2055),U_2054))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2053),U_2054))
    | ~ class_Lattices_Olattice(U_2053) ),
    inference(clausify,[status(thm)],[f_403_2]) ).

fof(f_404_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).

fof(f_404_2,plain,
    ! [U_2058,U_2057,U_2056] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2056),U_2058),c_Big__Operators_Olattice__class_OInf__fin(U_2056,U_2057)) = c_Big__Operators_Olattice__class_OInf__fin(U_2056,U_2057)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2056),U_2058),U_2057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2056),U_2057))
      | ~ class_Lattices_Olattice(U_2056) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

cnf(f_404_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2056),U_2058),c_Big__Operators_Olattice__class_OInf__fin(U_2056,U_2057)) = c_Big__Operators_Olattice__class_OInf__fin(U_2056,U_2057)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2056),U_2058),U_2057))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2056),U_2057))
    | ~ class_Lattices_Olattice(U_2056) ),
    inference(clausify,[status(thm)],[f_404_2]) ).

fof(f_405_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).

fof(f_405_2,plain,
    ! [U_2063,U_2062,U_2061,U_2060,U_2059] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2060,U_2059),U_2063),hAPP(hAPP(c_Set_Oinsert(U_2060),U_2062),U_2061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2059),hAPP(U_2063,U_2062)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2060,U_2059),U_2063),U_2061))
      | hBOOL(hAPP(hAPP(c_member(U_2060),U_2062),U_2061))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2060),U_2061))
      | ~ class_Groups_Ocomm__monoid__add(U_2059) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

cnf(f_405_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2060,U_2059),U_2063),hAPP(hAPP(c_Set_Oinsert(U_2060),U_2062),U_2061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2059),hAPP(U_2063,U_2062)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2060,U_2059),U_2063),U_2061))
    | hBOOL(hAPP(hAPP(c_member(U_2060),U_2062),U_2061))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2060),U_2061))
    | ~ class_Groups_Ocomm__monoid__add(U_2059) ),
    inference(clausify,[status(thm)],[f_405_2]) ).

fof(f_406_1,plain,
    ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).

fof(f_406_2,plain,
    ! [U_2068,U_2067,U_2066,U_2065,U_2064] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2065,U_2064),U_2068),hAPP(hAPP(c_Set_Oinsert(U_2065),U_2067),U_2066)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2064),hAPP(U_2068,U_2067)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2065,U_2064),U_2068),U_2066))
      | hBOOL(hAPP(hAPP(c_member(U_2065),U_2067),U_2066))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2065),U_2066))
      | ~ class_Groups_Ocomm__monoid__add(U_2064) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

cnf(f_406_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2065,U_2064),U_2068),hAPP(hAPP(c_Set_Oinsert(U_2065),U_2067),U_2066)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2064),hAPP(U_2068,U_2067)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2065,U_2064),U_2068),U_2066))
    | hBOOL(hAPP(hAPP(c_member(U_2065),U_2067),U_2066))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2065),U_2066))
    | ~ class_Groups_Ocomm__monoid__add(U_2064) ),
    inference(clausify,[status(thm)],[f_406_2]) ).

fof(f_407_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).

fof(f_407_2,plain,
    ! [U_2073,U_2072,U_2071,U_2070,U_2069] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2070,tc_HOL_Obool)),U_2071),U_2072))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2070,tc_HOL_Obool)),U_2071),U_2072))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),U_2071)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),U_2072))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2070),U_2072))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2070),U_2071))
      | ~ class_Groups_Ocomm__monoid__add(U_2069) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

cnf(f_407_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2070,tc_HOL_Obool)),U_2071),U_2072))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2070,tc_HOL_Obool)),U_2071),U_2072))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),U_2071)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2070,U_2069),U_2073),U_2072))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2070),U_2072))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2070),U_2071))
    | ~ class_Groups_Ocomm__monoid__add(U_2069) ),
    inference(clausify,[status(thm)],[f_407_2]) ).

fof(f_408_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).

fof(f_408_2,plain,
    ! [U_2076,U_2075,U_2074] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_2074,hAPP(hAPP(c_Set_Oinsert(U_2074),U_2076),U_2075)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2074,U_2074,c_Lattices_Osemilattice__sup__class_Osup(U_2074)),U_2076),U_2075)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2074),U_2075))
      | ~ class_Lattices_Olattice(U_2074) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2074,hAPP(hAPP(c_Set_Oinsert(U_2074),U_2076),U_2075)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2074,U_2074,c_Lattices_Osemilattice__sup__class_Osup(U_2074)),U_2076),U_2075)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2074),U_2075))
    | ~ class_Lattices_Olattice(U_2074) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).

fof(f_409_2,plain,
    ! [U_2079,U_2078,U_2077] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2077,tc_HOL_Obool)),U_2079),U_2078) = hAPP(hAPP(c_Finite__Set_Ofold(U_2077,tc_fun(U_2077,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_2077,tc_HOL_Obool),tc_fun(tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),U_2077),hAPP(c_COMBC(tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_2077,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_2077,tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),c_Set_Oinsert(U_2077)),c_Orderings_Obot__class_Obot(tc_fun(U_2077,tc_HOL_Obool))))),U_2079),U_2078)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2077),U_2078)) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2077,tc_HOL_Obool)),U_2079),U_2078) = hAPP(hAPP(c_Finite__Set_Ofold(U_2077,tc_fun(U_2077,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_2077,tc_HOL_Obool),tc_fun(tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),U_2077),hAPP(c_COMBC(tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_2077,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_2077,tc_fun(U_2077,tc_HOL_Obool),tc_fun(U_2077,tc_HOL_Obool)),c_Set_Oinsert(U_2077)),c_Orderings_Obot__class_Obot(tc_fun(U_2077,tc_HOL_Obool))))),U_2079),U_2078)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2077),U_2078)) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(f_410_2,plain,
    ! [U_2084,U_2083,U_2082,U_2081,U_2080] :
      ( hAPP(U_2082,hAPP(hAPP(c_Set_Oinsert(U_2080),U_2084),U_2083)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2080,U_2080,U_2081),U_2084),U_2083)
      | hBOOL(hAPP(hAPP(c_member(U_2080),U_2084),U_2083))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2080),U_2083))
      | ~ c_Finite__Set_Ofolding__one(U_2080,U_2081,U_2082) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    ( hAPP(U_2082,hAPP(hAPP(c_Set_Oinsert(U_2080),U_2084),U_2083)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2080,U_2080,U_2081),U_2084),U_2083)
    | hBOOL(hAPP(hAPP(c_member(U_2080),U_2084),U_2083))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2080),U_2083))
    | ~ c_Finite__Set_Ofolding__one(U_2080,U_2081,U_2082) ),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).

fof(f_411_2,plain,
    ! [U_2087,U_2086,U_2085] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2085,hAPP(hAPP(c_Set_Oinsert(U_2085),U_2087),U_2086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2085),U_2087),c_Big__Operators_Olattice__class_OInf__fin(U_2085,U_2086))
      | U_2086 = c_Orderings_Obot__class_Obot(tc_fun(U_2085,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2085),U_2086))
      | ~ class_Lattices_Olattice(U_2085) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

cnf(f_411_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2085,hAPP(hAPP(c_Set_Oinsert(U_2085),U_2087),U_2086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2085),U_2087),c_Big__Operators_Olattice__class_OInf__fin(U_2085,U_2086))
    | U_2086 = c_Orderings_Obot__class_Obot(tc_fun(U_2085,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2085),U_2086))
    | ~ class_Lattices_Olattice(U_2085) ),
    inference(clausify,[status(thm)],[f_411_2]) ).

fof(f_412_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).

fof(f_412_2,plain,
    ! [U_2090,U_2089,U_2088] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2088,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2088,tc_HOL_Obool)),U_2089),U_2090)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2088),c_Big__Operators_Olattice__class_OInf__fin(U_2088,U_2089)),c_Big__Operators_Olattice__class_OInf__fin(U_2088,U_2090))
      | U_2090 = c_Orderings_Obot__class_Obot(tc_fun(U_2088,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2088),U_2090))
      | U_2089 = c_Orderings_Obot__class_Obot(tc_fun(U_2088,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2088),U_2089))
      | ~ class_Lattices_Olattice(U_2088) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2088,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2088,tc_HOL_Obool)),U_2089),U_2090)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2088),c_Big__Operators_Olattice__class_OInf__fin(U_2088,U_2089)),c_Big__Operators_Olattice__class_OInf__fin(U_2088,U_2090))
    | U_2090 = c_Orderings_Obot__class_Obot(tc_fun(U_2088,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2088),U_2090))
    | U_2089 = c_Orderings_Obot__class_Obot(tc_fun(U_2088,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2088),U_2089))
    | ~ class_Lattices_Olattice(U_2088) ),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,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_413_2,plain,
    ! [U_2098,U_2097,U_2096,U_2095,U_2094,U_2093,U_2092,U_2091] :
      ( hAPP(hAPP(U_2093,hAPP(U_2095,U_2098)),hAPP(U_2096,U_2097)) = hAPP(U_2096,U_2097)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2092),U_2098),U_2097))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2092),U_2097))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_2091,U_2092,U_2093,U_2094,U_2095,U_2096) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_2098,U_2097,U_2096,U_2095,U_2094,U_2093,U_2092] :
      ( ! [U_2091] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_2091,U_2092,U_2093,U_2094,U_2095,U_2096)
      | hAPP(hAPP(U_2093,hAPP(U_2095,U_2098)),hAPP(U_2096,U_2097)) = hAPP(U_2096,U_2097)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2092),U_2098),U_2097))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2092),U_2097)) ),
    inference(miniscope,[status(thm)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_2091,U_2092,U_2093,U_2094,U_2095,U_2096)
    | hAPP(hAPP(U_2093,hAPP(U_2095,U_2098)),hAPP(U_2096,U_2097)) = hAPP(U_2096,U_2097)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2092),U_2098),U_2097))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2092),U_2097)) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,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_414_2,plain,
    ! [U_2106,U_2105,U_2104,U_2103,U_2102,U_2101,U_2100,U_2099] :
      ( hAPP(U_2104,hAPP(hAPP(c_Set_Oinsert(U_2100),U_2106),U_2105)) = hAPP(hAPP(U_2101,hAPP(U_2103,U_2106)),hAPP(U_2104,U_2105))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2100),U_2105))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_2099,U_2100,U_2101,U_2102,U_2103,U_2104) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_2106,U_2105,U_2104,U_2103,U_2102,U_2101,U_2100] :
      ( ! [U_2099] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_2099,U_2100,U_2101,U_2102,U_2103,U_2104)
      | hAPP(U_2104,hAPP(hAPP(c_Set_Oinsert(U_2100),U_2106),U_2105)) = hAPP(hAPP(U_2101,hAPP(U_2103,U_2106)),hAPP(U_2104,U_2105))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2100),U_2105)) ),
    inference(miniscope,[status(thm)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_2099,U_2100,U_2101,U_2102,U_2103,U_2104)
    | hAPP(U_2104,hAPP(hAPP(c_Set_Oinsert(U_2100),U_2106),U_2105)) = hAPP(hAPP(U_2101,hAPP(U_2103,U_2106)),hAPP(U_2104,U_2105))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2100),U_2105)) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).

fof(f_415_2,plain,
    ! [U_2111,U_2110,U_2109,U_2108,U_2107] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2108,U_2107),U_2110),hAPP(hAPP(c_Set_Oinsert(U_2108),U_2111),U_2109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2107),hAPP(U_2110,U_2111)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2108,U_2107),U_2110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2108,tc_HOL_Obool)),U_2109),hAPP(hAPP(c_Set_Oinsert(U_2108),U_2111),c_Orderings_Obot__class_Obot(tc_fun(U_2108,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2108),U_2109))
      | ~ class_Groups_Ocomm__monoid__add(U_2107) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2108,U_2107),U_2110),hAPP(hAPP(c_Set_Oinsert(U_2108),U_2111),U_2109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2107),hAPP(U_2110,U_2111)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2108,U_2107),U_2110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2108,tc_HOL_Obool)),U_2109),hAPP(hAPP(c_Set_Oinsert(U_2108),U_2111),c_Orderings_Obot__class_Obot(tc_fun(U_2108,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2108),U_2109))
    | ~ class_Groups_Ocomm__monoid__add(U_2107) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).

fof(f_416_2,plain,
    ! [U_2116,U_2115,U_2114,U_2113,U_2112] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2113,tc_HOL_Obool)),U_2114),U_2115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),U_2114)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),U_2115))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2113,tc_HOL_Obool)),U_2114),U_2115) != c_Orderings_Obot__class_Obot(tc_fun(U_2113,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2113),U_2115))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2113),U_2114))
      | ~ class_Groups_Ocomm__monoid__add(U_2112) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2113,tc_HOL_Obool)),U_2114),U_2115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),U_2114)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2113,U_2112),U_2116),U_2115))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2113,tc_HOL_Obool)),U_2114),U_2115) != c_Orderings_Obot__class_Obot(tc_fun(U_2113,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2113),U_2115))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2113),U_2114))
    | ~ class_Groups_Ocomm__monoid__add(U_2112) ),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).

fof(f_417_2,plain,
    ! [U_2122,U_2121,U_2120,U_2119,U_2118,U_2117] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2117,U_2118,U_2119),U_2122),U_2120) = hAPP(hAPP(U_2119,U_2121),hAPP(hAPP(c_Finite__Set_Ofold(U_2117,U_2118,U_2119),U_2122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2117,tc_HOL_Obool)),U_2120),hAPP(hAPP(c_Set_Oinsert(U_2117),U_2121),c_Orderings_Obot__class_Obot(tc_fun(U_2117,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2117),U_2121),U_2120))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2117),U_2120))
      | ~ c_Finite__Set_Ofun__left__comm(U_2117,U_2118,U_2119) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2117,U_2118,U_2119),U_2122),U_2120) = hAPP(hAPP(U_2119,U_2121),hAPP(hAPP(c_Finite__Set_Ofold(U_2117,U_2118,U_2119),U_2122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2117,tc_HOL_Obool)),U_2120),hAPP(hAPP(c_Set_Oinsert(U_2117),U_2121),c_Orderings_Obot__class_Obot(tc_fun(U_2117,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2117),U_2121),U_2120))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2117),U_2120))
    | ~ c_Finite__Set_Ofun__left__comm(U_2117,U_2118,U_2119) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).

fof(f_418_2,plain,
    ! [U_2128,U_2127,U_2126,U_2125,U_2124,U_2123] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2123,U_2124,U_2125),U_2127),hAPP(hAPP(c_Set_Oinsert(U_2123),U_2128),U_2126)) = hAPP(hAPP(U_2125,U_2128),hAPP(hAPP(c_Finite__Set_Ofold(U_2123,U_2124,U_2125),U_2127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2123,tc_HOL_Obool)),U_2126),hAPP(hAPP(c_Set_Oinsert(U_2123),U_2128),c_Orderings_Obot__class_Obot(tc_fun(U_2123,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2123),U_2126))
      | ~ c_Finite__Set_Ofun__left__comm(U_2123,U_2124,U_2125) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2123,U_2124,U_2125),U_2127),hAPP(hAPP(c_Set_Oinsert(U_2123),U_2128),U_2126)) = hAPP(hAPP(U_2125,U_2128),hAPP(hAPP(c_Finite__Set_Ofold(U_2123,U_2124,U_2125),U_2127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2123,tc_HOL_Obool)),U_2126),hAPP(hAPP(c_Set_Oinsert(U_2123),U_2128),c_Orderings_Obot__class_Obot(tc_fun(U_2123,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2123),U_2126))
    | ~ c_Finite__Set_Ofun__left__comm(U_2123,U_2124,U_2125) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).

fof(f_419_2,plain,
    ! [U_2132,U_2131] :
      ( hBOOL(hAPP(hAPP(c_member(U_2131),c_Big__Operators_Olattice__class_OInf__fin(U_2131,U_2132)),U_2132))
      | ? [U_2130,U_2129] : ~ hBOOL(hAPP(hAPP(c_member(U_2131),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2131),U_2130),U_2129)),hAPP(hAPP(c_Set_Oinsert(U_2131),U_2130),hAPP(hAPP(c_Set_Oinsert(U_2131),U_2129),c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))))))
      | U_2132 = c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2131),U_2132))
      | ~ class_Lattices_Olattice(U_2131) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_2132,U_2131] :
      ( hBOOL(hAPP(hAPP(c_member(U_2131),c_Big__Operators_Olattice__class_OInf__fin(U_2131,U_2132)),U_2132))
      | ? [U_2129] : ~ hBOOL(hAPP(hAPP(c_member(U_2131),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2131),sK37(U_2132,U_2131)),U_2129)),hAPP(hAPP(c_Set_Oinsert(U_2131),sK37(U_2132,U_2131)),hAPP(hAPP(c_Set_Oinsert(U_2131),U_2129),c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))))))
      | U_2132 = c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2131),U_2132))
      | ~ class_Lattices_Olattice(U_2131) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2130,sK37(U_2132,U_2131))],[f_419_2]) ).

fof(f_419_4,plain,
    ! [U_2132,U_2131] :
      ( hBOOL(hAPP(hAPP(c_member(U_2131),c_Big__Operators_Olattice__class_OInf__fin(U_2131,U_2132)),U_2132))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2131),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2131),sK37(U_2132,U_2131)),sK38(U_2132,U_2131))),hAPP(hAPP(c_Set_Oinsert(U_2131),sK37(U_2132,U_2131)),hAPP(hAPP(c_Set_Oinsert(U_2131),sK38(U_2132,U_2131)),c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))))))
      | U_2132 = c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2131),U_2132))
      | ~ class_Lattices_Olattice(U_2131) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2129,sK38(U_2132,U_2131))],[f_419_3]) ).

cnf(f_419_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2131),c_Big__Operators_Olattice__class_OInf__fin(U_2131,U_2132)),U_2132))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2131),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2131),sK37(U_2132,U_2131)),sK38(U_2132,U_2131))),hAPP(hAPP(c_Set_Oinsert(U_2131),sK37(U_2132,U_2131)),hAPP(hAPP(c_Set_Oinsert(U_2131),sK38(U_2132,U_2131)),c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))))))
    | U_2132 = c_Orderings_Obot__class_Obot(tc_fun(U_2131,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2131),U_2132))
    | ~ class_Lattices_Olattice(U_2131) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

fof(f_420_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_420_2,plain,
    ! [U_2135,U_2134,U_2133] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),U_2135)),U_2135) = U_2134
      | ~ class_Groups_Ogroup__add(U_2133) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),U_2135)),U_2135) = U_2134
    | ~ class_Groups_Ogroup__add(U_2133) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_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_421_2,plain,
    ! [U_2138,U_2137,U_2136] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2136),U_2137),U_2138)),U_2138) = U_2137
      | ~ class_Groups_Ogroup__add(U_2136) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2136),U_2137),U_2138)),U_2138) = U_2137
    | ~ class_Groups_Ogroup__add(U_2136) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).

fof(f_422_2,plain,
    ! [U_2143,U_2142,U_2141] :
      ( hAPP(U_2142,c_Big__Operators_Olattice__class_OInf__fin(U_2141,U_2143)) = c_Big__Operators_Olattice__class_OInf__fin(U_2141,hAPP(c_Set_Oimage(U_2141,U_2141,U_2142),U_2143))
      | U_2143 = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),U_2143))
      | ? [U_2140,U_2139] : hAPP(U_2142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),U_2140),U_2139)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),hAPP(U_2142,U_2140)),hAPP(U_2142,U_2139))
      | ~ class_Lattices_Olattice(U_2141) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_2143,U_2142,U_2141] :
      ( hAPP(U_2142,c_Big__Operators_Olattice__class_OInf__fin(U_2141,U_2143)) = c_Big__Operators_Olattice__class_OInf__fin(U_2141,hAPP(c_Set_Oimage(U_2141,U_2141,U_2142),U_2143))
      | U_2143 = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),U_2143))
      | ? [U_2139] : hAPP(U_2142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),sK39(U_2143,U_2142,U_2141)),U_2139)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),hAPP(U_2142,sK39(U_2143,U_2142,U_2141))),hAPP(U_2142,U_2139))
      | ~ class_Lattices_Olattice(U_2141) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2140,sK39(U_2143,U_2142,U_2141))],[f_422_2]) ).

fof(f_422_4,plain,
    ! [U_2143,U_2142,U_2141] :
      ( hAPP(U_2142,c_Big__Operators_Olattice__class_OInf__fin(U_2141,U_2143)) = c_Big__Operators_Olattice__class_OInf__fin(U_2141,hAPP(c_Set_Oimage(U_2141,U_2141,U_2142),U_2143))
      | U_2143 = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),U_2143))
      | hAPP(U_2142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),sK39(U_2143,U_2142,U_2141)),sK40(U_2143,U_2142,U_2141))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),hAPP(U_2142,sK39(U_2143,U_2142,U_2141))),hAPP(U_2142,sK40(U_2143,U_2142,U_2141)))
      | ~ class_Lattices_Olattice(U_2141) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2139,sK40(U_2143,U_2142,U_2141))],[f_422_3]) ).

cnf(f_422_5,plain,
    ( hAPP(U_2142,c_Big__Operators_Olattice__class_OInf__fin(U_2141,U_2143)) = c_Big__Operators_Olattice__class_OInf__fin(U_2141,hAPP(c_Set_Oimage(U_2141,U_2141,U_2142),U_2143))
    | U_2143 = c_Orderings_Obot__class_Obot(tc_fun(U_2141,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),U_2143))
    | hAPP(U_2142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),sK39(U_2143,U_2142,U_2141)),sK40(U_2143,U_2142,U_2141))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2141),hAPP(U_2142,sK39(U_2143,U_2142,U_2141))),hAPP(U_2142,sK40(U_2143,U_2142,U_2141)))
    | ~ class_Lattices_Olattice(U_2141) ),
    inference(clausify,[status(thm)],[f_422_4]) ).

fof(f_423_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).

fof(f_423_2,plain,
    ! [U_2147,U_2146,U_2145,U_2144] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2145,U_2144),U_2146),U_2147) = hAPP(hAPP(c_Finite__Set_Ofold(U_2145,U_2144,hAPP(hAPP(c_COMBB(U_2144,tc_fun(U_2144,U_2144),U_2145),c_Lattices_Osemilattice__sup__class_Osup(U_2144)),U_2147)),c_Orderings_Obot__class_Obot(U_2144)),U_2146)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2145),U_2146))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2144) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2145,U_2144),U_2146),U_2147) = hAPP(hAPP(c_Finite__Set_Ofold(U_2145,U_2144,hAPP(hAPP(c_COMBB(U_2144,tc_fun(U_2144,U_2144),U_2145),c_Lattices_Osemilattice__sup__class_Osup(U_2144)),U_2147)),c_Orderings_Obot__class_Obot(U_2144)),U_2146)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2145),U_2146))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2144) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(f_424_2,plain,
    ! [U_2153,U_2152,U_2151,U_2150,U_2149,U_2148] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2148,U_2149,U_2150),U_2153),hAPP(hAPP(c_Set_Oinsert(U_2148),U_2152),U_2151)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2148,U_2149,U_2150),hAPP(hAPP(U_2150,U_2152),U_2153)),U_2151)
      | hBOOL(hAPP(hAPP(c_member(U_2148),U_2152),U_2151))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),U_2151))
      | ~ c_Finite__Set_Ofun__left__comm(U_2148,U_2149,U_2150) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2148,U_2149,U_2150),U_2153),hAPP(hAPP(c_Set_Oinsert(U_2148),U_2152),U_2151)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2148,U_2149,U_2150),hAPP(hAPP(U_2150,U_2152),U_2153)),U_2151)
    | hBOOL(hAPP(hAPP(c_member(U_2148),U_2152),U_2151))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),U_2151))
    | ~ c_Finite__Set_Ofun__left__comm(U_2148,U_2149,U_2150) ),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(f_425_2,plain,
    ! [U_2159,U_2158,U_2157,U_2156,U_2155,U_2154] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2154,U_2155,U_2156),U_2159),hAPP(hAPP(c_Set_Oinsert(U_2154),U_2158),U_2157)) = hAPP(hAPP(U_2156,U_2158),hAPP(hAPP(c_Finite__Set_Ofold(U_2154,U_2155,U_2156),U_2159),U_2157))
      | hBOOL(hAPP(hAPP(c_member(U_2154),U_2158),U_2157))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2154),U_2157))
      | ~ c_Finite__Set_Ofun__left__comm(U_2154,U_2155,U_2156) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2154,U_2155,U_2156),U_2159),hAPP(hAPP(c_Set_Oinsert(U_2154),U_2158),U_2157)) = hAPP(hAPP(U_2156,U_2158),hAPP(hAPP(c_Finite__Set_Ofold(U_2154,U_2155,U_2156),U_2159),U_2157))
    | hBOOL(hAPP(hAPP(c_member(U_2154),U_2158),U_2157))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2154),U_2157))
    | ~ c_Finite__Set_Ofun__left__comm(U_2154,U_2155,U_2156) ),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [V_A_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).

fof(f_426_2,plain,
    ! [U_2161,U_2160] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2160,U_2161) = hAPP(hAPP(c_Finite__Set_Ofold(U_2160,U_2160,c_Lattices_Osemilattice__sup__class_Osup(U_2160)),c_Orderings_Obot__class_Obot(U_2160)),U_2161)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2161))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2160) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2160,U_2161) = hAPP(hAPP(c_Finite__Set_Ofold(U_2160,U_2160,c_Lattices_Osemilattice__sup__class_Osup(U_2160)),c_Orderings_Obot__class_Obot(U_2160)),U_2161)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2161))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2160) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).

fof(f_427_2,plain,
    ! [U_2167,U_2166,U_2165,U_2164,U_2163,U_2162] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2162,tc_fun(U_2167,tc_HOL_Obool)),U_2164),U_2165),U_2166))
      | ~ hBOOL(hAPP(hAPP(U_2165,U_2163),U_2166))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2162),U_2163),U_2164)) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2162,tc_fun(U_2167,tc_HOL_Obool)),U_2164),U_2165),U_2166))
    | ~ hBOOL(hAPP(hAPP(U_2165,U_2163),U_2166))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2162),U_2163),U_2164)) ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,plain,
    ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).

fof(f_428_2,plain,
    ! [U_2175,U_2174,U_2173,U_2172,U_2171,U_2170,U_2169,U_2168] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2168,tc_fun(U_2174,tc_fun(U_2175,tc_HOL_Obool))),U_2170),U_2171),U_2172),U_2173))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_2171,U_2169),U_2172),U_2173))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2168),U_2169),U_2170)) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2168,tc_fun(U_2174,tc_fun(U_2175,tc_HOL_Obool))),U_2170),U_2171),U_2172),U_2173))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_2171,U_2169),U_2172),U_2173))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2168),U_2169),U_2170)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( 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_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).

fof(f_429_2,plain,
    ! [U_2181,U_2180,U_2179,U_2178,U_2177,U_2176] :
      ( hAPP(hAPP(U_2178,U_2179),hAPP(hAPP(U_2178,U_2180),U_2181)) = hAPP(hAPP(U_2178,U_2180),hAPP(hAPP(U_2178,U_2179),U_2181))
      | ~ c_Finite__Set_Ofun__left__comm(U_2176,U_2177,U_2178) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_2181,U_2180,U_2179,U_2178] :
      ( ! [U_2177,U_2176] : ~ c_Finite__Set_Ofun__left__comm(U_2176,U_2177,U_2178)
      | hAPP(hAPP(U_2178,U_2179),hAPP(hAPP(U_2178,U_2180),U_2181)) = hAPP(hAPP(U_2178,U_2180),hAPP(hAPP(U_2178,U_2179),U_2181)) ),
    inference(miniscope,[status(thm)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_2176,U_2177,U_2178)
    | hAPP(hAPP(U_2178,U_2179),hAPP(hAPP(U_2178,U_2180),U_2181)) = hAPP(hAPP(U_2178,U_2180),hAPP(hAPP(U_2178,U_2179),U_2181)) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).

fof(f_430_2,plain,
    ! [U_2186,U_2185,U_2184,U_2183,U_2182] :
      ( c_Finite__Set_Ofun__left__comm(U_2185,U_2183,hAPP(hAPP(c_COMBB(U_2182,tc_fun(U_2183,U_2183),U_2185),U_2184),U_2186))
      | ~ c_Finite__Set_Ofun__left__comm(U_2182,U_2183,U_2184) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_2185,U_2183,hAPP(hAPP(c_COMBB(U_2182,tc_fun(U_2183,U_2183),U_2185),U_2184),U_2186))
    | ~ c_Finite__Set_Ofun__left__comm(U_2182,U_2183,U_2184) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).

fof(f_431_2,plain,
    ! [U_2192,U_2191,U_2190,U_2189] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192)))
          | ? [U_2188] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,U_2188)))
              & hBOOL(hAPP(hAPP(c_member(U_2189),U_2188),U_2190)) ) )
        & ( ! [U_2187] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,U_2187)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2189),U_2187),U_2190)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2189),U_2190)) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ! [U_2192,U_2191,U_2190,U_2189] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,sK41(U_2192,U_2191,U_2190,U_2189))))
            & hBOOL(hAPP(hAPP(c_member(U_2189),sK41(U_2192,U_2191,U_2190,U_2189)),U_2190)) ) )
        & ( ! [U_2187] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,U_2187)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2189),U_2187),U_2190)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2189),U_2190)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2188,sK41(U_2192,U_2191,U_2190,U_2189))],[f_431_2]) ).

cnf(f_431_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,U_2187)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2189),U_2187),U_2190))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2189),U_2190)) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2189),sK41(U_2192,U_2191,U_2190,U_2189)),U_2190))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2189),U_2190)) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(U_2192,sK41(U_2192,U_2191,U_2190,U_2189))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2189,tc_fun(U_2191,tc_HOL_Obool)),U_2190),U_2192)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2189),U_2190)) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2),
    inference(fof_nnf,[status(thm)],[fact_UN__o]) ).

fof(f_432_2,plain,
    ! [U_2198,U_2197,U_2196,U_2195,U_2194,U_2193] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2193,tc_fun(U_2194,tc_HOL_Obool)),U_2195),hAPP(c_Fun_Ocomp(U_2196,tc_fun(U_2194,tc_HOL_Obool),U_2193,U_2197),U_2198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2196,tc_fun(U_2194,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2193,U_2196,U_2198),U_2195)),U_2197),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2193,tc_fun(U_2194,tc_HOL_Obool)),U_2195),hAPP(c_Fun_Ocomp(U_2196,tc_fun(U_2194,tc_HOL_Obool),U_2193,U_2197),U_2198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2196,tc_fun(U_2194,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2193,U_2196,U_2198),U_2195)),U_2197),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).

fof(f_433_2,plain,
    ! [U_2200,U_2199] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2199,tc_HOL_Obool)),U_2200))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2199),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2199,tc_HOL_Obool),U_2200))) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2199,tc_HOL_Obool)),U_2200))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2199),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2199,tc_HOL_Obool),U_2200))) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm]) ).

fof(f_434_2,plain,
    ! [U_2205,U_2204,U_2203,U_2202,U_2201] :
      ( hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2204)),hAPP(U_2203,U_2205)) = hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2205)),hAPP(U_2203,U_2204))
      | ~ c_Finite__Set_Ofun__left__comm(U_2201,U_2202,U_2203) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_2205,U_2204,U_2203,U_2202] :
      ( ! [U_2201] : ~ c_Finite__Set_Ofun__left__comm(U_2201,U_2202,U_2203)
      | hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2204)),hAPP(U_2203,U_2205)) = hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2205)),hAPP(U_2203,U_2204)) ),
    inference(miniscope,[status(thm)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_2201,U_2202,U_2203)
    | hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2204)),hAPP(U_2203,U_2205)) = hAPP(c_Fun_Ocomp(U_2202,U_2202,U_2202,hAPP(U_2203,U_2205)),hAPP(U_2203,U_2204)) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_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_435_2,plain,
    ! [U_2209,U_2208,U_2207,U_2206] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2207),U_2208)),U_2209) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2208),U_2209))
      | ~ class_Groups_Oab__semigroup__add(U_2206) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2207),U_2208)),U_2209) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2206),U_2208),U_2209))
    | ~ class_Groups_Oab__semigroup__add(U_2206) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_a),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_436_2,plain,
    ! [U_2213,U_2212,U_2211,U_2210] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2213)
          | U_2212 != U_2213 )
        & ( U_2212 = U_2213
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2212) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2213) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_2210) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    ( U_2212 = U_2213
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2212) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2213)
    | ~ class_Groups_Ocancel__semigroup__add(U_2210) ),
    inference(clausify,[status(thm)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2210),U_2211),U_2213)
    | U_2212 != U_2213
    | ~ class_Groups_Ocancel__semigroup__add(U_2210) ),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_1,plain,
    ! [V_c_2,V_a_2,V_b_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_a),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_437_2,plain,
    ! [U_2217,U_2216,U_2215,U_2214] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2215),U_2216) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2217),U_2216)
          | U_2215 != U_2217 )
        & ( U_2215 = U_2217
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2215),U_2216) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2217),U_2216) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_2214) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( U_2215 = U_2217
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2215),U_2216) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2217),U_2216)
    | ~ class_Groups_Ocancel__semigroup__add(U_2214) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2215),U_2216) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),U_2217),U_2216)
    | U_2215 != U_2217
    | ~ class_Groups_Ocancel__semigroup__add(U_2214) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_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_438_2,plain,
    ! [U_2221,U_2220,U_2219,U_2218] :
      ( U_2220 = U_2221
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2218),U_2219),U_2220) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2218),U_2219),U_2221)
      | ~ class_Groups_Ocancel__semigroup__add(U_2218) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( U_2220 = U_2221
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2218),U_2219),U_2220) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2218),U_2219),U_2221)
    | ~ class_Groups_Ocancel__semigroup__add(U_2218) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_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_439_2,plain,
    ! [U_2225,U_2224,U_2223,U_2222] :
      ( U_2224 = U_2225
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2223),U_2224) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2223),U_2225)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_2222) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    ( U_2224 = U_2225
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2223),U_2224) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),U_2223),U_2225)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_2222) ),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_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_440_2,plain,
    ! [U_2229,U_2228,U_2227,U_2226] :
      ( U_2227 = U_2229
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2227),U_2228) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2229),U_2228)
      | ~ class_Groups_Ocancel__semigroup__add(U_2226) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    ( U_2227 = U_2229
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2227),U_2228) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2226),U_2229),U_2228)
    | ~ class_Groups_Ocancel__semigroup__add(U_2226) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( 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_a),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_441_2,plain,
    ! [U_2234,U_2233,U_2232,U_2231,U_2230] :
      ( ( ( U_2231 = U_2232
          | U_2233 != U_2234 )
        & ( U_2233 = U_2234
          | U_2231 != U_2232 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2231),U_2232) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2233),U_2234)
      | ~ class_Groups_Oab__group__add(U_2230) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    ( U_2233 = U_2234
    | U_2231 != U_2232
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2231),U_2232) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2233),U_2234)
    | ~ class_Groups_Oab__group__add(U_2230) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( U_2231 = U_2232
    | U_2233 != U_2234
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2231),U_2232) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2230),U_2233),U_2234)
    | ~ class_Groups_Oab__group__add(U_2230) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).

fof(f_442_2,plain,
    ! [U_2240,U_2239,U_2238,U_2237,U_2236,U_2235] :
      ( hAPP(hAPP(U_2237,U_2239),hAPP(hAPP(c_Finite__Set_Ofold(U_2235,U_2236,U_2237),U_2240),U_2238)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2235,U_2236,U_2237),hAPP(hAPP(U_2237,U_2239),U_2240)),U_2238)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2235),U_2238))
      | ~ c_Finite__Set_Ofun__left__comm(U_2235,U_2236,U_2237) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hAPP(hAPP(U_2237,U_2239),hAPP(hAPP(c_Finite__Set_Ofold(U_2235,U_2236,U_2237),U_2240),U_2238)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2235,U_2236,U_2237),hAPP(hAPP(U_2237,U_2239),U_2240)),U_2238)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2235),U_2238))
    | ~ c_Finite__Set_Ofun__left__comm(U_2235,U_2236,U_2237) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).

fof(f_443_2,plain,
    ! [U_2243,U_2242,U_2241] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2241),U_2243),c_Complete__Lattice_OSup__class_OSup(U_2241,U_2242)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2241,U_2241,c_Lattices_Osemilattice__sup__class_Osup(U_2241)),U_2243),U_2242)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2241),U_2242))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2241) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2241),U_2243),c_Complete__Lattice_OSup__class_OSup(U_2241,U_2242)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2241,U_2241,c_Lattices_Osemilattice__sup__class_Osup(U_2241)),U_2243),U_2242)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2241),U_2242))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2241) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).

fof(f_444_2,plain,
    ! [U_2245,U_2244] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_2244,U_2245) = c_Complete__Lattice_OSup__class_OSup(U_2244,U_2245)
      | U_2245 = c_Orderings_Obot__class_Obot(tc_fun(U_2244,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2244),U_2245))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2244) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2244,U_2245) = c_Complete__Lattice_OSup__class_OSup(U_2244,U_2245)
    | U_2245 = c_Orderings_Obot__class_Obot(tc_fun(U_2244,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2244),U_2245))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2244) ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).

fof(f_445_2,plain,
    ! [U_2250,U_2249,U_2248,U_2247,U_2246] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2246),U_2249),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2247,U_2246),U_2248),U_2250)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2247,U_2246,hAPP(hAPP(c_COMBB(U_2246,tc_fun(U_2246,U_2246),U_2247),c_Lattices_Osemilattice__sup__class_Osup(U_2246)),U_2250)),U_2249),U_2248)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2247),U_2248))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2246) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2246),U_2249),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2247,U_2246),U_2248),U_2250)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2247,U_2246,hAPP(hAPP(c_COMBB(U_2246,tc_fun(U_2246,U_2246),U_2247),c_Lattices_Osemilattice__sup__class_Osup(U_2246)),U_2250)),U_2249),U_2248)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2247),U_2248))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2246) ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).

fof(f_446_2,plain,
    ! [U_2253,U_2252,U_2251] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2251,hAPP(hAPP(c_Set_Oinsert(U_2251),U_2252),hAPP(hAPP(c_Set_Oinsert(U_2251),U_2253),c_Orderings_Obot__class_Obot(tc_fun(U_2251,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2251),U_2252),U_2253)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2251) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

cnf(f_446_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2251,hAPP(hAPP(c_Set_Oinsert(U_2251),U_2252),hAPP(hAPP(c_Set_Oinsert(U_2251),U_2253),c_Orderings_Obot__class_Obot(tc_fun(U_2251,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2251),U_2252),U_2253)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2251) ),
    inference(clausify,[status(thm)],[f_446_2]) ).

fof(f_447_1,plain,
    ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,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))))),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq__UN]) ).

fof(f_447_2,plain,
    ! [U_2257,U_2256,U_2255,U_2254] : hAPP(c_Set_Ovimage(U_2254,U_2255,U_2256),U_2257) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2255,tc_fun(U_2254,tc_HOL_Obool)),U_2257),hAPP(hAPP(c_COMBB(tc_fun(U_2255,tc_HOL_Obool),tc_fun(U_2254,tc_HOL_Obool),U_2255),c_Set_Ovimage(U_2254,U_2255,U_2256)),hAPP(hAPP(c_COMBC(U_2255,tc_fun(U_2255,tc_HOL_Obool),tc_fun(U_2255,tc_HOL_Obool)),c_Set_Oinsert(U_2255)),c_Orderings_Obot__class_Obot(tc_fun(U_2255,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    hAPP(c_Set_Ovimage(U_2254,U_2255,U_2256),U_2257) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2255,tc_fun(U_2254,tc_HOL_Obool)),U_2257),hAPP(hAPP(c_COMBB(tc_fun(U_2255,tc_HOL_Obool),tc_fun(U_2254,tc_HOL_Obool),U_2255),c_Set_Ovimage(U_2254,U_2255,U_2256)),hAPP(hAPP(c_COMBC(U_2255,tc_fun(U_2255,tc_HOL_Obool),tc_fun(U_2255,tc_HOL_Obool)),c_Set_Oinsert(U_2255)),c_Orderings_Obot__class_Obot(tc_fun(U_2255,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_1,plain,
    ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).

fof(f_448_2,plain,
    ! [U_2261,U_2260,U_2259,U_2258] : hAPP(c_Set_Oimage(U_2258,U_2259,U_2260),U_2261) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2258,tc_fun(U_2259,tc_HOL_Obool)),U_2261),hAPP(hAPP(c_COMBC(U_2258,tc_fun(U_2259,tc_HOL_Obool),tc_fun(U_2259,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_2259,tc_fun(tc_fun(U_2259,tc_HOL_Obool),tc_fun(U_2259,tc_HOL_Obool)),U_2258),c_Set_Oinsert(U_2259)),U_2260)),c_Orderings_Obot__class_Obot(tc_fun(U_2259,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    hAPP(c_Set_Oimage(U_2258,U_2259,U_2260),U_2261) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2258,tc_fun(U_2259,tc_HOL_Obool)),U_2261),hAPP(hAPP(c_COMBC(U_2258,tc_fun(U_2259,tc_HOL_Obool),tc_fun(U_2259,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_2259,tc_fun(tc_fun(U_2259,tc_HOL_Obool),tc_fun(U_2259,tc_HOL_Obool)),U_2258),c_Set_Oinsert(U_2259)),U_2260)),c_Orderings_Obot__class_Obot(tc_fun(U_2259,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_1,plain,
    ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__I]) ).

fof(f_449_2,plain,
    ! [U_2267,U_2266,U_2265,U_2264,U_2263,U_2262] :
      ( hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2262,tc_fun(U_2265,tc_HOL_Obool)),U_2264),U_2267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(U_2267,U_2263)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2262),U_2263),U_2264)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2262,tc_fun(U_2265,tc_HOL_Obool)),U_2264),U_2267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(U_2267,U_2263)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2262),U_2263),U_2264)) ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).

fof(f_450_2,plain,
    ! [U_2270,U_2269,U_2268] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2268,hAPP(hAPP(c_Set_Oinsert(U_2268),U_2269),U_2270)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2268),U_2269),c_Complete__Lattice_OSup__class_OSup(U_2268,U_2270))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2268) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2268,hAPP(hAPP(c_Set_Oinsert(U_2268),U_2269),U_2270)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2268),U_2269),c_Complete__Lattice_OSup__class_OSup(U_2268,U_2270))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2268) ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_1,plain,
    ! [V_a_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).

fof(f_451_2,plain,
    ! [U_2272,U_2271] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2271,hAPP(hAPP(c_Set_Oinsert(U_2271),U_2272),c_Orderings_Obot__class_Obot(tc_fun(U_2271,tc_HOL_Obool)))) = U_2272
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2271) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2271,hAPP(hAPP(c_Set_Oinsert(U_2271),U_2272),c_Orderings_Obot__class_Obot(tc_fun(U_2271,tc_HOL_Obool)))) = U_2272
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2271) ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_1,plain,
    ! [T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).

fof(f_452_2,plain,
    ! [U_2273] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2273,c_Orderings_Obot__class_Obot(tc_fun(U_2273,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_2273)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2273) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2273,c_Orderings_Obot__class_Obot(tc_fun(U_2273,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_2273)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2273) ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_1,plain,
    ! [V_M_2,T_a,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).

fof(f_453_2,plain,
    ! [U_2277,U_2276,U_2275,U_2274] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2276,U_2274),U_2275),hAPP(c_COMBK(U_2274,U_2276),U_2277)) = U_2277
      | U_2275 = c_Orderings_Obot__class_Obot(tc_fun(U_2276,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2274) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

cnf(f_453_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2276,U_2274),U_2275),hAPP(c_COMBK(U_2274,U_2276),U_2277)) = U_2277
    | U_2275 = c_Orderings_Obot__class_Obot(tc_fun(U_2276,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2274) ),
    inference(clausify,[status(thm)],[f_453_2]) ).

fof(f_454_1,plain,
    ! [V_A_2,V_C_2,V_X_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnionI]) ).

fof(f_454_2,plain,
    ! [U_2281,U_2280,U_2279,U_2278] :
      ( hBOOL(hAPP(hAPP(c_member(U_2278),U_2281),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2278,tc_HOL_Obool),U_2280)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2278),U_2281),U_2279))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2278,tc_HOL_Obool)),U_2279),U_2280)) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2278),U_2281),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2278,tc_HOL_Obool),U_2280)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2278),U_2281),U_2279))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2278,tc_HOL_Obool)),U_2279),U_2280)) ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).

fof(f_455_2,plain,
    ! [U_2286,U_2285,U_2284,U_2283,U_2282] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2282,tc_fun(U_2283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2282),U_2284),U_2285)),U_2286) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2283,tc_HOL_Obool)),hAPP(U_2286,U_2284)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2282,tc_fun(U_2283,tc_HOL_Obool)),U_2285),U_2286)),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2282,tc_fun(U_2283,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2282),U_2284),U_2285)),U_2286) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2283,tc_HOL_Obool)),hAPP(U_2286,U_2284)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2282,tc_fun(U_2283,tc_HOL_Obool)),U_2285),U_2286)),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,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_a),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).

fof(f_456_2,plain,
    ! [U_2293,U_2292,U_2291,U_2290,U_2289] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2289,tc_fun(U_2290,tc_HOL_Obool)),U_2291),U_2292),U_2293))
        | ! [U_2288] :
            ( ~ hBOOL(hAPP(hAPP(U_2292,U_2288),U_2293))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2289),U_2288),U_2291)) ) )
      & ( ? [U_2287] :
            ( hBOOL(hAPP(hAPP(U_2292,U_2287),U_2293))
            & hBOOL(hAPP(hAPP(c_member(U_2289),U_2287),U_2291)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2289,tc_fun(U_2290,tc_HOL_Obool)),U_2291),U_2292),U_2293)) ) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ( ! [U_2303,U_2301,U_2299,U_2297,U_2295] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2295,tc_fun(U_2297,tc_HOL_Obool)),U_2299),U_2301),U_2303))
        | ! [U_2288] :
            ( ~ hBOOL(hAPP(hAPP(U_2301,U_2288),U_2303))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2295),U_2288),U_2299)) ) )
    & ! [U_2302,U_2300,U_2298,U_2296,U_2294] :
        ( ? [U_2287] :
            ( hBOOL(hAPP(hAPP(U_2300,U_2287),U_2302))
            & hBOOL(hAPP(hAPP(c_member(U_2294),U_2287),U_2298)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2294,tc_fun(U_2296,tc_HOL_Obool)),U_2298),U_2300),U_2302)) ) ),
    inference(miniscope,[status(thm)],[f_456_2]) ).

fof(f_456_4,plain,
    ( ! [U_2303,U_2301,U_2299,U_2297,U_2295] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2295,tc_fun(U_2297,tc_HOL_Obool)),U_2299),U_2301),U_2303))
        | ! [U_2288] :
            ( ~ hBOOL(hAPP(hAPP(U_2301,U_2288),U_2303))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2295),U_2288),U_2299)) ) )
    & ! [U_2302,U_2300,U_2298,U_2296,U_2294] :
        ( ( hBOOL(hAPP(hAPP(U_2300,sK42(U_2302,U_2300,U_2298,U_2296,U_2294)),U_2302))
          & hBOOL(hAPP(hAPP(c_member(U_2294),sK42(U_2302,U_2300,U_2298,U_2296,U_2294)),U_2298)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2294,tc_fun(U_2296,tc_HOL_Obool)),U_2298),U_2300),U_2302)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2287,sK42(U_2302,U_2300,U_2298,U_2296,U_2294))],[f_456_3]) ).

cnf(f_456_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2294),sK42(U_2302,U_2300,U_2298,U_2296,U_2294)),U_2298))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2294,tc_fun(U_2296,tc_HOL_Obool)),U_2298),U_2300),U_2302)) ),
    inference(clausify,[status(thm)],[f_456_4]) ).

cnf(f_456_6,plain,
    ( hBOOL(hAPP(hAPP(U_2300,sK42(U_2302,U_2300,U_2298,U_2296,U_2294)),U_2302))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2294,tc_fun(U_2296,tc_HOL_Obool)),U_2298),U_2300),U_2302)) ),
    inference(clausify,[status(thm)],[f_456_4]) ).

cnf(f_456_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2295,tc_fun(U_2297,tc_HOL_Obool)),U_2299),U_2301),U_2303))
    | ~ hBOOL(hAPP(hAPP(U_2301,U_2288),U_2303))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2295),U_2288),U_2299)) ),
    inference(clausify,[status(thm)],[f_456_4]) ).

fof(f_457_1,plain,
    ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).

fof(f_457_2,plain,
    ! [U_2307,U_2306,U_2305,U_2304] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2304,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2305,tc_fun(U_2304,tc_HOL_Obool),U_2306),U_2307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2305,tc_fun(U_2304,tc_HOL_Obool)),U_2307),U_2306),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

cnf(f_457_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2304,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2305,tc_fun(U_2304,tc_HOL_Obool),U_2306),U_2307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2305,tc_fun(U_2304,tc_HOL_Obool)),U_2307),U_2306),
    inference(clausify,[status(thm)],[f_457_2]) ).

fof(f_458_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(f_458_2,plain,
    ! [U_2311,U_2310,U_2309,U_2308] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2308,tc_fun(U_2309,tc_HOL_Obool)),U_2310),U_2311) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2309,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2308,tc_fun(U_2309,tc_HOL_Obool),U_2311),U_2310)),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

cnf(f_458_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2308,tc_fun(U_2309,tc_HOL_Obool)),U_2310),U_2311) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2309,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2308,tc_fun(U_2309,tc_HOL_Obool),U_2311),U_2310)),
    inference(clausify,[status(thm)],[f_458_2]) ).

fof(f_459_1,plain,
    ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Union__def]) ).

fof(f_459_2,plain,
    ! [U_2313,U_2312] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2312,tc_HOL_Obool),U_2313) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2312,tc_HOL_Obool),tc_fun(U_2312,tc_HOL_Obool)),U_2313),c_COMBI(tc_fun(U_2312,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

cnf(f_459_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2312,tc_HOL_Obool),U_2313) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2312,tc_HOL_Obool),tc_fun(U_2312,tc_HOL_Obool)),U_2313),c_COMBI(tc_fun(U_2312,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_459_2]) ).

fof(f_460_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(f_460_2,plain,
    ! [U_2317,U_2316,U_2315,U_2314] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2314,tc_HOL_Obool),tc_fun(U_2315,tc_HOL_Obool)),U_2316),hAPP(hAPP(c_COMBC(tc_fun(U_2314,tc_HOL_Obool),tc_fun(U_2314,tc_fun(U_2315,tc_HOL_Obool)),tc_fun(U_2315,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2314,tc_fun(U_2315,tc_HOL_Obool))),U_2317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2314,tc_fun(U_2315,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2314,tc_HOL_Obool),U_2316)),U_2317),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

cnf(f_460_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2314,tc_HOL_Obool),tc_fun(U_2315,tc_HOL_Obool)),U_2316),hAPP(hAPP(c_COMBC(tc_fun(U_2314,tc_HOL_Obool),tc_fun(U_2314,tc_fun(U_2315,tc_HOL_Obool)),tc_fun(U_2315,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2314,tc_fun(U_2315,tc_HOL_Obool))),U_2317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2314,tc_fun(U_2315,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2314,tc_HOL_Obool),U_2316)),U_2317),
    inference(clausify,[status(thm)],[f_460_2]) ).

fof(f_461_1,plain,
    ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(f_461_2,plain,
    ! [U_2323,U_2322,U_2321,U_2320,U_2319,U_2318] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2318,tc_fun(U_2319,tc_HOL_Obool)),U_2320),hAPP(hAPP(c_COMBC(U_2318,tc_fun(U_2321,tc_fun(U_2319,tc_HOL_Obool)),tc_fun(U_2319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2321,tc_HOL_Obool),tc_fun(tc_fun(U_2321,tc_fun(U_2319,tc_HOL_Obool)),tc_fun(U_2319,tc_HOL_Obool)),U_2318),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2321,tc_fun(U_2319,tc_HOL_Obool))),U_2322)),U_2323)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2321,tc_fun(U_2319,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2318,tc_fun(U_2321,tc_HOL_Obool)),U_2320),U_2322)),U_2323),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

cnf(f_461_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2318,tc_fun(U_2319,tc_HOL_Obool)),U_2320),hAPP(hAPP(c_COMBC(U_2318,tc_fun(U_2321,tc_fun(U_2319,tc_HOL_Obool)),tc_fun(U_2319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2321,tc_HOL_Obool),tc_fun(tc_fun(U_2321,tc_fun(U_2319,tc_HOL_Obool)),tc_fun(U_2319,tc_HOL_Obool)),U_2318),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2321,tc_fun(U_2319,tc_HOL_Obool))),U_2322)),U_2323)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2321,tc_fun(U_2319,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2318,tc_fun(U_2321,tc_HOL_Obool)),U_2320),U_2322)),U_2323),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(f_462_2,plain,
    ! [U_2327,U_2326,U_2325,U_2324] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2324,tc_fun(U_2325,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2324,tc_HOL_Obool),U_2326)),U_2327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2324,tc_HOL_Obool),tc_fun(U_2325,tc_HOL_Obool)),U_2326),hAPP(hAPP(c_COMBC(tc_fun(U_2324,tc_HOL_Obool),tc_fun(U_2324,tc_fun(U_2325,tc_HOL_Obool)),tc_fun(U_2325,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2324,tc_fun(U_2325,tc_HOL_Obool))),U_2327)),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2324,tc_fun(U_2325,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2324,tc_HOL_Obool),U_2326)),U_2327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2324,tc_HOL_Obool),tc_fun(U_2325,tc_HOL_Obool)),U_2326),hAPP(hAPP(c_COMBC(tc_fun(U_2324,tc_HOL_Obool),tc_fun(U_2324,tc_fun(U_2325,tc_HOL_Obool)),tc_fun(U_2325,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2324,tc_fun(U_2325,tc_HOL_Obool))),U_2327)),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(V_P_2,B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(V_P_2,B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).

fof(f_463_2,plain,
    ! [U_2338,U_2337,U_2336,U_2335,U_2334] :
      ( ( ! [U_2333] :
            ( hBOOL(hAPP(U_2338,U_2333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2334),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2335,tc_fun(U_2334,tc_HOL_Obool)),U_2336),U_2337))) )
        | ? [U_2332] :
            ( ? [U_2331] :
                ( ~ hBOOL(hAPP(U_2338,U_2331))
                & hBOOL(hAPP(hAPP(c_member(U_2334),U_2331),hAPP(U_2337,U_2332))) )
            & hBOOL(hAPP(hAPP(c_member(U_2335),U_2332),U_2336)) ) )
      & ( ! [U_2330] :
            ( ! [U_2329] :
                ( hBOOL(hAPP(U_2338,U_2329))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2334),U_2329),hAPP(U_2337,U_2330))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2335),U_2330),U_2336)) )
        | ? [U_2328] :
            ( ~ hBOOL(hAPP(U_2338,U_2328))
            & hBOOL(hAPP(hAPP(c_member(U_2334),U_2328),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2335,tc_fun(U_2334,tc_HOL_Obool)),U_2336),U_2337))) ) ) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ( ! [U_2348,U_2346,U_2344,U_2342,U_2340] :
        ( ! [U_2333] :
            ( hBOOL(hAPP(U_2348,U_2333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) )
        | ? [U_2332] :
            ( ? [U_2331] :
                ( ~ hBOOL(hAPP(U_2348,U_2331))
                & hBOOL(hAPP(hAPP(c_member(U_2340),U_2331),hAPP(U_2346,U_2332))) )
            & hBOOL(hAPP(hAPP(c_member(U_2342),U_2332),U_2344)) ) )
    & ! [U_2347,U_2345,U_2343,U_2341,U_2339] :
        ( ! [U_2330] :
            ( ! [U_2329] :
                ( hBOOL(hAPP(U_2347,U_2329))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) )
        | ? [U_2328] :
            ( ~ hBOOL(hAPP(U_2347,U_2328))
            & hBOOL(hAPP(hAPP(c_member(U_2339),U_2328),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2341,tc_fun(U_2339,tc_HOL_Obool)),U_2343),U_2345))) ) ) ),
    inference(miniscope,[status(thm)],[f_463_2]) ).

fof(f_463_4,plain,
    ( ! [U_2348,U_2346,U_2344,U_2342,U_2340] :
        ( ! [U_2333] :
            ( hBOOL(hAPP(U_2348,U_2333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) )
        | ? [U_2332] :
            ( ? [U_2331] :
                ( ~ hBOOL(hAPP(U_2348,U_2331))
                & hBOOL(hAPP(hAPP(c_member(U_2340),U_2331),hAPP(U_2346,U_2332))) )
            & hBOOL(hAPP(hAPP(c_member(U_2342),U_2332),U_2344)) ) )
    & ! [U_2347,U_2345,U_2343,U_2341,U_2339] :
        ( ! [U_2330] :
            ( ! [U_2329] :
                ( hBOOL(hAPP(U_2347,U_2329))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) )
        | ( ~ hBOOL(hAPP(U_2347,sK43(U_2347,U_2345,U_2343,U_2341,U_2339)))
          & hBOOL(hAPP(hAPP(c_member(U_2339),sK43(U_2347,U_2345,U_2343,U_2341,U_2339)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2341,tc_fun(U_2339,tc_HOL_Obool)),U_2343),U_2345))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2328,sK43(U_2347,U_2345,U_2343,U_2341,U_2339))],[f_463_3]) ).

fof(f_463_5,plain,
    ( ! [U_2348,U_2346,U_2344,U_2342,U_2340] :
        ( ! [U_2333] :
            ( hBOOL(hAPP(U_2348,U_2333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) )
        | ( ? [U_2331] :
              ( ~ hBOOL(hAPP(U_2348,U_2331))
              & hBOOL(hAPP(hAPP(c_member(U_2340),U_2331),hAPP(U_2346,sK44(U_2348,U_2346,U_2344,U_2342,U_2340)))) )
          & hBOOL(hAPP(hAPP(c_member(U_2342),sK44(U_2348,U_2346,U_2344,U_2342,U_2340)),U_2344)) ) )
    & ! [U_2347,U_2345,U_2343,U_2341,U_2339] :
        ( ! [U_2330] :
            ( ! [U_2329] :
                ( hBOOL(hAPP(U_2347,U_2329))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) )
        | ( ~ hBOOL(hAPP(U_2347,sK43(U_2347,U_2345,U_2343,U_2341,U_2339)))
          & hBOOL(hAPP(hAPP(c_member(U_2339),sK43(U_2347,U_2345,U_2343,U_2341,U_2339)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2341,tc_fun(U_2339,tc_HOL_Obool)),U_2343),U_2345))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2332,sK44(U_2348,U_2346,U_2344,U_2342,U_2340))],[f_463_4]) ).

fof(f_463_6,plain,
    ( ! [U_2348,U_2346,U_2344,U_2342,U_2340] :
        ( ! [U_2333] :
            ( hBOOL(hAPP(U_2348,U_2333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) )
        | ( ~ hBOOL(hAPP(U_2348,sK45(U_2348,U_2346,U_2344,U_2342,U_2340)))
          & hBOOL(hAPP(hAPP(c_member(U_2340),sK45(U_2348,U_2346,U_2344,U_2342,U_2340)),hAPP(U_2346,sK44(U_2348,U_2346,U_2344,U_2342,U_2340))))
          & hBOOL(hAPP(hAPP(c_member(U_2342),sK44(U_2348,U_2346,U_2344,U_2342,U_2340)),U_2344)) ) )
    & ! [U_2347,U_2345,U_2343,U_2341,U_2339] :
        ( ! [U_2330] :
            ( ! [U_2329] :
                ( hBOOL(hAPP(U_2347,U_2329))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) )
        | ( ~ hBOOL(hAPP(U_2347,sK43(U_2347,U_2345,U_2343,U_2341,U_2339)))
          & hBOOL(hAPP(hAPP(c_member(U_2339),sK43(U_2347,U_2345,U_2343,U_2341,U_2339)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2341,tc_fun(U_2339,tc_HOL_Obool)),U_2343),U_2345))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2331,sK45(U_2348,U_2346,U_2344,U_2342,U_2340))],[f_463_5]) ).

cnf(f_463_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2339),sK43(U_2347,U_2345,U_2343,U_2341,U_2339)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2341,tc_fun(U_2339,tc_HOL_Obool)),U_2343),U_2345)))
    | hBOOL(hAPP(U_2347,U_2329))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) ),
    inference(clausify,[status(thm)],[f_463_6]) ).

cnf(f_463_8,plain,
    ( ~ hBOOL(hAPP(U_2347,sK43(U_2347,U_2345,U_2343,U_2341,U_2339)))
    | hBOOL(hAPP(U_2347,U_2329))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2329),hAPP(U_2345,U_2330)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2341),U_2330),U_2343)) ),
    inference(clausify,[status(thm)],[f_463_6]) ).

cnf(f_463_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2342),sK44(U_2348,U_2346,U_2344,U_2342,U_2340)),U_2344))
    | hBOOL(hAPP(U_2348,U_2333))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) ),
    inference(clausify,[status(thm)],[f_463_6]) ).

cnf(f_463_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2340),sK45(U_2348,U_2346,U_2344,U_2342,U_2340)),hAPP(U_2346,sK44(U_2348,U_2346,U_2344,U_2342,U_2340))))
    | hBOOL(hAPP(U_2348,U_2333))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) ),
    inference(clausify,[status(thm)],[f_463_6]) ).

cnf(f_463_11,plain,
    ( ~ hBOOL(hAPP(U_2348,sK45(U_2348,U_2346,U_2344,U_2342,U_2340)))
    | hBOOL(hAPP(U_2348,U_2333))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2340),U_2333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2342,tc_fun(U_2340,tc_HOL_Obool)),U_2344),U_2346))) ),
    inference(clausify,[status(thm)],[f_463_6]) ).

fof(f_464_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(f_464_2,plain,
    ! [U_2354,U_2353,U_2352,U_2351,U_2350,U_2349] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2349,tc_fun(U_2350,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2351,tc_fun(U_2349,tc_HOL_Obool)),U_2352),U_2353)),U_2354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2351,tc_fun(U_2350,tc_HOL_Obool)),U_2352),hAPP(hAPP(c_COMBC(U_2351,tc_fun(U_2349,tc_fun(U_2350,tc_HOL_Obool)),tc_fun(U_2350,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2349,tc_HOL_Obool),tc_fun(tc_fun(U_2349,tc_fun(U_2350,tc_HOL_Obool)),tc_fun(U_2350,tc_HOL_Obool)),U_2351),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2349,tc_fun(U_2350,tc_HOL_Obool))),U_2353)),U_2354)),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2349,tc_fun(U_2350,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2351,tc_fun(U_2349,tc_HOL_Obool)),U_2352),U_2353)),U_2354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2351,tc_fun(U_2350,tc_HOL_Obool)),U_2352),hAPP(hAPP(c_COMBC(U_2351,tc_fun(U_2349,tc_fun(U_2350,tc_HOL_Obool)),tc_fun(U_2350,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2349,tc_HOL_Obool),tc_fun(tc_fun(U_2349,tc_fun(U_2350,tc_HOL_Obool)),tc_fun(U_2350,tc_HOL_Obool)),U_2351),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2349,tc_fun(U_2350,tc_HOL_Obool))),U_2353)),U_2354)),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).

fof(f_465_2,plain,
    ! [U_2360,U_2359,U_2358,U_2357,U_2356,U_2355] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2355,tc_fun(U_2356,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2357,tc_fun(U_2355,tc_HOL_Obool)),U_2358),U_2359)),U_2360) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2357,tc_fun(U_2356,tc_HOL_Obool)),U_2358),hAPP(hAPP(c_COMBC(U_2357,tc_fun(U_2355,tc_fun(U_2356,tc_HOL_Obool)),tc_fun(U_2356,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2355,tc_HOL_Obool),tc_fun(tc_fun(U_2355,tc_fun(U_2356,tc_HOL_Obool)),tc_fun(U_2356,tc_HOL_Obool)),U_2357),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2355,tc_fun(U_2356,tc_HOL_Obool))),U_2359)),U_2360)),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2355,tc_fun(U_2356,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2357,tc_fun(U_2355,tc_HOL_Obool)),U_2358),U_2359)),U_2360) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2357,tc_fun(U_2356,tc_HOL_Obool)),U_2358),hAPP(hAPP(c_COMBC(U_2357,tc_fun(U_2355,tc_fun(U_2356,tc_HOL_Obool)),tc_fun(U_2356,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2355,tc_HOL_Obool),tc_fun(tc_fun(U_2355,tc_fun(U_2356,tc_HOL_Obool)),tc_fun(U_2356,tc_HOL_Obool)),U_2357),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2355,tc_fun(U_2356,tc_HOL_Obool))),U_2359)),U_2360)),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,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_a),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_a),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,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_466_2,plain,
    ! [U_2369,U_2368,U_2367,U_2366,U_2365,U_2364,U_2363] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2363,tc_fun(U_2364,tc_fun(U_2365,tc_HOL_Obool))),U_2366),U_2367),U_2368),U_2369))
        | ! [U_2362] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_2367,U_2362),U_2368),U_2369))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2363),U_2362),U_2366)) ) )
      & ( ? [U_2361] :
            ( hBOOL(hAPP(hAPP(hAPP(U_2367,U_2361),U_2368),U_2369))
            & hBOOL(hAPP(hAPP(c_member(U_2363),U_2361),U_2366)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2363,tc_fun(U_2364,tc_fun(U_2365,tc_HOL_Obool))),U_2366),U_2367),U_2368),U_2369)) ) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ( ! [U_2383,U_2381,U_2379,U_2377,U_2375,U_2373,U_2371] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2371,tc_fun(U_2373,tc_fun(U_2375,tc_HOL_Obool))),U_2377),U_2379),U_2381),U_2383))
        | ! [U_2362] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_2379,U_2362),U_2381),U_2383))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2371),U_2362),U_2377)) ) )
    & ! [U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370] :
        ( ? [U_2361] :
            ( hBOOL(hAPP(hAPP(hAPP(U_2378,U_2361),U_2380),U_2382))
            & hBOOL(hAPP(hAPP(c_member(U_2370),U_2361),U_2376)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2370,tc_fun(U_2372,tc_fun(U_2374,tc_HOL_Obool))),U_2376),U_2378),U_2380),U_2382)) ) ),
    inference(miniscope,[status(thm)],[f_466_2]) ).

fof(f_466_4,plain,
    ( ! [U_2383,U_2381,U_2379,U_2377,U_2375,U_2373,U_2371] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2371,tc_fun(U_2373,tc_fun(U_2375,tc_HOL_Obool))),U_2377),U_2379),U_2381),U_2383))
        | ! [U_2362] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_2379,U_2362),U_2381),U_2383))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2371),U_2362),U_2377)) ) )
    & ! [U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_2378,sK46(U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370)),U_2380),U_2382))
          & hBOOL(hAPP(hAPP(c_member(U_2370),sK46(U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370)),U_2376)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2370,tc_fun(U_2372,tc_fun(U_2374,tc_HOL_Obool))),U_2376),U_2378),U_2380),U_2382)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2361,sK46(U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370))],[f_466_3]) ).

cnf(f_466_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2370),sK46(U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370)),U_2376))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2370,tc_fun(U_2372,tc_fun(U_2374,tc_HOL_Obool))),U_2376),U_2378),U_2380),U_2382)) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

cnf(f_466_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_2378,sK46(U_2382,U_2380,U_2378,U_2376,U_2374,U_2372,U_2370)),U_2380),U_2382))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2370,tc_fun(U_2372,tc_fun(U_2374,tc_HOL_Obool))),U_2376),U_2378),U_2380),U_2382)) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

cnf(f_466_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2371,tc_fun(U_2373,tc_fun(U_2375,tc_HOL_Obool))),U_2377),U_2379),U_2381),U_2383))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_2379,U_2362),U_2381),U_2383))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2371),U_2362),U_2377)) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

fof(f_467_1,plain,
    ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).

fof(f_467_2,plain,
    ! [U_2384] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2384,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2384,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2384,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

cnf(f_467_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2384,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2384,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2384,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_467_2]) ).

fof(f_468_1,plain,
    ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).

fof(f_468_2,plain,
    ! [U_2387,U_2386,U_2385] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2385,tc_HOL_Obool),tc_HOL_Obool)),U_2386),U_2387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2385,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),U_2386)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),U_2387)),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2385,tc_HOL_Obool),tc_HOL_Obool)),U_2386),U_2387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2385,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),U_2386)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2385,tc_HOL_Obool),U_2387)),
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).

fof(f_469_2,plain,
    ! [U_2390,U_2389,U_2388] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2388,tc_HOL_Obool)),U_2389),U_2390) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2388,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2388,tc_HOL_Obool)),U_2389),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2388,tc_HOL_Obool)),U_2390),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2388,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2388,tc_HOL_Obool)),U_2389),U_2390) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2388,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2388,tc_HOL_Obool)),U_2389),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2388,tc_HOL_Obool)),U_2390),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2388,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).

fof(f_470_2,plain,
    ! [U_2393,U_2392,U_2391] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2391,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2391,tc_HOL_Obool)),U_2392),U_2393)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2391,tc_HOL_Obool)),U_2392),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2391,tc_HOL_Obool),U_2393)),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2391,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2391,tc_HOL_Obool)),U_2392),U_2393)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2391,tc_HOL_Obool)),U_2392),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2391,tc_HOL_Obool),U_2393)),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).

fof(f_471_2,plain,
    ! [U_2400,U_2399,U_2398,U_2397,U_2396] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2396),U_2397),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2398,tc_fun(U_2396,tc_HOL_Obool)),U_2399),U_2400)))
        | ! [U_2395] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_2396),U_2397),hAPP(U_2400,U_2395)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2398),U_2395),U_2399)) ) )
      & ( ? [U_2394] :
            ( hBOOL(hAPP(hAPP(c_member(U_2396),U_2397),hAPP(U_2400,U_2394)))
            & hBOOL(hAPP(hAPP(c_member(U_2398),U_2394),U_2399)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2396),U_2397),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2398,tc_fun(U_2396,tc_HOL_Obool)),U_2399),U_2400))) ) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ( ! [U_2410,U_2408,U_2406,U_2404,U_2402] :
        ( hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2406,tc_fun(U_2402,tc_HOL_Obool)),U_2408),U_2410)))
        | ! [U_2395] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(U_2410,U_2395)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2395),U_2408)) ) )
    & ! [U_2409,U_2407,U_2405,U_2403,U_2401] :
        ( ? [U_2394] :
            ( hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(U_2409,U_2394)))
            & hBOOL(hAPP(hAPP(c_member(U_2405),U_2394),U_2407)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2405,tc_fun(U_2401,tc_HOL_Obool)),U_2407),U_2409))) ) ),
    inference(miniscope,[status(thm)],[f_471_2]) ).

fof(f_471_4,plain,
    ( ! [U_2410,U_2408,U_2406,U_2404,U_2402] :
        ( hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2406,tc_fun(U_2402,tc_HOL_Obool)),U_2408),U_2410)))
        | ! [U_2395] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(U_2410,U_2395)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2395),U_2408)) ) )
    & ! [U_2409,U_2407,U_2405,U_2403,U_2401] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(U_2409,sK47(U_2409,U_2407,U_2405,U_2403,U_2401))))
          & hBOOL(hAPP(hAPP(c_member(U_2405),sK47(U_2409,U_2407,U_2405,U_2403,U_2401)),U_2407)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2405,tc_fun(U_2401,tc_HOL_Obool)),U_2407),U_2409))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_2394,sK47(U_2409,U_2407,U_2405,U_2403,U_2401))],[f_471_3]) ).

cnf(f_471_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2405),sK47(U_2409,U_2407,U_2405,U_2403,U_2401)),U_2407))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2405,tc_fun(U_2401,tc_HOL_Obool)),U_2407),U_2409))) ),
    inference(clausify,[status(thm)],[f_471_4]) ).

cnf(f_471_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(U_2409,sK47(U_2409,U_2407,U_2405,U_2403,U_2401))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2403),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2405,tc_fun(U_2401,tc_HOL_Obool)),U_2407),U_2409))) ),
    inference(clausify,[status(thm)],[f_471_4]) ).

cnf(f_471_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2406,tc_fun(U_2402,tc_HOL_Obool)),U_2408),U_2410)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2404),hAPP(U_2410,U_2395)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2395),U_2408)) ),
    inference(clausify,[status(thm)],[f_471_4]) ).

fof(f_472_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).

fof(f_472_2,plain,
    ! [U_2416,U_2415,U_2414,U_2413] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2414,tc_fun(U_2413,tc_HOL_Obool)),U_2415),U_2416)
        | ? [U_2412] :
            ( hAPP(U_2416,U_2412) != c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_2414),U_2412),U_2415)) ) )
      & ( ! [U_2411] :
            ( hAPP(U_2416,U_2411) = c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2414),U_2411),U_2415)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2414,tc_fun(U_2413,tc_HOL_Obool)),U_2415),U_2416) ) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ( ! [U_2424,U_2422,U_2420,U_2418] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2420,tc_fun(U_2418,tc_HOL_Obool)),U_2422),U_2424)
        | ? [U_2412] :
            ( hAPP(U_2424,U_2412) != c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_2420),U_2412),U_2422)) ) )
    & ! [U_2423,U_2421,U_2419,U_2417] :
        ( ! [U_2411] :
            ( hAPP(U_2423,U_2411) = c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2419),U_2411),U_2421)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2419,tc_fun(U_2417,tc_HOL_Obool)),U_2421),U_2423) ) ),
    inference(miniscope,[status(thm)],[f_472_2]) ).

fof(f_472_4,plain,
    ( ! [U_2424,U_2422,U_2420,U_2418] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2420,tc_fun(U_2418,tc_HOL_Obool)),U_2422),U_2424)
        | ( hAPP(U_2424,sK48(U_2424,U_2422,U_2420,U_2418)) != c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_2420),sK48(U_2424,U_2422,U_2420,U_2418)),U_2422)) ) )
    & ! [U_2423,U_2421,U_2419,U_2417] :
        ( ! [U_2411] :
            ( hAPP(U_2423,U_2411) = c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2419),U_2411),U_2421)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2419,tc_fun(U_2417,tc_HOL_Obool)),U_2421),U_2423) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_2412,sK48(U_2424,U_2422,U_2420,U_2418))],[f_472_3]) ).

cnf(f_472_5,plain,
    ( hAPP(U_2423,U_2411) = c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2419),U_2411),U_2421))
    | c_Orderings_Obot__class_Obot(tc_fun(U_2417,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2419,tc_fun(U_2417,tc_HOL_Obool)),U_2421),U_2423) ),
    inference(clausify,[status(thm)],[f_472_4]) ).

cnf(f_472_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2420),sK48(U_2424,U_2422,U_2420,U_2418)),U_2422))
    | c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2420,tc_fun(U_2418,tc_HOL_Obool)),U_2422),U_2424) ),
    inference(clausify,[status(thm)],[f_472_4]) ).

cnf(f_472_7,plain,
    ( hAPP(U_2424,sK48(U_2424,U_2422,U_2420,U_2418)) != c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(U_2418,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2420,tc_fun(U_2418,tc_HOL_Obool)),U_2422),U_2424) ),
    inference(clausify,[status(thm)],[f_472_4]) ).

fof(f_473_1,plain,
    ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).

fof(f_473_2,plain,
    ! [U_2427,U_2426,U_2425] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2425,tc_fun(U_2426,tc_HOL_Obool)),U_2427),hAPP(c_COMBK(tc_fun(U_2426,tc_HOL_Obool),U_2425),c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

cnf(f_473_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2425,tc_fun(U_2426,tc_HOL_Obool)),U_2427),hAPP(c_COMBK(tc_fun(U_2426,tc_HOL_Obool),U_2425),c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).

fof(f_474_2,plain,
    ! [U_2431,U_2430,U_2429,U_2428] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2429,tc_fun(U_2430,tc_HOL_Obool)),U_2428),hAPP(c_COMBK(tc_fun(U_2430,tc_HOL_Obool),U_2429),U_2431)) = U_2431
        | U_2428 = c_Orderings_Obot__class_Obot(tc_fun(U_2429,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2429,tc_fun(U_2430,tc_HOL_Obool)),U_2428),hAPP(c_COMBK(tc_fun(U_2430,tc_HOL_Obool),U_2429),U_2431)) = c_Orderings_Obot__class_Obot(tc_fun(U_2430,tc_HOL_Obool))
        | U_2428 != c_Orderings_Obot__class_Obot(tc_fun(U_2429,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ( ! [U_2439,U_2437,U_2435,U_2433] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2435,tc_fun(U_2437,tc_HOL_Obool)),U_2433),hAPP(c_COMBK(tc_fun(U_2437,tc_HOL_Obool),U_2435),U_2439)) = U_2439
        | U_2433 = c_Orderings_Obot__class_Obot(tc_fun(U_2435,tc_HOL_Obool)) )
    & ! [U_2438,U_2436,U_2434,U_2432] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2434,tc_fun(U_2436,tc_HOL_Obool)),U_2432),hAPP(c_COMBK(tc_fun(U_2436,tc_HOL_Obool),U_2434),U_2438)) = c_Orderings_Obot__class_Obot(tc_fun(U_2436,tc_HOL_Obool))
        | U_2432 != c_Orderings_Obot__class_Obot(tc_fun(U_2434,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_474_2]) ).

cnf(f_474_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2434,tc_fun(U_2436,tc_HOL_Obool)),U_2432),hAPP(c_COMBK(tc_fun(U_2436,tc_HOL_Obool),U_2434),U_2438)) = c_Orderings_Obot__class_Obot(tc_fun(U_2436,tc_HOL_Obool))
    | U_2432 != c_Orderings_Obot__class_Obot(tc_fun(U_2434,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

cnf(f_474_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2435,tc_fun(U_2437,tc_HOL_Obool)),U_2433),hAPP(c_COMBK(tc_fun(U_2437,tc_HOL_Obool),U_2435),U_2439)) = U_2439
    | U_2433 = c_Orderings_Obot__class_Obot(tc_fun(U_2435,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).

fof(f_475_2,plain,
    ! [U_2445,U_2444,U_2443,U_2442] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2442,tc_fun(U_2443,tc_HOL_Obool)),U_2444),U_2445) = c_Orderings_Obot__class_Obot(tc_fun(U_2443,tc_HOL_Obool))
        | ? [U_2441] :
            ( hAPP(U_2445,U_2441) != c_Orderings_Obot__class_Obot(tc_fun(U_2443,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_2442),U_2441),U_2444)) ) )
      & ( ! [U_2440] :
            ( hAPP(U_2445,U_2440) = c_Orderings_Obot__class_Obot(tc_fun(U_2443,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2442),U_2440),U_2444)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2442,tc_fun(U_2443,tc_HOL_Obool)),U_2444),U_2445) != c_Orderings_Obot__class_Obot(tc_fun(U_2443,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ( ! [U_2453,U_2451,U_2449,U_2447] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2447,tc_fun(U_2449,tc_HOL_Obool)),U_2451),U_2453) = c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool))
        | ? [U_2441] :
            ( hAPP(U_2453,U_2441) != c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_2447),U_2441),U_2451)) ) )
    & ! [U_2452,U_2450,U_2448,U_2446] :
        ( ! [U_2440] :
            ( hAPP(U_2452,U_2440) = c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2446),U_2440),U_2450)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2446,tc_fun(U_2448,tc_HOL_Obool)),U_2450),U_2452) != c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_475_2]) ).

fof(f_475_4,plain,
    ( ! [U_2453,U_2451,U_2449,U_2447] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2447,tc_fun(U_2449,tc_HOL_Obool)),U_2451),U_2453) = c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool))
        | ( hAPP(U_2453,sK49(U_2453,U_2451,U_2449,U_2447)) != c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_2447),sK49(U_2453,U_2451,U_2449,U_2447)),U_2451)) ) )
    & ! [U_2452,U_2450,U_2448,U_2446] :
        ( ! [U_2440] :
            ( hAPP(U_2452,U_2440) = c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2446),U_2440),U_2450)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2446,tc_fun(U_2448,tc_HOL_Obool)),U_2450),U_2452) != c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_2441,sK49(U_2453,U_2451,U_2449,U_2447))],[f_475_3]) ).

cnf(f_475_5,plain,
    ( hAPP(U_2452,U_2440) = c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2446),U_2440),U_2450))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2446,tc_fun(U_2448,tc_HOL_Obool)),U_2450),U_2452) != c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

cnf(f_475_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2447),sK49(U_2453,U_2451,U_2449,U_2447)),U_2451))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2447,tc_fun(U_2449,tc_HOL_Obool)),U_2451),U_2453) = c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

cnf(f_475_7,plain,
    ( hAPP(U_2453,sK49(U_2453,U_2451,U_2449,U_2447)) != c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2447,tc_fun(U_2449,tc_HOL_Obool)),U_2451),U_2453) = c_Orderings_Obot__class_Obot(tc_fun(U_2449,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

fof(f_476_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(f_476_2,plain,
    ! [U_2459,U_2458,U_2457,U_2456,U_2455,U_2454] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2454,tc_fun(U_2455,tc_HOL_Obool)),U_2456),hAPP(hAPP(c_COMBB(U_2457,tc_fun(U_2455,tc_HOL_Obool),U_2454),U_2458),U_2459)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2457,tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2454,U_2457,U_2459),U_2456)),U_2458),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

cnf(f_476_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2454,tc_fun(U_2455,tc_HOL_Obool)),U_2456),hAPP(hAPP(c_COMBB(U_2457,tc_fun(U_2455,tc_HOL_Obool),U_2454),U_2458),U_2459)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2457,tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2454,U_2457,U_2459),U_2456)),U_2458),
    inference(clausify,[status(thm)],[f_476_2]) ).

fof(f_477_1,plain,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__UN]) ).

fof(f_477_2,plain,
    ! [U_2465,U_2464,U_2463,U_2462,U_2461,U_2460] : hAPP(c_Set_Oimage(U_2460,U_2461,U_2462),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2463,tc_fun(U_2460,tc_HOL_Obool)),U_2464),U_2465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2463,tc_fun(U_2461,tc_HOL_Obool)),U_2464),hAPP(hAPP(c_COMBB(tc_fun(U_2460,tc_HOL_Obool),tc_fun(U_2461,tc_HOL_Obool),U_2463),c_Set_Oimage(U_2460,U_2461,U_2462)),U_2465)),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    hAPP(c_Set_Oimage(U_2460,U_2461,U_2462),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2463,tc_fun(U_2460,tc_HOL_Obool)),U_2464),U_2465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2463,tc_fun(U_2461,tc_HOL_Obool)),U_2464),hAPP(hAPP(c_COMBB(tc_fun(U_2460,tc_HOL_Obool),tc_fun(U_2461,tc_HOL_Obool),U_2463),c_Set_Oimage(U_2460,U_2461,U_2462)),U_2465)),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(f_478_2,plain,
    ! [U_2471,U_2470,U_2469,U_2468,U_2467,U_2466] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2466,tc_fun(U_2467,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2468,U_2466,U_2469),U_2470)),U_2471) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2468,tc_fun(U_2467,tc_HOL_Obool)),U_2470),hAPP(hAPP(c_COMBB(U_2466,tc_fun(U_2467,tc_HOL_Obool),U_2468),U_2471),U_2469)),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2466,tc_fun(U_2467,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2468,U_2466,U_2469),U_2470)),U_2471) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2468,tc_fun(U_2467,tc_HOL_Obool)),U_2470),hAPP(hAPP(c_COMBB(U_2466,tc_fun(U_2467,tc_HOL_Obool),U_2468),U_2471),U_2469)),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_1,plain,
    ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),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_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Union]) ).

fof(f_479_2,plain,
    ! [U_2475,U_2474,U_2473,U_2472] : hAPP(c_Set_Oimage(U_2472,U_2473,U_2474),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2472,tc_HOL_Obool),U_2475)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2472,tc_HOL_Obool),tc_fun(U_2473,tc_HOL_Obool)),U_2475),c_Set_Oimage(U_2472,U_2473,U_2474)),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    hAPP(c_Set_Oimage(U_2472,U_2473,U_2474),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2472,tc_HOL_Obool),U_2475)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2472,tc_HOL_Obool),tc_fun(U_2473,tc_HOL_Obool)),U_2475),c_Set_Oimage(U_2472,U_2473,U_2474)),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).

fof(f_480_2,plain,
    ! [U_2480,U_2479,U_2478,U_2477,U_2476] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),hAPP(hAPP(c_COMBS(U_2476,tc_fun(U_2477,tc_HOL_Obool),tc_fun(U_2477,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2477,tc_HOL_Obool),tc_fun(tc_fun(U_2477,tc_HOL_Obool),tc_fun(U_2477,tc_HOL_Obool)),U_2476),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2477,tc_HOL_Obool))),U_2479)),U_2480)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2477,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),U_2479)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),U_2480)),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),hAPP(hAPP(c_COMBS(U_2476,tc_fun(U_2477,tc_HOL_Obool),tc_fun(U_2477,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2477,tc_HOL_Obool),tc_fun(tc_fun(U_2477,tc_HOL_Obool),tc_fun(U_2477,tc_HOL_Obool)),U_2476),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2477,tc_HOL_Obool))),U_2479)),U_2480)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2477,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),U_2479)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2476,tc_fun(U_2477,tc_HOL_Obool)),U_2478),U_2480)),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).

fof(f_481_2,plain,
    ! [U_2485,U_2484,U_2483,U_2482,U_2481] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2481,tc_HOL_Obool)),U_2483),U_2484)),U_2485) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2482,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),U_2483),U_2485)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),U_2484),U_2485)),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

cnf(f_481_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2481,tc_HOL_Obool)),U_2483),U_2484)),U_2485) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2482,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),U_2483),U_2485)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2481,tc_fun(U_2482,tc_HOL_Obool)),U_2484),U_2485)),
    inference(clausify,[status(thm)],[f_481_2]) ).

fof(f_482_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).

fof(f_482_2,plain,
    ! [U_2490,U_2489,U_2488,U_2487,U_2486] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2486,tc_fun(U_2487,tc_HOL_Obool)),U_2488),hAPP(hAPP(c_COMBS(U_2486,tc_fun(U_2487,tc_HOL_Obool),tc_fun(U_2487,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2487,tc_HOL_Obool),tc_fun(tc_fun(U_2487,tc_HOL_Obool),tc_fun(U_2487,tc_HOL_Obool)),U_2486),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2487,tc_HOL_Obool))),U_2489)),U_2490)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2487,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2487,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2486,tc_fun(U_2487,tc_HOL_Obool),U_2489),U_2488))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2487,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2486,tc_fun(U_2487,tc_HOL_Obool),U_2490),U_2488))),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2486,tc_fun(U_2487,tc_HOL_Obool)),U_2488),hAPP(hAPP(c_COMBS(U_2486,tc_fun(U_2487,tc_HOL_Obool),tc_fun(U_2487,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2487,tc_HOL_Obool),tc_fun(tc_fun(U_2487,tc_HOL_Obool),tc_fun(U_2487,tc_HOL_Obool)),U_2486),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2487,tc_HOL_Obool))),U_2489)),U_2490)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2487,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2487,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2486,tc_fun(U_2487,tc_HOL_Obool),U_2489),U_2488))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2487,tc_HOL_Obool),hAPP(c_Set_Oimage(U_2486,tc_fun(U_2487,tc_HOL_Obool),U_2490),U_2488))),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_1,plain,
    ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(f_483_2,plain,
    ! [U_2497,U_2496,U_2495,U_2494,U_2493,U_2492,U_2491] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2492,tc_fun(U_2491,tc_HOL_Obool)),U_2493),U_2494)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2495,tc_fun(U_2491,tc_HOL_Obool)),U_2496),U_2497)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2492,tc_fun(U_2491,tc_HOL_Obool)),U_2493),hAPP(hAPP(c_COMBB(tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2491,tc_HOL_Obool),U_2492),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2495,tc_fun(U_2491,tc_HOL_Obool)),U_2496)),hAPP(hAPP(c_COMBC(U_2492,tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool)),tc_fun(tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool))),U_2492),c_COMBB(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool),U_2495)),hAPP(hAPP(c_COMBB(tc_fun(U_2491,tc_HOL_Obool),tc_fun(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool)),U_2492),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2491,tc_HOL_Obool))),U_2494))),U_2497))),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2492,tc_fun(U_2491,tc_HOL_Obool)),U_2493),U_2494)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2495,tc_fun(U_2491,tc_HOL_Obool)),U_2496),U_2497)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2492,tc_fun(U_2491,tc_HOL_Obool)),U_2493),hAPP(hAPP(c_COMBB(tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2491,tc_HOL_Obool),U_2492),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2495,tc_fun(U_2491,tc_HOL_Obool)),U_2496)),hAPP(hAPP(c_COMBC(U_2492,tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool)),tc_fun(tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool)),tc_fun(U_2495,tc_fun(U_2491,tc_HOL_Obool))),U_2492),c_COMBB(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool),U_2495)),hAPP(hAPP(c_COMBB(tc_fun(U_2491,tc_HOL_Obool),tc_fun(tc_fun(U_2491,tc_HOL_Obool),tc_fun(U_2491,tc_HOL_Obool)),U_2492),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2491,tc_HOL_Obool))),U_2494))),U_2497))),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(f_484_2,plain,
    ! [U_2502,U_2501,U_2500,U_2499,U_2498] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2498,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2499,tc_fun(U_2498,tc_HOL_Obool)),U_2500),U_2501)),U_2502) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2499,tc_fun(U_2498,tc_HOL_Obool)),U_2500),hAPP(hAPP(c_COMBC(U_2499,tc_fun(U_2498,tc_HOL_Obool),tc_fun(U_2498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2498,tc_HOL_Obool),tc_fun(tc_fun(U_2498,tc_HOL_Obool),tc_fun(U_2498,tc_HOL_Obool)),U_2499),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2498,tc_HOL_Obool))),U_2501)),U_2502)),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

cnf(f_484_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2498,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2499,tc_fun(U_2498,tc_HOL_Obool)),U_2500),U_2501)),U_2502) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2499,tc_fun(U_2498,tc_HOL_Obool)),U_2500),hAPP(hAPP(c_COMBC(U_2499,tc_fun(U_2498,tc_HOL_Obool),tc_fun(U_2498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2498,tc_HOL_Obool),tc_fun(tc_fun(U_2498,tc_HOL_Obool),tc_fun(U_2498,tc_HOL_Obool)),U_2499),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2498,tc_HOL_Obool))),U_2501)),U_2502)),
    inference(clausify,[status(thm)],[f_484_2]) ).

fof(f_485_1,plain,
    ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).

fof(f_485_2,plain,
    ! [U_2507,U_2506,U_2505,U_2504,U_2503] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2503,tc_HOL_Obool)),U_2504),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2505,tc_fun(U_2503,tc_HOL_Obool)),U_2506),U_2507)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2505,tc_fun(U_2503,tc_HOL_Obool)),U_2506),hAPP(hAPP(c_COMBB(tc_fun(U_2503,tc_HOL_Obool),tc_fun(U_2503,tc_HOL_Obool),U_2505),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2503,tc_HOL_Obool)),U_2504)),U_2507)),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

cnf(f_485_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2503,tc_HOL_Obool)),U_2504),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2505,tc_fun(U_2503,tc_HOL_Obool)),U_2506),U_2507)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2505,tc_fun(U_2503,tc_HOL_Obool)),U_2506),hAPP(hAPP(c_COMBB(tc_fun(U_2503,tc_HOL_Obool),tc_fun(U_2503,tc_HOL_Obool),U_2505),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2503,tc_HOL_Obool)),U_2504)),U_2507)),
    inference(clausify,[status(thm)],[f_485_2]) ).

fof(f_486_1,plain,
    ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(f_486_2,plain,
    ! [U_2512,U_2511,U_2510,U_2509,U_2508] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2509),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2510,tc_fun(U_2508,tc_HOL_Obool)),U_2511),U_2512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2510,tc_fun(U_2508,tc_HOL_Obool)),U_2511),hAPP(hAPP(c_COMBB(tc_fun(U_2508,tc_HOL_Obool),tc_fun(U_2508,tc_HOL_Obool),U_2510),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2509)),U_2512)),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

cnf(f_486_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2509),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2510,tc_fun(U_2508,tc_HOL_Obool)),U_2511),U_2512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2510,tc_fun(U_2508,tc_HOL_Obool)),U_2511),hAPP(hAPP(c_COMBB(tc_fun(U_2508,tc_HOL_Obool),tc_fun(U_2508,tc_HOL_Obool),U_2510),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2509)),U_2512)),
    inference(clausify,[status(thm)],[f_486_2]) ).

fof(f_487_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(f_487_2,plain,
    ! [U_2517,U_2516,U_2515,U_2514,U_2513] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2513,tc_fun(U_2514,tc_HOL_Obool)),U_2515),hAPP(hAPP(c_COMBC(U_2513,tc_fun(U_2514,tc_HOL_Obool),tc_fun(U_2514,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2514,tc_HOL_Obool),tc_fun(tc_fun(U_2514,tc_HOL_Obool),tc_fun(U_2514,tc_HOL_Obool)),U_2513),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2514,tc_HOL_Obool))),U_2516)),U_2517)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2514,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2513,tc_fun(U_2514,tc_HOL_Obool)),U_2515),U_2516)),U_2517),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2513,tc_fun(U_2514,tc_HOL_Obool)),U_2515),hAPP(hAPP(c_COMBC(U_2513,tc_fun(U_2514,tc_HOL_Obool),tc_fun(U_2514,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2514,tc_HOL_Obool),tc_fun(tc_fun(U_2514,tc_HOL_Obool),tc_fun(U_2514,tc_HOL_Obool)),U_2513),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2514,tc_HOL_Obool))),U_2516)),U_2517)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2514,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2513,tc_fun(U_2514,tc_HOL_Obool)),U_2515),U_2516)),U_2517),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(f_488_2,plain,
    ! [U_2522,U_2521,U_2520,U_2519,U_2518] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2518,tc_fun(U_2519,tc_HOL_Obool)),U_2520),hAPP(hAPP(c_COMBB(tc_fun(U_2519,tc_HOL_Obool),tc_fun(U_2519,tc_HOL_Obool),U_2518),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2519,tc_HOL_Obool)),U_2521)),U_2522)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2519,tc_HOL_Obool)),U_2521),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2518,tc_fun(U_2519,tc_HOL_Obool)),U_2520),U_2522)),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2518,tc_fun(U_2519,tc_HOL_Obool)),U_2520),hAPP(hAPP(c_COMBB(tc_fun(U_2519,tc_HOL_Obool),tc_fun(U_2519,tc_HOL_Obool),U_2518),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2519,tc_HOL_Obool)),U_2521)),U_2522)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2519,tc_HOL_Obool)),U_2521),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2518,tc_fun(U_2519,tc_HOL_Obool)),U_2520),U_2522)),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_1,plain,
    ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).

fof(f_489_2,plain,
    ! [U_2525,U_2524,U_2523] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2523,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2523,tc_HOL_Obool),U_2524)),U_2525) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool)),U_2524),hAPP(hAPP(c_COMBC(tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2523,tc_HOL_Obool))),U_2525)),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2523,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2523,tc_HOL_Obool),U_2524)),U_2525) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool)),U_2524),hAPP(hAPP(c_COMBC(tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool),tc_fun(U_2523,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2523,tc_HOL_Obool))),U_2525)),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).

fof(f_490_2,plain,
    ! [U_2528,U_2527,U_2526] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2526,tc_HOL_Obool)),U_2527),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2526,tc_HOL_Obool),U_2528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2526,tc_HOL_Obool),tc_fun(U_2526,tc_HOL_Obool)),U_2528),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2526,tc_HOL_Obool)),U_2527)),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2526,tc_HOL_Obool)),U_2527),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2526,tc_HOL_Obool),U_2528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2526,tc_HOL_Obool),tc_fun(U_2526,tc_HOL_Obool)),U_2528),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2526,tc_HOL_Obool)),U_2527)),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).

fof(f_491_2,plain,
    ! [U_2534,U_2533,U_2532,U_2531,U_2530,U_2529] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2530,tc_fun(U_2531,U_2529)),U_2532),U_2533),U_2534) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2530,U_2529),U_2532),hAPP(hAPP(c_COMBC(U_2530,U_2531,U_2529),U_2533),U_2534))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2529) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2530,tc_fun(U_2531,U_2529)),U_2532),U_2533),U_2534) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2530,U_2529),U_2532),hAPP(hAPP(c_COMBC(U_2530,U_2531,U_2529),U_2533),U_2534))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2529) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).

fof(f_492_2,plain,
    ! [U_2540,U_2539,U_2538,U_2537,U_2536,U_2535] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2536,U_2535),U_2537),hAPP(hAPP(c_COMBB(tc_fun(U_2538,U_2535),U_2535,U_2536),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2538,U_2535),U_2539)),U_2540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2538,U_2535),U_2539),hAPP(hAPP(c_COMBB(tc_fun(U_2536,U_2535),U_2535,U_2538),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2536,U_2535),U_2537)),hAPP(c_COMBC(U_2536,U_2538,U_2535),U_2540)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2535) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

cnf(f_492_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2536,U_2535),U_2537),hAPP(hAPP(c_COMBB(tc_fun(U_2538,U_2535),U_2535,U_2536),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2538,U_2535),U_2539)),U_2540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2538,U_2535),U_2539),hAPP(hAPP(c_COMBB(tc_fun(U_2536,U_2535),U_2535,U_2538),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2536,U_2535),U_2537)),hAPP(c_COMBC(U_2536,U_2538,U_2535),U_2540)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2535) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(f_493_2,plain,
    ! [U_2545,U_2544,U_2543,U_2542,U_2541] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2541,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2542,tc_fun(U_2541,tc_HOL_Obool)),U_2543),U_2544)),U_2545) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2542,tc_fun(U_2541,tc_HOL_Obool)),U_2543),hAPP(hAPP(c_COMBC(U_2542,tc_fun(U_2541,tc_HOL_Obool),tc_fun(U_2541,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2541,tc_HOL_Obool),tc_fun(tc_fun(U_2541,tc_HOL_Obool),tc_fun(U_2541,tc_HOL_Obool)),U_2542),c_Groups_Ominus__class_Ominus(tc_fun(U_2541,tc_HOL_Obool))),U_2544)),U_2545)),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

cnf(f_493_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2541,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2542,tc_fun(U_2541,tc_HOL_Obool)),U_2543),U_2544)),U_2545) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2542,tc_fun(U_2541,tc_HOL_Obool)),U_2543),hAPP(hAPP(c_COMBC(U_2542,tc_fun(U_2541,tc_HOL_Obool),tc_fun(U_2541,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2541,tc_HOL_Obool),tc_fun(tc_fun(U_2541,tc_HOL_Obool),tc_fun(U_2541,tc_HOL_Obool)),U_2542),c_Groups_Ominus__class_Ominus(tc_fun(U_2541,tc_HOL_Obool))),U_2544)),U_2545)),
    inference(clausify,[status(thm)],[f_493_2]) ).

fof(f_494_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(f_494_2,plain,
    ! [U_2550,U_2549,U_2548,U_2547,U_2546] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2546,tc_fun(U_2547,tc_HOL_Obool)),U_2548),hAPP(hAPP(c_COMBC(U_2546,tc_fun(U_2547,tc_HOL_Obool),tc_fun(U_2547,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2547,tc_HOL_Obool),tc_fun(tc_fun(U_2547,tc_HOL_Obool),tc_fun(U_2547,tc_HOL_Obool)),U_2546),c_Groups_Ominus__class_Ominus(tc_fun(U_2547,tc_HOL_Obool))),U_2549)),U_2550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2547,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2546,tc_fun(U_2547,tc_HOL_Obool)),U_2548),U_2549)),U_2550),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

cnf(f_494_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2546,tc_fun(U_2547,tc_HOL_Obool)),U_2548),hAPP(hAPP(c_COMBC(U_2546,tc_fun(U_2547,tc_HOL_Obool),tc_fun(U_2547,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2547,tc_HOL_Obool),tc_fun(tc_fun(U_2547,tc_HOL_Obool),tc_fun(U_2547,tc_HOL_Obool)),U_2546),c_Groups_Ominus__class_Ominus(tc_fun(U_2547,tc_HOL_Obool))),U_2549)),U_2550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2547,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2546,tc_fun(U_2547,tc_HOL_Obool)),U_2548),U_2549)),U_2550),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_1,plain,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UN]) ).

fof(f_495_2,plain,
    ! [U_2556,U_2555,U_2554,U_2553,U_2552,U_2551] : hAPP(c_Set_Ovimage(U_2551,U_2552,U_2553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2554,tc_fun(U_2552,tc_HOL_Obool)),U_2555),U_2556)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2554,tc_fun(U_2551,tc_HOL_Obool)),U_2555),hAPP(hAPP(c_COMBB(tc_fun(U_2552,tc_HOL_Obool),tc_fun(U_2551,tc_HOL_Obool),U_2554),c_Set_Ovimage(U_2551,U_2552,U_2553)),U_2556)),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

cnf(f_495_3,plain,
    hAPP(c_Set_Ovimage(U_2551,U_2552,U_2553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2554,tc_fun(U_2552,tc_HOL_Obool)),U_2555),U_2556)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2554,tc_fun(U_2551,tc_HOL_Obool)),U_2555),hAPP(hAPP(c_COMBB(tc_fun(U_2552,tc_HOL_Obool),tc_fun(U_2551,tc_HOL_Obool),U_2554),c_Set_Ovimage(U_2551,U_2552,U_2553)),U_2556)),
    inference(clausify,[status(thm)],[f_495_2]) ).

fof(f_496_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Union]) ).

fof(f_496_2,plain,
    ! [U_2560,U_2559,U_2558,U_2557] : hAPP(c_Set_Ovimage(U_2557,U_2558,U_2559),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2558,tc_HOL_Obool),U_2560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2558,tc_HOL_Obool),tc_fun(U_2557,tc_HOL_Obool)),U_2560),c_Set_Ovimage(U_2557,U_2558,U_2559)),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

cnf(f_496_3,plain,
    hAPP(c_Set_Ovimage(U_2557,U_2558,U_2559),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2558,tc_HOL_Obool),U_2560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_2558,tc_HOL_Obool),tc_fun(U_2557,tc_HOL_Obool)),U_2560),c_Set_Ovimage(U_2557,U_2558,U_2559)),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_1,plain,
    ! [V_A_2,V_C_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) ) )
      & ( ! [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).

fof(f_497_2,plain,
    ! [U_2565,U_2564,U_2563] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2563,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2563,tc_HOL_Obool),U_2564)),U_2565) = c_Orderings_Obot__class_Obot(tc_fun(U_2563,tc_HOL_Obool))
        | ? [U_2562] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2563,tc_HOL_Obool)),U_2562),U_2565) != c_Orderings_Obot__class_Obot(tc_fun(U_2563,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2563,tc_HOL_Obool)),U_2562),U_2564)) ) )
      & ( ! [U_2561] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2563,tc_HOL_Obool)),U_2561),U_2565) = c_Orderings_Obot__class_Obot(tc_fun(U_2563,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2563,tc_HOL_Obool)),U_2561),U_2564)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2563,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2563,tc_HOL_Obool),U_2564)),U_2565) != c_Orderings_Obot__class_Obot(tc_fun(U_2563,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_2571,U_2569,U_2567] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2567,tc_HOL_Obool),U_2569)),U_2571) = c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool))
        | ? [U_2562] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),U_2562),U_2571) != c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2567,tc_HOL_Obool)),U_2562),U_2569)) ) )
    & ! [U_2570,U_2568,U_2566] :
        ( ! [U_2561] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2570) = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2568)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2566,tc_HOL_Obool),U_2568)),U_2570) != c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_497_2]) ).

fof(f_497_4,plain,
    ( ! [U_2571,U_2569,U_2567] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2567,tc_HOL_Obool),U_2569)),U_2571) = c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),sK50(U_2571,U_2569,U_2567)),U_2571) != c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2567,tc_HOL_Obool)),sK50(U_2571,U_2569,U_2567)),U_2569)) ) )
    & ! [U_2570,U_2568,U_2566] :
        ( ! [U_2561] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2570) = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2568)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2566,tc_HOL_Obool),U_2568)),U_2570) != c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2562,sK50(U_2571,U_2569,U_2567))],[f_497_3]) ).

cnf(f_497_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2570) = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2566,tc_HOL_Obool)),U_2561),U_2568))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2566,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2566,tc_HOL_Obool),U_2568)),U_2570) != c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_497_4]) ).

cnf(f_497_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2567,tc_HOL_Obool)),sK50(U_2571,U_2569,U_2567)),U_2569))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2567,tc_HOL_Obool),U_2569)),U_2571) = c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_497_4]) ).

cnf(f_497_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),sK50(U_2571,U_2569,U_2567)),U_2571) != c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2567,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2567,tc_HOL_Obool),U_2569)),U_2571) = c_Orderings_Obot__class_Obot(tc_fun(U_2567,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_497_4]) ).

fof(f_498_1,plain,
    ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).

fof(f_498_2,plain,
    ! [U_2577,U_2576,U_2575,U_2574,U_2573,U_2572] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2572,tc_fun(U_2575,tc_HOL_Obool)),U_2574),hAPP(hAPP(c_COMBB(tc_fun(U_2575,tc_HOL_Obool),tc_fun(U_2575,tc_HOL_Obool),U_2572),hAPP(c_Set_Oinsert(U_2575),U_2576)),U_2577)) = hAPP(hAPP(c_Set_Oinsert(U_2575),U_2576),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2572,tc_fun(U_2575,tc_HOL_Obool)),U_2574),U_2577))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2574)) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

cnf(f_498_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2572,tc_fun(U_2575,tc_HOL_Obool)),U_2574),hAPP(hAPP(c_COMBB(tc_fun(U_2575,tc_HOL_Obool),tc_fun(U_2575,tc_HOL_Obool),U_2572),hAPP(c_Set_Oinsert(U_2575),U_2576)),U_2577)) = hAPP(hAPP(c_Set_Oinsert(U_2575),U_2576),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2572,tc_fun(U_2575,tc_HOL_Obool)),U_2574),U_2577))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2574)) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

fof(f_499_1,plain,
    ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).

fof(f_499_2,plain,
    ! [U_2582,U_2581,U_2580,U_2579,U_2578] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2581,tc_HOL_Obool)),hAPP(U_2582,U_2579)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2578,tc_fun(U_2581,tc_HOL_Obool)),U_2580),U_2582)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2578,tc_fun(U_2581,tc_HOL_Obool)),U_2580),U_2582)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2578),U_2579),U_2580)) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

cnf(f_499_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2581,tc_HOL_Obool)),hAPP(U_2582,U_2579)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2578,tc_fun(U_2581,tc_HOL_Obool)),U_2580),U_2582)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2578,tc_fun(U_2581,tc_HOL_Obool)),U_2580),U_2582)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2578),U_2579),U_2580)) ),
    inference(clausify,[status(thm)],[f_499_2]) ).

fof(f_500_1,plain,
    ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).

fof(f_500_2,plain,
    ! [U_2587,U_2586,U_2585,U_2584,U_2583] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2584,tc_fun(U_2585,tc_HOL_Obool)),U_2583),hAPP(hAPP(c_COMBB(tc_fun(U_2585,tc_HOL_Obool),tc_fun(U_2585,tc_HOL_Obool),U_2584),hAPP(c_Set_Oinsert(U_2585),U_2586)),U_2587)) = hAPP(hAPP(c_Set_Oinsert(U_2585),U_2586),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2584,tc_fun(U_2585,tc_HOL_Obool)),U_2583),U_2587))
        | U_2583 = c_Orderings_Obot__class_Obot(tc_fun(U_2584,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2584,tc_fun(U_2585,tc_HOL_Obool)),U_2583),hAPP(hAPP(c_COMBB(tc_fun(U_2585,tc_HOL_Obool),tc_fun(U_2585,tc_HOL_Obool),U_2584),hAPP(c_Set_Oinsert(U_2585),U_2586)),U_2587)) = c_Orderings_Obot__class_Obot(tc_fun(U_2585,tc_HOL_Obool))
        | U_2583 != c_Orderings_Obot__class_Obot(tc_fun(U_2584,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ( ! [U_2597,U_2595,U_2593,U_2591,U_2589] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2591,tc_fun(U_2593,tc_HOL_Obool)),U_2589),hAPP(hAPP(c_COMBB(tc_fun(U_2593,tc_HOL_Obool),tc_fun(U_2593,tc_HOL_Obool),U_2591),hAPP(c_Set_Oinsert(U_2593),U_2595)),U_2597)) = hAPP(hAPP(c_Set_Oinsert(U_2593),U_2595),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2591,tc_fun(U_2593,tc_HOL_Obool)),U_2589),U_2597))
        | U_2589 = c_Orderings_Obot__class_Obot(tc_fun(U_2591,tc_HOL_Obool)) )
    & ! [U_2596,U_2594,U_2592,U_2590,U_2588] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2590,tc_fun(U_2592,tc_HOL_Obool)),U_2588),hAPP(hAPP(c_COMBB(tc_fun(U_2592,tc_HOL_Obool),tc_fun(U_2592,tc_HOL_Obool),U_2590),hAPP(c_Set_Oinsert(U_2592),U_2594)),U_2596)) = c_Orderings_Obot__class_Obot(tc_fun(U_2592,tc_HOL_Obool))
        | U_2588 != c_Orderings_Obot__class_Obot(tc_fun(U_2590,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2590,tc_fun(U_2592,tc_HOL_Obool)),U_2588),hAPP(hAPP(c_COMBB(tc_fun(U_2592,tc_HOL_Obool),tc_fun(U_2592,tc_HOL_Obool),U_2590),hAPP(c_Set_Oinsert(U_2592),U_2594)),U_2596)) = c_Orderings_Obot__class_Obot(tc_fun(U_2592,tc_HOL_Obool))
    | U_2588 != c_Orderings_Obot__class_Obot(tc_fun(U_2590,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

cnf(f_500_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2591,tc_fun(U_2593,tc_HOL_Obool)),U_2589),hAPP(hAPP(c_COMBB(tc_fun(U_2593,tc_HOL_Obool),tc_fun(U_2593,tc_HOL_Obool),U_2591),hAPP(c_Set_Oinsert(U_2593),U_2595)),U_2597)) = hAPP(hAPP(c_Set_Oinsert(U_2593),U_2595),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2591,tc_fun(U_2593,tc_HOL_Obool)),U_2589),U_2597))
    | U_2589 = c_Orderings_Obot__class_Obot(tc_fun(U_2591,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).

fof(f_501_2,plain,
    ! [U_2599,U_2598] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2598,tc_fun(U_2598,tc_HOL_Obool)),U_2599),hAPP(hAPP(c_COMBC(U_2598,tc_fun(U_2598,tc_HOL_Obool),tc_fun(U_2598,tc_HOL_Obool)),c_Set_Oinsert(U_2598)),c_Orderings_Obot__class_Obot(tc_fun(U_2598,tc_HOL_Obool)))) = U_2599,
    inference(variable_rename,[status(thm)],[f_501_1]) ).

cnf(f_501_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2598,tc_fun(U_2598,tc_HOL_Obool)),U_2599),hAPP(hAPP(c_COMBC(U_2598,tc_fun(U_2598,tc_HOL_Obool),tc_fun(U_2598,tc_HOL_Obool)),c_Set_Oinsert(U_2598)),c_Orderings_Obot__class_Obot(tc_fun(U_2598,tc_HOL_Obool)))) = U_2599,
    inference(clausify,[status(thm)],[f_501_2]) ).

fof(f_502_1,plain,
    ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_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_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).

fof(f_502_2,plain,
    ! [U_2604,U_2603,U_2602,U_2601,U_2600] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_2602),U_2603),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2601,tc_fun(U_2602,tc_HOL_Obool)),U_2600),U_2604)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2601,tc_fun(U_2602,tc_HOL_Obool)),U_2600),hAPP(hAPP(c_COMBB(tc_fun(U_2602,tc_HOL_Obool),tc_fun(U_2602,tc_HOL_Obool),U_2601),hAPP(c_Set_Oinsert(U_2602),U_2603)),U_2604))
        | U_2600 = c_Orderings_Obot__class_Obot(tc_fun(U_2601,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_2602),U_2603),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2601,tc_fun(U_2602,tc_HOL_Obool)),U_2600),U_2604)) = hAPP(hAPP(c_Set_Oinsert(U_2602),U_2603),c_Orderings_Obot__class_Obot(tc_fun(U_2602,tc_HOL_Obool)))
        | U_2600 != c_Orderings_Obot__class_Obot(tc_fun(U_2601,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ( ! [U_2614,U_2612,U_2610,U_2608,U_2606] :
        ( hAPP(hAPP(c_Set_Oinsert(U_2610),U_2612),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2608,tc_fun(U_2610,tc_HOL_Obool)),U_2606),U_2614)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2608,tc_fun(U_2610,tc_HOL_Obool)),U_2606),hAPP(hAPP(c_COMBB(tc_fun(U_2610,tc_HOL_Obool),tc_fun(U_2610,tc_HOL_Obool),U_2608),hAPP(c_Set_Oinsert(U_2610),U_2612)),U_2614))
        | U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2608,tc_HOL_Obool)) )
    & ! [U_2613,U_2611,U_2609,U_2607,U_2605] :
        ( hAPP(hAPP(c_Set_Oinsert(U_2609),U_2611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2607,tc_fun(U_2609,tc_HOL_Obool)),U_2605),U_2613)) = hAPP(hAPP(c_Set_Oinsert(U_2609),U_2611),c_Orderings_Obot__class_Obot(tc_fun(U_2609,tc_HOL_Obool)))
        | U_2605 != c_Orderings_Obot__class_Obot(tc_fun(U_2607,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_502_2]) ).

cnf(f_502_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2609),U_2611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2607,tc_fun(U_2609,tc_HOL_Obool)),U_2605),U_2613)) = hAPP(hAPP(c_Set_Oinsert(U_2609),U_2611),c_Orderings_Obot__class_Obot(tc_fun(U_2609,tc_HOL_Obool)))
    | U_2605 != c_Orderings_Obot__class_Obot(tc_fun(U_2607,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2610),U_2612),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2608,tc_fun(U_2610,tc_HOL_Obool)),U_2606),U_2614)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2608,tc_fun(U_2610,tc_HOL_Obool)),U_2606),hAPP(hAPP(c_COMBB(tc_fun(U_2610,tc_HOL_Obool),tc_fun(U_2610,tc_HOL_Obool),U_2608),hAPP(c_Set_Oinsert(U_2610),U_2612)),U_2614))
    | U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2608,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).

fof(f_503_2,plain,
    ! [U_2619,U_2618,U_2617,U_2616,U_2615] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2616,tc_fun(U_2617,tc_HOL_Obool)),U_2615),hAPP(hAPP(c_COMBB(tc_fun(U_2617,tc_HOL_Obool),tc_fun(U_2617,tc_HOL_Obool),U_2616),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2617,tc_HOL_Obool)),U_2618)),U_2619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2617,tc_HOL_Obool)),U_2618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2616,tc_fun(U_2617,tc_HOL_Obool)),U_2615),U_2619))
        | U_2615 = c_Orderings_Obot__class_Obot(tc_fun(U_2616,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2616,tc_fun(U_2617,tc_HOL_Obool)),U_2615),hAPP(hAPP(c_COMBB(tc_fun(U_2617,tc_HOL_Obool),tc_fun(U_2617,tc_HOL_Obool),U_2616),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2617,tc_HOL_Obool)),U_2618)),U_2619)) = c_Orderings_Obot__class_Obot(tc_fun(U_2617,tc_HOL_Obool))
        | U_2615 != c_Orderings_Obot__class_Obot(tc_fun(U_2616,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ( ! [U_2629,U_2627,U_2625,U_2623,U_2621] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2623,tc_fun(U_2625,tc_HOL_Obool)),U_2621),hAPP(hAPP(c_COMBB(tc_fun(U_2625,tc_HOL_Obool),tc_fun(U_2625,tc_HOL_Obool),U_2623),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2625,tc_HOL_Obool)),U_2627)),U_2629)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2625,tc_HOL_Obool)),U_2627),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2623,tc_fun(U_2625,tc_HOL_Obool)),U_2621),U_2629))
        | U_2621 = c_Orderings_Obot__class_Obot(tc_fun(U_2623,tc_HOL_Obool)) )
    & ! [U_2628,U_2626,U_2624,U_2622,U_2620] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2622,tc_fun(U_2624,tc_HOL_Obool)),U_2620),hAPP(hAPP(c_COMBB(tc_fun(U_2624,tc_HOL_Obool),tc_fun(U_2624,tc_HOL_Obool),U_2622),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2624,tc_HOL_Obool)),U_2626)),U_2628)) = c_Orderings_Obot__class_Obot(tc_fun(U_2624,tc_HOL_Obool))
        | U_2620 != c_Orderings_Obot__class_Obot(tc_fun(U_2622,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2622,tc_fun(U_2624,tc_HOL_Obool)),U_2620),hAPP(hAPP(c_COMBB(tc_fun(U_2624,tc_HOL_Obool),tc_fun(U_2624,tc_HOL_Obool),U_2622),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2624,tc_HOL_Obool)),U_2626)),U_2628)) = c_Orderings_Obot__class_Obot(tc_fun(U_2624,tc_HOL_Obool))
    | U_2620 != c_Orderings_Obot__class_Obot(tc_fun(U_2622,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

cnf(f_503_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2623,tc_fun(U_2625,tc_HOL_Obool)),U_2621),hAPP(hAPP(c_COMBB(tc_fun(U_2625,tc_HOL_Obool),tc_fun(U_2625,tc_HOL_Obool),U_2623),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2625,tc_HOL_Obool)),U_2627)),U_2629)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2625,tc_HOL_Obool)),U_2627),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2623,tc_fun(U_2625,tc_HOL_Obool)),U_2621),U_2629))
    | U_2621 = c_Orderings_Obot__class_Obot(tc_fun(U_2623,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).

fof(f_504_2,plain,
    ! [U_2634,U_2633,U_2632,U_2631,U_2630] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2631,tc_fun(U_2632,tc_HOL_Obool)),U_2630),hAPP(hAPP(c_COMBC(U_2631,tc_fun(U_2632,tc_HOL_Obool),tc_fun(U_2632,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2632,tc_HOL_Obool),tc_fun(tc_fun(U_2632,tc_HOL_Obool),tc_fun(U_2632,tc_HOL_Obool)),U_2631),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2632,tc_HOL_Obool))),U_2633)),U_2634)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2632,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2631,tc_fun(U_2632,tc_HOL_Obool)),U_2630),U_2633)),U_2634)
        | U_2630 = c_Orderings_Obot__class_Obot(tc_fun(U_2631,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2631,tc_fun(U_2632,tc_HOL_Obool)),U_2630),hAPP(hAPP(c_COMBC(U_2631,tc_fun(U_2632,tc_HOL_Obool),tc_fun(U_2632,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2632,tc_HOL_Obool),tc_fun(tc_fun(U_2632,tc_HOL_Obool),tc_fun(U_2632,tc_HOL_Obool)),U_2631),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2632,tc_HOL_Obool))),U_2633)),U_2634)) = c_Orderings_Obot__class_Obot(tc_fun(U_2632,tc_HOL_Obool))
        | U_2630 != c_Orderings_Obot__class_Obot(tc_fun(U_2631,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_2644,U_2642,U_2640,U_2638,U_2636] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2638,tc_fun(U_2640,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_COMBC(U_2638,tc_fun(U_2640,tc_HOL_Obool),tc_fun(U_2640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2640,tc_HOL_Obool),tc_fun(tc_fun(U_2640,tc_HOL_Obool),tc_fun(U_2640,tc_HOL_Obool)),U_2638),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2640,tc_HOL_Obool))),U_2642)),U_2644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2640,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2638,tc_fun(U_2640,tc_HOL_Obool)),U_2636),U_2642)),U_2644)
        | U_2636 = c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)) )
    & ! [U_2643,U_2641,U_2639,U_2637,U_2635] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2637,tc_fun(U_2639,tc_HOL_Obool)),U_2635),hAPP(hAPP(c_COMBC(U_2637,tc_fun(U_2639,tc_HOL_Obool),tc_fun(U_2639,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2639,tc_HOL_Obool),tc_fun(tc_fun(U_2639,tc_HOL_Obool),tc_fun(U_2639,tc_HOL_Obool)),U_2637),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2639,tc_HOL_Obool))),U_2641)),U_2643)) = c_Orderings_Obot__class_Obot(tc_fun(U_2639,tc_HOL_Obool))
        | U_2635 != c_Orderings_Obot__class_Obot(tc_fun(U_2637,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_504_2]) ).

cnf(f_504_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2637,tc_fun(U_2639,tc_HOL_Obool)),U_2635),hAPP(hAPP(c_COMBC(U_2637,tc_fun(U_2639,tc_HOL_Obool),tc_fun(U_2639,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2639,tc_HOL_Obool),tc_fun(tc_fun(U_2639,tc_HOL_Obool),tc_fun(U_2639,tc_HOL_Obool)),U_2637),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2639,tc_HOL_Obool))),U_2641)),U_2643)) = c_Orderings_Obot__class_Obot(tc_fun(U_2639,tc_HOL_Obool))
    | U_2635 != c_Orderings_Obot__class_Obot(tc_fun(U_2637,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2638,tc_fun(U_2640,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_COMBC(U_2638,tc_fun(U_2640,tc_HOL_Obool),tc_fun(U_2640,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2640,tc_HOL_Obool),tc_fun(tc_fun(U_2640,tc_HOL_Obool),tc_fun(U_2640,tc_HOL_Obool)),U_2638),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2640,tc_HOL_Obool))),U_2642)),U_2644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2640,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2638,tc_fun(U_2640,tc_HOL_Obool)),U_2636),U_2642)),U_2644)
    | U_2636 = c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).

fof(f_505_2,plain,
    ! [U_2649,U_2648,U_2647,U_2646,U_2645] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2647,tc_HOL_Obool)),U_2648),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2646,tc_fun(U_2647,tc_HOL_Obool)),U_2645),U_2649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2646,tc_fun(U_2647,tc_HOL_Obool)),U_2645),hAPP(hAPP(c_COMBB(tc_fun(U_2647,tc_HOL_Obool),tc_fun(U_2647,tc_HOL_Obool),U_2646),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2647,tc_HOL_Obool)),U_2648)),U_2649))
        | U_2645 = c_Orderings_Obot__class_Obot(tc_fun(U_2646,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2647,tc_HOL_Obool)),U_2648),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2646,tc_fun(U_2647,tc_HOL_Obool)),U_2645),U_2649)) = U_2648
        | U_2645 != c_Orderings_Obot__class_Obot(tc_fun(U_2646,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_2659,U_2657,U_2655,U_2653,U_2651] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2655,tc_HOL_Obool)),U_2657),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2653,tc_fun(U_2655,tc_HOL_Obool)),U_2651),U_2659)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2653,tc_fun(U_2655,tc_HOL_Obool)),U_2651),hAPP(hAPP(c_COMBB(tc_fun(U_2655,tc_HOL_Obool),tc_fun(U_2655,tc_HOL_Obool),U_2653),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2655,tc_HOL_Obool)),U_2657)),U_2659))
        | U_2651 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool)) )
    & ! [U_2658,U_2656,U_2654,U_2652,U_2650] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2654,tc_HOL_Obool)),U_2656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2652,tc_fun(U_2654,tc_HOL_Obool)),U_2650),U_2658)) = U_2656
        | U_2650 != c_Orderings_Obot__class_Obot(tc_fun(U_2652,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_505_2]) ).

cnf(f_505_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2654,tc_HOL_Obool)),U_2656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2652,tc_fun(U_2654,tc_HOL_Obool)),U_2650),U_2658)) = U_2656
    | U_2650 != c_Orderings_Obot__class_Obot(tc_fun(U_2652,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2655,tc_HOL_Obool)),U_2657),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2653,tc_fun(U_2655,tc_HOL_Obool)),U_2651),U_2659)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2653,tc_fun(U_2655,tc_HOL_Obool)),U_2651),hAPP(hAPP(c_COMBB(tc_fun(U_2655,tc_HOL_Obool),tc_fun(U_2655,tc_HOL_Obool),U_2653),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2655,tc_HOL_Obool)),U_2657)),U_2659))
    | U_2651 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( 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_a,tc_fun(T_b,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_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).

fof(f_506_2,plain,
    ! [U_2664,U_2663,U_2662,U_2661,U_2660] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2662,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2661,tc_fun(U_2662,tc_HOL_Obool)),U_2660),U_2663)),U_2664) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2661,tc_fun(U_2662,tc_HOL_Obool)),U_2660),hAPP(hAPP(c_COMBC(U_2661,tc_fun(U_2662,tc_HOL_Obool),tc_fun(U_2662,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2662,tc_HOL_Obool),tc_fun(tc_fun(U_2662,tc_HOL_Obool),tc_fun(U_2662,tc_HOL_Obool)),U_2661),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2662,tc_HOL_Obool))),U_2663)),U_2664))
        | U_2660 = c_Orderings_Obot__class_Obot(tc_fun(U_2661,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2662,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2661,tc_fun(U_2662,tc_HOL_Obool)),U_2660),U_2663)),U_2664) = U_2664
        | U_2660 != c_Orderings_Obot__class_Obot(tc_fun(U_2661,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_2674,U_2672,U_2670,U_2668,U_2666] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2670,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2668,tc_fun(U_2670,tc_HOL_Obool)),U_2666),U_2672)),U_2674) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2668,tc_fun(U_2670,tc_HOL_Obool)),U_2666),hAPP(hAPP(c_COMBC(U_2668,tc_fun(U_2670,tc_HOL_Obool),tc_fun(U_2670,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2670,tc_HOL_Obool),tc_fun(tc_fun(U_2670,tc_HOL_Obool),tc_fun(U_2670,tc_HOL_Obool)),U_2668),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2670,tc_HOL_Obool))),U_2672)),U_2674))
        | U_2666 = c_Orderings_Obot__class_Obot(tc_fun(U_2668,tc_HOL_Obool)) )
    & ! [U_2673,U_2671,U_2669,U_2667,U_2665] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2669,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2667,tc_fun(U_2669,tc_HOL_Obool)),U_2665),U_2671)),U_2673) = U_2673
        | U_2665 != c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_506_2]) ).

cnf(f_506_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2669,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2667,tc_fun(U_2669,tc_HOL_Obool)),U_2665),U_2671)),U_2673) = U_2673
    | U_2665 != c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2670,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2668,tc_fun(U_2670,tc_HOL_Obool)),U_2666),U_2672)),U_2674) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2668,tc_fun(U_2670,tc_HOL_Obool)),U_2666),hAPP(hAPP(c_COMBC(U_2668,tc_fun(U_2670,tc_HOL_Obool),tc_fun(U_2670,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2670,tc_HOL_Obool),tc_fun(tc_fun(U_2670,tc_HOL_Obool),tc_fun(U_2670,tc_HOL_Obool)),U_2668),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2670,tc_HOL_Obool))),U_2672)),U_2674))
    | U_2666 = c_Orderings_Obot__class_Obot(tc_fun(U_2668,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
      | ? [B_M] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).

fof(f_507_2,plain,
    ! [U_2677,U_2676] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2677)))
      | ? [U_2675] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),U_2675))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2676,tc_HOL_Obool)),U_2675),U_2677)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2676,tc_HOL_Obool)),U_2677)) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_2677,U_2676] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2677)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),sK51(U_2677,U_2676)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2676,tc_HOL_Obool)),sK51(U_2677,U_2676)),U_2677)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2676,tc_HOL_Obool)),U_2677)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2675,sK51(U_2677,U_2676))],[f_507_2]) ).

cnf(f_507_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2676,tc_HOL_Obool)),sK51(U_2677,U_2676)),U_2677))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2677)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2676,tc_HOL_Obool)),U_2677)) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),sK51(U_2677,U_2676)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2676),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2677)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2676,tc_HOL_Obool)),U_2677)) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_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_508_2,plain,
    ! [U_2680,U_2679,U_2678] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2678),U_2679)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2680),U_2679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2678),U_2680),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

cnf(f_508_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2678),U_2679)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2680),U_2679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2678),U_2680),
    inference(clausify,[status(thm)],[f_508_2]) ).

fof(f_509_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_509_2,plain,
    ! [U_2683,U_2682,U_2681] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2681),U_2682)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2681),U_2683)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2682),U_2683),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

cnf(f_509_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2681),U_2682)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2681),U_2683)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2682),U_2683),
    inference(clausify,[status(thm)],[f_509_2]) ).

fof(f_510_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_510_2,plain,
    ! [U_2686,U_2685,U_2684] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2684),U_2685)),U_2686) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2685),U_2686)),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

cnf(f_510_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2684),U_2685)),U_2686) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2685),U_2686)),
    inference(clausify,[status(thm)],[f_510_2]) ).

fof(f_511_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_511_2,plain,
    ! [U_2688,U_2687] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2687),U_2688)),U_2687) = U_2688,
    inference(variable_rename,[status(thm)],[f_511_1]) ).

cnf(f_511_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2687),U_2688)),U_2687) = U_2688,
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_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_512_2,plain,
    ! [U_2690,U_2689] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2689),U_2690)),U_2690) = U_2689,
    inference(variable_rename,[status(thm)],[f_512_1]) ).

cnf(f_512_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2689),U_2690)),U_2690) = U_2689,
    inference(clausify,[status(thm)],[f_512_2]) ).

fof(f_513_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN__I]) ).

fof(f_513_2,plain,
    ! [U_2695,U_2694,U_2693,U_2692] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2692,tc_fun(U_2694,tc_HOL_Obool)),U_2693),U_2695)))
      | ? [U_2691] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(U_2695,U_2691)))
          & hBOOL(hAPP(hAPP(c_member(U_2692),U_2691),U_2693)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2692),U_2693)) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_2695,U_2694,U_2693,U_2692] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2692,tc_fun(U_2694,tc_HOL_Obool)),U_2693),U_2695)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(U_2695,sK52(U_2695,U_2694,U_2693,U_2692))))
        & hBOOL(hAPP(hAPP(c_member(U_2692),sK52(U_2695,U_2694,U_2693,U_2692)),U_2693)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2692),U_2693)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_2691,sK52(U_2695,U_2694,U_2693,U_2692))],[f_513_2]) ).

cnf(f_513_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2692),sK52(U_2695,U_2694,U_2693,U_2692)),U_2693))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2692,tc_fun(U_2694,tc_HOL_Obool)),U_2693),U_2695)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2692),U_2693)) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

cnf(f_513_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(U_2695,sK52(U_2695,U_2694,U_2693,U_2692))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2692,tc_fun(U_2694,tc_HOL_Obool)),U_2693),U_2695)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2692),U_2693)) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_1,plain,
    ! [V_F_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ? [B_x] :
          ( ? [B_xa] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
              & B_x != B_xa
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).

fof(f_514_2,plain,
    ! [U_2700,U_2699,U_2698] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
      | ? [U_2697] :
          ( ? [U_2696] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2697),U_2696) != c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
              & U_2697 != U_2696
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2696),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2697),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_2700,U_2699,U_2698] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
      | ( ? [U_2696] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),U_2696) != c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
            & sK53(U_2700,U_2699,U_2698) != U_2696
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2696),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_2697,sK53(U_2700,U_2699,U_2698))],[f_514_2]) ).

fof(f_514_4,plain,
    ! [U_2700,U_2699,U_2698] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),sK54(U_2700,U_2699,U_2698)) != c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
        & sK53(U_2700,U_2699,U_2698) != sK54(U_2700,U_2699,U_2698)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),sK54(U_2700,U_2699,U_2698)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_2696,sK54(U_2700,U_2699,U_2698))],[f_514_3]) ).

cnf(f_514_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(clausify,[status(thm)],[f_514_4]) ).

cnf(f_514_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),sK54(U_2700,U_2699,U_2698)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(clausify,[status(thm)],[f_514_4]) ).

cnf(f_514_7,plain,
    ( sK53(U_2700,U_2699,U_2698) != sK54(U_2700,U_2699,U_2698)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(clausify,[status(thm)],[f_514_4]) ).

cnf(f_514_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),sK53(U_2700,U_2699,U_2698)),sK54(U_2700,U_2699,U_2698)) != c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2698,tc_HOL_Obool)),U_2699),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2698,tc_HOL_Obool),U_2700)) = c_Orderings_Obot__class_Obot(tc_fun(U_2698,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2698,tc_HOL_Obool)),U_2699),U_2700)) ),
    inference(clausify,[status(thm)],[f_514_4]) ).

fof(f_515_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).

fof(f_515_2,plain,
    ! [U_2705,U_2704,U_2703,U_2702,U_2701] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2701),U_2704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2702,U_2701),U_2703),U_2705)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2702,U_2701,hAPP(hAPP(c_COMBB(U_2701,tc_fun(U_2701,U_2701),U_2702),c_Lattices_Osemilattice__inf__class_Oinf(U_2701)),U_2705)),U_2704),U_2703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2702),U_2703))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2701) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2701),U_2704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2702,U_2701),U_2703),U_2705)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2702,U_2701,hAPP(hAPP(c_COMBB(U_2701,tc_fun(U_2701,U_2701),U_2702),c_Lattices_Osemilattice__inf__class_Oinf(U_2701)),U_2705)),U_2704),U_2703)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2702),U_2703))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2701) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_1,plain,
    ! [V_C_2,V_A_2,T_a] :
      ( ? [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnionE]) ).

fof(f_516_2,plain,
    ! [U_2709,U_2708,U_2707] :
      ( ? [U_2706] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2707,tc_HOL_Obool)),U_2706),U_2709))
          & hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),U_2706)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2707,tc_HOL_Obool),U_2709))) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_2709,U_2708,U_2707] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2707,tc_HOL_Obool)),sK55(U_2709,U_2708,U_2707)),U_2709))
        & hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),sK55(U_2709,U_2708,U_2707))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2707,tc_HOL_Obool),U_2709))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2706,sK55(U_2709,U_2708,U_2707))],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),sK55(U_2709,U_2708,U_2707)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2707,tc_HOL_Obool),U_2709))) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

cnf(f_516_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2707,tc_HOL_Obool)),sK55(U_2709,U_2708,U_2707)),U_2709))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2707),U_2708),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2707,tc_HOL_Obool),U_2709))) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).

fof(f_517_2,plain,
    ! [U_2715,U_2714,U_2713,U_2712,U_2711,U_2710] :
      ( hBOOL(hAPP(hAPP(U_2713,U_2715),U_2714))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2710),U_2715),U_2712))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2710,tc_fun(U_2711,tc_HOL_Obool)),U_2712),U_2713),U_2714)) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

cnf(f_517_3,plain,
    ( hBOOL(hAPP(hAPP(U_2713,U_2715),U_2714))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2710),U_2715),U_2712))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2710,tc_fun(U_2711,tc_HOL_Obool)),U_2712),U_2713),U_2714)) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

fof(f_518_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).

fof(f_518_2,plain,
    ! [U_2721,U_2720,U_2719,U_2718,U_2717,U_2716] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2721),U_2718))
      | hBOOL(hAPP(hAPP(U_2719,U_2721),U_2720))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2716,tc_fun(U_2717,tc_HOL_Obool)),U_2718),U_2719),U_2720)) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

cnf(f_518_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2721),U_2718))
    | hBOOL(hAPP(hAPP(U_2719,U_2721),U_2720))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2716,tc_fun(U_2717,tc_HOL_Obool)),U_2718),U_2719),U_2720)) ),
    inference(clausify,[status(thm)],[f_518_2]) ).

fof(f_519_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__D]) ).

fof(f_519_2,plain,
    ! [U_2727,U_2726,U_2725,U_2724,U_2723,U_2722] :
      ( hBOOL(hAPP(hAPP(c_member(U_2722),U_2723),hAPP(U_2726,U_2727)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2724),U_2727),U_2725))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2722),U_2723),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2724,tc_fun(U_2722,tc_HOL_Obool)),U_2725),U_2726))) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

cnf(f_519_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2722),U_2723),hAPP(U_2726,U_2727)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2724),U_2727),U_2725))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2722),U_2723),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2724,tc_fun(U_2722,tc_HOL_Obool)),U_2725),U_2726))) ),
    inference(clausify,[status(thm)],[f_519_2]) ).

fof(f_520_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__E]) ).

fof(f_520_2,plain,
    ! [U_2733,U_2732,U_2731,U_2730,U_2729,U_2728] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2730),U_2733),U_2731))
      | hBOOL(hAPP(hAPP(c_member(U_2728),U_2729),hAPP(U_2732,U_2733)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2728),U_2729),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2730,tc_fun(U_2728,tc_HOL_Obool)),U_2731),U_2732))) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

cnf(f_520_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2730),U_2733),U_2731))
    | hBOOL(hAPP(hAPP(c_member(U_2728),U_2729),hAPP(U_2732,U_2733)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2728),U_2729),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2730,tc_fun(U_2728,tc_HOL_Obool)),U_2731),U_2732))) ),
    inference(clausify,[status(thm)],[f_520_2]) ).

fof(f_521_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,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_521_2,plain,
    ! [U_2741,U_2740,U_2739,U_2738,U_2737,U_2736,U_2735,U_2734] :
      ( hBOOL(hAPP(hAPP(hAPP(U_2738,U_2741),U_2739),U_2740))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2734),U_2741),U_2737))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2734,tc_fun(U_2735,tc_fun(U_2736,tc_HOL_Obool))),U_2737),U_2738),U_2739),U_2740)) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

cnf(f_521_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_2738,U_2741),U_2739),U_2740))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2734),U_2741),U_2737))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2734,tc_fun(U_2735,tc_fun(U_2736,tc_HOL_Obool))),U_2737),U_2738),U_2739),U_2740)) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

fof(f_522_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_fun(T_b,tc_fun(T_c,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_522_2,plain,
    ! [U_2749,U_2748,U_2747,U_2746,U_2745,U_2744,U_2743,U_2742] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2742),U_2749),U_2745))
      | hBOOL(hAPP(hAPP(hAPP(U_2746,U_2749),U_2747),U_2748))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2742,tc_fun(U_2743,tc_fun(U_2744,tc_HOL_Obool))),U_2745),U_2746),U_2747),U_2748)) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

cnf(f_522_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2742),U_2749),U_2745))
    | hBOOL(hAPP(hAPP(hAPP(U_2746,U_2749),U_2747),U_2748))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2742,tc_fun(U_2743,tc_fun(U_2744,tc_HOL_Obool))),U_2745),U_2746),U_2747),U_2748)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

fof(f_523_1,plain,
    ! [V_A_2,T_b,V_I_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).

fof(f_523_2,plain,
    ! [U_2754,U_2753,U_2752,U_2751] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2751,tc_fun(U_2753,tc_HOL_Obool)),U_2752),U_2754)))
      | ! [U_2750] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),hAPP(U_2754,U_2750)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2751),U_2750),U_2752)) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

cnf(f_523_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2751,tc_fun(U_2753,tc_HOL_Obool)),U_2752),U_2754)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),hAPP(U_2754,U_2750)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2751),U_2750),U_2752)) ),
    inference(clausify,[status(thm)],[f_523_2]) ).

fof(f_524_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).

fof(f_524_2,plain,
    ! [U_2760,U_2759,U_2758,U_2757,U_2756,U_2755] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2756,tc_fun(U_2757,U_2755)),U_2758),U_2759),U_2760) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2756,U_2755),U_2758),hAPP(hAPP(c_COMBC(U_2756,U_2757,U_2755),U_2759),U_2760))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2755) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

cnf(f_524_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2756,tc_fun(U_2757,U_2755)),U_2758),U_2759),U_2760) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2756,U_2755),U_2758),hAPP(hAPP(c_COMBC(U_2756,U_2757,U_2755),U_2759),U_2760))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2755) ),
    inference(clausify,[status(thm)],[f_524_2]) ).

fof(f_525_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(f_525_2,plain,
    ! [U_2764,U_2763,U_2762,U_2761] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2761,tc_fun(U_2762,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2761,tc_HOL_Obool),U_2763)),U_2764) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_2761,tc_HOL_Obool),tc_fun(U_2762,tc_HOL_Obool)),U_2763),hAPP(hAPP(c_COMBC(tc_fun(U_2761,tc_HOL_Obool),tc_fun(U_2761,tc_fun(U_2762,tc_HOL_Obool)),tc_fun(U_2762,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2761,tc_fun(U_2762,tc_HOL_Obool))),U_2764)),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

cnf(f_525_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2761,tc_fun(U_2762,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2761,tc_HOL_Obool),U_2763)),U_2764) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_2761,tc_HOL_Obool),tc_fun(U_2762,tc_HOL_Obool)),U_2763),hAPP(hAPP(c_COMBC(tc_fun(U_2761,tc_HOL_Obool),tc_fun(U_2761,tc_fun(U_2762,tc_HOL_Obool)),tc_fun(U_2762,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2761,tc_fun(U_2762,tc_HOL_Obool))),U_2764)),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(f_526_2,plain,
    ! [U_2768,U_2767,U_2766,U_2765] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_2765,tc_HOL_Obool),tc_fun(U_2766,tc_HOL_Obool)),U_2767),hAPP(hAPP(c_COMBC(tc_fun(U_2765,tc_HOL_Obool),tc_fun(U_2765,tc_fun(U_2766,tc_HOL_Obool)),tc_fun(U_2766,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2765,tc_fun(U_2766,tc_HOL_Obool))),U_2768)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2765,tc_fun(U_2766,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2765,tc_HOL_Obool),U_2767)),U_2768),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

cnf(f_526_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_2765,tc_HOL_Obool),tc_fun(U_2766,tc_HOL_Obool)),U_2767),hAPP(hAPP(c_COMBC(tc_fun(U_2765,tc_HOL_Obool),tc_fun(U_2765,tc_fun(U_2766,tc_HOL_Obool)),tc_fun(U_2766,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2765,tc_fun(U_2766,tc_HOL_Obool))),U_2768)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2765,tc_fun(U_2766,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2765,tc_HOL_Obool),U_2767)),U_2768),
    inference(clausify,[status(thm)],[f_526_2]) ).

fof(f_527_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).

fof(f_527_2,plain,
    ! [U_2774,U_2773,U_2772,U_2771,U_2770,U_2769] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2770,U_2769),U_2771),hAPP(hAPP(c_COMBB(tc_fun(U_2772,U_2769),U_2769,U_2770),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2772,U_2769),U_2773)),U_2774)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2772,U_2769),U_2773),hAPP(hAPP(c_COMBB(tc_fun(U_2770,U_2769),U_2769,U_2772),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2770,U_2769),U_2771)),hAPP(c_COMBC(U_2770,U_2772,U_2769),U_2774)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2769) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

cnf(f_527_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2770,U_2769),U_2771),hAPP(hAPP(c_COMBB(tc_fun(U_2772,U_2769),U_2769,U_2770),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2772,U_2769),U_2773)),U_2774)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2772,U_2769),U_2773),hAPP(hAPP(c_COMBB(tc_fun(U_2770,U_2769),U_2769,U_2772),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2770,U_2769),U_2771)),hAPP(c_COMBC(U_2770,U_2772,U_2769),U_2774)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2769) ),
    inference(clausify,[status(thm)],[f_527_2]) ).

fof(f_528_1,plain,
    ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).

fof(f_528_2,plain,
    ! [U_2781,U_2780,U_2779,U_2778,U_2777] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2779,tc_fun(U_2777,tc_HOL_Obool)),U_2780),U_2781)))
        | ? [U_2776] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),hAPP(U_2781,U_2776)))
            & hBOOL(hAPP(hAPP(c_member(U_2779),U_2776),U_2780)) ) )
      & ( ! [U_2775] :
            ( hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),hAPP(U_2781,U_2775)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2779),U_2775),U_2780)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2779,tc_fun(U_2777,tc_HOL_Obool)),U_2780),U_2781))) ) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ( ! [U_2791,U_2789,U_2787,U_2785,U_2783] :
        ( hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2787,tc_fun(U_2783,tc_HOL_Obool)),U_2789),U_2791)))
        | ? [U_2776] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(U_2791,U_2776)))
            & hBOOL(hAPP(hAPP(c_member(U_2787),U_2776),U_2789)) ) )
    & ! [U_2790,U_2788,U_2786,U_2784,U_2782] :
        ( ! [U_2775] :
            ( hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(U_2790,U_2775)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2786),U_2775),U_2788)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2786,tc_fun(U_2782,tc_HOL_Obool)),U_2788),U_2790))) ) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

fof(f_528_4,plain,
    ( ! [U_2791,U_2789,U_2787,U_2785,U_2783] :
        ( hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2787,tc_fun(U_2783,tc_HOL_Obool)),U_2789),U_2791)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(U_2791,sK56(U_2791,U_2789,U_2787,U_2785,U_2783))))
          & hBOOL(hAPP(hAPP(c_member(U_2787),sK56(U_2791,U_2789,U_2787,U_2785,U_2783)),U_2789)) ) )
    & ! [U_2790,U_2788,U_2786,U_2784,U_2782] :
        ( ! [U_2775] :
            ( hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(U_2790,U_2775)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2786),U_2775),U_2788)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2786,tc_fun(U_2782,tc_HOL_Obool)),U_2788),U_2790))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2776,sK56(U_2791,U_2789,U_2787,U_2785,U_2783))],[f_528_3]) ).

cnf(f_528_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(U_2790,U_2775)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2786),U_2775),U_2788))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2786,tc_fun(U_2782,tc_HOL_Obool)),U_2788),U_2790))) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

cnf(f_528_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2787),sK56(U_2791,U_2789,U_2787,U_2785,U_2783)),U_2789))
    | hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2787,tc_fun(U_2783,tc_HOL_Obool)),U_2789),U_2791))) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

cnf(f_528_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(U_2791,sK56(U_2791,U_2789,U_2787,U_2785,U_2783))))
    | hBOOL(hAPP(hAPP(c_member(U_2783),U_2785),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2787,tc_fun(U_2783,tc_HOL_Obool)),U_2789),U_2791))) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

fof(f_529_1,plain,
    ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(f_529_2,plain,
    ! [U_2796,U_2795,U_2794,U_2793,U_2792] : hAPP(hAPP(c_Set_Oinsert(U_2792),U_2793),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2794,tc_fun(U_2792,tc_HOL_Obool)),U_2795),U_2796)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2794,tc_fun(U_2792,tc_HOL_Obool)),U_2795),hAPP(hAPP(c_COMBB(tc_fun(U_2792,tc_HOL_Obool),tc_fun(U_2792,tc_HOL_Obool),U_2794),hAPP(c_Set_Oinsert(U_2792),U_2793)),U_2796)),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

cnf(f_529_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_2792),U_2793),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2794,tc_fun(U_2792,tc_HOL_Obool)),U_2795),U_2796)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2794,tc_fun(U_2792,tc_HOL_Obool)),U_2795),hAPP(hAPP(c_COMBB(tc_fun(U_2792,tc_HOL_Obool),tc_fun(U_2792,tc_HOL_Obool),U_2794),hAPP(c_Set_Oinsert(U_2792),U_2793)),U_2796)),
    inference(clausify,[status(thm)],[f_529_2]) ).

fof(f_530_1,plain,
    ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(f_530_2,plain,
    ! [U_2801,U_2800,U_2799,U_2798,U_2797] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2797,tc_fun(U_2798,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_COMBB(tc_fun(U_2798,tc_HOL_Obool),tc_fun(U_2798,tc_HOL_Obool),U_2797),hAPP(c_Set_Oinsert(U_2798),U_2800)),U_2801)) = hAPP(hAPP(c_Set_Oinsert(U_2798),U_2800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2797,tc_fun(U_2798,tc_HOL_Obool)),U_2799),U_2801)),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

cnf(f_530_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2797,tc_fun(U_2798,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_COMBB(tc_fun(U_2798,tc_HOL_Obool),tc_fun(U_2798,tc_HOL_Obool),U_2797),hAPP(c_Set_Oinsert(U_2798),U_2800)),U_2801)) = hAPP(hAPP(c_Set_Oinsert(U_2798),U_2800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2797,tc_fun(U_2798,tc_HOL_Obool)),U_2799),U_2801)),
    inference(clausify,[status(thm)],[f_530_2]) ).

fof(f_531_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(f_531_2,plain,
    ! [U_2807,U_2806,U_2805,U_2804,U_2803,U_2802] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2802,tc_fun(U_2803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2804,U_2802,U_2805),U_2806)),U_2807) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2804,tc_fun(U_2803,tc_HOL_Obool)),U_2806),hAPP(hAPP(c_COMBB(U_2802,tc_fun(U_2803,tc_HOL_Obool),U_2804),U_2807),U_2805)),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

cnf(f_531_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2802,tc_fun(U_2803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2804,U_2802,U_2805),U_2806)),U_2807) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2804,tc_fun(U_2803,tc_HOL_Obool)),U_2806),hAPP(hAPP(c_COMBB(U_2802,tc_fun(U_2803,tc_HOL_Obool),U_2804),U_2807),U_2805)),
    inference(clausify,[status(thm)],[f_531_2]) ).

fof(f_532_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(f_532_2,plain,
    ! [U_2813,U_2812,U_2811,U_2810,U_2809,U_2808] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2808,tc_fun(U_2809,tc_HOL_Obool)),U_2810),hAPP(hAPP(c_COMBB(U_2811,tc_fun(U_2809,tc_HOL_Obool),U_2808),U_2812),U_2813)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2811,tc_fun(U_2809,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2808,U_2811,U_2813),U_2810)),U_2812),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

cnf(f_532_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2808,tc_fun(U_2809,tc_HOL_Obool)),U_2810),hAPP(hAPP(c_COMBB(U_2811,tc_fun(U_2809,tc_HOL_Obool),U_2808),U_2812),U_2813)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2811,tc_fun(U_2809,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2808,U_2811,U_2813),U_2810)),U_2812),
    inference(clausify,[status(thm)],[f_532_2]) ).

fof(f_533_1,plain,
    ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).

fof(f_533_2,plain,
    ! [U_2820,U_2819,U_2818,U_2817,U_2816,U_2815,U_2814] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2814,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2815,tc_fun(U_2814,tc_HOL_Obool)),U_2816),U_2817)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2818,tc_fun(U_2814,tc_HOL_Obool)),U_2819),U_2820)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2815,tc_fun(U_2814,tc_HOL_Obool)),U_2816),hAPP(hAPP(c_COMBB(tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2814,tc_HOL_Obool),U_2815),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2818,tc_fun(U_2814,tc_HOL_Obool)),U_2819)),hAPP(hAPP(c_COMBC(U_2815,tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool)),tc_fun(tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool))),U_2815),c_COMBB(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool),U_2818)),hAPP(hAPP(c_COMBB(tc_fun(U_2814,tc_HOL_Obool),tc_fun(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool)),U_2815),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2814,tc_HOL_Obool))),U_2817))),U_2820))),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

cnf(f_533_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2814,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2815,tc_fun(U_2814,tc_HOL_Obool)),U_2816),U_2817)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2818,tc_fun(U_2814,tc_HOL_Obool)),U_2819),U_2820)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2815,tc_fun(U_2814,tc_HOL_Obool)),U_2816),hAPP(hAPP(c_COMBB(tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2814,tc_HOL_Obool),U_2815),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2818,tc_fun(U_2814,tc_HOL_Obool)),U_2819)),hAPP(hAPP(c_COMBC(U_2815,tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool)),tc_fun(tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool)),tc_fun(U_2818,tc_fun(U_2814,tc_HOL_Obool))),U_2815),c_COMBB(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool),U_2818)),hAPP(hAPP(c_COMBB(tc_fun(U_2814,tc_HOL_Obool),tc_fun(tc_fun(U_2814,tc_HOL_Obool),tc_fun(U_2814,tc_HOL_Obool)),U_2815),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2814,tc_HOL_Obool))),U_2817))),U_2820))),
    inference(clausify,[status(thm)],[f_533_2]) ).

fof(f_534_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(f_534_2,plain,
    ! [U_2825,U_2824,U_2823,U_2822,U_2821] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2821,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2822,tc_fun(U_2821,tc_HOL_Obool)),U_2823),U_2824)),U_2825) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2822,tc_fun(U_2821,tc_HOL_Obool)),U_2823),hAPP(hAPP(c_COMBC(U_2822,tc_fun(U_2821,tc_HOL_Obool),tc_fun(U_2821,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2821,tc_HOL_Obool),tc_fun(tc_fun(U_2821,tc_HOL_Obool),tc_fun(U_2821,tc_HOL_Obool)),U_2822),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2821,tc_HOL_Obool))),U_2824)),U_2825)),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

cnf(f_534_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2821,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2822,tc_fun(U_2821,tc_HOL_Obool)),U_2823),U_2824)),U_2825) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2822,tc_fun(U_2821,tc_HOL_Obool)),U_2823),hAPP(hAPP(c_COMBC(U_2822,tc_fun(U_2821,tc_HOL_Obool),tc_fun(U_2821,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2821,tc_HOL_Obool),tc_fun(tc_fun(U_2821,tc_HOL_Obool),tc_fun(U_2821,tc_HOL_Obool)),U_2822),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2821,tc_HOL_Obool))),U_2824)),U_2825)),
    inference(clausify,[status(thm)],[f_534_2]) ).

fof(f_535_1,plain,
    ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).

fof(f_535_2,plain,
    ! [U_2830,U_2829,U_2828,U_2827,U_2826] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2826,tc_HOL_Obool)),U_2827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2829),U_2830)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2829),hAPP(hAPP(c_COMBB(tc_fun(U_2826,tc_HOL_Obool),tc_fun(U_2826,tc_HOL_Obool),U_2828),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2826,tc_HOL_Obool)),U_2827)),U_2830)),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2826,tc_HOL_Obool)),U_2827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2829),U_2830)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2828,tc_fun(U_2826,tc_HOL_Obool)),U_2829),hAPP(hAPP(c_COMBB(tc_fun(U_2826,tc_HOL_Obool),tc_fun(U_2826,tc_HOL_Obool),U_2828),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2826,tc_HOL_Obool)),U_2827)),U_2830)),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(f_536_2,plain,
    ! [U_2835,U_2834,U_2833,U_2832,U_2831] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2831,tc_HOL_Obool)),U_2832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2833,tc_fun(U_2831,tc_HOL_Obool)),U_2834),U_2835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2833,tc_fun(U_2831,tc_HOL_Obool)),U_2834),hAPP(hAPP(c_COMBB(tc_fun(U_2831,tc_HOL_Obool),tc_fun(U_2831,tc_HOL_Obool),U_2833),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2831,tc_HOL_Obool)),U_2832)),U_2835)),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2831,tc_HOL_Obool)),U_2832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2833,tc_fun(U_2831,tc_HOL_Obool)),U_2834),U_2835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2833,tc_fun(U_2831,tc_HOL_Obool)),U_2834),hAPP(hAPP(c_COMBB(tc_fun(U_2831,tc_HOL_Obool),tc_fun(U_2831,tc_HOL_Obool),U_2833),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2831,tc_HOL_Obool)),U_2832)),U_2835)),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(f_537_2,plain,
    ! [U_2840,U_2839,U_2838,U_2837,U_2836] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2836,tc_fun(U_2837,tc_HOL_Obool)),U_2838),hAPP(hAPP(c_COMBC(U_2836,tc_fun(U_2837,tc_HOL_Obool),tc_fun(U_2837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2837,tc_HOL_Obool),tc_fun(tc_fun(U_2837,tc_HOL_Obool),tc_fun(U_2837,tc_HOL_Obool)),U_2836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2837,tc_HOL_Obool))),U_2839)),U_2840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2836,tc_fun(U_2837,tc_HOL_Obool)),U_2838),U_2839)),U_2840),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

cnf(f_537_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2836,tc_fun(U_2837,tc_HOL_Obool)),U_2838),hAPP(hAPP(c_COMBC(U_2836,tc_fun(U_2837,tc_HOL_Obool),tc_fun(U_2837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2837,tc_HOL_Obool),tc_fun(tc_fun(U_2837,tc_HOL_Obool),tc_fun(U_2837,tc_HOL_Obool)),U_2836),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2837,tc_HOL_Obool))),U_2839)),U_2840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2836,tc_fun(U_2837,tc_HOL_Obool)),U_2838),U_2839)),U_2840),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(f_538_2,plain,
    ! [U_2845,U_2844,U_2843,U_2842,U_2841] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2841,tc_fun(U_2842,tc_HOL_Obool)),U_2843),hAPP(hAPP(c_COMBB(tc_fun(U_2842,tc_HOL_Obool),tc_fun(U_2842,tc_HOL_Obool),U_2841),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2842,tc_HOL_Obool)),U_2844)),U_2845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2842,tc_HOL_Obool)),U_2844),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2841,tc_fun(U_2842,tc_HOL_Obool)),U_2843),U_2845)),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

cnf(f_538_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2841,tc_fun(U_2842,tc_HOL_Obool)),U_2843),hAPP(hAPP(c_COMBB(tc_fun(U_2842,tc_HOL_Obool),tc_fun(U_2842,tc_HOL_Obool),U_2841),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2842,tc_HOL_Obool)),U_2844)),U_2845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2842,tc_HOL_Obool)),U_2844),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2841,tc_fun(U_2842,tc_HOL_Obool)),U_2843),U_2845)),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).

fof(f_539_2,plain,
    ! [U_2850,U_2849,U_2848,U_2847,U_2846] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),hAPP(hAPP(c_COMBS(U_2846,tc_fun(U_2847,tc_HOL_Obool),tc_fun(U_2847,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2847,tc_HOL_Obool),tc_fun(tc_fun(U_2847,tc_HOL_Obool),tc_fun(U_2847,tc_HOL_Obool)),U_2846),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2847,tc_HOL_Obool))),U_2849)),U_2850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2847,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),U_2849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),U_2850)),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),hAPP(hAPP(c_COMBS(U_2846,tc_fun(U_2847,tc_HOL_Obool),tc_fun(U_2847,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2847,tc_HOL_Obool),tc_fun(tc_fun(U_2847,tc_HOL_Obool),tc_fun(U_2847,tc_HOL_Obool)),U_2846),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2847,tc_HOL_Obool))),U_2849)),U_2850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2847,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),U_2849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2846,tc_fun(U_2847,tc_HOL_Obool)),U_2848),U_2850)),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(f_540_2,plain,
    ! [U_2856,U_2855,U_2854,U_2853,U_2852,U_2851] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2851,tc_fun(U_2852,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2853,tc_fun(U_2851,tc_HOL_Obool)),U_2854),U_2855)),U_2856) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2853,tc_fun(U_2852,tc_HOL_Obool)),U_2854),hAPP(hAPP(c_COMBC(U_2853,tc_fun(U_2851,tc_fun(U_2852,tc_HOL_Obool)),tc_fun(U_2852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2851,tc_HOL_Obool),tc_fun(tc_fun(U_2851,tc_fun(U_2852,tc_HOL_Obool)),tc_fun(U_2852,tc_HOL_Obool)),U_2853),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2851,tc_fun(U_2852,tc_HOL_Obool))),U_2855)),U_2856)),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

cnf(f_540_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2851,tc_fun(U_2852,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2853,tc_fun(U_2851,tc_HOL_Obool)),U_2854),U_2855)),U_2856) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2853,tc_fun(U_2852,tc_HOL_Obool)),U_2854),hAPP(hAPP(c_COMBC(U_2853,tc_fun(U_2851,tc_fun(U_2852,tc_HOL_Obool)),tc_fun(U_2852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2851,tc_HOL_Obool),tc_fun(tc_fun(U_2851,tc_fun(U_2852,tc_HOL_Obool)),tc_fun(U_2852,tc_HOL_Obool)),U_2853),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2851,tc_fun(U_2852,tc_HOL_Obool))),U_2855)),U_2856)),
    inference(clausify,[status(thm)],[f_540_2]) ).

fof(f_541_1,plain,
    ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),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_C_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(f_541_2,plain,
    ! [U_2862,U_2861,U_2860,U_2859,U_2858,U_2857] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2857,tc_fun(U_2858,tc_HOL_Obool)),U_2859),hAPP(hAPP(c_COMBC(U_2857,tc_fun(U_2860,tc_fun(U_2858,tc_HOL_Obool)),tc_fun(U_2858,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2860,tc_HOL_Obool),tc_fun(tc_fun(U_2860,tc_fun(U_2858,tc_HOL_Obool)),tc_fun(U_2858,tc_HOL_Obool)),U_2857),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2860,tc_fun(U_2858,tc_HOL_Obool))),U_2861)),U_2862)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2860,tc_fun(U_2858,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2857,tc_fun(U_2860,tc_HOL_Obool)),U_2859),U_2861)),U_2862),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2857,tc_fun(U_2858,tc_HOL_Obool)),U_2859),hAPP(hAPP(c_COMBC(U_2857,tc_fun(U_2860,tc_fun(U_2858,tc_HOL_Obool)),tc_fun(U_2858,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2860,tc_HOL_Obool),tc_fun(tc_fun(U_2860,tc_fun(U_2858,tc_HOL_Obool)),tc_fun(U_2858,tc_HOL_Obool)),U_2857),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2860,tc_fun(U_2858,tc_HOL_Obool))),U_2861)),U_2862)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2860,tc_fun(U_2858,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2857,tc_fun(U_2860,tc_HOL_Obool)),U_2859),U_2861)),U_2862),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_1,plain,
    ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__INT]) ).

fof(f_542_2,plain,
    ! [U_2868,U_2867,U_2866,U_2865,U_2864,U_2863] : hAPP(c_Set_Ovimage(U_2863,U_2864,U_2865),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2866,tc_fun(U_2864,tc_HOL_Obool)),U_2867),U_2868)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2866,tc_fun(U_2863,tc_HOL_Obool)),U_2867),hAPP(hAPP(c_COMBB(tc_fun(U_2864,tc_HOL_Obool),tc_fun(U_2863,tc_HOL_Obool),U_2866),c_Set_Ovimage(U_2863,U_2864,U_2865)),U_2868)),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

cnf(f_542_3,plain,
    hAPP(c_Set_Ovimage(U_2863,U_2864,U_2865),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2866,tc_fun(U_2864,tc_HOL_Obool)),U_2867),U_2868)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2866,tc_fun(U_2863,tc_HOL_Obool)),U_2867),hAPP(hAPP(c_COMBB(tc_fun(U_2864,tc_HOL_Obool),tc_fun(U_2863,tc_HOL_Obool),U_2866),c_Set_Ovimage(U_2863,U_2864,U_2865)),U_2868)),
    inference(clausify,[status(thm)],[f_542_2]) ).

fof(f_543_1,plain,
    ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).

fof(f_543_2,plain,
    ! [U_2874,U_2873,U_2872,U_2871,U_2870,U_2869] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2869,tc_fun(U_2872,tc_HOL_Obool)),U_2871),hAPP(hAPP(c_COMBB(tc_fun(U_2872,tc_HOL_Obool),tc_fun(U_2872,tc_HOL_Obool),U_2869),hAPP(c_Set_Oinsert(U_2872),U_2873)),U_2874)) = hAPP(hAPP(c_Set_Oinsert(U_2872),U_2873),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2869,tc_fun(U_2872,tc_HOL_Obool)),U_2871),U_2874))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2869),U_2870),U_2871)) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

cnf(f_543_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2869,tc_fun(U_2872,tc_HOL_Obool)),U_2871),hAPP(hAPP(c_COMBB(tc_fun(U_2872,tc_HOL_Obool),tc_fun(U_2872,tc_HOL_Obool),U_2869),hAPP(c_Set_Oinsert(U_2872),U_2873)),U_2874)) = hAPP(hAPP(c_Set_Oinsert(U_2872),U_2873),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2869,tc_fun(U_2872,tc_HOL_Obool)),U_2871),U_2874))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2869),U_2870),U_2871)) ),
    inference(clausify,[status(thm)],[f_543_2]) ).

fof(f_544_1,plain,
    ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).

fof(f_544_2,plain,
    ! [U_2879,U_2878,U_2877,U_2876,U_2875] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2878,tc_HOL_Obool)),hAPP(U_2879,U_2876)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2875,tc_fun(U_2878,tc_HOL_Obool)),U_2877),U_2879)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2875,tc_fun(U_2878,tc_HOL_Obool)),U_2877),U_2879)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2875),U_2876),U_2877)) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

cnf(f_544_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2878,tc_HOL_Obool)),hAPP(U_2879,U_2876)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2875,tc_fun(U_2878,tc_HOL_Obool)),U_2877),U_2879)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2875,tc_fun(U_2878,tc_HOL_Obool)),U_2877),U_2879)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2875),U_2876),U_2877)) ),
    inference(clausify,[status(thm)],[f_544_2]) ).

fof(f_545_1,plain,
    ! [V_M_2,T_a,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__const]) ).

fof(f_545_2,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2882,U_2880),U_2881),hAPP(c_COMBK(U_2880,U_2882),U_2883)) = U_2883
      | U_2881 = c_Orderings_Obot__class_Obot(tc_fun(U_2882,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2880) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

cnf(f_545_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2882,U_2880),U_2881),hAPP(c_COMBK(U_2880,U_2882),U_2883)) = U_2883
    | U_2881 = c_Orderings_Obot__class_Obot(tc_fun(U_2882,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2880) ),
    inference(clausify,[status(thm)],[f_545_2]) ).

fof(f_546_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( 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_a,tc_fun(T_b,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_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).

fof(f_546_2,plain,
    ! [U_2888,U_2887,U_2886,U_2885,U_2884] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2886,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2885,tc_fun(U_2886,tc_HOL_Obool)),U_2884),U_2887)),U_2888) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2885,tc_fun(U_2886,tc_HOL_Obool)),U_2884),hAPP(hAPP(c_COMBC(U_2885,tc_fun(U_2886,tc_HOL_Obool),tc_fun(U_2886,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2886,tc_HOL_Obool),tc_fun(tc_fun(U_2886,tc_HOL_Obool),tc_fun(U_2886,tc_HOL_Obool)),U_2885),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2886,tc_HOL_Obool))),U_2887)),U_2888))
        | U_2884 = c_Orderings_Obot__class_Obot(tc_fun(U_2885,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2886,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2885,tc_fun(U_2886,tc_HOL_Obool)),U_2884),U_2887)),U_2888) = U_2888
        | U_2884 != c_Orderings_Obot__class_Obot(tc_fun(U_2885,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ( ! [U_2898,U_2896,U_2894,U_2892,U_2890] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2894,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2892,tc_fun(U_2894,tc_HOL_Obool)),U_2890),U_2896)),U_2898) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2892,tc_fun(U_2894,tc_HOL_Obool)),U_2890),hAPP(hAPP(c_COMBC(U_2892,tc_fun(U_2894,tc_HOL_Obool),tc_fun(U_2894,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2894,tc_HOL_Obool),tc_fun(tc_fun(U_2894,tc_HOL_Obool),tc_fun(U_2894,tc_HOL_Obool)),U_2892),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2894,tc_HOL_Obool))),U_2896)),U_2898))
        | U_2890 = c_Orderings_Obot__class_Obot(tc_fun(U_2892,tc_HOL_Obool)) )
    & ! [U_2897,U_2895,U_2893,U_2891,U_2889] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2893,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2891,tc_fun(U_2893,tc_HOL_Obool)),U_2889),U_2895)),U_2897) = U_2897
        | U_2889 != c_Orderings_Obot__class_Obot(tc_fun(U_2891,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2893,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2891,tc_fun(U_2893,tc_HOL_Obool)),U_2889),U_2895)),U_2897) = U_2897
    | U_2889 != c_Orderings_Obot__class_Obot(tc_fun(U_2891,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2894,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2892,tc_fun(U_2894,tc_HOL_Obool)),U_2890),U_2896)),U_2898) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2892,tc_fun(U_2894,tc_HOL_Obool)),U_2890),hAPP(hAPP(c_COMBC(U_2892,tc_fun(U_2894,tc_HOL_Obool),tc_fun(U_2894,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_2894,tc_HOL_Obool),tc_fun(tc_fun(U_2894,tc_HOL_Obool),tc_fun(U_2894,tc_HOL_Obool)),U_2892),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2894,tc_HOL_Obool))),U_2896)),U_2898))
    | U_2890 = c_Orderings_Obot__class_Obot(tc_fun(U_2892,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).

fof(f_547_2,plain,
    ! [U_2903,U_2902,U_2901,U_2900,U_2899] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2901,tc_HOL_Obool)),U_2902),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2900,tc_fun(U_2901,tc_HOL_Obool)),U_2899),U_2903)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2900,tc_fun(U_2901,tc_HOL_Obool)),U_2899),hAPP(hAPP(c_COMBB(tc_fun(U_2901,tc_HOL_Obool),tc_fun(U_2901,tc_HOL_Obool),U_2900),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2901,tc_HOL_Obool)),U_2902)),U_2903))
        | U_2899 = c_Orderings_Obot__class_Obot(tc_fun(U_2900,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2901,tc_HOL_Obool)),U_2902),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2900,tc_fun(U_2901,tc_HOL_Obool)),U_2899),U_2903)) = U_2902
        | U_2899 != c_Orderings_Obot__class_Obot(tc_fun(U_2900,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ( ! [U_2913,U_2911,U_2909,U_2907,U_2905] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2909,tc_HOL_Obool)),U_2911),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2907,tc_fun(U_2909,tc_HOL_Obool)),U_2905),U_2913)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2907,tc_fun(U_2909,tc_HOL_Obool)),U_2905),hAPP(hAPP(c_COMBB(tc_fun(U_2909,tc_HOL_Obool),tc_fun(U_2909,tc_HOL_Obool),U_2907),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2909,tc_HOL_Obool)),U_2911)),U_2913))
        | U_2905 = c_Orderings_Obot__class_Obot(tc_fun(U_2907,tc_HOL_Obool)) )
    & ! [U_2912,U_2910,U_2908,U_2906,U_2904] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2908,tc_HOL_Obool)),U_2910),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2906,tc_fun(U_2908,tc_HOL_Obool)),U_2904),U_2912)) = U_2910
        | U_2904 != c_Orderings_Obot__class_Obot(tc_fun(U_2906,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2908,tc_HOL_Obool)),U_2910),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2906,tc_fun(U_2908,tc_HOL_Obool)),U_2904),U_2912)) = U_2910
    | U_2904 != c_Orderings_Obot__class_Obot(tc_fun(U_2906,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

cnf(f_547_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2909,tc_HOL_Obool)),U_2911),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2907,tc_fun(U_2909,tc_HOL_Obool)),U_2905),U_2913)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2907,tc_fun(U_2909,tc_HOL_Obool)),U_2905),hAPP(hAPP(c_COMBB(tc_fun(U_2909,tc_HOL_Obool),tc_fun(U_2909,tc_HOL_Obool),U_2907),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2909,tc_HOL_Obool)),U_2911)),U_2913))
    | U_2905 = c_Orderings_Obot__class_Obot(tc_fun(U_2907,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).

fof(f_548_2,plain,
    ! [U_2918,U_2917,U_2916,U_2915,U_2914] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2914,tc_fun(U_2915,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2914),U_2916),U_2917)),U_2918) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2915,tc_HOL_Obool)),hAPP(U_2918,U_2916)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2914,tc_fun(U_2915,tc_HOL_Obool)),U_2917),U_2918)),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2914,tc_fun(U_2915,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2914),U_2916),U_2917)),U_2918) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2915,tc_HOL_Obool)),hAPP(U_2918,U_2916)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2914,tc_fun(U_2915,tc_HOL_Obool)),U_2917),U_2918)),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).

fof(f_549_2,plain,
    ! [U_2923,U_2922,U_2921,U_2920,U_2919] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2919,tc_HOL_Obool)),U_2921),U_2922)),U_2923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2923)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),U_2922),U_2923)),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

cnf(f_549_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2919,tc_HOL_Obool)),U_2921),U_2922)),U_2923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),U_2921),U_2923)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2919,tc_fun(U_2920,tc_HOL_Obool)),U_2922),U_2923)),
    inference(clausify,[status(thm)],[f_549_2]) ).

fof(f_550_1,plain,
    ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(f_550_2,plain,
    ! [U_2928,U_2927,U_2926,U_2925,U_2924] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2924,tc_HOL_Obool)),U_2925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2926,tc_fun(U_2924,tc_HOL_Obool)),U_2927),U_2928)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2926,tc_fun(U_2924,tc_HOL_Obool)),U_2927),hAPP(hAPP(c_COMBB(tc_fun(U_2924,tc_HOL_Obool),tc_fun(U_2924,tc_HOL_Obool),U_2926),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2924,tc_HOL_Obool)),U_2925)),U_2928)),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

cnf(f_550_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2924,tc_HOL_Obool)),U_2925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2926,tc_fun(U_2924,tc_HOL_Obool)),U_2927),U_2928)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2926,tc_fun(U_2924,tc_HOL_Obool)),U_2927),hAPP(hAPP(c_COMBB(tc_fun(U_2924,tc_HOL_Obool),tc_fun(U_2924,tc_HOL_Obool),U_2926),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2924,tc_HOL_Obool)),U_2925)),U_2928)),
    inference(clausify,[status(thm)],[f_550_2]) ).

fof(f_551_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(f_551_2,plain,
    ! [U_2933,U_2932,U_2931,U_2930,U_2929] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2929,tc_fun(U_2930,tc_HOL_Obool)),U_2931),hAPP(hAPP(c_COMBB(tc_fun(U_2930,tc_HOL_Obool),tc_fun(U_2930,tc_HOL_Obool),U_2929),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2930,tc_HOL_Obool)),U_2932)),U_2933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2930,tc_HOL_Obool)),U_2932),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2929,tc_fun(U_2930,tc_HOL_Obool)),U_2931),U_2933)),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

cnf(f_551_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2929,tc_fun(U_2930,tc_HOL_Obool)),U_2931),hAPP(hAPP(c_COMBB(tc_fun(U_2930,tc_HOL_Obool),tc_fun(U_2930,tc_HOL_Obool),U_2929),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2930,tc_HOL_Obool)),U_2932)),U_2933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2930,tc_HOL_Obool)),U_2932),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2929,tc_fun(U_2930,tc_HOL_Obool)),U_2931),U_2933)),
    inference(clausify,[status(thm)],[f_551_2]) ).

fof(f_552_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).

fof(f_552_2,plain,
    ! [U_2938,U_2937,U_2936,U_2935,U_2934] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2936,tc_HOL_Obool)),U_2937),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2935,tc_fun(U_2936,tc_HOL_Obool)),U_2934),U_2938)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2935,tc_fun(U_2936,tc_HOL_Obool)),U_2934),hAPP(hAPP(c_COMBB(tc_fun(U_2936,tc_HOL_Obool),tc_fun(U_2936,tc_HOL_Obool),U_2935),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2936,tc_HOL_Obool)),U_2937)),U_2938))
        | U_2934 = c_Orderings_Obot__class_Obot(tc_fun(U_2935,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2936,tc_HOL_Obool)),U_2937),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2935,tc_fun(U_2936,tc_HOL_Obool)),U_2934),U_2938)) = U_2937
        | U_2934 != c_Orderings_Obot__class_Obot(tc_fun(U_2935,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ( ! [U_2948,U_2946,U_2944,U_2942,U_2940] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2944,tc_HOL_Obool)),U_2946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2942,tc_fun(U_2944,tc_HOL_Obool)),U_2940),U_2948)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2942,tc_fun(U_2944,tc_HOL_Obool)),U_2940),hAPP(hAPP(c_COMBB(tc_fun(U_2944,tc_HOL_Obool),tc_fun(U_2944,tc_HOL_Obool),U_2942),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2944,tc_HOL_Obool)),U_2946)),U_2948))
        | U_2940 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool)) )
    & ! [U_2947,U_2945,U_2943,U_2941,U_2939] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2943,tc_HOL_Obool)),U_2945),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2941,tc_fun(U_2943,tc_HOL_Obool)),U_2939),U_2947)) = U_2945
        | U_2939 != c_Orderings_Obot__class_Obot(tc_fun(U_2941,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2943,tc_HOL_Obool)),U_2945),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2941,tc_fun(U_2943,tc_HOL_Obool)),U_2939),U_2947)) = U_2945
    | U_2939 != c_Orderings_Obot__class_Obot(tc_fun(U_2941,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

cnf(f_552_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2944,tc_HOL_Obool)),U_2946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2942,tc_fun(U_2944,tc_HOL_Obool)),U_2940),U_2948)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2942,tc_fun(U_2944,tc_HOL_Obool)),U_2940),hAPP(hAPP(c_COMBB(tc_fun(U_2944,tc_HOL_Obool),tc_fun(U_2944,tc_HOL_Obool),U_2942),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2944,tc_HOL_Obool)),U_2946)),U_2948))
    | U_2940 = c_Orderings_Obot__class_Obot(tc_fun(U_2942,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_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_553_2,plain,
    ! [U_2951,U_2950,U_2949] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2949),U_2950) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2951),U_2950)
        | U_2949 != U_2951 )
      & ( U_2949 = U_2951
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2949),U_2950) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2951),U_2950) ) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ( ! [U_2957,U_2955,U_2953] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2953),U_2955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2957),U_2955)
        | U_2953 != U_2957 )
    & ! [U_2956,U_2954,U_2952] :
        ( U_2952 = U_2956
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2952),U_2954) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2956),U_2954) ) ),
    inference(miniscope,[status(thm)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( U_2952 = U_2956
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2952),U_2954) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2956),U_2954) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

cnf(f_553_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2953),U_2955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2957),U_2955)
    | U_2953 != U_2957 ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_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_554_2,plain,
    ! [U_2960,U_2959,U_2958] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2958),U_2959) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2958),U_2960)
        | U_2959 != U_2960 )
      & ( U_2959 = U_2960
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2958),U_2959) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2958),U_2960) ) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ( ! [U_2966,U_2964] :
        ( ! [U_2962] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),U_2964) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),U_2966)
        | U_2964 != U_2966 )
    & ! [U_2965,U_2963] :
        ( ! [U_2961] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2961),U_2963) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2961),U_2965)
        | U_2963 = U_2965 ) ),
    inference(miniscope,[status(thm)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2961),U_2963) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2961),U_2965)
    | U_2963 = U_2965 ),
    inference(clausify,[status(thm)],[f_554_3]) ).

cnf(f_554_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),U_2964) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),U_2966)
    | U_2964 != U_2966 ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_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_555_2,plain,
    ! [U_2969,U_2968,U_2967] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2967),U_2968)),U_2969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2968),U_2969)),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

cnf(f_555_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2967),U_2968)),U_2969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2968),U_2969)),
    inference(clausify,[status(thm)],[f_555_2]) ).

fof(f_556_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_556_2,plain,
    ! [U_2972,U_2971,U_2970] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2971),U_2972)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2970),U_2972)),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

cnf(f_556_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2971),U_2972)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2970),U_2972)),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_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_557_2,plain,
    ! [U_2974,U_2973] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2973),U_2974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2974),U_2973),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2973),U_2974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2974),U_2973),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_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_558_2,plain,
    ! [U_2977,U_2976,U_2975] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2975),U_2976)),U_2977) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2975),U_2977)),U_2976),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

cnf(f_558_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2975),U_2976)),U_2977) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2975),U_2977)),U_2976),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).

fof(f_559_2,plain,
    ! [U_2981,U_2980,U_2979,U_2978] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2979,U_2978),U_2980),U_2981) = hAPP(hAPP(c_Finite__Set_Ofold(U_2979,U_2978,hAPP(hAPP(c_COMBB(U_2978,tc_fun(U_2978,U_2978),U_2979),c_Lattices_Osemilattice__inf__class_Oinf(U_2978)),U_2981)),c_Orderings_Otop__class_Otop(U_2978)),U_2980)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2979),U_2980))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2978) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_2979,U_2978),U_2980),U_2981) = hAPP(hAPP(c_Finite__Set_Ofold(U_2979,U_2978,hAPP(hAPP(c_COMBB(U_2978,tc_fun(U_2978,U_2978),U_2979),c_Lattices_Osemilattice__inf__class_Oinf(U_2978)),U_2981)),c_Orderings_Otop__class_Otop(U_2978)),U_2980)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2979),U_2980))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2978) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    ! [V_P_2,V_F_2,T_a] :
      ( hBOOL(hAPP(V_P_2,V_F_2))
      | ? [B_x,B_F] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F)))
          & hBOOL(hAPP(V_P_2,B_F))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) )
      | ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).

fof(f_560_2,plain,
    ! [U_2986,U_2985,U_2984] :
      ( hBOOL(hAPP(U_2986,U_2985))
      | ? [U_2983,U_2982] :
          ( ~ hBOOL(hAPP(U_2986,hAPP(hAPP(c_Set_Oinsert(U_2984),U_2983),U_2982)))
          & hBOOL(hAPP(U_2986,U_2982))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2984),U_2983),U_2982))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2982)) )
      | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_2986,U_2985,U_2984] :
      ( hBOOL(hAPP(U_2986,U_2985))
      | ? [U_2982] :
          ( ~ hBOOL(hAPP(U_2986,hAPP(hAPP(c_Set_Oinsert(U_2984),sK57(U_2986,U_2985,U_2984)),U_2982)))
          & hBOOL(hAPP(U_2986,U_2982))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2984),sK57(U_2986,U_2985,U_2984)),U_2982))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2982)) )
      | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2983,sK57(U_2986,U_2985,U_2984))],[f_560_2]) ).

fof(f_560_4,plain,
    ! [U_2986,U_2985,U_2984] :
      ( hBOOL(hAPP(U_2986,U_2985))
      | ( ~ hBOOL(hAPP(U_2986,hAPP(hAPP(c_Set_Oinsert(U_2984),sK57(U_2986,U_2985,U_2984)),sK58(U_2986,U_2985,U_2984))))
        & hBOOL(hAPP(U_2986,sK58(U_2986,U_2985,U_2984)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_2984),sK57(U_2986,U_2985,U_2984)),sK58(U_2986,U_2985,U_2984)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),sK58(U_2986,U_2985,U_2984))) )
      | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2982,sK58(U_2986,U_2985,U_2984))],[f_560_3]) ).

cnf(f_560_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),sK58(U_2986,U_2985,U_2984)))
    | hBOOL(hAPP(U_2986,U_2985))
    | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2984),sK57(U_2986,U_2985,U_2984)),sK58(U_2986,U_2985,U_2984)))
    | hBOOL(hAPP(U_2986,U_2985))
    | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_7,plain,
    ( hBOOL(hAPP(U_2986,sK58(U_2986,U_2985,U_2984)))
    | hBOOL(hAPP(U_2986,U_2985))
    | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_8,plain,
    ( ~ hBOOL(hAPP(U_2986,hAPP(hAPP(c_Set_Oinsert(U_2984),sK57(U_2986,U_2985,U_2984)),sK58(U_2986,U_2985,U_2984))))
    | hBOOL(hAPP(U_2986,U_2985))
    | ~ hBOOL(hAPP(U_2986,c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2984),U_2985)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

fof(f_561_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( c_Nitpick_Ofold__graph_H(T_a,T_b,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_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).

fof(f_561_2,plain,
    ! [U_2993,U_2992,U_2991,U_2990,U_2989,U_2988,U_2987] :
      ( c_Nitpick_Ofold__graph_H(U_2987,U_2990,U_2991,U_2992,U_2989,hAPP(hAPP(U_2991,U_2988),U_2993))
      | ~ c_Nitpick_Ofold__graph_H(U_2987,U_2990,U_2991,U_2992,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2987,tc_HOL_Obool)),U_2989),hAPP(hAPP(c_Set_Oinsert(U_2987),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool)))),U_2993)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2987),U_2988),U_2989)) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_3,plain,
    ( c_Nitpick_Ofold__graph_H(U_2987,U_2990,U_2991,U_2992,U_2989,hAPP(hAPP(U_2991,U_2988),U_2993))
    | ~ c_Nitpick_Ofold__graph_H(U_2987,U_2990,U_2991,U_2992,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2987,tc_HOL_Obool)),U_2989),hAPP(hAPP(c_Set_Oinsert(U_2987),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool)))),U_2993)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2987),U_2988),U_2989)) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2,
    inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).

fof(f_562_2,plain,
    ! [U_2999,U_2998,U_2997,U_2996,U_2995,U_2994] : hAPP(hAPP(c_Fun_Ocomp(U_2994,U_2995,U_2996,hAPP(c_COMBK(U_2995,U_2994),U_2997)),U_2998),U_2999) = U_2997,
    inference(variable_rename,[status(thm)],[f_562_1]) ).

cnf(f_562_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_2994,U_2995,U_2996,hAPP(c_COMBK(U_2995,U_2994),U_2997)),U_2998),U_2999) = U_2997,
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,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_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).

fof(f_563_2,plain,
    ! [U_3006,U_3005,U_3004,U_3003,U_3002,U_3001,U_3000] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3000,U_3001,U_3002,U_3003,U_3004),hAPP(hAPP(U_3002,U_3005),U_3006)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3000),U_3005),U_3004))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3000,U_3001,U_3002,U_3003,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3000,tc_HOL_Obool)),U_3004),hAPP(hAPP(c_Set_Oinsert(U_3000),U_3005),c_Orderings_Obot__class_Obot(tc_fun(U_3000,tc_HOL_Obool))))),U_3006)) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

cnf(f_563_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3000,U_3001,U_3002,U_3003,U_3004),hAPP(hAPP(U_3002,U_3005),U_3006)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3000),U_3005),U_3004))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3000,U_3001,U_3002,U_3003,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3000,tc_HOL_Obool)),U_3004),hAPP(hAPP(c_Set_Oinsert(U_3000),U_3005),c_Orderings_Obot__class_Obot(tc_fun(U_3000,tc_HOL_Obool))))),U_3006)) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__E]) ).

fof(f_564_2,plain,
    ! [U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008] :
      ( ? [U_3007] :
          ( hBOOL(hAPP(hAPP(hAPP(U_3012,U_3007),U_3013),U_3014))
          & hBOOL(hAPP(hAPP(c_member(U_3008),U_3007),U_3011)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3008,tc_fun(U_3009,tc_fun(U_3010,tc_HOL_Obool))),U_3011),U_3012),U_3013),U_3014)) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008] :
      ( ( hBOOL(hAPP(hAPP(hAPP(U_3012,sK59(U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008)),U_3013),U_3014))
        & hBOOL(hAPP(hAPP(c_member(U_3008),sK59(U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008)),U_3011)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3008,tc_fun(U_3009,tc_fun(U_3010,tc_HOL_Obool))),U_3011),U_3012),U_3013),U_3014)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3007,sK59(U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008))],[f_564_2]) ).

cnf(f_564_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3008),sK59(U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008)),U_3011))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3008,tc_fun(U_3009,tc_fun(U_3010,tc_HOL_Obool))),U_3011),U_3012),U_3013),U_3014)) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

cnf(f_564_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_3012,sK59(U_3014,U_3013,U_3012,U_3011,U_3010,U_3009,U_3008)),U_3013),U_3014))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3008,tc_fun(U_3009,tc_fun(U_3010,tc_HOL_Obool))),U_3011),U_3012),U_3013),U_3014)) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).

fof(f_565_2,plain,
    ! [U_3017,U_3016,U_3015] :
      ( hAPP(c_Finite__Set_Ocard(U_3015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3015,tc_HOL_Obool)),U_3016),U_3017)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3015),U_3016)),hAPP(c_Finite__Set_Ocard(U_3015),U_3017))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3015,tc_HOL_Obool)),U_3016),U_3017) != c_Orderings_Obot__class_Obot(tc_fun(U_3015,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3017))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3016)) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3015,tc_HOL_Obool)),U_3016),U_3017)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3015),U_3016)),hAPP(c_Finite__Set_Ocard(U_3015),U_3017))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3015,tc_HOL_Obool)),U_3016),U_3017) != c_Orderings_Obot__class_Obot(tc_fun(U_3015,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3017))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3015),U_3016)) ),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).

fof(f_566_2,plain,
    ! [U_3022,U_3021,U_3020,U_3019,U_3018] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3019,U_3018),U_3021),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3019,tc_HOL_Obool)),U_3020),U_3022)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3019,U_3018),hAPP(hAPP(c_COMBC(U_3019,U_3018,U_3018),hAPP(hAPP(c_COMBS(U_3019,U_3018,tc_fun(U_3018,U_3018)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3018,tc_fun(U_3018,U_3018)),U_3019),c_If(U_3018)),hAPP(hAPP(c_COMBC(U_3019,tc_fun(U_3019,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3019)),U_3022))),U_3021)),c_Groups_Ozero__class_Ozero(U_3018))),U_3020)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3019),U_3020))
      | ~ class_Groups_Ocomm__monoid__add(U_3018) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3019,U_3018),U_3021),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3019,tc_HOL_Obool)),U_3020),U_3022)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3019,U_3018),hAPP(hAPP(c_COMBC(U_3019,U_3018,U_3018),hAPP(hAPP(c_COMBS(U_3019,U_3018,tc_fun(U_3018,U_3018)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3018,tc_fun(U_3018,U_3018)),U_3019),c_If(U_3018)),hAPP(hAPP(c_COMBC(U_3019,tc_fun(U_3019,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3019)),U_3022))),U_3021)),c_Groups_Ozero__class_Ozero(U_3018))),U_3020)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3019),U_3020))
    | ~ class_Groups_Ocomm__monoid__add(U_3018) ),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).

fof(f_567_2,plain,
    ! [U_3024,U_3023] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3023,U_3024) = c_Complete__Lattice_OInf__class_OInf(U_3023,U_3024)
      | U_3024 = c_Orderings_Obot__class_Obot(tc_fun(U_3023,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3023),U_3024))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3023) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3023,U_3024) = c_Complete__Lattice_OInf__class_OInf(U_3023,U_3024)
    | U_3024 = c_Orderings_Obot__class_Obot(tc_fun(U_3023,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3023),U_3024))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3023) ),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_1,plain,
    ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).

fof(f_568_2,plain,
    ! [U_3026,U_3025] : hBOOL(hAPP(hAPP(c_member(U_3025),U_3026),c_Orderings_Otop__class_Otop(tc_fun(U_3025,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_3025),U_3026),c_Orderings_Otop__class_Otop(tc_fun(U_3025,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    ! [V_M_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).

fof(f_569_2,plain,
    ! [U_3029,U_3028] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3028,tc_HOL_Obool),U_3029)))
      | ! [U_3027] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),U_3027))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3028,tc_HOL_Obool)),U_3027),U_3029)) ) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3028,tc_HOL_Obool),U_3029)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),U_3027))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3028,tc_HOL_Obool)),U_3027),U_3029)) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterE]) ).

fof(f_570_2,plain,
    ! [U_3033,U_3032,U_3031,U_3030] :
      ( hBOOL(hAPP(hAPP(c_member(U_3030),U_3031),U_3033))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3030,tc_HOL_Obool)),U_3033),U_3032))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3030),U_3031),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3030,tc_HOL_Obool),U_3032))) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

cnf(f_570_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3030),U_3031),U_3033))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3030,tc_HOL_Obool)),U_3033),U_3032))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3030),U_3031),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3030,tc_HOL_Obool),U_3032))) ),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterD]) ).

fof(f_571_2,plain,
    ! [U_3037,U_3036,U_3035,U_3034] :
      ( hBOOL(hAPP(hAPP(c_member(U_3034),U_3035),U_3037))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3034,tc_HOL_Obool)),U_3037),U_3036))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3034),U_3035),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3034,tc_HOL_Obool),U_3036))) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3034),U_3035),U_3037))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3034,tc_HOL_Obool)),U_3037),U_3036))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3034),U_3035),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3034,tc_HOL_Obool),U_3036))) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).

fof(f_572_2,plain,
    ! [U_3038] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3038,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3038,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3038,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3038,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3038,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3038,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,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_a),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).

fof(f_573_2,plain,
    ! [U_3045,U_3044,U_3043,U_3042,U_3041] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3041,tc_fun(U_3042,tc_HOL_Obool)),U_3043),U_3044),U_3045))
        | ? [U_3040] :
            ( ~ hBOOL(hAPP(hAPP(U_3044,U_3040),U_3045))
            & hBOOL(hAPP(hAPP(c_member(U_3041),U_3040),U_3043)) ) )
      & ( ! [U_3039] :
            ( hBOOL(hAPP(hAPP(U_3044,U_3039),U_3045))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3041),U_3039),U_3043)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3041,tc_fun(U_3042,tc_HOL_Obool)),U_3043),U_3044),U_3045)) ) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ( ! [U_3055,U_3053,U_3051,U_3049,U_3047] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3047,tc_fun(U_3049,tc_HOL_Obool)),U_3051),U_3053),U_3055))
        | ? [U_3040] :
            ( ~ hBOOL(hAPP(hAPP(U_3053,U_3040),U_3055))
            & hBOOL(hAPP(hAPP(c_member(U_3047),U_3040),U_3051)) ) )
    & ! [U_3054,U_3052,U_3050,U_3048,U_3046] :
        ( ! [U_3039] :
            ( hBOOL(hAPP(hAPP(U_3052,U_3039),U_3054))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3046),U_3039),U_3050)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3046,tc_fun(U_3048,tc_HOL_Obool)),U_3050),U_3052),U_3054)) ) ),
    inference(miniscope,[status(thm)],[f_573_2]) ).

fof(f_573_4,plain,
    ( ! [U_3055,U_3053,U_3051,U_3049,U_3047] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3047,tc_fun(U_3049,tc_HOL_Obool)),U_3051),U_3053),U_3055))
        | ( ~ hBOOL(hAPP(hAPP(U_3053,sK60(U_3055,U_3053,U_3051,U_3049,U_3047)),U_3055))
          & hBOOL(hAPP(hAPP(c_member(U_3047),sK60(U_3055,U_3053,U_3051,U_3049,U_3047)),U_3051)) ) )
    & ! [U_3054,U_3052,U_3050,U_3048,U_3046] :
        ( ! [U_3039] :
            ( hBOOL(hAPP(hAPP(U_3052,U_3039),U_3054))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3046),U_3039),U_3050)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3046,tc_fun(U_3048,tc_HOL_Obool)),U_3050),U_3052),U_3054)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3040,sK60(U_3055,U_3053,U_3051,U_3049,U_3047))],[f_573_3]) ).

cnf(f_573_5,plain,
    ( hBOOL(hAPP(hAPP(U_3052,U_3039),U_3054))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3046),U_3039),U_3050))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3046,tc_fun(U_3048,tc_HOL_Obool)),U_3050),U_3052),U_3054)) ),
    inference(clausify,[status(thm)],[f_573_4]) ).

cnf(f_573_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3047),sK60(U_3055,U_3053,U_3051,U_3049,U_3047)),U_3051))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3047,tc_fun(U_3049,tc_HOL_Obool)),U_3051),U_3053),U_3055)) ),
    inference(clausify,[status(thm)],[f_573_4]) ).

cnf(f_573_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3053,sK60(U_3055,U_3053,U_3051,U_3049,U_3047)),U_3055))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3047,tc_fun(U_3049,tc_HOL_Obool)),U_3051),U_3053),U_3055)) ),
    inference(clausify,[status(thm)],[f_573_4]) ).

fof(f_574_1,plain,
    ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).

fof(f_574_2,plain,
    ! [U_3056] : hAPP(c_Finite__Set_Ocard(U_3056),c_Orderings_Obot__class_Obot(tc_fun(U_3056,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

cnf(f_574_3,plain,
    hAPP(c_Finite__Set_Ocard(U_3056),c_Orderings_Obot__class_Obot(tc_fun(U_3056,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,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_a),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_a),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,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_575_2,plain,
    ! [U_3065,U_3064,U_3063,U_3062,U_3061,U_3060,U_3059] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3059,tc_fun(U_3060,tc_fun(U_3061,tc_HOL_Obool))),U_3062),U_3063),U_3064),U_3065))
        | ? [U_3058] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_3063,U_3058),U_3064),U_3065))
            & hBOOL(hAPP(hAPP(c_member(U_3059),U_3058),U_3062)) ) )
      & ( ! [U_3057] :
            ( hBOOL(hAPP(hAPP(hAPP(U_3063,U_3057),U_3064),U_3065))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3059),U_3057),U_3062)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3059,tc_fun(U_3060,tc_fun(U_3061,tc_HOL_Obool))),U_3062),U_3063),U_3064),U_3065)) ) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ( ! [U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3067,tc_fun(U_3069,tc_fun(U_3071,tc_HOL_Obool))),U_3073),U_3075),U_3077),U_3079))
        | ? [U_3058] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_3075,U_3058),U_3077),U_3079))
            & hBOOL(hAPP(hAPP(c_member(U_3067),U_3058),U_3073)) ) )
    & ! [U_3078,U_3076,U_3074,U_3072,U_3070,U_3068,U_3066] :
        ( ! [U_3057] :
            ( hBOOL(hAPP(hAPP(hAPP(U_3074,U_3057),U_3076),U_3078))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3066),U_3057),U_3072)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3066,tc_fun(U_3068,tc_fun(U_3070,tc_HOL_Obool))),U_3072),U_3074),U_3076),U_3078)) ) ),
    inference(miniscope,[status(thm)],[f_575_2]) ).

fof(f_575_4,plain,
    ( ! [U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3067,tc_fun(U_3069,tc_fun(U_3071,tc_HOL_Obool))),U_3073),U_3075),U_3077),U_3079))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_3075,sK61(U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067)),U_3077),U_3079))
          & hBOOL(hAPP(hAPP(c_member(U_3067),sK61(U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067)),U_3073)) ) )
    & ! [U_3078,U_3076,U_3074,U_3072,U_3070,U_3068,U_3066] :
        ( ! [U_3057] :
            ( hBOOL(hAPP(hAPP(hAPP(U_3074,U_3057),U_3076),U_3078))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3066),U_3057),U_3072)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3066,tc_fun(U_3068,tc_fun(U_3070,tc_HOL_Obool))),U_3072),U_3074),U_3076),U_3078)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3058,sK61(U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067))],[f_575_3]) ).

cnf(f_575_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_3074,U_3057),U_3076),U_3078))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3066),U_3057),U_3072))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3066,tc_fun(U_3068,tc_fun(U_3070,tc_HOL_Obool))),U_3072),U_3074),U_3076),U_3078)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3067),sK61(U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067)),U_3073))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3067,tc_fun(U_3069,tc_fun(U_3071,tc_HOL_Obool))),U_3073),U_3075),U_3077),U_3079)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_7,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_3075,sK61(U_3079,U_3077,U_3075,U_3073,U_3071,U_3069,U_3067)),U_3077),U_3079))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3067,tc_fun(U_3069,tc_fun(U_3071,tc_HOL_Obool))),U_3073),U_3075),U_3077),U_3079)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

fof(f_576_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ozero__class_Ozero(T_a) != V_x_2 ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).

fof(f_576_2,plain,
    ! [U_3081,U_3080] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_3080) = U_3081
          | U_3081 != c_Groups_Ozero__class_Ozero(U_3080) )
        & ( U_3081 = c_Groups_Ozero__class_Ozero(U_3080)
          | c_Groups_Ozero__class_Ozero(U_3080) != U_3081 ) )
      | ~ class_Groups_Ozero(U_3080) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( U_3081 = c_Groups_Ozero__class_Ozero(U_3080)
    | c_Groups_Ozero__class_Ozero(U_3080) != U_3081
    | ~ class_Groups_Ozero(U_3080) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_3080) = U_3081
    | U_3081 != c_Groups_Ozero__class_Ozero(U_3080)
    | ~ class_Groups_Ozero(U_3080) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_1,plain,
    ! [V_x_2,T_b,T_a] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Orderings_Otop(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_top__apply]) ).

fof(f_577_2,plain,
    ! [U_3084,U_3083,U_3082] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_3083,U_3082)),U_3084) = c_Orderings_Otop__class_Otop(U_3082)
      | ~ class_Orderings_Otop(U_3082) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

cnf(f_577_3,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_3083,U_3082)),U_3084) = c_Orderings_Otop__class_Otop(U_3082)
    | ~ class_Orderings_Otop(U_3082) ),
    inference(clausify,[status(thm)],[f_577_2]) ).

fof(f_578_1,plain,
    ! [V_A_2,T_a] :
      ( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(T_a),V_A_2) != hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).

fof(f_578_2,plain,
    ! [U_3086,U_3085] :
      ( U_3086 = c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_3085),U_3086) != hAPP(c_Finite__Set_Ocard(U_3085),c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3085),c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( U_3086 = c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3085),U_3086) != hAPP(c_Finite__Set_Ocard(U_3085),c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3085),c_Orderings_Otop__class_Otop(tc_fun(U_3085,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_1,plain,
    ! [V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).

fof(f_579_2,plain,
    ! [U_3088,U_3087] :
      ( hAPP(c_Finite__Set_Ocard(U_3087),U_3088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088)) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3087),U_3088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088)) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    ! [T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).

fof(f_580_2,plain,
    ! [U_3089] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3089)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3089),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),c_Orderings_Otop__class_Otop(tc_fun(U_3089,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3089),c_Orderings_Otop__class_Otop(tc_fun(U_3089,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3089)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3089),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ( ! [U_3091] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3091)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3091),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3091),c_Orderings_Otop__class_Otop(tc_fun(U_3091,tc_HOL_Obool)))) )
    & ! [U_3090] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),c_Orderings_Otop__class_Otop(tc_fun(U_3090,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3090)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3090),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_580_2]) ).

cnf(f_580_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),c_Orderings_Otop__class_Otop(tc_fun(U_3090,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3090)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3090),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

cnf(f_580_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3091)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3091),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3091),c_Orderings_Otop__class_Otop(tc_fun(U_3091,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_1,plain,
    ! [T_b,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).

fof(f_581_2,plain,
    ! [U_3093,U_3092] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3092,U_3093)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3092,U_3093),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),c_Orderings_Otop__class_Otop(tc_fun(U_3092,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),c_Orderings_Otop__class_Otop(tc_fun(U_3092,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3092,U_3093)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3092,U_3093),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ( ! [U_3097,U_3095] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3095,U_3097)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3095,U_3097),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3097),c_Orderings_Otop__class_Otop(tc_fun(U_3097,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3095),c_Orderings_Otop__class_Otop(tc_fun(U_3095,tc_HOL_Obool)))) )
    & ! [U_3096,U_3094] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3096),c_Orderings_Otop__class_Otop(tc_fun(U_3096,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3094),c_Orderings_Otop__class_Otop(tc_fun(U_3094,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3094,U_3096)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3094,U_3096),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3094),c_Orderings_Otop__class_Otop(tc_fun(U_3094,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3094,U_3096)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3094,U_3096),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

cnf(f_581_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3096),c_Orderings_Otop__class_Otop(tc_fun(U_3096,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3094,U_3096)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3094,U_3096),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

cnf(f_581_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3095,U_3097)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3095,U_3097),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3097),c_Orderings_Otop__class_Otop(tc_fun(U_3097,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3095),c_Orderings_Otop__class_Otop(tc_fun(U_3095,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_1,plain,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).

fof(f_582_2,plain,
    ! [U_3099,U_3098] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_3098,U_3099)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_3098,U_3099),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3099),c_Orderings_Otop__class_Otop(tc_fun(U_3099,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3098),c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_3098,U_3099)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_3098,U_3099),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3099),c_Orderings_Otop__class_Otop(tc_fun(U_3099,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3098),c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_1,plain,
    ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(f_583_2,plain,
    ! [U_3101,U_3100] : hBOOL(hAPP(hAPP(c_member(U_3100),U_3101),c_Orderings_Otop__class_Otop(tc_fun(U_3100,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_3100),U_3101),c_Orderings_Otop__class_Otop(tc_fun(U_3100,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_1,plain,
    ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).

fof(f_584_2,plain,
    ! [U_3102] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3102,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3102,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3102,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3102,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3102,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3102,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).

fof(f_585_2,plain,
    ! [U_3108,U_3107,U_3106,U_3105] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_3105,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3106,tc_fun(U_3105,tc_HOL_Obool)),U_3107),U_3108)
        | ? [U_3104] :
            ( hAPP(U_3108,U_3104) != c_Orderings_Otop__class_Otop(tc_fun(U_3105,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_3106),U_3104),U_3107)) ) )
      & ( ! [U_3103] :
            ( hAPP(U_3108,U_3103) = c_Orderings_Otop__class_Otop(tc_fun(U_3105,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3106),U_3103),U_3107)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_3105,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3106,tc_fun(U_3105,tc_HOL_Obool)),U_3107),U_3108) ) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_3116,U_3114,U_3112,U_3110] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3112,tc_fun(U_3110,tc_HOL_Obool)),U_3114),U_3116)
        | ? [U_3104] :
            ( hAPP(U_3116,U_3104) != c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_3112),U_3104),U_3114)) ) )
    & ! [U_3115,U_3113,U_3111,U_3109] :
        ( ! [U_3103] :
            ( hAPP(U_3115,U_3103) = c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3111),U_3103),U_3113)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3111,tc_fun(U_3109,tc_HOL_Obool)),U_3113),U_3115) ) ),
    inference(miniscope,[status(thm)],[f_585_2]) ).

fof(f_585_4,plain,
    ( ! [U_3116,U_3114,U_3112,U_3110] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3112,tc_fun(U_3110,tc_HOL_Obool)),U_3114),U_3116)
        | ( hAPP(U_3116,sK62(U_3116,U_3114,U_3112,U_3110)) != c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_3112),sK62(U_3116,U_3114,U_3112,U_3110)),U_3114)) ) )
    & ! [U_3115,U_3113,U_3111,U_3109] :
        ( ! [U_3103] :
            ( hAPP(U_3115,U_3103) = c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3111),U_3103),U_3113)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3111,tc_fun(U_3109,tc_HOL_Obool)),U_3113),U_3115) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3104,sK62(U_3116,U_3114,U_3112,U_3110))],[f_585_3]) ).

cnf(f_585_5,plain,
    ( hAPP(U_3115,U_3103) = c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3111),U_3103),U_3113))
    | c_Orderings_Otop__class_Otop(tc_fun(U_3109,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3111,tc_fun(U_3109,tc_HOL_Obool)),U_3113),U_3115) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3112),sK62(U_3116,U_3114,U_3112,U_3110)),U_3114))
    | c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3112,tc_fun(U_3110,tc_HOL_Obool)),U_3114),U_3116) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_7,plain,
    ( hAPP(U_3116,sK62(U_3116,U_3114,U_3112,U_3110)) != c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool))
    | c_Orderings_Otop__class_Otop(tc_fun(U_3110,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3112,tc_fun(U_3110,tc_HOL_Obool)),U_3114),U_3116) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

fof(f_586_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).

fof(f_586_2,plain,
    ! [U_3122,U_3121,U_3120,U_3119] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3119,tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122) = c_Orderings_Otop__class_Otop(tc_fun(U_3120,tc_HOL_Obool))
        | ? [U_3118] :
            ( hAPP(U_3122,U_3118) != c_Orderings_Otop__class_Otop(tc_fun(U_3120,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_3119),U_3118),U_3121)) ) )
      & ( ! [U_3117] :
            ( hAPP(U_3122,U_3117) = c_Orderings_Otop__class_Otop(tc_fun(U_3120,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3119),U_3117),U_3121)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3119,tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122) != c_Orderings_Otop__class_Otop(tc_fun(U_3120,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ( ! [U_3130,U_3128,U_3126,U_3124] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3124,tc_fun(U_3126,tc_HOL_Obool)),U_3128),U_3130) = c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool))
        | ? [U_3118] :
            ( hAPP(U_3130,U_3118) != c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_3124),U_3118),U_3128)) ) )
    & ! [U_3129,U_3127,U_3125,U_3123] :
        ( ! [U_3117] :
            ( hAPP(U_3129,U_3117) = c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3123),U_3117),U_3127)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3123,tc_fun(U_3125,tc_HOL_Obool)),U_3127),U_3129) != c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_586_2]) ).

fof(f_586_4,plain,
    ( ! [U_3130,U_3128,U_3126,U_3124] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3124,tc_fun(U_3126,tc_HOL_Obool)),U_3128),U_3130) = c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool))
        | ( hAPP(U_3130,sK63(U_3130,U_3128,U_3126,U_3124)) != c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_3124),sK63(U_3130,U_3128,U_3126,U_3124)),U_3128)) ) )
    & ! [U_3129,U_3127,U_3125,U_3123] :
        ( ! [U_3117] :
            ( hAPP(U_3129,U_3117) = c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_3123),U_3117),U_3127)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3123,tc_fun(U_3125,tc_HOL_Obool)),U_3127),U_3129) != c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3118,sK63(U_3130,U_3128,U_3126,U_3124))],[f_586_3]) ).

cnf(f_586_5,plain,
    ( hAPP(U_3129,U_3117) = c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3123),U_3117),U_3127))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3123,tc_fun(U_3125,tc_HOL_Obool)),U_3127),U_3129) != c_Orderings_Otop__class_Otop(tc_fun(U_3125,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3124),sK63(U_3130,U_3128,U_3126,U_3124)),U_3128))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3124,tc_fun(U_3126,tc_HOL_Obool)),U_3128),U_3130) = c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_7,plain,
    ( hAPP(U_3130,sK63(U_3130,U_3128,U_3126,U_3124)) != c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3124,tc_fun(U_3126,tc_HOL_Obool)),U_3128),U_3130) = c_Orderings_Otop__class_Otop(tc_fun(U_3126,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

fof(f_587_1,plain,
    ! [T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).

fof(f_587_2,plain,
    ! [U_3131] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3131,c_Orderings_Otop__class_Otop(tc_fun(U_3131,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_3131)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3131) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3131,c_Orderings_Otop__class_Otop(tc_fun(U_3131,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_3131)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3131) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_1,plain,
    ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).

fof(f_588_2,plain,
    ! [U_3133,U_3132] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3132,tc_HOL_Obool),U_3133) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_3132,tc_HOL_Obool),tc_fun(U_3132,tc_HOL_Obool)),U_3133),c_COMBI(tc_fun(U_3132,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

cnf(f_588_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3132,tc_HOL_Obool),U_3133) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_3132,tc_HOL_Obool),tc_fun(U_3132,tc_HOL_Obool)),U_3133),c_COMBI(tc_fun(U_3132,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_588_2]) ).

fof(f_589_1,plain,
    ! [T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).

fof(f_589_2,plain,
    ! [U_3134] :
      ( c_Complete__Lattice_OSup__class_OSup(U_3134,c_Orderings_Otop__class_Otop(tc_fun(U_3134,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_3134)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3134) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_3134,c_Orderings_Otop__class_Otop(tc_fun(U_3134,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_3134)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3134) ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_1,plain,
    ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).

fof(f_590_2,plain,
    ! [U_3135] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3135,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3135,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3135,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3135,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3135,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3135,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_1,plain,
    ! [T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).

fof(f_591_2,plain,
    ! [U_3136] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3136,c_Orderings_Obot__class_Obot(tc_fun(U_3136,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_3136)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3136) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3136,c_Orderings_Obot__class_Obot(tc_fun(U_3136,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_3136)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3136) ),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_1,plain,
    ! [V_A_2,T_a] :
      ( ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(T_a),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).

fof(f_592_2,plain,
    ! [U_3138,U_3137] :
      ( ( hAPP(c_Finite__Set_Ocard(U_3137),U_3138) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3137),U_3138))
          & U_3138 != c_Orderings_Obot__class_Obot(tc_fun(U_3137,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3137),U_3138))
        | U_3138 = c_Orderings_Obot__class_Obot(tc_fun(U_3137,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_3137),U_3138) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_3142,U_3140] :
        ( hAPP(c_Finite__Set_Ocard(U_3140),U_3142) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3140),U_3142))
          & U_3142 != c_Orderings_Obot__class_Obot(tc_fun(U_3140,tc_HOL_Obool)) ) )
    & ! [U_3141,U_3139] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3139),U_3141))
        | U_3141 = c_Orderings_Obot__class_Obot(tc_fun(U_3139,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_3139),U_3141) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_592_2]) ).

cnf(f_592_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3139),U_3141))
    | U_3141 = c_Orderings_Obot__class_Obot(tc_fun(U_3139,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3139),U_3141) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_5,plain,
    ( U_3142 != c_Orderings_Obot__class_Obot(tc_fun(U_3140,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3140),U_3142) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3140),U_3142))
    | hAPP(c_Finite__Set_Ocard(U_3140),U_3142) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(f_593_2,plain,
    ! [U_3146,U_3145,U_3144,U_3143] : c_Nitpick_Ofold__graph_H(U_3143,U_3144,U_3145,U_3146,c_Orderings_Obot__class_Obot(tc_fun(U_3143,tc_HOL_Obool)),U_3146),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    c_Nitpick_Ofold__graph_H(U_3143,U_3144,U_3145,U_3146,c_Orderings_Obot__class_Obot(tc_fun(U_3143,tc_HOL_Obool)),U_3146),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_1,plain,
    ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(f_594_2,plain,
    ! [U_3150,U_3149,U_3148,U_3147] : c_Nitpick_Ofold__graph_H(U_3147,U_3148,U_3149,U_3150,c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool)),U_3150),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    c_Nitpick_Ofold__graph_H(U_3147,U_3148,U_3149,U_3150,c_Orderings_Obot__class_Obot(tc_fun(U_3147,tc_HOL_Obool)),U_3150),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_1,plain,
    ! [T_b,T_a] :
      ( 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_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).

fof(f_595_2,plain,
    ! [U_3152,U_3151] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),c_Orderings_Otop__class_Otop(tc_fun(U_3152,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3151,U_3152)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3151,U_3152),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_3152] :
      ( ! [U_3151] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3151,U_3152)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3151,U_3152),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),c_Orderings_Otop__class_Otop(tc_fun(U_3152,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_595_2]) ).

cnf(f_595_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3151,U_3152)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3151,U_3152),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3152),c_Orderings_Otop__class_Otop(tc_fun(U_3152,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).

fof(f_596_2,plain,
    ! [U_3153] : c_Orderings_Otop__class_Otop(tc_fun(U_3153,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_3153,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_3153,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_3153,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).

fof(f_597_2,plain,
    ! [U_3154] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),c_Orderings_Otop__class_Otop(tc_fun(U_3154,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_3154) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

cnf(f_597_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),c_Orderings_Otop__class_Otop(tc_fun(U_3154,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_3154) ),
    inference(clausify,[status(thm)],[f_597_2]) ).

fof(f_598_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_598_2,plain,
    ! [U_3156,U_3155] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3156),c_Groups_Ozero__class_Ozero(U_3155)) = U_3156
      | ~ class_Groups_Ocomm__monoid__add(U_3155) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

cnf(f_598_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3156),c_Groups_Ozero__class_Ozero(U_3155)) = U_3156
    | ~ class_Groups_Ocomm__monoid__add(U_3155) ),
    inference(clausify,[status(thm)],[f_598_2]) ).

fof(f_599_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_599_2,plain,
    ! [U_3158,U_3157] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3157),U_3158),c_Groups_Ozero__class_Ozero(U_3157)) = U_3158
      | ~ class_Groups_Omonoid__add(U_3157) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

cnf(f_599_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3157),U_3158),c_Groups_Ozero__class_Ozero(U_3157)) = U_3158
    | ~ class_Groups_Omonoid__add(U_3157) ),
    inference(clausify,[status(thm)],[f_599_2]) ).

fof(f_600_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ozero__class_Ozero(T_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).

fof(f_600_2,plain,
    ! [U_3160,U_3159] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_3159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3159),U_3160),U_3160)
          | U_3160 != c_Groups_Ozero__class_Ozero(U_3159) )
        & ( U_3160 = c_Groups_Ozero__class_Ozero(U_3159)
          | c_Groups_Ozero__class_Ozero(U_3159) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3159),U_3160),U_3160) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3159) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

cnf(f_600_3,plain,
    ( U_3160 = c_Groups_Ozero__class_Ozero(U_3159)
    | c_Groups_Ozero__class_Ozero(U_3159) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3159),U_3160),U_3160)
    | ~ class_Groups_Olinordered__ab__group__add(U_3159) ),
    inference(clausify,[status(thm)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_3159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3159),U_3160),U_3160)
    | U_3160 != c_Groups_Ozero__class_Ozero(U_3159)
    | ~ class_Groups_Olinordered__ab__group__add(U_3159) ),
    inference(clausify,[status(thm)],[f_600_2]) ).

fof(f_601_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_601_2,plain,
    ! [U_3162,U_3161] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3161),c_Groups_Ozero__class_Ozero(U_3161)),U_3162) = U_3162
      | ~ class_Groups_Ocomm__monoid__add(U_3161) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

cnf(f_601_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3161),c_Groups_Ozero__class_Ozero(U_3161)),U_3162) = U_3162
    | ~ class_Groups_Ocomm__monoid__add(U_3161) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

fof(f_602_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_602_2,plain,
    ! [U_3164,U_3163] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3163),c_Groups_Ozero__class_Ozero(U_3163)),U_3164) = U_3164
      | ~ class_Groups_Omonoid__add(U_3163) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

cnf(f_602_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3163),c_Groups_Ozero__class_Ozero(U_3163)),U_3164) = U_3164
    | ~ class_Groups_Omonoid__add(U_3163) ),
    inference(clausify,[status(thm)],[f_602_2]) ).

fof(f_603_1,plain,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).

fof(f_603_2,plain,
    ! [U_3166,U_3165] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3165,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3165,tc_HOL_Obool))),U_3166) = c_Orderings_Otop__class_Otop(tc_fun(U_3165,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

cnf(f_603_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3165,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3165,tc_HOL_Obool))),U_3166) = c_Orderings_Otop__class_Otop(tc_fun(U_3165,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_603_2]) ).

fof(f_604_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).

fof(f_604_2,plain,
    ! [U_3168,U_3167] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3167,tc_HOL_Obool)),U_3168),c_Orderings_Otop__class_Otop(tc_fun(U_3167,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3167,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

cnf(f_604_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3167,tc_HOL_Obool)),U_3168),c_Orderings_Otop__class_Otop(tc_fun(U_3167,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3167,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_1,plain,
    ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).

fof(f_605_2,plain,
    ! [U_3170,U_3169] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3169,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3169,tc_HOL_Obool))),U_3170) = U_3170,
    inference(variable_rename,[status(thm)],[f_605_1]) ).

cnf(f_605_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3169,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3169,tc_HOL_Obool))),U_3170) = U_3170,
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).

fof(f_606_2,plain,
    ! [U_3172,U_3171] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3171,tc_HOL_Obool)),U_3172),c_Orderings_Otop__class_Otop(tc_fun(U_3171,tc_HOL_Obool))) = U_3172,
    inference(variable_rename,[status(thm)],[f_606_1]) ).

cnf(f_606_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3171,tc_HOL_Obool)),U_3172),c_Orderings_Otop__class_Otop(tc_fun(U_3171,tc_HOL_Obool))) = U_3172,
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).

fof(f_607_2,plain,
    ! [U_3175,U_3174,U_3173] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3173),U_3174),U_3175) = c_Groups_Ozero__class_Ozero(U_3173)
          | U_3174 != U_3175 )
        & ( U_3174 = U_3175
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3173),U_3174),U_3175) != c_Groups_Ozero__class_Ozero(U_3173) ) )
      | ~ class_Groups_Ogroup__add(U_3173) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    ( U_3174 = U_3175
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3173),U_3174),U_3175) != c_Groups_Ozero__class_Ozero(U_3173)
    | ~ class_Groups_Ogroup__add(U_3173) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

cnf(f_607_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3173),U_3174),U_3175) = c_Groups_Ozero__class_Ozero(U_3173)
    | U_3174 != U_3175
    | ~ class_Groups_Ogroup__add(U_3173) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != V_b_2 ) )
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).

fof(f_608_2,plain,
    ! [U_3178,U_3177,U_3176] :
      ( ( ( U_3177 = U_3178
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),U_3178) != c_Groups_Ozero__class_Ozero(U_3176) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),U_3178) = c_Groups_Ozero__class_Ozero(U_3176)
          | U_3177 != U_3178 ) )
      | ~ class_Groups_Oab__group__add(U_3176) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

cnf(f_608_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),U_3178) = c_Groups_Ozero__class_Ozero(U_3176)
    | U_3177 != U_3178
    | ~ class_Groups_Oab__group__add(U_3176) ),
    inference(clausify,[status(thm)],[f_608_2]) ).

cnf(f_608_4,plain,
    ( U_3177 = U_3178
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),U_3178) != c_Groups_Ozero__class_Ozero(U_3176)
    | ~ class_Groups_Oab__group__add(U_3176) ),
    inference(clausify,[status(thm)],[f_608_2]) ).

fof(f_609_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_609_2,plain,
    ! [U_3180,U_3179] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3179),U_3180),U_3180) = c_Groups_Ozero__class_Ozero(U_3179)
      | ~ class_Groups_Ogroup__add(U_3179) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

cnf(f_609_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3179),U_3180),U_3180) = c_Groups_Ozero__class_Ozero(U_3179)
    | ~ class_Groups_Ogroup__add(U_3179) ),
    inference(clausify,[status(thm)],[f_609_2]) ).

fof(f_610_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_610_2,plain,
    ! [U_3182,U_3181] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3181),U_3182),c_Groups_Ozero__class_Ozero(U_3181)) = U_3182
      | ~ class_Groups_Ogroup__add(U_3181) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

cnf(f_610_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3181),U_3182),c_Groups_Ozero__class_Ozero(U_3181)) = U_3182
    | ~ class_Groups_Ogroup__add(U_3181) ),
    inference(clausify,[status(thm)],[f_610_2]) ).

fof(f_611_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_611_2,plain,
    ! [U_3183] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3183) = U_3183,
    inference(variable_rename,[status(thm)],[f_611_1]) ).

cnf(f_611_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3183) = U_3183,
    inference(clausify,[status(thm)],[f_611_2]) ).

fof(f_612_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_612_2,plain,
    ! [U_3184] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3184),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3184,
    inference(variable_rename,[status(thm)],[f_612_1]) ).

cnf(f_612_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3184),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3184,
    inference(clausify,[status(thm)],[f_612_2]) ).

fof(f_613_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_613_2,plain,
    ! [U_3186,U_3185] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3185),U_3186) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3185 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_3186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3185),U_3186) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ( ! [U_3190,U_3188] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3188),U_3190) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3190 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3189,U_3187] :
        ( ( U_3189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3187 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3187),U_3189) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( U_3187 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3187),U_3189) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

cnf(f_613_5,plain,
    ( U_3189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3187),U_3189) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

cnf(f_613_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3188),U_3190) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3190 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_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_614_2,plain,
    ! [U_3192,U_3191] :
      ( U_3192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3191),U_3192) != U_3191 ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_3192] :
      ( ! [U_3191] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3191),U_3192) != U_3191
      | U_3192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3191),U_3192) != U_3191
    | U_3192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_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_615_2,plain,
    ! [U_3194,U_3193] :
      ( U_3193 = U_3194
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3194),U_3193) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3193),U_3194) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

cnf(f_615_3,plain,
    ( U_3193 = U_3194
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3194),U_3193) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3193),U_3194) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_615_2]) ).

fof(f_616_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_616_2,plain,
    ! [U_3195] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3195),U_3195) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

cnf(f_616_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3195),U_3195) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_616_2]) ).

fof(f_617_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_617_2,plain,
    ! [U_3196] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3196),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3196,
    inference(variable_rename,[status(thm)],[f_617_1]) ).

cnf(f_617_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3196),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3196,
    inference(clausify,[status(thm)],[f_617_2]) ).

fof(f_618_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_618_2,plain,
    ! [U_3197] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3197) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

cnf(f_618_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3197) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_618_2]) ).

fof(f_619_1,plain,
    ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,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_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UNIV]) ).

fof(f_619_2,plain,
    ! [U_3200,U_3199,U_3198] : hAPP(c_Set_Ovimage(U_3198,U_3199,U_3200),c_Orderings_Otop__class_Otop(tc_fun(U_3199,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3198,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

cnf(f_619_3,plain,
    hAPP(c_Set_Ovimage(U_3198,U_3199,U_3200),c_Orderings_Otop__class_Otop(tc_fun(U_3199,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3198,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_619_2]) ).

fof(f_620_1,plain,
    ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(f_620_2,plain,
    ! [U_3204,U_3203,U_3202,U_3201] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3201,U_3202,U_3203,U_3204,c_Orderings_Obot__class_Obot(tc_fun(U_3201,tc_HOL_Obool))),U_3204)),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

cnf(f_620_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3201,U_3202,U_3203,U_3204,c_Orderings_Obot__class_Obot(tc_fun(U_3201,tc_HOL_Obool))),U_3204)),
    inference(clausify,[status(thm)],[f_620_2]) ).

fof(f_621_1,plain,
    ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(f_621_2,plain,
    ! [U_3208,U_3207,U_3206,U_3205] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3205,U_3206,U_3207,U_3208,c_Orderings_Obot__class_Obot(tc_fun(U_3205,tc_HOL_Obool))),U_3208)),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

cnf(f_621_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3205,U_3206,U_3207,U_3208,c_Orderings_Obot__class_Obot(tc_fun(U_3205,tc_HOL_Obool))),U_3208)),
    inference(clausify,[status(thm)],[f_621_2]) ).

fof(f_622_1,plain,
    ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
      ( V_x_2 = V_z_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).

fof(f_622_2,plain,
    ! [U_3213,U_3212,U_3211,U_3210,U_3209] :
      ( U_3213 = U_3212
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3209,U_3210,U_3211,U_3212,c_Orderings_Obot__class_Obot(tc_fun(U_3209,tc_HOL_Obool))),U_3213)) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_3213,U_3212] :
      ( ! [U_3211,U_3210,U_3209] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3209,U_3210,U_3211,U_3212,c_Orderings_Obot__class_Obot(tc_fun(U_3209,tc_HOL_Obool))),U_3213))
      | U_3213 = U_3212 ),
    inference(miniscope,[status(thm)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3209,U_3210,U_3211,U_3212,c_Orderings_Obot__class_Obot(tc_fun(U_3209,tc_HOL_Obool))),U_3213))
    | U_3213 = U_3212 ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_1,plain,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).

fof(f_623_2,plain,
    ! [U_3219,U_3218,U_3217,U_3216,U_3215,U_3214] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3214),U_3218))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3214,U_3215,U_3216,U_3217,U_3218),U_3219)) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

cnf(f_623_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3214),U_3218))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3214,U_3215,U_3216,U_3217,U_3218),U_3219)) ),
    inference(clausify,[status(thm)],[f_623_2]) ).

fof(f_624_1,plain,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).

fof(f_624_2,plain,
    ! [U_3223,U_3222,U_3221,U_3220] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3220,tc_fun(U_3221,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3220,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3221,tc_HOL_Obool),tc_fun(U_3221,tc_HOL_Obool),U_3220),hAPP(c_COMBC(U_3221,tc_fun(U_3221,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3221))),U_3222)),U_3223))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3221),U_3223),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3220,tc_fun(U_3221,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3220,tc_HOL_Obool))),U_3222))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_3221),U_3223),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3220,tc_fun(U_3221,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3220,tc_HOL_Obool))),U_3222)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3220,tc_fun(U_3221,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3220,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3221,tc_HOL_Obool),tc_fun(U_3221,tc_HOL_Obool),U_3220),hAPP(c_COMBC(U_3221,tc_fun(U_3221,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3221))),U_3222)),U_3223)) ) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ( ! [U_3231,U_3229,U_3227,U_3225] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3225,tc_fun(U_3227,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3227,tc_HOL_Obool),tc_fun(U_3227,tc_HOL_Obool),U_3225),hAPP(c_COMBC(U_3227,tc_fun(U_3227,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3227))),U_3229)),U_3231))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3227),U_3231),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3225,tc_fun(U_3227,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3225,tc_HOL_Obool))),U_3229))) )
    & ! [U_3230,U_3228,U_3226,U_3224] :
        ( hBOOL(hAPP(hAPP(c_member(U_3226),U_3230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3224,tc_fun(U_3226,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3224,tc_HOL_Obool))),U_3228)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3224,tc_fun(U_3226,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3224,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3226,tc_HOL_Obool),tc_fun(U_3226,tc_HOL_Obool),U_3224),hAPP(c_COMBC(U_3226,tc_fun(U_3226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3226))),U_3228)),U_3230)) ) ),
    inference(miniscope,[status(thm)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3226),U_3230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3224,tc_fun(U_3226,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3224,tc_HOL_Obool))),U_3228)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3224,tc_fun(U_3226,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3224,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3226,tc_HOL_Obool),tc_fun(U_3226,tc_HOL_Obool),U_3224),hAPP(c_COMBC(U_3226,tc_fun(U_3226,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3226))),U_3228)),U_3230)) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3225,tc_fun(U_3227,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3227,tc_HOL_Obool),tc_fun(U_3227,tc_HOL_Obool),U_3225),hAPP(c_COMBC(U_3227,tc_fun(U_3227,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3227))),U_3229)),U_3231))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3227),U_3231),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3225,tc_fun(U_3227,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3225,tc_HOL_Obool))),U_3229))) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [V_c_2,T_b,T_a,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).

fof(f_625_2,plain,
    ! [U_3235,U_3234,U_3233,U_3232] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3233,tc_fun(U_3234,tc_HOL_Obool)),U_3232),hAPP(c_COMBK(tc_fun(U_3234,tc_HOL_Obool),U_3233),U_3235)) = U_3235
        | U_3232 = c_Orderings_Obot__class_Obot(tc_fun(U_3233,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3233,tc_fun(U_3234,tc_HOL_Obool)),U_3232),hAPP(c_COMBK(tc_fun(U_3234,tc_HOL_Obool),U_3233),U_3235)) = c_Orderings_Otop__class_Otop(tc_fun(U_3234,tc_HOL_Obool))
        | U_3232 != c_Orderings_Obot__class_Obot(tc_fun(U_3233,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ( ! [U_3243,U_3241,U_3239,U_3237] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3239,tc_fun(U_3241,tc_HOL_Obool)),U_3237),hAPP(c_COMBK(tc_fun(U_3241,tc_HOL_Obool),U_3239),U_3243)) = U_3243
        | U_3237 = c_Orderings_Obot__class_Obot(tc_fun(U_3239,tc_HOL_Obool)) )
    & ! [U_3242,U_3240,U_3238,U_3236] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3238,tc_fun(U_3240,tc_HOL_Obool)),U_3236),hAPP(c_COMBK(tc_fun(U_3240,tc_HOL_Obool),U_3238),U_3242)) = c_Orderings_Otop__class_Otop(tc_fun(U_3240,tc_HOL_Obool))
        | U_3236 != c_Orderings_Obot__class_Obot(tc_fun(U_3238,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_625_2]) ).

cnf(f_625_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3238,tc_fun(U_3240,tc_HOL_Obool)),U_3236),hAPP(c_COMBK(tc_fun(U_3240,tc_HOL_Obool),U_3238),U_3242)) = c_Orderings_Otop__class_Otop(tc_fun(U_3240,tc_HOL_Obool))
    | U_3236 != c_Orderings_Obot__class_Obot(tc_fun(U_3238,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3239,tc_fun(U_3241,tc_HOL_Obool)),U_3237),hAPP(c_COMBK(tc_fun(U_3241,tc_HOL_Obool),U_3239),U_3243)) = U_3243
    | U_3237 = c_Orderings_Obot__class_Obot(tc_fun(U_3239,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_1,plain,
    ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).

fof(f_626_2,plain,
    ! [U_3246,U_3245,U_3244] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3244,tc_fun(U_3245,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_3244,tc_HOL_Obool))),U_3246) = c_Orderings_Otop__class_Otop(tc_fun(U_3245,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

cnf(f_626_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3244,tc_fun(U_3245,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_3244,tc_HOL_Obool))),U_3246) = c_Orderings_Otop__class_Otop(tc_fun(U_3245,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_626_2]) ).

fof(f_627_1,plain,
    ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_range__composition]) ).

fof(f_627_2,plain,
    ! [U_3251,U_3250,U_3249,U_3248,U_3247] : hAPP(c_Set_Oimage(U_3247,U_3248,hAPP(hAPP(c_COMBB(U_3249,U_3248,U_3247),U_3250),U_3251)),c_Orderings_Otop__class_Otop(tc_fun(U_3247,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_3249,U_3248,U_3250),hAPP(c_Set_Oimage(U_3247,U_3249,U_3251),c_Orderings_Otop__class_Otop(tc_fun(U_3247,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

cnf(f_627_3,plain,
    hAPP(c_Set_Oimage(U_3247,U_3248,hAPP(hAPP(c_COMBB(U_3249,U_3248,U_3247),U_3250),U_3251)),c_Orderings_Otop__class_Otop(tc_fun(U_3247,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_3249,U_3248,U_3250),hAPP(c_Set_Oimage(U_3247,U_3249,U_3251),c_Orderings_Otop__class_Otop(tc_fun(U_3247,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_627_2]) ).

fof(f_628_1,plain,
    ! [V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).

fof(f_628_2,plain,
    ! [U_3254,U_3253,U_3252] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3253,U_3252),hAPP(c_COMBK(U_3252,U_3253),c_Groups_Ozero__class_Ozero(U_3252))),U_3254) = c_Groups_Ozero__class_Ozero(U_3252)
      | ~ class_Groups_Ocomm__monoid__add(U_3252) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

cnf(f_628_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3253,U_3252),hAPP(c_COMBK(U_3252,U_3253),c_Groups_Ozero__class_Ozero(U_3252))),U_3254) = c_Groups_Ozero__class_Ozero(U_3252)
    | ~ class_Groups_Ocomm__monoid__add(U_3252) ),
    inference(clausify,[status(thm)],[f_628_2]) ).

fof(f_629_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).

fof(f_629_2,plain,
    ! [U_3257,U_3256,U_3255] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3255,tc_HOL_Obool)),U_3256),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3255,tc_HOL_Obool),U_3257)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_3255,tc_HOL_Obool),tc_fun(U_3255,tc_HOL_Obool)),U_3257),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3255,tc_HOL_Obool)),U_3256)),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

cnf(f_629_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3255,tc_HOL_Obool)),U_3256),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3255,tc_HOL_Obool),U_3257)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_3255,tc_HOL_Obool),tc_fun(U_3255,tc_HOL_Obool)),U_3257),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3255,tc_HOL_Obool)),U_3256)),
    inference(clausify,[status(thm)],[f_629_2]) ).

fof(f_630_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( V_y_2 = V_x_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).

fof(f_630_2,plain,
    ! [U_3264,U_3263,U_3262,U_3261,U_3260,U_3259,U_3258] :
      ( U_3264 = U_3263
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3258,U_3259,U_3260,U_3261,U_3262),U_3264))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3258,U_3259,U_3260,U_3261,U_3262),U_3263))
      | ~ c_Finite__Set_Ofun__left__comm(U_3258,U_3259,U_3260) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

cnf(f_630_3,plain,
    ( U_3264 = U_3263
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3258,U_3259,U_3260,U_3261,U_3262),U_3264))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3258,U_3259,U_3260,U_3261,U_3262),U_3263))
    | ~ c_Finite__Set_Ofun__left__comm(U_3258,U_3259,U_3260) ),
    inference(clausify,[status(thm)],[f_630_2]) ).

fof(f_631_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_631_2,plain,
    ! [U_3266,U_3265] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3265),c_Orderings_Otop__class_Otop(U_3265)),U_3266) = c_Orderings_Otop__class_Otop(U_3265)
      | ~ class_Lattices_Obounded__lattice__top(U_3265) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

cnf(f_631_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3265),c_Orderings_Otop__class_Otop(U_3265)),U_3266) = c_Orderings_Otop__class_Otop(U_3265)
    | ~ class_Lattices_Obounded__lattice__top(U_3265) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

fof(f_632_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_632_2,plain,
    ! [U_3268,U_3267] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3267),U_3268),c_Orderings_Otop__class_Otop(U_3267)) = c_Orderings_Otop__class_Otop(U_3267)
      | ~ class_Lattices_Obounded__lattice__top(U_3267) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

cnf(f_632_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3267),U_3268),c_Orderings_Otop__class_Otop(U_3267)) = c_Orderings_Otop__class_Otop(U_3267)
    | ~ class_Lattices_Obounded__lattice__top(U_3267) ),
    inference(clausify,[status(thm)],[f_632_2]) ).

fof(f_633_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_633_2,plain,
    ! [U_3270,U_3269] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3269),c_Orderings_Otop__class_Otop(U_3269)),U_3270) = U_3270
      | ~ class_Lattices_Obounded__lattice__top(U_3269) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

cnf(f_633_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3269),c_Orderings_Otop__class_Otop(U_3269)),U_3270) = U_3270
    | ~ class_Lattices_Obounded__lattice__top(U_3269) ),
    inference(clausify,[status(thm)],[f_633_2]) ).

fof(f_634_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_634_2,plain,
    ! [U_3272,U_3271] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3271),U_3272),c_Orderings_Otop__class_Otop(U_3271)) = U_3272
      | ~ class_Lattices_Obounded__lattice__top(U_3271) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

cnf(f_634_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3271),U_3272),c_Orderings_Otop__class_Otop(U_3271)) = U_3272
    | ~ class_Lattices_Obounded__lattice__top(U_3271) ),
    inference(clausify,[status(thm)],[f_634_2]) ).

fof(f_635_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
          | V_y_2 != c_Orderings_Otop__class_Otop(T_a)
          | V_x_2 != c_Orderings_Otop__class_Otop(T_a) )
        & ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_a)
            & V_x_2 = c_Orderings_Otop__class_Otop(T_a) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_a) ) )
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).

fof(f_635_2,plain,
    ! [U_3275,U_3274,U_3273] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3273),U_3274),U_3275) = c_Orderings_Otop__class_Otop(U_3273)
          | U_3275 != c_Orderings_Otop__class_Otop(U_3273)
          | U_3274 != c_Orderings_Otop__class_Otop(U_3273) )
        & ( ( U_3275 = c_Orderings_Otop__class_Otop(U_3273)
            & U_3274 = c_Orderings_Otop__class_Otop(U_3273) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3273),U_3274),U_3275) != c_Orderings_Otop__class_Otop(U_3273) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_3273) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

cnf(f_635_3,plain,
    ( U_3274 = c_Orderings_Otop__class_Otop(U_3273)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3273),U_3274),U_3275) != c_Orderings_Otop__class_Otop(U_3273)
    | ~ class_Lattices_Obounded__lattice__top(U_3273) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( U_3275 = c_Orderings_Otop__class_Otop(U_3273)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3273),U_3274),U_3275) != c_Orderings_Otop__class_Otop(U_3273)
    | ~ class_Lattices_Obounded__lattice__top(U_3273) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

cnf(f_635_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3273),U_3274),U_3275) = c_Orderings_Otop__class_Otop(U_3273)
    | U_3275 != c_Orderings_Otop__class_Otop(U_3273)
    | U_3274 != c_Orderings_Otop__class_Otop(U_3273)
    | ~ class_Lattices_Obounded__lattice__top(U_3273) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

fof(f_636_1,plain,
    ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).

fof(f_636_2,plain,
    ! [U_3279,U_3278,U_3277,U_3276] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3276,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3277,tc_fun(U_3276,tc_HOL_Obool),U_3278),U_3279)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3277,tc_fun(U_3276,tc_HOL_Obool)),U_3279),U_3278),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

cnf(f_636_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3276,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3277,tc_fun(U_3276,tc_HOL_Obool),U_3278),U_3279)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3277,tc_fun(U_3276,tc_HOL_Obool)),U_3279),U_3278),
    inference(clausify,[status(thm)],[f_636_2]) ).

fof(f_637_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(f_637_2,plain,
    ! [U_3283,U_3282,U_3281,U_3280] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3280,tc_fun(U_3281,tc_HOL_Obool)),U_3282),U_3283) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3281,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3280,tc_fun(U_3281,tc_HOL_Obool),U_3283),U_3282)),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

cnf(f_637_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3280,tc_fun(U_3281,tc_HOL_Obool)),U_3282),U_3283) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3281,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3280,tc_fun(U_3281,tc_HOL_Obool),U_3283),U_3282)),
    inference(clausify,[status(thm)],[f_637_2]) ).

fof(f_638_1,plain,
    ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | V_b_2 != hAPP(V_f_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).

fof(f_638_2,plain,
    ! [U_3288,U_3287,U_3286,U_3285,U_3284] :
      ( hBOOL(hAPP(hAPP(c_member(U_3287),U_3284),hAPP(c_Set_Oimage(U_3288,U_3287,U_3285),c_Orderings_Otop__class_Otop(tc_fun(U_3288,tc_HOL_Obool)))))
      | U_3284 != hAPP(U_3285,U_3286) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

cnf(f_638_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3287),U_3284),hAPP(c_Set_Oimage(U_3288,U_3287,U_3285),c_Orderings_Otop__class_Otop(tc_fun(U_3288,tc_HOL_Obool)))))
    | U_3284 != hAPP(U_3285,U_3286) ),
    inference(clausify,[status(thm)],[f_638_2]) ).

fof(f_639_1,plain,
    ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_rangeI]) ).

fof(f_639_2,plain,
    ! [U_3292,U_3291,U_3290,U_3289] : hBOOL(hAPP(hAPP(c_member(U_3289),hAPP(U_3290,U_3291)),hAPP(c_Set_Oimage(U_3292,U_3289,U_3290),c_Orderings_Otop__class_Otop(tc_fun(U_3292,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

cnf(f_639_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_3289),hAPP(U_3290,U_3291)),hAPP(c_Set_Oimage(U_3292,U_3289,U_3290),c_Orderings_Otop__class_Otop(tc_fun(U_3292,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_1,plain,
    ! [V_A_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).

fof(f_640_2,plain,
    ! [U_3294,U_3293] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3293,U_3294) = hAPP(hAPP(c_Finite__Set_Ofold(U_3293,U_3293,c_Lattices_Osemilattice__inf__class_Oinf(U_3293)),c_Orderings_Otop__class_Otop(U_3293)),U_3294)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3293),U_3294))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3293) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3293,U_3294) = hAPP(hAPP(c_Finite__Set_Ofold(U_3293,U_3293,c_Lattices_Osemilattice__inf__class_Oinf(U_3293)),c_Orderings_Otop__class_Otop(U_3293)),U_3294)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3293),U_3294))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3293) ),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).

fof(f_641_2,plain,
    ! [U_3296,U_3295] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3295,tc_HOL_Obool)),U_3296),c_Orderings_Otop__class_Otop(tc_fun(U_3295,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3295,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

cnf(f_641_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3295,tc_HOL_Obool)),U_3296),c_Orderings_Otop__class_Otop(tc_fun(U_3295,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3295,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_641_2]) ).

fof(f_642_1,plain,
    ! [V_g_2,T_c,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_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))
      | hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_comp__surj]) ).

fof(f_642_2,plain,
    ! [U_3301,U_3300,U_3299,U_3298,U_3297] :
      ( hAPP(c_Set_Oimage(U_3297,U_3300,hAPP(c_Fun_Ocomp(U_3298,U_3300,U_3297,U_3301),U_3299)),c_Orderings_Otop__class_Otop(tc_fun(U_3297,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3300,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_3298,U_3300,U_3301),c_Orderings_Otop__class_Otop(tc_fun(U_3298,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3300,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_3297,U_3298,U_3299),c_Orderings_Otop__class_Otop(tc_fun(U_3297,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3298,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

cnf(f_642_3,plain,
    ( hAPP(c_Set_Oimage(U_3297,U_3300,hAPP(c_Fun_Ocomp(U_3298,U_3300,U_3297,U_3301),U_3299)),c_Orderings_Otop__class_Otop(tc_fun(U_3297,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3300,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_3298,U_3300,U_3301),c_Orderings_Otop__class_Otop(tc_fun(U_3298,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3300,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_3297,U_3298,U_3299),c_Orderings_Otop__class_Otop(tc_fun(U_3297,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3298,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_642_2]) ).

fof(f_643_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).

fof(f_643_2,plain,
    ! [U_3304,U_3303,U_3302] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3303,U_3302),U_3304),c_Orderings_Obot__class_Obot(tc_fun(U_3303,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3302)
      | ~ class_Groups_Ocomm__monoid__add(U_3302) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

cnf(f_643_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3303,U_3302),U_3304),c_Orderings_Obot__class_Obot(tc_fun(U_3303,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3302)
    | ~ class_Groups_Ocomm__monoid__add(U_3302) ),
    inference(clausify,[status(thm)],[f_643_2]) ).

fof(f_644_1,plain,
    ! [V_g_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).

fof(f_644_2,plain,
    ! [U_3307,U_3306,U_3305] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3306,U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3305)
      | ~ class_Groups_Ocomm__monoid__add(U_3305) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

cnf(f_644_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3306,U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3305)
    | ~ class_Groups_Ocomm__monoid__add(U_3305) ),
    inference(clausify,[status(thm)],[f_644_2]) ).

fof(f_645_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(f_645_2,plain,
    ! [U_3311,U_3310,U_3309,U_3308] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3309,U_3308),U_3311),U_3310) = c_Groups_Ozero__class_Ozero(U_3308)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3310))
      | ~ class_Groups_Ocomm__monoid__add(U_3308) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3309,U_3308),U_3311),U_3310) = c_Groups_Ozero__class_Ozero(U_3308)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3310))
    | ~ class_Groups_Ocomm__monoid__add(U_3308) ),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).

fof(f_646_2,plain,
    ! [U_3315,U_3314,U_3313,U_3312] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3313,U_3312),U_3315),U_3314) = c_Groups_Ozero__class_Ozero(U_3312)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3313),U_3314))
      | ~ class_Groups_Ocomm__monoid__add(U_3312) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3313,U_3312),U_3315),U_3314) = c_Groups_Ozero__class_Ozero(U_3312)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3313),U_3314))
    | ~ class_Groups_Ocomm__monoid__add(U_3312) ),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq]) ).

fof(f_647_2,plain,
    ! [U_3319,U_3318,U_3317,U_3316] :
      ( hAPP(c_Set_Oimage(U_3316,U_3317,U_3318),hAPP(c_Set_Ovimage(U_3316,U_3317,U_3318),U_3319)) = U_3319
      | hAPP(c_Set_Oimage(U_3316,U_3317,U_3318),c_Orderings_Otop__class_Otop(tc_fun(U_3316,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3317,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

cnf(f_647_3,plain,
    ( hAPP(c_Set_Oimage(U_3316,U_3317,U_3318),hAPP(c_Set_Ovimage(U_3316,U_3317,U_3318),U_3319)) = U_3319
    | hAPP(c_Set_Oimage(U_3316,U_3317,U_3318),c_Orderings_Otop__class_Otop(tc_fun(U_3316,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3317,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_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_648_2,plain,
    ! [U_3321,U_3320] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3320),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3320),U_3321)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

cnf(f_648_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3320),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3320),U_3321)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_648_2]) ).

fof(f_649_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),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_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(f_649_2,plain,
    ! [U_3328,U_3327,U_3326,U_3325,U_3324,U_3323,U_3322] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3322,U_3325,U_3326,U_3327,hAPP(hAPP(c_Set_Oinsert(U_3322),U_3323),U_3324)),hAPP(hAPP(U_3326,U_3323),U_3328)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3322,U_3325,U_3326,U_3327,U_3324),U_3328))
      | hBOOL(hAPP(hAPP(c_member(U_3322),U_3323),U_3324)) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

cnf(f_649_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3322,U_3325,U_3326,U_3327,hAPP(hAPP(c_Set_Oinsert(U_3322),U_3323),U_3324)),hAPP(hAPP(U_3326,U_3323),U_3328)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3322,U_3325,U_3326,U_3327,U_3324),U_3328))
    | hBOOL(hAPP(hAPP(c_member(U_3322),U_3323),U_3324)) ),
    inference(clausify,[status(thm)],[f_649_2]) ).

fof(f_650_1,plain,
    ! [V_f_2,V_F_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_a),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).

fof(f_650_2,plain,
    ! [U_3333,U_3332,U_3331] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_3330] :
              ( hAPP(U_3333,U_3330) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_3331),U_3330),U_3332)) ) )
        & ( ! [U_3329] :
              ( hAPP(U_3333,U_3329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3331),U_3329),U_3332)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3331),U_3332)) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_3333,U_3332,U_3331] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_3333,sK64(U_3333,U_3332,U_3331)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3331),sK64(U_3333,U_3332,U_3331)),U_3332)) ) )
        & ( ! [U_3329] :
              ( hAPP(U_3333,U_3329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3331),U_3329),U_3332)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3331),U_3332)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3330,sK64(U_3333,U_3332,U_3331))],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hAPP(U_3333,U_3329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3331),U_3329),U_3332))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3331),U_3332)) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3331),sK64(U_3333,U_3332,U_3331)),U_3332))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3331),U_3332)) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_6,plain,
    ( hAPP(U_3333,sK64(U_3333,U_3332,U_3331)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3331,tc_Nat_Onat),U_3333),U_3332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3331),U_3332)) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_1,plain,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).

fof(f_651_2,plain,
    ! [U_3337,U_3336,U_3335,U_3334] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3334,tc_fun(U_3335,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3334,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3335,tc_HOL_Obool),tc_fun(U_3335,tc_HOL_Obool),U_3334),hAPP(c_COMBC(U_3335,tc_fun(U_3335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3335))),U_3336)),U_3337))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3335),U_3337),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3334,tc_fun(U_3335,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3334,tc_HOL_Obool))),U_3336))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_3335),U_3337),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3334,tc_fun(U_3335,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3334,tc_HOL_Obool))),U_3336)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3334,tc_fun(U_3335,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3334,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3335,tc_HOL_Obool),tc_fun(U_3335,tc_HOL_Obool),U_3334),hAPP(c_COMBC(U_3335,tc_fun(U_3335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3335))),U_3336)),U_3337)) ) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ( ! [U_3345,U_3343,U_3341,U_3339] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3339,tc_fun(U_3341,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3339,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3341,tc_HOL_Obool),tc_fun(U_3341,tc_HOL_Obool),U_3339),hAPP(c_COMBC(U_3341,tc_fun(U_3341,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3341))),U_3343)),U_3345))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3341),U_3345),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3339,tc_fun(U_3341,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3339,tc_HOL_Obool))),U_3343))) )
    & ! [U_3344,U_3342,U_3340,U_3338] :
        ( hBOOL(hAPP(hAPP(c_member(U_3340),U_3344),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3338,tc_fun(U_3340,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3338,tc_HOL_Obool))),U_3342)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3338,tc_fun(U_3340,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3340,tc_HOL_Obool),tc_fun(U_3340,tc_HOL_Obool),U_3338),hAPP(c_COMBC(U_3340,tc_fun(U_3340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3340))),U_3342)),U_3344)) ) ),
    inference(miniscope,[status(thm)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3340),U_3344),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3338,tc_fun(U_3340,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3338,tc_HOL_Obool))),U_3342)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3338,tc_fun(U_3340,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3340,tc_HOL_Obool),tc_fun(U_3340,tc_HOL_Obool),U_3338),hAPP(c_COMBC(U_3340,tc_fun(U_3340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3340))),U_3342)),U_3344)) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

cnf(f_651_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3339,tc_fun(U_3341,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3339,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_3341,tc_HOL_Obool),tc_fun(U_3341,tc_HOL_Obool),U_3339),hAPP(c_COMBC(U_3341,tc_fun(U_3341,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3341))),U_3343)),U_3345))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3341),U_3345),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3339,tc_fun(U_3341,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3339,tc_HOL_Obool))),U_3343))) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [V_f_2,T_c,V_g_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).

fof(f_652_2,plain,
    ! [U_3350,U_3349,U_3348,U_3347,U_3346] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3349),hAPP(c_Set_Oimage(U_3347,U_3349,hAPP(hAPP(c_COMBB(U_3346,U_3349,U_3347),U_3350),U_3348)),c_Orderings_Otop__class_Otop(tc_fun(U_3347,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3346),hAPP(c_Set_Oimage(U_3347,U_3346,U_3348),c_Orderings_Otop__class_Otop(tc_fun(U_3347,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3349),hAPP(c_Set_Oimage(U_3347,U_3349,hAPP(hAPP(c_COMBB(U_3346,U_3349,U_3347),U_3350),U_3348)),c_Orderings_Otop__class_Otop(tc_fun(U_3347,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3346),hAPP(c_Set_Oimage(U_3347,U_3346,U_3348),c_Orderings_Otop__class_Otop(tc_fun(U_3347,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).

fof(f_653_2,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3352,tc_fun(U_3353,tc_HOL_Obool)),U_3351),hAPP(hAPP(c_COMBB(tc_fun(U_3353,tc_HOL_Obool),tc_fun(U_3353,tc_HOL_Obool),U_3352),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3353,tc_HOL_Obool)),U_3354)),U_3355)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3353,tc_HOL_Obool)),U_3354),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3352,tc_fun(U_3353,tc_HOL_Obool)),U_3351),U_3355))
        | U_3351 = c_Orderings_Obot__class_Obot(tc_fun(U_3352,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3352,tc_fun(U_3353,tc_HOL_Obool)),U_3351),hAPP(hAPP(c_COMBB(tc_fun(U_3353,tc_HOL_Obool),tc_fun(U_3353,tc_HOL_Obool),U_3352),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3353,tc_HOL_Obool)),U_3354)),U_3355)) = c_Orderings_Otop__class_Otop(tc_fun(U_3353,tc_HOL_Obool))
        | U_3351 != c_Orderings_Obot__class_Obot(tc_fun(U_3352,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ( ! [U_3365,U_3363,U_3361,U_3359,U_3357] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3359,tc_fun(U_3361,tc_HOL_Obool)),U_3357),hAPP(hAPP(c_COMBB(tc_fun(U_3361,tc_HOL_Obool),tc_fun(U_3361,tc_HOL_Obool),U_3359),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3361,tc_HOL_Obool)),U_3363)),U_3365)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3361,tc_HOL_Obool)),U_3363),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3359,tc_fun(U_3361,tc_HOL_Obool)),U_3357),U_3365))
        | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3359,tc_HOL_Obool)) )
    & ! [U_3364,U_3362,U_3360,U_3358,U_3356] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3358,tc_fun(U_3360,tc_HOL_Obool)),U_3356),hAPP(hAPP(c_COMBB(tc_fun(U_3360,tc_HOL_Obool),tc_fun(U_3360,tc_HOL_Obool),U_3358),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3362)),U_3364)) = c_Orderings_Otop__class_Otop(tc_fun(U_3360,tc_HOL_Obool))
        | U_3356 != c_Orderings_Obot__class_Obot(tc_fun(U_3358,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3358,tc_fun(U_3360,tc_HOL_Obool)),U_3356),hAPP(hAPP(c_COMBB(tc_fun(U_3360,tc_HOL_Obool),tc_fun(U_3360,tc_HOL_Obool),U_3358),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3362)),U_3364)) = c_Orderings_Otop__class_Otop(tc_fun(U_3360,tc_HOL_Obool))
    | U_3356 != c_Orderings_Obot__class_Obot(tc_fun(U_3358,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

cnf(f_653_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3359,tc_fun(U_3361,tc_HOL_Obool)),U_3357),hAPP(hAPP(c_COMBB(tc_fun(U_3361,tc_HOL_Obool),tc_fun(U_3361,tc_HOL_Obool),U_3359),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3361,tc_HOL_Obool)),U_3363)),U_3365)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3361,tc_HOL_Obool)),U_3363),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3359,tc_fun(U_3361,tc_HOL_Obool)),U_3357),U_3365))
    | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3359,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(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))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).

fof(f_654_2,plain,
    ! [U_3370,U_3369,U_3368,U_3367,U_3366] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3367,tc_fun(U_3368,tc_HOL_Obool)),U_3366),hAPP(hAPP(c_COMBC(U_3367,tc_fun(U_3368,tc_HOL_Obool),tc_fun(U_3368,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3368,tc_HOL_Obool),tc_fun(tc_fun(U_3368,tc_HOL_Obool),tc_fun(U_3368,tc_HOL_Obool)),U_3367),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3368,tc_HOL_Obool))),U_3369)),U_3370)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3368,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3367,tc_fun(U_3368,tc_HOL_Obool)),U_3366),U_3369)),U_3370)
        | U_3366 = c_Orderings_Obot__class_Obot(tc_fun(U_3367,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3367,tc_fun(U_3368,tc_HOL_Obool)),U_3366),hAPP(hAPP(c_COMBC(U_3367,tc_fun(U_3368,tc_HOL_Obool),tc_fun(U_3368,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3368,tc_HOL_Obool),tc_fun(tc_fun(U_3368,tc_HOL_Obool),tc_fun(U_3368,tc_HOL_Obool)),U_3367),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3368,tc_HOL_Obool))),U_3369)),U_3370)) = c_Orderings_Otop__class_Otop(tc_fun(U_3368,tc_HOL_Obool))
        | U_3366 != c_Orderings_Obot__class_Obot(tc_fun(U_3367,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ( ! [U_3380,U_3378,U_3376,U_3374,U_3372] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3374,tc_fun(U_3376,tc_HOL_Obool)),U_3372),hAPP(hAPP(c_COMBC(U_3374,tc_fun(U_3376,tc_HOL_Obool),tc_fun(U_3376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3376,tc_HOL_Obool),tc_fun(tc_fun(U_3376,tc_HOL_Obool),tc_fun(U_3376,tc_HOL_Obool)),U_3374),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3376,tc_HOL_Obool))),U_3378)),U_3380)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3376,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3374,tc_fun(U_3376,tc_HOL_Obool)),U_3372),U_3378)),U_3380)
        | U_3372 = c_Orderings_Obot__class_Obot(tc_fun(U_3374,tc_HOL_Obool)) )
    & ! [U_3379,U_3377,U_3375,U_3373,U_3371] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3373,tc_fun(U_3375,tc_HOL_Obool)),U_3371),hAPP(hAPP(c_COMBC(U_3373,tc_fun(U_3375,tc_HOL_Obool),tc_fun(U_3375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3375,tc_HOL_Obool),tc_fun(tc_fun(U_3375,tc_HOL_Obool),tc_fun(U_3375,tc_HOL_Obool)),U_3373),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3375,tc_HOL_Obool))),U_3377)),U_3379)) = c_Orderings_Otop__class_Otop(tc_fun(U_3375,tc_HOL_Obool))
        | U_3371 != c_Orderings_Obot__class_Obot(tc_fun(U_3373,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_654_2]) ).

cnf(f_654_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3373,tc_fun(U_3375,tc_HOL_Obool)),U_3371),hAPP(hAPP(c_COMBC(U_3373,tc_fun(U_3375,tc_HOL_Obool),tc_fun(U_3375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3375,tc_HOL_Obool),tc_fun(tc_fun(U_3375,tc_HOL_Obool),tc_fun(U_3375,tc_HOL_Obool)),U_3373),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3375,tc_HOL_Obool))),U_3377)),U_3379)) = c_Orderings_Otop__class_Otop(tc_fun(U_3375,tc_HOL_Obool))
    | U_3371 != c_Orderings_Obot__class_Obot(tc_fun(U_3373,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

cnf(f_654_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3374,tc_fun(U_3376,tc_HOL_Obool)),U_3372),hAPP(hAPP(c_COMBC(U_3374,tc_fun(U_3376,tc_HOL_Obool),tc_fun(U_3376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3376,tc_HOL_Obool),tc_fun(tc_fun(U_3376,tc_HOL_Obool),tc_fun(U_3376,tc_HOL_Obool)),U_3374),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3376,tc_HOL_Obool))),U_3378)),U_3380)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3376,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3374,tc_fun(U_3376,tc_HOL_Obool)),U_3372),U_3378)),U_3380)
    | U_3372 = c_Orderings_Obot__class_Obot(tc_fun(U_3374,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(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))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).

fof(f_655_2,plain,
    ! [U_3385,U_3384,U_3383,U_3382,U_3381] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3382,tc_fun(U_3383,tc_HOL_Obool)),U_3381),hAPP(hAPP(c_COMBC(U_3382,tc_fun(U_3383,tc_HOL_Obool),tc_fun(U_3383,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3383,tc_HOL_Obool),tc_fun(tc_fun(U_3383,tc_HOL_Obool),tc_fun(U_3383,tc_HOL_Obool)),U_3382),c_Groups_Ominus__class_Ominus(tc_fun(U_3383,tc_HOL_Obool))),U_3384)),U_3385)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3383,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3382,tc_fun(U_3383,tc_HOL_Obool)),U_3381),U_3384)),U_3385)
        | U_3381 = c_Orderings_Obot__class_Obot(tc_fun(U_3382,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3382,tc_fun(U_3383,tc_HOL_Obool)),U_3381),hAPP(hAPP(c_COMBC(U_3382,tc_fun(U_3383,tc_HOL_Obool),tc_fun(U_3383,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3383,tc_HOL_Obool),tc_fun(tc_fun(U_3383,tc_HOL_Obool),tc_fun(U_3383,tc_HOL_Obool)),U_3382),c_Groups_Ominus__class_Ominus(tc_fun(U_3383,tc_HOL_Obool))),U_3384)),U_3385)) = c_Orderings_Otop__class_Otop(tc_fun(U_3383,tc_HOL_Obool))
        | U_3381 != c_Orderings_Obot__class_Obot(tc_fun(U_3382,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ( ! [U_3395,U_3393,U_3391,U_3389,U_3387] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3389,tc_fun(U_3391,tc_HOL_Obool)),U_3387),hAPP(hAPP(c_COMBC(U_3389,tc_fun(U_3391,tc_HOL_Obool),tc_fun(U_3391,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3391,tc_HOL_Obool),tc_fun(tc_fun(U_3391,tc_HOL_Obool),tc_fun(U_3391,tc_HOL_Obool)),U_3389),c_Groups_Ominus__class_Ominus(tc_fun(U_3391,tc_HOL_Obool))),U_3393)),U_3395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3391,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3389,tc_fun(U_3391,tc_HOL_Obool)),U_3387),U_3393)),U_3395)
        | U_3387 = c_Orderings_Obot__class_Obot(tc_fun(U_3389,tc_HOL_Obool)) )
    & ! [U_3394,U_3392,U_3390,U_3388,U_3386] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3388,tc_fun(U_3390,tc_HOL_Obool)),U_3386),hAPP(hAPP(c_COMBC(U_3388,tc_fun(U_3390,tc_HOL_Obool),tc_fun(U_3390,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3390,tc_HOL_Obool),tc_fun(tc_fun(U_3390,tc_HOL_Obool),tc_fun(U_3390,tc_HOL_Obool)),U_3388),c_Groups_Ominus__class_Ominus(tc_fun(U_3390,tc_HOL_Obool))),U_3392)),U_3394)) = c_Orderings_Otop__class_Otop(tc_fun(U_3390,tc_HOL_Obool))
        | U_3386 != c_Orderings_Obot__class_Obot(tc_fun(U_3388,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_655_2]) ).

cnf(f_655_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3388,tc_fun(U_3390,tc_HOL_Obool)),U_3386),hAPP(hAPP(c_COMBC(U_3388,tc_fun(U_3390,tc_HOL_Obool),tc_fun(U_3390,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3390,tc_HOL_Obool),tc_fun(tc_fun(U_3390,tc_HOL_Obool),tc_fun(U_3390,tc_HOL_Obool)),U_3388),c_Groups_Ominus__class_Ominus(tc_fun(U_3390,tc_HOL_Obool))),U_3392)),U_3394)) = c_Orderings_Otop__class_Otop(tc_fun(U_3390,tc_HOL_Obool))
    | U_3386 != c_Orderings_Obot__class_Obot(tc_fun(U_3388,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

cnf(f_655_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3389,tc_fun(U_3391,tc_HOL_Obool)),U_3387),hAPP(hAPP(c_COMBC(U_3389,tc_fun(U_3391,tc_HOL_Obool),tc_fun(U_3391,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3391,tc_HOL_Obool),tc_fun(tc_fun(U_3391,tc_HOL_Obool),tc_fun(U_3391,tc_HOL_Obool)),U_3389),c_Groups_Ominus__class_Ominus(tc_fun(U_3391,tc_HOL_Obool))),U_3393)),U_3395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3391,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3389,tc_fun(U_3391,tc_HOL_Obool)),U_3387),U_3393)),U_3395)
    | U_3387 = c_Orderings_Obot__class_Obot(tc_fun(U_3389,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_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_B_2)
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).

fof(f_656_2,plain,
    ! [U_3400,U_3399,U_3398,U_3397,U_3396] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3398,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3397,tc_fun(U_3398,tc_HOL_Obool)),U_3396),U_3399)),U_3400) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3397,tc_fun(U_3398,tc_HOL_Obool)),U_3396),hAPP(hAPP(c_COMBC(U_3397,tc_fun(U_3398,tc_HOL_Obool),tc_fun(U_3398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3398,tc_HOL_Obool),tc_fun(tc_fun(U_3398,tc_HOL_Obool),tc_fun(U_3398,tc_HOL_Obool)),U_3397),c_Groups_Ominus__class_Ominus(tc_fun(U_3398,tc_HOL_Obool))),U_3399)),U_3400))
        | U_3396 = c_Orderings_Obot__class_Obot(tc_fun(U_3397,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3398,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3397,tc_fun(U_3398,tc_HOL_Obool)),U_3396),U_3399)),U_3400) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3398,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3398,tc_HOL_Obool))),U_3400)
        | U_3396 != c_Orderings_Obot__class_Obot(tc_fun(U_3397,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ( ! [U_3410,U_3408,U_3406,U_3404,U_3402] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3406,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3404,tc_fun(U_3406,tc_HOL_Obool)),U_3402),U_3408)),U_3410) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3404,tc_fun(U_3406,tc_HOL_Obool)),U_3402),hAPP(hAPP(c_COMBC(U_3404,tc_fun(U_3406,tc_HOL_Obool),tc_fun(U_3406,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3406,tc_HOL_Obool),tc_fun(tc_fun(U_3406,tc_HOL_Obool),tc_fun(U_3406,tc_HOL_Obool)),U_3404),c_Groups_Ominus__class_Ominus(tc_fun(U_3406,tc_HOL_Obool))),U_3408)),U_3410))
        | U_3402 = c_Orderings_Obot__class_Obot(tc_fun(U_3404,tc_HOL_Obool)) )
    & ! [U_3409,U_3407,U_3405,U_3403,U_3401] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3405,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3403,tc_fun(U_3405,tc_HOL_Obool)),U_3401),U_3407)),U_3409) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3405,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3405,tc_HOL_Obool))),U_3409)
        | U_3401 != c_Orderings_Obot__class_Obot(tc_fun(U_3403,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_656_2]) ).

cnf(f_656_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3405,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3403,tc_fun(U_3405,tc_HOL_Obool)),U_3401),U_3407)),U_3409) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3405,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3405,tc_HOL_Obool))),U_3409)
    | U_3401 != c_Orderings_Obot__class_Obot(tc_fun(U_3403,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3406,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3404,tc_fun(U_3406,tc_HOL_Obool)),U_3402),U_3408)),U_3410) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3404,tc_fun(U_3406,tc_HOL_Obool)),U_3402),hAPP(hAPP(c_COMBC(U_3404,tc_fun(U_3406,tc_HOL_Obool),tc_fun(U_3406,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3406,tc_HOL_Obool),tc_fun(tc_fun(U_3406,tc_HOL_Obool),tc_fun(U_3406,tc_HOL_Obool)),U_3404),c_Groups_Ominus__class_Ominus(tc_fun(U_3406,tc_HOL_Obool))),U_3408)),U_3410))
    | U_3402 = c_Orderings_Obot__class_Obot(tc_fun(U_3404,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).

fof(f_657_2,plain,
    ! [U_3413,U_3412,U_3411] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3411,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3411,tc_HOL_Obool)),U_3412),U_3413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3411,tc_HOL_Obool)),U_3412),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3411,tc_HOL_Obool),U_3413)),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3411,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3411,tc_HOL_Obool)),U_3412),U_3413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3411,tc_HOL_Obool)),U_3412),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3411,tc_HOL_Obool),U_3413)),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_1,plain,
    ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(f_658_2,plain,
    ! [U_3416,U_3415,U_3414] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_3414,tc_HOL_Obool),tc_HOL_Obool)),U_3415),U_3416)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),U_3415)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),U_3416)),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

cnf(f_658_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_3414,tc_HOL_Obool),tc_HOL_Obool)),U_3415),U_3416)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),U_3415)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3414,tc_HOL_Obool),U_3416)),
    inference(clausify,[status(thm)],[f_658_2]) ).

fof(f_659_1,plain,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).

fof(f_659_2,plain,
    ! [U_3422,U_3421,U_3420,U_3419,U_3418,U_3417] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_3417,U_3418,U_3419),U_3420),U_3421) = U_3422
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3417,U_3418,U_3419,U_3420,U_3421),U_3422))
      | ~ c_Finite__Set_Ofun__left__comm(U_3417,U_3418,U_3419) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

cnf(f_659_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_3417,U_3418,U_3419),U_3420),U_3421) = U_3422
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3417,U_3418,U_3419,U_3420,U_3421),U_3422))
    | ~ c_Finite__Set_Ofun__left__comm(U_3417,U_3418,U_3419) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

fof(f_660_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).

fof(f_660_2,plain,
    ! [U_3427,U_3426,U_3425,U_3424,U_3423] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3423,tc_fun(U_3424,tc_HOL_Obool)),U_3425),hAPP(hAPP(c_COMBS(U_3423,tc_fun(U_3424,tc_HOL_Obool),tc_fun(U_3424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3424,tc_HOL_Obool),tc_fun(tc_fun(U_3424,tc_HOL_Obool),tc_fun(U_3424,tc_HOL_Obool)),U_3423),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3424,tc_HOL_Obool))),U_3426)),U_3427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3424,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3424,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3423,tc_fun(U_3424,tc_HOL_Obool),U_3426),U_3425))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3424,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3423,tc_fun(U_3424,tc_HOL_Obool),U_3427),U_3425))),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3423,tc_fun(U_3424,tc_HOL_Obool)),U_3425),hAPP(hAPP(c_COMBS(U_3423,tc_fun(U_3424,tc_HOL_Obool),tc_fun(U_3424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_3424,tc_HOL_Obool),tc_fun(tc_fun(U_3424,tc_HOL_Obool),tc_fun(U_3424,tc_HOL_Obool)),U_3423),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3424,tc_HOL_Obool))),U_3426)),U_3427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3424,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3424,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3423,tc_fun(U_3424,tc_HOL_Obool),U_3426),U_3425))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3424,tc_HOL_Obool),hAPP(c_Set_Oimage(U_3423,tc_fun(U_3424,tc_HOL_Obool),U_3427),U_3425))),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_1,plain,
    ! [V_a_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).

fof(f_661_2,plain,
    ! [U_3429,U_3428] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3428,hAPP(hAPP(c_Set_Oinsert(U_3428),U_3429),c_Orderings_Obot__class_Obot(tc_fun(U_3428,tc_HOL_Obool)))) = U_3429
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3428) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

cnf(f_661_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3428,hAPP(hAPP(c_Set_Oinsert(U_3428),U_3429),c_Orderings_Obot__class_Obot(tc_fun(U_3428,tc_HOL_Obool)))) = U_3429
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3428) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

fof(f_662_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).

fof(f_662_2,plain,
    ! [U_3432,U_3431,U_3430] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3430,hAPP(hAPP(c_Set_Oinsert(U_3430),U_3431),U_3432)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3430),U_3431),c_Complete__Lattice_OInf__class_OInf(U_3430,U_3432))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3430) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3430,hAPP(hAPP(c_Set_Oinsert(U_3430),U_3431),U_3432)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3430),U_3431),c_Complete__Lattice_OInf__class_OInf(U_3430,U_3432))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3430) ),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_1,plain,
    ! [V_F_2,V_h_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
      | hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageD]) ).

fof(f_663_2,plain,
    ! [U_3436,U_3435,U_3434,U_3433] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3434),U_3436))
      | hAPP(c_Set_Oimage(U_3433,U_3434,U_3435),c_Orderings_Otop__class_Otop(tc_fun(U_3433,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3433),hAPP(c_Set_Ovimage(U_3433,U_3434,U_3435),U_3436))) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3434),U_3436))
    | hAPP(c_Set_Oimage(U_3433,U_3434,U_3435),c_Orderings_Otop__class_Otop(tc_fun(U_3433,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3434,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3433),hAPP(c_Set_Ovimage(U_3433,U_3434,U_3435),U_3436))) ),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_1,plain,
    ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__def]) ).

fof(f_664_2,plain,
    ! [U_3441,U_3440,U_3439,U_3438,U_3437] : hAPP(hAPP(c_Finite__Set_Ofold(U_3437,U_3438,U_3439),U_3440),U_3441) = c_HOL_OThe(U_3438,c_Finite__Set_Ofold__graph(U_3437,U_3438,U_3439,U_3440,U_3441)),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

cnf(f_664_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_3437,U_3438,U_3439),U_3440),U_3441) = c_HOL_OThe(U_3438,c_Finite__Set_Ofold__graph(U_3437,U_3438,U_3439,U_3440,U_3441)),
    inference(clausify,[status(thm)],[f_664_2]) ).

fof(f_665_1,plain,
    ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__eq]) ).

fof(f_665_2,plain,
    ! [U_3445,U_3444,U_3443,U_3442] : hAPP(c_Set_Oimage(U_3442,U_3443,U_3444),hAPP(c_Set_Ovimage(U_3442,U_3443,U_3444),U_3445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3443,tc_HOL_Obool)),U_3445),hAPP(c_Set_Oimage(U_3442,U_3443,U_3444),c_Orderings_Otop__class_Otop(tc_fun(U_3442,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

cnf(f_665_3,plain,
    hAPP(c_Set_Oimage(U_3442,U_3443,U_3444),hAPP(c_Set_Ovimage(U_3442,U_3443,U_3444),U_3445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3443,tc_HOL_Obool)),U_3445),hAPP(c_Set_Oimage(U_3442,U_3443,U_3444),c_Orderings_Otop__class_Otop(tc_fun(U_3442,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_665_2]) ).

fof(f_666_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) != V_c_2 ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).

fof(f_666_2,plain,
    ! [U_3452,U_3451,U_3450,U_3449,U_3448,U_3447,U_3446] :
      ( hAPP(U_3449,hAPP(U_3450,U_3452)) = hAPP(U_3451,U_3452)
      | hAPP(c_Fun_Ocomp(U_3446,U_3447,U_3448,U_3449),U_3450) != U_3451 ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_3452,U_3451,U_3450,U_3449] :
      ( ! [U_3448,U_3447,U_3446] : hAPP(c_Fun_Ocomp(U_3446,U_3447,U_3448,U_3449),U_3450) != U_3451
      | hAPP(U_3449,hAPP(U_3450,U_3452)) = hAPP(U_3451,U_3452) ),
    inference(miniscope,[status(thm)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( hAPP(c_Fun_Ocomp(U_3446,U_3447,U_3448,U_3449),U_3450) != U_3451
    | hAPP(U_3449,hAPP(U_3450,U_3452)) = hAPP(U_3451,U_3452) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(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))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).

fof(f_667_2,plain,
    ! [U_3457,U_3456,U_3455,U_3454,U_3453] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3454,tc_fun(U_3455,tc_HOL_Obool)),U_3453),hAPP(hAPP(c_COMBB(tc_fun(U_3455,tc_HOL_Obool),tc_fun(U_3455,tc_HOL_Obool),U_3454),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3455,tc_HOL_Obool)),U_3456)),U_3457)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3455,tc_HOL_Obool)),U_3456),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3454,tc_fun(U_3455,tc_HOL_Obool)),U_3453),U_3457))
        | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3454,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3454,tc_fun(U_3455,tc_HOL_Obool)),U_3453),hAPP(hAPP(c_COMBB(tc_fun(U_3455,tc_HOL_Obool),tc_fun(U_3455,tc_HOL_Obool),U_3454),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3455,tc_HOL_Obool)),U_3456)),U_3457)) = c_Orderings_Otop__class_Otop(tc_fun(U_3455,tc_HOL_Obool))
        | U_3453 != c_Orderings_Obot__class_Obot(tc_fun(U_3454,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ( ! [U_3467,U_3465,U_3463,U_3461,U_3459] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3461,tc_fun(U_3463,tc_HOL_Obool)),U_3459),hAPP(hAPP(c_COMBB(tc_fun(U_3463,tc_HOL_Obool),tc_fun(U_3463,tc_HOL_Obool),U_3461),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3463,tc_HOL_Obool)),U_3465)),U_3467)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3463,tc_HOL_Obool)),U_3465),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3461,tc_fun(U_3463,tc_HOL_Obool)),U_3459),U_3467))
        | U_3459 = c_Orderings_Obot__class_Obot(tc_fun(U_3461,tc_HOL_Obool)) )
    & ! [U_3466,U_3464,U_3462,U_3460,U_3458] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3460,tc_fun(U_3462,tc_HOL_Obool)),U_3458),hAPP(hAPP(c_COMBB(tc_fun(U_3462,tc_HOL_Obool),tc_fun(U_3462,tc_HOL_Obool),U_3460),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3462,tc_HOL_Obool)),U_3464)),U_3466)) = c_Orderings_Otop__class_Otop(tc_fun(U_3462,tc_HOL_Obool))
        | U_3458 != c_Orderings_Obot__class_Obot(tc_fun(U_3460,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_667_2]) ).

cnf(f_667_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3460,tc_fun(U_3462,tc_HOL_Obool)),U_3458),hAPP(hAPP(c_COMBB(tc_fun(U_3462,tc_HOL_Obool),tc_fun(U_3462,tc_HOL_Obool),U_3460),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3462,tc_HOL_Obool)),U_3464)),U_3466)) = c_Orderings_Otop__class_Otop(tc_fun(U_3462,tc_HOL_Obool))
    | U_3458 != c_Orderings_Obot__class_Obot(tc_fun(U_3460,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

cnf(f_667_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_3461,tc_fun(U_3463,tc_HOL_Obool)),U_3459),hAPP(hAPP(c_COMBB(tc_fun(U_3463,tc_HOL_Obool),tc_fun(U_3463,tc_HOL_Obool),U_3461),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3463,tc_HOL_Obool)),U_3465)),U_3467)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3463,tc_HOL_Obool)),U_3465),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3461,tc_fun(U_3463,tc_HOL_Obool)),U_3459),U_3467))
    | U_3459 = c_Orderings_Obot__class_Obot(tc_fun(U_3461,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [T_b,V_A_2,V_c_2,T_a] :
      ( ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      & ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).

fof(f_668_2,plain,
    ! [U_3471,U_3470,U_3469,U_3468] :
      ( ( hAPP(c_Set_Ovimage(U_3471,U_3468,hAPP(c_COMBK(U_3468,U_3471),U_3469)),U_3470) = c_Orderings_Obot__class_Obot(tc_fun(U_3471,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_3468),U_3469),U_3470)) )
      & ( hAPP(c_Set_Ovimage(U_3471,U_3468,hAPP(c_COMBK(U_3468,U_3471),U_3469)),U_3470) = c_Orderings_Otop__class_Otop(tc_fun(U_3471,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3468),U_3469),U_3470)) ) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ( ! [U_3479,U_3477,U_3475,U_3473] :
        ( hAPP(c_Set_Ovimage(U_3479,U_3473,hAPP(c_COMBK(U_3473,U_3479),U_3475)),U_3477) = c_Orderings_Obot__class_Obot(tc_fun(U_3479,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_3473),U_3475),U_3477)) )
    & ! [U_3478,U_3476,U_3474,U_3472] :
        ( hAPP(c_Set_Ovimage(U_3478,U_3472,hAPP(c_COMBK(U_3472,U_3478),U_3474)),U_3476) = c_Orderings_Otop__class_Otop(tc_fun(U_3478,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3472),U_3474),U_3476)) ) ),
    inference(miniscope,[status(thm)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( hAPP(c_Set_Ovimage(U_3478,U_3472,hAPP(c_COMBK(U_3472,U_3478),U_3474)),U_3476) = c_Orderings_Otop__class_Otop(tc_fun(U_3478,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3472),U_3474),U_3476)) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

cnf(f_668_5,plain,
    ( hAPP(c_Set_Ovimage(U_3479,U_3473,hAPP(c_COMBK(U_3473,U_3479),U_3475)),U_3477) = c_Orderings_Obot__class_Obot(tc_fun(U_3479,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_3473),U_3475),U_3477)) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).

fof(f_669_2,plain,
    ! [U_3484,U_3483,U_3482,U_3481,U_3480] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),hAPP(hAPP(c_COMBC(U_3481,U_3480,U_3480),hAPP(hAPP(c_COMBS(U_3481,U_3480,tc_fun(U_3480,U_3480)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3480,tc_fun(U_3480,U_3480)),U_3481),c_If(U_3480)),hAPP(hAPP(c_COMBC(U_3481,U_3481,tc_HOL_Obool),c_fequal),U_3483))),U_3484)),c_Groups_Ozero__class_Ozero(U_3480))),U_3482) = c_Groups_Ozero__class_Ozero(U_3480)
          | hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),hAPP(hAPP(c_COMBC(U_3481,U_3480,U_3480),hAPP(hAPP(c_COMBS(U_3481,U_3480,tc_fun(U_3480,U_3480)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3480,tc_fun(U_3480,U_3480)),U_3481),c_If(U_3480)),hAPP(hAPP(c_COMBC(U_3481,U_3481,tc_HOL_Obool),c_fequal),U_3483))),U_3484)),c_Groups_Ozero__class_Ozero(U_3480))),U_3482) = hAPP(U_3484,U_3483)
          | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
      | ~ class_Groups_Ocomm__monoid__add(U_3480) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),hAPP(hAPP(c_COMBC(U_3481,U_3480,U_3480),hAPP(hAPP(c_COMBS(U_3481,U_3480,tc_fun(U_3480,U_3480)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3480,tc_fun(U_3480,U_3480)),U_3481),c_If(U_3480)),hAPP(hAPP(c_COMBC(U_3481,U_3481,tc_HOL_Obool),c_fequal),U_3483))),U_3484)),c_Groups_Ozero__class_Ozero(U_3480))),U_3482) = hAPP(U_3484,U_3483)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Groups_Ocomm__monoid__add(U_3480) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

cnf(f_669_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),hAPP(hAPP(c_COMBC(U_3481,U_3480,U_3480),hAPP(hAPP(c_COMBS(U_3481,U_3480,tc_fun(U_3480,U_3480)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3480,tc_fun(U_3480,U_3480)),U_3481),c_If(U_3480)),hAPP(hAPP(c_COMBC(U_3481,U_3481,tc_HOL_Obool),c_fequal),U_3483))),U_3484)),c_Groups_Ozero__class_Ozero(U_3480))),U_3482) = c_Groups_Ozero__class_Ozero(U_3480)
    | hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Groups_Ocomm__monoid__add(U_3480) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).

fof(f_670_2,plain,
    ! [U_3489,U_3488,U_3487,U_3486,U_3485] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3486,U_3485),hAPP(hAPP(c_COMBC(U_3486,U_3485,U_3485),hAPP(hAPP(c_COMBS(U_3486,U_3485,tc_fun(U_3485,U_3485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3485,tc_fun(U_3485,U_3485)),U_3486),c_If(U_3485)),hAPP(c_fequal,U_3488))),U_3489)),c_Groups_Ozero__class_Ozero(U_3485))),U_3487) = c_Groups_Ozero__class_Ozero(U_3485)
          | hBOOL(hAPP(hAPP(c_member(U_3486),U_3488),U_3487)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3486,U_3485),hAPP(hAPP(c_COMBC(U_3486,U_3485,U_3485),hAPP(hAPP(c_COMBS(U_3486,U_3485,tc_fun(U_3485,U_3485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3485,tc_fun(U_3485,U_3485)),U_3486),c_If(U_3485)),hAPP(c_fequal,U_3488))),U_3489)),c_Groups_Ozero__class_Ozero(U_3485))),U_3487) = hAPP(U_3489,U_3488)
          | ~ hBOOL(hAPP(hAPP(c_member(U_3486),U_3488),U_3487)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3486),U_3487))
      | ~ class_Groups_Ocomm__monoid__add(U_3485) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

cnf(f_670_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3486,U_3485),hAPP(hAPP(c_COMBC(U_3486,U_3485,U_3485),hAPP(hAPP(c_COMBS(U_3486,U_3485,tc_fun(U_3485,U_3485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3485,tc_fun(U_3485,U_3485)),U_3486),c_If(U_3485)),hAPP(c_fequal,U_3488))),U_3489)),c_Groups_Ozero__class_Ozero(U_3485))),U_3487) = hAPP(U_3489,U_3488)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3486),U_3488),U_3487))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3486),U_3487))
    | ~ class_Groups_Ocomm__monoid__add(U_3485) ),
    inference(clausify,[status(thm)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3486,U_3485),hAPP(hAPP(c_COMBC(U_3486,U_3485,U_3485),hAPP(hAPP(c_COMBS(U_3486,U_3485,tc_fun(U_3485,U_3485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3485,tc_fun(U_3485,U_3485)),U_3486),c_If(U_3485)),hAPP(c_fequal,U_3488))),U_3489)),c_Groups_Ozero__class_Ozero(U_3485))),U_3487) = c_Groups_Ozero__class_Ozero(U_3485)
    | hBOOL(hAPP(hAPP(c_member(U_3486),U_3488),U_3487))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3486),U_3487))
    | ~ class_Groups_Ocomm__monoid__add(U_3485) ),
    inference(clausify,[status(thm)],[f_670_2]) ).

fof(f_671_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).

fof(f_671_2,plain,
    ! [U_3492,U_3491,U_3490] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3490,tc_HOL_Obool)),U_3491),U_3492))),hAPP(c_Finite__Set_Ocard(U_3490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3490,tc_HOL_Obool)),U_3491),U_3492))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3490),U_3491)),hAPP(c_Finite__Set_Ocard(U_3490),U_3492))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3490),U_3492))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3490),U_3491)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

cnf(f_671_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3490,tc_HOL_Obool)),U_3491),U_3492))),hAPP(c_Finite__Set_Ocard(U_3490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3490,tc_HOL_Obool)),U_3491),U_3492))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3490),U_3491)),hAPP(c_Finite__Set_Ocard(U_3490),U_3492))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3490),U_3492))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3490),U_3491)) ),
    inference(clausify,[status(thm)],[f_671_2]) ).

fof(f_672_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).

fof(f_672_2,plain,
    ! [U_3495,U_3494,U_3493] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3493),U_3494)),hAPP(c_Finite__Set_Ocard(U_3493),U_3495)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3493,tc_HOL_Obool)),U_3494),U_3495))),hAPP(c_Finite__Set_Ocard(U_3493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3493,tc_HOL_Obool)),U_3494),U_3495)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3495))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3494)) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3493),U_3494)),hAPP(c_Finite__Set_Ocard(U_3493),U_3495)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3493,tc_HOL_Obool)),U_3494),U_3495))),hAPP(c_Finite__Set_Ocard(U_3493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3493,tc_HOL_Obool)),U_3494),U_3495)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3495))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3493),U_3494)) ),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).

fof(f_673_2,plain,
    ! [U_3498,U_3497,U_3496] :
      ( hAPP(c_Finite__Set_Ocard(U_3496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3496),U_3497)),hAPP(c_Finite__Set_Ocard(U_3496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498))) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3496),U_3497)),hAPP(c_Finite__Set_Ocard(U_3496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3496,tc_HOL_Obool)),U_3497),U_3498))) ),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).

fof(f_674_2,plain,
    ! [U_3501,U_3500,U_3499] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3499,tc_HOL_Obool)),U_3500),U_3501) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3499,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3499,tc_HOL_Obool)),U_3500),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3499,tc_HOL_Obool)),U_3501),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3499,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3499,tc_HOL_Obool)),U_3500),U_3501) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3499,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3499,tc_HOL_Obool)),U_3500),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3499,tc_HOL_Obool)),U_3501),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3499,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_1,plain,
    ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).

fof(f_675_2,plain,
    ! [U_3506,U_3505,U_3504,U_3503,U_3502] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3502,U_3503,U_3504,U_3506,U_3505),hAPP(hAPP(c_Finite__Set_Ofold(U_3502,U_3503,U_3504),U_3506),U_3505)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3502),U_3505))
      | ~ c_Finite__Set_Ofun__left__comm(U_3502,U_3503,U_3504) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3502,U_3503,U_3504,U_3506,U_3505),hAPP(hAPP(c_Finite__Set_Ofold(U_3502,U_3503,U_3504),U_3506),U_3505)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3502),U_3505))
    | ~ c_Finite__Set_Ofun__left__comm(U_3502,U_3503,U_3504) ),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).

fof(f_676_2,plain,
    ! [U_3509,U_3508,U_3507] :
      ( c_Complete__Lattice_OInf__class_OInf(U_3507,hAPP(hAPP(c_Set_Oinsert(U_3507),U_3508),hAPP(hAPP(c_Set_Oinsert(U_3507),U_3509),c_Orderings_Obot__class_Obot(tc_fun(U_3507,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3507),U_3508),U_3509)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3507) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

cnf(f_676_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_3507,hAPP(hAPP(c_Set_Oinsert(U_3507),U_3508),hAPP(hAPP(c_Set_Oinsert(U_3507),U_3509),c_Orderings_Obot__class_Obot(tc_fun(U_3507,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3507),U_3508),U_3509)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3507) ),
    inference(clausify,[status(thm)],[f_676_2]) ).

fof(f_677_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).

fof(f_677_2,plain,
    ! [U_3513,U_3512,U_3511,U_3510] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3513),U_3512) = c_Groups_Ozero__class_Ozero(U_3510)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3513),U_3512) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3510,U_3511,c_Groups_Oplus__class_Oplus(U_3510)),U_3513),c_Groups_Ozero__class_Ozero(U_3510)),U_3512)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_3510) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

cnf(f_677_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3513),U_3512) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3510,U_3511,c_Groups_Oplus__class_Oplus(U_3510)),U_3513),c_Groups_Ozero__class_Ozero(U_3510)),U_3512)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512))
    | ~ class_Groups_Ocomm__monoid__add(U_3510) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

cnf(f_677_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3511,U_3510),U_3513),U_3512) = c_Groups_Ozero__class_Ozero(U_3510)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3511),U_3512))
    | ~ class_Groups_Ocomm__monoid__add(U_3510) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

fof(f_678_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).

fof(f_678_2,plain,
    ! [U_3517,U_3516,U_3515,U_3514] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3515,U_3514),U_3517),U_3516) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3514,U_3515,c_Groups_Oplus__class_Oplus(U_3514)),U_3517),c_Groups_Ozero__class_Ozero(U_3514)),U_3516)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3515),U_3516))
      | ~ class_Groups_Ocomm__monoid__add(U_3514) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

cnf(f_678_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3515,U_3514),U_3517),U_3516) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3514,U_3515,c_Groups_Oplus__class_Oplus(U_3514)),U_3517),c_Groups_Ozero__class_Ozero(U_3514)),U_3516)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3515),U_3516))
    | ~ class_Groups_Ocomm__monoid__add(U_3514) ),
    inference(clausify,[status(thm)],[f_678_2]) ).

fof(f_679_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).

fof(f_679_2,plain,
    ! [U_3520,U_3519,U_3518] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3518),U_3520),c_Complete__Lattice_OInf__class_OInf(U_3518,U_3519)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3518,U_3518,c_Lattices_Osemilattice__inf__class_Oinf(U_3518)),U_3520),U_3519)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3518),U_3519))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3518) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

cnf(f_679_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3518),U_3520),c_Complete__Lattice_OInf__class_OInf(U_3518,U_3519)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3518,U_3518,c_Lattices_Osemilattice__inf__class_Oinf(U_3518)),U_3520),U_3519)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3518),U_3519))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3518) ),
    inference(clausify,[status(thm)],[f_679_2]) ).

fof(f_680_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_680_2,plain,
    ! [U_3525,U_3524,U_3523,U_3522,U_3521] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_3521,U_3522,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3521),U_3523),U_3524),U_3525)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

cnf(f_680_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(U_3521,U_3522,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3521),U_3523),U_3524),U_3525)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_680_2]) ).

fof(f_681_1,plain,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(f_681_2,plain,
    ! [U_3530,U_3529,U_3528,U_3527,U_3526] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3526,U_3527,hAPP(hAPP(c_Set_Oinsert(U_3526),U_3528),U_3529)),U_3530))
      | hBOOL(hAPP(hAPP(c_member(U_3526),U_3528),U_3529))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3526,U_3526,U_3527,U_3528,U_3529),U_3530)) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

cnf(f_681_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3526,U_3527,hAPP(hAPP(c_Set_Oinsert(U_3526),U_3528),U_3529)),U_3530))
    | hBOOL(hAPP(hAPP(c_member(U_3526),U_3528),U_3529))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3526,U_3526,U_3527,U_3528,U_3529),U_3530)) ),
    inference(clausify,[status(thm)],[f_681_2]) ).

fof(f_682_1,plain,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
      ( ? [B_y_H] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).

fof(f_682_2,plain,
    ! [U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532] :
      ( ? [U_3531] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3532,tc_HOL_Obool)),U_3536),hAPP(hAPP(c_Set_Oinsert(U_3532),U_3538),c_Orderings_Obot__class_Obot(tc_fun(U_3532,tc_HOL_Obool))))),U_3531))
          & U_3537 = hAPP(hAPP(U_3534,U_3538),U_3531) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_3532),U_3538),U_3536))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,U_3536),U_3537))
      | ~ c_Finite__Set_Ofun__left__comm(U_3532,U_3533,U_3534) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3532,tc_HOL_Obool)),U_3536),hAPP(hAPP(c_Set_Oinsert(U_3532),U_3538),c_Orderings_Obot__class_Obot(tc_fun(U_3532,tc_HOL_Obool))))),sK65(U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532)))
        & U_3537 = hAPP(hAPP(U_3534,U_3538),sK65(U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_3532),U_3538),U_3536))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,U_3536),U_3537))
      | ~ c_Finite__Set_Ofun__left__comm(U_3532,U_3533,U_3534) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3531,sK65(U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532))],[f_682_2]) ).

cnf(f_682_4,plain,
    ( U_3537 = hAPP(hAPP(U_3534,U_3538),sK65(U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3532),U_3538),U_3536))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,U_3536),U_3537))
    | ~ c_Finite__Set_Ofun__left__comm(U_3532,U_3533,U_3534) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

cnf(f_682_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3532,tc_HOL_Obool)),U_3536),hAPP(hAPP(c_Set_Oinsert(U_3532),U_3538),c_Orderings_Obot__class_Obot(tc_fun(U_3532,tc_HOL_Obool))))),sK65(U_3538,U_3537,U_3536,U_3535,U_3534,U_3533,U_3532)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3532),U_3538),U_3536))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3532,U_3533,U_3534,U_3535,U_3536),U_3537))
    | ~ c_Finite__Set_Ofun__left__comm(U_3532,U_3533,U_3534) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).

fof(f_683_2,plain,
    ! [U_3544,U_3543,U_3542,U_3541,U_3540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3543))
      | ? [U_3539] :
          ( hAPP(U_3544,U_3539) != c_Groups_Ozero__class_Ozero(U_3540)
          & hBOOL(hAPP(hAPP(c_member(U_3541),U_3539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3543))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
      | ~ class_Groups_Ocomm__monoid__add(U_3540) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ! [U_3544,U_3543,U_3542,U_3541,U_3540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3543))
      | ( hAPP(U_3544,sK66(U_3544,U_3543,U_3542,U_3541,U_3540)) != c_Groups_Ozero__class_Ozero(U_3540)
        & hBOOL(hAPP(hAPP(c_member(U_3541),sK66(U_3544,U_3543,U_3542,U_3541,U_3540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3543))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
      | ~ class_Groups_Ocomm__monoid__add(U_3540) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3539,sK66(U_3544,U_3543,U_3542,U_3541,U_3540))],[f_683_2]) ).

cnf(f_683_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3541),sK66(U_3544,U_3543,U_3542,U_3541,U_3540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3543))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3543))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
    | ~ class_Groups_Ocomm__monoid__add(U_3540) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( hAPP(U_3544,sK66(U_3544,U_3543,U_3542,U_3541,U_3540)) != c_Groups_Ozero__class_Ozero(U_3540)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3541,tc_HOL_Obool)),U_3542),U_3543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3544),U_3543))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3543))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
    | ~ class_Groups_Ocomm__monoid__add(U_3540) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).

fof(f_684_2,plain,
    ! [U_3550,U_3549,U_3548,U_3547,U_3546] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3548)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3549))
      | ? [U_3545] :
          ( hAPP(U_3550,U_3545) != c_Groups_Ozero__class_Ozero(U_3546)
          & hBOOL(hAPP(hAPP(c_member(U_3547),U_3545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3549))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3548))
      | ~ class_Groups_Ocomm__monoid__add(U_3546) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ! [U_3550,U_3549,U_3548,U_3547,U_3546] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3548)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3549))
      | ( hAPP(U_3550,sK67(U_3550,U_3549,U_3548,U_3547,U_3546)) != c_Groups_Ozero__class_Ozero(U_3546)
        & hBOOL(hAPP(hAPP(c_member(U_3547),sK67(U_3550,U_3549,U_3548,U_3547,U_3546)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3549))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3548))
      | ~ class_Groups_Ocomm__monoid__add(U_3546) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3545,sK67(U_3550,U_3549,U_3548,U_3547,U_3546))],[f_684_2]) ).

cnf(f_684_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3547),sK67(U_3550,U_3549,U_3548,U_3547,U_3546)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3548)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3549))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3549))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3548))
    | ~ class_Groups_Ocomm__monoid__add(U_3546) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( hAPP(U_3550,sK67(U_3550,U_3549,U_3548,U_3547,U_3546)) != c_Groups_Ozero__class_Ozero(U_3546)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3547,tc_HOL_Obool)),U_3548),U_3549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3548)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3547,U_3546),U_3550),U_3549))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3549))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3547),U_3548))
    | ~ class_Groups_Ocomm__monoid__add(U_3546) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,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_c)
              & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
              & B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero]) ).

fof(f_685_2,plain,
    ! [U_3558,U_3557,U_3556,U_3555,U_3554,U_3553] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
      | ? [U_3552] :
          ( ? [U_3551] :
              ( hAPP(U_3557,hAPP(U_3556,U_3552)) != c_Groups_Ozero__class_Ozero(U_3553)
              & hAPP(U_3556,U_3552) = hAPP(U_3556,U_3551)
              & U_3552 != U_3551
              & hBOOL(hAPP(hAPP(c_member(U_3554),U_3551),U_3555)) )
          & hBOOL(hAPP(hAPP(c_member(U_3554),U_3552),U_3555)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
      | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ! [U_3558,U_3557,U_3556,U_3555,U_3554,U_3553] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
      | ( ? [U_3551] :
            ( hAPP(U_3557,hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))) != c_Groups_Ozero__class_Ozero(U_3553)
            & hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)) = hAPP(U_3556,U_3551)
            & sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553) != U_3551
            & hBOOL(hAPP(hAPP(c_member(U_3554),U_3551),U_3555)) )
        & hBOOL(hAPP(hAPP(c_member(U_3554),sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)),U_3555)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
      | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3552,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))],[f_685_2]) ).

fof(f_685_4,plain,
    ! [U_3558,U_3557,U_3556,U_3555,U_3554,U_3553] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
      | ( hAPP(U_3557,hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))) != c_Groups_Ozero__class_Ozero(U_3553)
        & hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)) = hAPP(U_3556,sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))
        & sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553) != sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)
        & hBOOL(hAPP(hAPP(c_member(U_3554),sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)),U_3555))
        & hBOOL(hAPP(hAPP(c_member(U_3554),sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)),U_3555)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
      | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3551,sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))],[f_685_3]) ).

cnf(f_685_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3554),sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)),U_3555))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
    | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3554),sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)),U_3555))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
    | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_7,plain,
    ( sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553) != sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
    | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_8,plain,
    ( hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553)) = hAPP(U_3556,sK69(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
    | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_9,plain,
    ( hAPP(U_3557,hAPP(U_3556,sK68(U_3558,U_3557,U_3556,U_3555,U_3554,U_3553))) != c_Groups_Ozero__class_Ozero(U_3553)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3553),U_3557),hAPP(c_Set_Oimage(U_3554,U_3558,U_3556),U_3555)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3554,U_3553),hAPP(c_Fun_Ocomp(U_3558,U_3553,U_3554,U_3557),U_3556)),U_3555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3554),U_3555))
    | ~ class_Groups_Ocomm__monoid__add(U_3553) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

fof(f_686_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).

fof(f_686_2,plain,
    ! [U_3561,U_3560,U_3559] :
      ( hAPP(c_Finite__Set_Ocard(U_3559),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3559,tc_HOL_Obool)),U_3560),hAPP(hAPP(c_Set_Oinsert(U_3559),U_3561),c_Orderings_Obot__class_Obot(tc_fun(U_3559,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3559),U_3560)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3559),U_3561),U_3560))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3559),U_3560)) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

cnf(f_686_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3559),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3559,tc_HOL_Obool)),U_3560),hAPP(hAPP(c_Set_Oinsert(U_3559),U_3561),c_Orderings_Obot__class_Obot(tc_fun(U_3559,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3559),U_3560)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3559),U_3561),U_3560))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3559),U_3560)) ),
    inference(clausify,[status(thm)],[f_686_2]) ).

fof(f_687_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(f_687_2,plain,
    ! [U_3564,U_3563,U_3562] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3562,tc_HOL_Obool)),U_3563),hAPP(hAPP(c_Set_Oinsert(U_3562),U_3564),c_Orderings_Obot__class_Obot(tc_fun(U_3562,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_3562),U_3563)
          | hBOOL(hAPP(hAPP(c_member(U_3562),U_3564),U_3563)) )
        & ( hAPP(c_Finite__Set_Ocard(U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3562,tc_HOL_Obool)),U_3563),hAPP(hAPP(c_Set_Oinsert(U_3562),U_3564),c_Orderings_Obot__class_Obot(tc_fun(U_3562,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3562),U_3563)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_3562),U_3564),U_3563)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3562),U_3563)) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3562,tc_HOL_Obool)),U_3563),hAPP(hAPP(c_Set_Oinsert(U_3562),U_3564),c_Orderings_Obot__class_Obot(tc_fun(U_3562,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3562),U_3563)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3562),U_3564),U_3563))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3562),U_3563)) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3562,tc_HOL_Obool)),U_3563),hAPP(hAPP(c_Set_Oinsert(U_3562),U_3564),c_Orderings_Obot__class_Obot(tc_fun(U_3562,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_3562),U_3563)
    | hBOOL(hAPP(hAPP(c_member(U_3562),U_3564),U_3563))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3562),U_3563)) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).

fof(f_688_2,plain,
    ! [U_3567,U_3566,U_3565] :
      ( hAPP(c_Finite__Set_Ocard(U_3565),U_3566) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3565,tc_HOL_Obool)),U_3566),hAPP(hAPP(c_Set_Oinsert(U_3565),U_3567),c_Orderings_Obot__class_Obot(tc_fun(U_3565,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3565),U_3567),U_3566))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3565),U_3566)) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3565),U_3566) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3565,tc_HOL_Obool)),U_3566),hAPP(hAPP(c_Set_Oinsert(U_3565),U_3567),c_Orderings_Obot__class_Obot(tc_fun(U_3565,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3565),U_3567),U_3566))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3565),U_3566)) ),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_1,plain,
    ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_top1I]) ).

fof(f_689_2,plain,
    ! [U_3569,U_3568] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_3568,tc_HOL_Obool)),U_3569)),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_3568,tc_HOL_Obool)),U_3569)),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_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]) ).

cnf(f_690_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_690_1]) ).

fof(f_691_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]) ).

cnf(f_691_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(clausify,[status(thm)],[f_691_1]) ).

fof(f_692_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Groups_Oone__class_Oone(T_a) = V_x_2
          | V_x_2 != c_Groups_Oone__class_Oone(T_a) )
        & ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
          | c_Groups_Oone__class_Oone(T_a) != V_x_2 ) )
      | ~ class_Groups_Oone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).

fof(f_692_2,plain,
    ! [U_3571,U_3570] :
      ( ( ( c_Groups_Oone__class_Oone(U_3570) = U_3571
          | U_3571 != c_Groups_Oone__class_Oone(U_3570) )
        & ( U_3571 = c_Groups_Oone__class_Oone(U_3570)
          | c_Groups_Oone__class_Oone(U_3570) != U_3571 ) )
      | ~ class_Groups_Oone(U_3570) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

cnf(f_692_3,plain,
    ( U_3571 = c_Groups_Oone__class_Oone(U_3570)
    | c_Groups_Oone__class_Oone(U_3570) != U_3571
    | ~ class_Groups_Oone(U_3570) ),
    inference(clausify,[status(thm)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( c_Groups_Oone__class_Oone(U_3570) = U_3571
    | U_3571 != c_Groups_Oone__class_Oone(U_3570)
    | ~ class_Groups_Oone(U_3570) ),
    inference(clausify,[status(thm)],[f_692_2]) ).

fof(f_693_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_a] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).

fof(f_693_2,plain,
    ! [U_3575,U_3574,U_3573,U_3572] :
      ( U_3574 != c_Orderings_Obot__class_Obot(tc_fun(U_3572,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3572,U_3573,U_3574),U_3575)) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    ( U_3574 != c_Orderings_Obot__class_Obot(tc_fun(U_3572,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3572,U_3573,U_3574),U_3575)) ),
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_1,plain,
    ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).

fof(f_694_2,plain,
    ! [U_3578,U_3577,U_3576] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3576,U_3577,c_Orderings_Obot__class_Obot(tc_fun(U_3576,tc_HOL_Obool))),U_3578)),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

cnf(f_694_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3576,U_3577,c_Orderings_Obot__class_Obot(tc_fun(U_3576,tc_HOL_Obool))),U_3578)),
    inference(clausify,[status(thm)],[f_694_2]) ).

fof(f_695_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_a),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_a),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_a),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).

fof(f_695_2,plain,
    ! [U_3585,U_3584,U_3583] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3582] :
              ( ? [U_3581] :
                  ( hAPP(U_3585,U_3581) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3582 != U_3581
                  & hBOOL(hAPP(hAPP(c_member(U_3583),U_3581),U_3584)) )
              | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584)) ) )
        & ( ? [U_3580] :
              ( ! [U_3579] :
                  ( hAPP(U_3585,U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_3580 = U_3579
                  | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3579),U_3584)) )
              & hAPP(U_3585,U_3580) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_3583),U_3580),U_3584)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_3585,U_3584,U_3583] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3582] :
              ( ? [U_3581] :
                  ( hAPP(U_3585,U_3581) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3582 != U_3581
                  & hBOOL(hAPP(hAPP(c_member(U_3583),U_3581),U_3584)) )
              | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584)) ) )
        & ( ( ! [U_3579] :
                ( hAPP(U_3585,U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK70(U_3585,U_3584,U_3583) = U_3579
                | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3579),U_3584)) )
            & hAPP(U_3585,sK70(U_3585,U_3584,U_3583)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3583),sK70(U_3585,U_3584,U_3583)),U_3584)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3580,sK70(U_3585,U_3584,U_3583))],[f_695_2]) ).

fof(f_695_4,plain,
    ! [U_3585,U_3584,U_3583] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3582] :
              ( ( hAPP(U_3585,sK71(U_3585,U_3584,U_3583,U_3582)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_3582 != sK71(U_3585,U_3584,U_3583,U_3582)
                & hBOOL(hAPP(hAPP(c_member(U_3583),sK71(U_3585,U_3584,U_3583,U_3582)),U_3584)) )
              | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584)) ) )
        & ( ( ! [U_3579] :
                ( hAPP(U_3585,U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK70(U_3585,U_3584,U_3583) = U_3579
                | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3579),U_3584)) )
            & hAPP(U_3585,sK70(U_3585,U_3584,U_3583)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3583),sK70(U_3585,U_3584,U_3583)),U_3584)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3581,sK71(U_3585,U_3584,U_3583,U_3582))],[f_695_3]) ).

cnf(f_695_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3583),sK70(U_3585,U_3584,U_3583)),U_3584))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

cnf(f_695_6,plain,
    ( hAPP(U_3585,sK70(U_3585,U_3584,U_3583)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

cnf(f_695_7,plain,
    ( hAPP(U_3585,U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK70(U_3585,U_3584,U_3583) = U_3579
    | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3579),U_3584))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

cnf(f_695_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3583),sK71(U_3585,U_3584,U_3583,U_3582)),U_3584))
    | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

cnf(f_695_9,plain,
    ( U_3582 != sK71(U_3585,U_3584,U_3583,U_3582)
    | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

cnf(f_695_10,plain,
    ( hAPP(U_3585,sK71(U_3585,U_3584,U_3583,U_3582)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_3585,U_3582) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3583),U_3582),U_3584))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3583,tc_Nat_Onat),U_3585),U_3584) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3583),U_3584)) ),
    inference(clausify,[status(thm)],[f_695_4]) ).

fof(f_696_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).

fof(f_696_2,plain,
    ! [U_3587,U_3586] : hAPP(c_Finite__Set_Ocard(U_3586),U_3587) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3586,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_3586),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3587),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

cnf(f_696_3,plain,
    hAPP(c_Finite__Set_Ocard(U_3586),U_3587) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3586,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_3586),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3587),
    inference(clausify,[status(thm)],[f_696_2]) ).

fof(f_697_1,plain,
    ! [V_A_2,T_a] :
      ( ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
      & ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),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_a),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__def]) ).

fof(f_697_2,plain,
    ! [U_3589,U_3588] :
      ( ( hAPP(c_Finite__Set_Ocard(U_3588),U_3589) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3588),U_3589)) )
      & ( hAPP(c_Finite__Set_Ocard(U_3588),U_3589) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_3588,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_3588),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3589)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3588),U_3589)) ) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ( ! [U_3593,U_3591] :
        ( hAPP(c_Finite__Set_Ocard(U_3591),U_3593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3591),U_3593)) )
    & ! [U_3592,U_3590] :
        ( hAPP(c_Finite__Set_Ocard(U_3590),U_3592) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_3590,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_3590),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3592)) ) ),
    inference(miniscope,[status(thm)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3590),U_3592) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_3590,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_3590),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3592)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3592)) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3591),U_3593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3591),U_3593)) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),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_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).

fof(f_698_2,plain,
    ! [U_3595,U_3594] :
      ( hAPP(c_Finite__Set_Ocard(U_3594),U_3595) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_3594,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_3594),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3595)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3594),U_3595)) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

cnf(f_698_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3594),U_3595) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_3594,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_3594),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3595)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3594),U_3595)) ),
    inference(clausify,[status(thm)],[f_698_2]) ).

fof(f_699_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).

fof(f_699_2,plain,
    ! [U_3599,U_3598,U_3597,U_3596] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3596,U_3597,hAPP(hAPP(c_Set_Oinsert(U_3596),U_3598),c_Orderings_Obot__class_Obot(tc_fun(U_3596,tc_HOL_Obool)))),U_3599))
        | U_3598 != U_3599 )
      & ( U_3598 = U_3599
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3596,U_3597,hAPP(hAPP(c_Set_Oinsert(U_3596),U_3598),c_Orderings_Obot__class_Obot(tc_fun(U_3596,tc_HOL_Obool)))),U_3599)) ) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ( ! [U_3607,U_3605] :
        ( ! [U_3603,U_3601] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3601,U_3603,hAPP(hAPP(c_Set_Oinsert(U_3601),U_3605),c_Orderings_Obot__class_Obot(tc_fun(U_3601,tc_HOL_Obool)))),U_3607))
        | U_3605 != U_3607 )
    & ! [U_3606,U_3604] :
        ( ! [U_3602,U_3600] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3600,U_3602,hAPP(hAPP(c_Set_Oinsert(U_3600),U_3604),c_Orderings_Obot__class_Obot(tc_fun(U_3600,tc_HOL_Obool)))),U_3606))
        | U_3604 = U_3606 ) ),
    inference(miniscope,[status(thm)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3600,U_3602,hAPP(hAPP(c_Set_Oinsert(U_3600),U_3604),c_Orderings_Obot__class_Obot(tc_fun(U_3600,tc_HOL_Obool)))),U_3606))
    | U_3604 = U_3606 ),
    inference(clausify,[status(thm)],[f_699_3]) ).

cnf(f_699_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3601,U_3603,hAPP(hAPP(c_Set_Oinsert(U_3601),U_3605),c_Orderings_Obot__class_Obot(tc_fun(U_3601,tc_HOL_Obool)))),U_3607))
    | U_3605 != U_3607 ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).

fof(f_700_2,plain,
    ! [U_3610,U_3609,U_3608] :
      ( hAPP(c_Finite__Set_Ocard(U_3608),hAPP(hAPP(c_Set_Oinsert(U_3608),U_3610),U_3609)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3608),U_3609))
      | hBOOL(hAPP(hAPP(c_member(U_3608),U_3610),U_3609))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3608),U_3609)) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3608),hAPP(hAPP(c_Set_Oinsert(U_3608),U_3610),U_3609)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3608),U_3609))
    | hBOOL(hAPP(hAPP(c_member(U_3608),U_3610),U_3609))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3608),U_3609)) ),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).

fof(f_701_2,plain,
    ! [U_3614,U_3613,U_3612,U_3611] :
      ( hAPP(c_Finite__Set_Ocard(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3611,tc_HOL_Obool)),U_3612),hAPP(hAPP(c_Set_Oinsert(U_3611),U_3613),U_3614))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3611,tc_HOL_Obool)),U_3612),U_3614))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_3611),U_3613),U_3614))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3611),U_3613),U_3612))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3611),U_3612)) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3611,tc_HOL_Obool)),U_3612),hAPP(hAPP(c_Set_Oinsert(U_3611),U_3613),U_3614))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3611,tc_HOL_Obool)),U_3612),U_3614))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_3611),U_3613),U_3614))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3611),U_3613),U_3612))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3611),U_3612)) ),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).

fof(f_702_2,plain,
    ! [U_3617,U_3616,U_3615] :
      ( hAPP(c_Finite__Set_Ocard(U_3615),hAPP(hAPP(c_Set_Oinsert(U_3615),U_3617),U_3616)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3615,tc_HOL_Obool)),U_3616),hAPP(hAPP(c_Set_Oinsert(U_3615),U_3617),c_Orderings_Obot__class_Obot(tc_fun(U_3615,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3615),U_3616)) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

cnf(f_702_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3615),hAPP(hAPP(c_Set_Oinsert(U_3615),U_3617),U_3616)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3615,tc_HOL_Obool)),U_3616),hAPP(hAPP(c_Set_Oinsert(U_3615),U_3617),c_Orderings_Obot__class_Obot(tc_fun(U_3615,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3615),U_3616)) ),
    inference(clausify,[status(thm)],[f_702_2]) ).

fof(f_703_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),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_703_2,plain,
    ! [U_3621,U_3620,U_3619,U_3618] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_3618)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3618),U_3619),U_3620),U_3621)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

cnf(f_703_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_3618)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3618),U_3619),U_3620),U_3621)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_703_2]) ).

fof(f_704_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),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_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).

fof(f_704_2,plain,
    ! [U_3625,U_3624,U_3623] :
      ( hAPP(c_Finite__Set_Ocard(U_3623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3623),U_3624)),hAPP(c_Finite__Set_Ocard(U_3623),U_3625))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_3622] : hBOOL(hAPP(hAPP(c_member(U_3623),U_3622),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3625))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3624)) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ! [U_3625,U_3624,U_3623] :
      ( hAPP(c_Finite__Set_Ocard(U_3623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3623),U_3624)),hAPP(c_Finite__Set_Ocard(U_3623),U_3625))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_3623),sK72(U_3625,U_3624,U_3623)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3625))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3624)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3622,sK72(U_3625,U_3624,U_3623))],[f_704_2]) ).

cnf(f_704_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3623),sK72(U_3625,U_3624,U_3623)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625)))
    | hAPP(c_Finite__Set_Ocard(U_3623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3623),U_3624)),hAPP(c_Finite__Set_Ocard(U_3623),U_3625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3624)) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_3623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3623,tc_HOL_Obool)),U_3624),U_3625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3623),U_3624)),hAPP(c_Finite__Set_Ocard(U_3623),U_3625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3623),U_3624)) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_1,plain,
    ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
      ( ( c_Nitpick_Ofold__graph_H(T_a,T_b,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_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y)
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_HOL_Obool)) ) ) )
      & ( ? [B_x,B_y] :
            ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_a),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_a,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(T_a,T_b,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_705_2,plain,
    ! [U_3636,U_3635,U_3634,U_3633,U_3632,U_3631,U_3630] :
      ( ( c_Nitpick_Ofold__graph_H(U_3630,U_3631,U_3632,U_3633,U_3634,hAPP(hAPP(U_3632,U_3635),U_3636))
        | ( ! [U_3629,U_3628] :
              ( ~ c_Nitpick_Ofold__graph_H(U_3630,U_3631,U_3632,U_3633,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3630,tc_HOL_Obool)),U_3634),hAPP(hAPP(c_Set_Oinsert(U_3630),U_3629),c_Orderings_Obot__class_Obot(tc_fun(U_3630,tc_HOL_Obool)))),U_3628)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3630),U_3629),U_3634))
              | hAPP(hAPP(U_3632,U_3635),U_3636) != hAPP(hAPP(U_3632,U_3629),U_3628) )
          & ( hAPP(hAPP(U_3632,U_3635),U_3636) != U_3633
            | U_3634 != c_Orderings_Obot__class_Obot(tc_fun(U_3630,tc_HOL_Obool)) ) ) )
      & ( ? [U_3627,U_3626] :
            ( c_Nitpick_Ofold__graph_H(U_3630,U_3631,U_3632,U_3633,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3630,tc_HOL_Obool)),U_3634),hAPP(hAPP(c_Set_Oinsert(U_3630),U_3627),c_Orderings_Obot__class_Obot(tc_fun(U_3630,tc_HOL_Obool)))),U_3626)
            & hBOOL(hAPP(hAPP(c_member(U_3630),U_3627),U_3634))
            & hAPP(hAPP(U_3632,U_3635),U_3636) = hAPP(hAPP(U_3632,U_3627),U_3626) )
        | ( hAPP(hAPP(U_3632,U_3635),U_3636) = U_3633
          & U_3634 = c_Orderings_Obot__class_Obot(tc_fun(U_3630,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_3630,U_3631,U_3632,U_3633,U_3634,hAPP(hAPP(U_3632,U_3635),U_3636)) ) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ( ! [U_3650,U_3648,U_3646,U_3644,U_3642,U_3640,U_3638] :
        ( c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,U_3646,hAPP(hAPP(U_3642,U_3648),U_3650))
        | ( ! [U_3629] :
              ( ! [U_3628] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3638,tc_HOL_Obool)),U_3646),hAPP(hAPP(c_Set_Oinsert(U_3638),U_3629),c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)))),U_3628)
                  | hAPP(hAPP(U_3642,U_3648),U_3650) != hAPP(hAPP(U_3642,U_3629),U_3628) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_3638),U_3629),U_3646)) )
          & ( hAPP(hAPP(U_3642,U_3648),U_3650) != U_3644
            | U_3646 != c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)) ) ) )
    & ! [U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637] :
        ( ? [U_3627] :
            ( ? [U_3626] :
                ( c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3645),hAPP(hAPP(c_Set_Oinsert(U_3637),U_3627),c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)))),U_3626)
                & hAPP(hAPP(U_3641,U_3647),U_3649) = hAPP(hAPP(U_3641,U_3627),U_3626) )
            & hBOOL(hAPP(hAPP(c_member(U_3637),U_3627),U_3645)) )
        | ( hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
          & U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ) ),
    inference(miniscope,[status(thm)],[f_705_2]) ).

fof(f_705_4,plain,
    ( ! [U_3650,U_3648,U_3646,U_3644,U_3642,U_3640,U_3638] :
        ( c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,U_3646,hAPP(hAPP(U_3642,U_3648),U_3650))
        | ( ! [U_3629] :
              ( ! [U_3628] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3638,tc_HOL_Obool)),U_3646),hAPP(hAPP(c_Set_Oinsert(U_3638),U_3629),c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)))),U_3628)
                  | hAPP(hAPP(U_3642,U_3648),U_3650) != hAPP(hAPP(U_3642,U_3629),U_3628) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_3638),U_3629),U_3646)) )
          & ( hAPP(hAPP(U_3642,U_3648),U_3650) != U_3644
            | U_3646 != c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)) ) ) )
    & ! [U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637] :
        ( ( ? [U_3626] :
              ( c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3645),hAPP(hAPP(c_Set_Oinsert(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)))),U_3626)
              & hAPP(hAPP(U_3641,U_3647),U_3649) = hAPP(hAPP(U_3641,sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),U_3626) )
          & hBOOL(hAPP(hAPP(c_member(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),U_3645)) )
        | ( hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
          & U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3627,sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))],[f_705_3]) ).

fof(f_705_5,plain,
    ( ! [U_3650,U_3648,U_3646,U_3644,U_3642,U_3640,U_3638] :
        ( c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,U_3646,hAPP(hAPP(U_3642,U_3648),U_3650))
        | ( ! [U_3629] :
              ( ! [U_3628] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3638,tc_HOL_Obool)),U_3646),hAPP(hAPP(c_Set_Oinsert(U_3638),U_3629),c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)))),U_3628)
                  | hAPP(hAPP(U_3642,U_3648),U_3650) != hAPP(hAPP(U_3642,U_3629),U_3628) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_3638),U_3629),U_3646)) )
          & ( hAPP(hAPP(U_3642,U_3648),U_3650) != U_3644
            | U_3646 != c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)) ) ) )
    & ! [U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637] :
        ( ( c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3645),hAPP(hAPP(c_Set_Oinsert(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)))),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
          & hAPP(hAPP(U_3641,U_3647),U_3649) = hAPP(hAPP(U_3641,sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
          & hBOOL(hAPP(hAPP(c_member(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),U_3645)) )
        | ( hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
          & U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3626,sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))],[f_705_4]) ).

cnf(f_705_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),U_3645))
    | U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_7,plain,
    ( hAPP(hAPP(U_3641,U_3647),U_3649) = hAPP(hAPP(U_3641,sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
    | U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3645),hAPP(hAPP(c_Set_Oinsert(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)))),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
    | U_3645 = c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),U_3645))
    | hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_10,plain,
    ( hAPP(hAPP(U_3641,U_3647),U_3649) = hAPP(hAPP(U_3641,sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
    | hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_11,plain,
    ( c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3645),hAPP(hAPP(c_Set_Oinsert(U_3637),sK73(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637)),c_Orderings_Obot__class_Obot(tc_fun(U_3637,tc_HOL_Obool)))),sK74(U_3649,U_3647,U_3645,U_3643,U_3641,U_3639,U_3637))
    | hAPP(hAPP(U_3641,U_3647),U_3649) = U_3643
    | ~ c_Nitpick_Ofold__graph_H(U_3637,U_3639,U_3641,U_3643,U_3645,hAPP(hAPP(U_3641,U_3647),U_3649)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_12,plain,
    ( hAPP(hAPP(U_3642,U_3648),U_3650) != U_3644
    | U_3646 != c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool))
    | c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,U_3646,hAPP(hAPP(U_3642,U_3648),U_3650)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

cnf(f_705_13,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3638,tc_HOL_Obool)),U_3646),hAPP(hAPP(c_Set_Oinsert(U_3638),U_3629),c_Orderings_Obot__class_Obot(tc_fun(U_3638,tc_HOL_Obool)))),U_3628)
    | hAPP(hAPP(U_3642,U_3648),U_3650) != hAPP(hAPP(U_3642,U_3629),U_3628)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3638),U_3629),U_3646))
    | c_Nitpick_Ofold__graph_H(U_3638,U_3640,U_3642,U_3644,U_3646,hAPP(hAPP(U_3642,U_3648),U_3650)) ),
    inference(clausify,[status(thm)],[f_705_5]) ).

fof(f_706_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_706_2,plain,
    ! [U_3651] :
      ( c_Groups_Ozero__class_Ozero(U_3651) != c_Groups_Oone__class_Oone(U_3651)
      | ~ class_Rings_Ozero__neq__one(U_3651) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

cnf(f_706_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_3651) != c_Groups_Oone__class_Oone(U_3651)
    | ~ class_Rings_Ozero__neq__one(U_3651) ),
    inference(clausify,[status(thm)],[f_706_2]) ).

fof(f_707_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_707_2,plain,
    ! [U_3652] :
      ( c_Groups_Oone__class_Oone(U_3652) != c_Groups_Ozero__class_Ozero(U_3652)
      | ~ class_Rings_Ozero__neq__one(U_3652) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

cnf(f_707_3,plain,
    ( c_Groups_Oone__class_Oone(U_3652) != c_Groups_Ozero__class_Ozero(U_3652)
    | ~ class_Rings_Ozero__neq__one(U_3652) ),
    inference(clausify,[status(thm)],[f_707_2]) ).

fof(f_708_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_708_2,plain,
    ! [U_3654,U_3653] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3653),c_Groups_Ozero__class_Ozero(U_3653)),U_3654) = U_3654
      | ~ class_Rings_Ocomm__semiring__1(U_3653) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

cnf(f_708_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3653),c_Groups_Ozero__class_Ozero(U_3653)),U_3654) = U_3654
    | ~ class_Rings_Ocomm__semiring__1(U_3653) ),
    inference(clausify,[status(thm)],[f_708_2]) ).

fof(f_709_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_709_2,plain,
    ! [U_3656,U_3655] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),c_Groups_Ozero__class_Ozero(U_3655)) = U_3656
      | ~ class_Rings_Ocomm__semiring__1(U_3655) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

cnf(f_709_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),c_Groups_Ozero__class_Ozero(U_3655)) = U_3656
    | ~ class_Rings_Ocomm__semiring__1(U_3655) ),
    inference(clausify,[status(thm)],[f_709_2]) ).

fof(f_710_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).

fof(f_710_2,plain,
    ! [U_3659,U_3658,U_3657] :
      ( ( ( U_3658 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3657),U_3658),U_3659)
          | U_3659 != c_Groups_Ozero__class_Ozero(U_3657) )
        & ( U_3659 = c_Groups_Ozero__class_Ozero(U_3657)
          | U_3658 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3657),U_3658),U_3659) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3657) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

cnf(f_710_3,plain,
    ( U_3659 = c_Groups_Ozero__class_Ozero(U_3657)
    | U_3658 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3657),U_3658),U_3659)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3657) ),
    inference(clausify,[status(thm)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( U_3658 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3657),U_3658),U_3659)
    | U_3659 != c_Groups_Ozero__class_Ozero(U_3657)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3657) ),
    inference(clausify,[status(thm)],[f_710_2]) ).

fof(f_711_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).

fof(f_711_2,plain,
    ! [U_3661,U_3660] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3660),U_3661),U_3661) = c_Groups_Ozero__class_Ozero(U_3660)
          | U_3661 != c_Groups_Ozero__class_Ozero(U_3660) )
        & ( U_3661 = c_Groups_Ozero__class_Ozero(U_3660)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3660),U_3661),U_3661) != c_Groups_Ozero__class_Ozero(U_3660) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3660) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

cnf(f_711_3,plain,
    ( U_3661 = c_Groups_Ozero__class_Ozero(U_3660)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3660),U_3661),U_3661) != c_Groups_Ozero__class_Ozero(U_3660)
    | ~ class_Groups_Olinordered__ab__group__add(U_3660) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3660),U_3661),U_3661) = c_Groups_Ozero__class_Ozero(U_3660)
    | U_3661 != c_Groups_Ozero__class_Ozero(U_3660)
    | ~ class_Groups_Olinordered__ab__group__add(U_3660) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

fof(f_712_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_712_2,plain,
    ! [U_3666,U_3665,U_3664,U_3663,U_3662] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3664)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3665),U_3666)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3665)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3664),U_3666))
      | ~ class_Rings_Ocomm__semiring__1(U_3662) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

cnf(f_712_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3664)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3665),U_3666)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3665)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3664),U_3666))
    | ~ class_Rings_Ocomm__semiring__1(U_3662) ),
    inference(clausify,[status(thm)],[f_712_2]) ).

fof(f_713_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_713_2,plain,
    ! [U_3670,U_3669,U_3668,U_3667] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),U_3668),U_3669)),U_3670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),U_3668),U_3670)),U_3669)
      | ~ class_Rings_Ocomm__semiring__1(U_3667) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

cnf(f_713_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),U_3668),U_3669)),U_3670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3667),U_3668),U_3670)),U_3669)
    | ~ class_Rings_Ocomm__semiring__1(U_3667) ),
    inference(clausify,[status(thm)],[f_713_2]) ).

fof(f_714_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_714_2,plain,
    ! [U_3674,U_3673,U_3672,U_3671] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),U_3673)),U_3674) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3673),U_3674))
      | ~ class_Rings_Ocomm__semiring__1(U_3671) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),U_3673)),U_3674) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3673),U_3674))
    | ~ class_Rings_Ocomm__semiring__1(U_3671) ),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_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_715_2,plain,
    ! [U_3678,U_3677,U_3676,U_3675] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3677),U_3678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3676),U_3677)),U_3678)
      | ~ class_Rings_Ocomm__semiring__1(U_3675) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

cnf(f_715_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3677),U_3678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3675),U_3676),U_3677)),U_3678)
    | ~ class_Rings_Ocomm__semiring__1(U_3675) ),
    inference(clausify,[status(thm)],[f_715_2]) ).

fof(f_716_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_716_2,plain,
    ! [U_3682,U_3681,U_3680,U_3679] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3681),U_3682)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3680),U_3682))
      | ~ class_Rings_Ocomm__semiring__1(U_3679) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

cnf(f_716_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3681),U_3682)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3679),U_3680),U_3682))
    | ~ class_Rings_Ocomm__semiring__1(U_3679) ),
    inference(clausify,[status(thm)],[f_716_2]) ).

fof(f_717_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_717_2,plain,
    ! [U_3685,U_3684,U_3683] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),U_3684),U_3685) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),U_3685),U_3684)
      | ~ class_Rings_Ocomm__semiring__1(U_3683) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

cnf(f_717_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),U_3684),U_3685) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),U_3685),U_3684)
    | ~ class_Rings_Ocomm__semiring__1(U_3683) ),
    inference(clausify,[status(thm)],[f_717_2]) ).

fof(f_718_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),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_a),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).

fof(f_718_2,plain,
    ! [U_3689,U_3688,U_3687,U_3686] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3686,U_3688)),c_Sum__Type_OPlus(U_3686,U_3688,U_3687,U_3689)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3688),U_3689))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3686,U_3688)),c_Sum__Type_OPlus(U_3686,U_3688,U_3687,U_3689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3686),U_3687)),hAPP(c_Finite__Set_Ocard(U_3688),U_3689))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3688),U_3689))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687)) ) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ( ! [U_3697,U_3695,U_3693,U_3691] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3691,U_3695)),c_Sum__Type_OPlus(U_3691,U_3695,U_3693,U_3697)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3695),U_3697))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3691),U_3693)) ) )
    & ! [U_3696,U_3694,U_3692,U_3690] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3690,U_3694)),c_Sum__Type_OPlus(U_3690,U_3694,U_3692,U_3696)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3690),U_3692)),hAPP(c_Finite__Set_Ocard(U_3694),U_3696))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3694),U_3696))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3692)) ) ),
    inference(miniscope,[status(thm)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3690,U_3694)),c_Sum__Type_OPlus(U_3690,U_3694,U_3692,U_3696)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3690),U_3692)),hAPP(c_Finite__Set_Ocard(U_3694),U_3696))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3694),U_3696))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3692)) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

cnf(f_718_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3691),U_3693))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_3691,U_3695)),c_Sum__Type_OPlus(U_3691,U_3695,U_3693,U_3697)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

cnf(f_718_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3695),U_3697))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_3691,U_3695)),c_Sum__Type_OPlus(U_3691,U_3695,U_3693,U_3697)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).

fof(f_719_2,plain,
    ! [U_3702,U_3701,U_3700,U_3699,U_3698] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3698),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),U_3700)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),U_3701))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3701) != c_Orderings_Obot__class_Obot(tc_fun(U_3699,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3701))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3700))
      | ~ class_Groups_Ocomm__monoid__mult(U_3698) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

cnf(f_719_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3698),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),U_3700)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3698,U_3699,c_Groups_Otimes__class_Otimes(U_3698)),U_3702),c_Groups_Oone__class_Oone(U_3698)),U_3701))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3701) != c_Orderings_Obot__class_Obot(tc_fun(U_3699,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3701))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3700))
    | ~ class_Groups_Ocomm__monoid__mult(U_3698) ),
    inference(clausify,[status(thm)],[f_719_2]) ).

fof(f_720_1,plain,
    ! [V_y_2,V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).

fof(f_720_2,plain,
    ! [U_3706,U_3705,U_3704,U_3703] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3703,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3703,tc_HOL_Obool)),U_3704),hAPP(hAPP(c_Set_Oinsert(U_3703),U_3705),c_Orderings_Obot__class_Obot(tc_fun(U_3703,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_3703),U_3706),c_Orderings_Obot__class_Obot(tc_fun(U_3703,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3703),U_3704)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3703),U_3706),U_3704))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3703),U_3705),U_3704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3703),U_3704)) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

cnf(f_720_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3703,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3703,tc_HOL_Obool)),U_3704),hAPP(hAPP(c_Set_Oinsert(U_3703),U_3705),c_Orderings_Obot__class_Obot(tc_fun(U_3703,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_3703),U_3706),c_Orderings_Obot__class_Obot(tc_fun(U_3703,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3703),U_3704)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3703),U_3706),U_3704))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3703),U_3705),U_3704))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3703),U_3704)) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

fof(f_721_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).

fof(f_721_2,plain,
    ! [U_3709,U_3708,U_3707] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3707,tc_HOL_Obool)),U_3708),hAPP(hAPP(c_Set_Oinsert(U_3707),U_3709),c_Orderings_Obot__class_Obot(tc_fun(U_3707,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3707),U_3708)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3707),U_3709),U_3708))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3707),U_3708)) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

cnf(f_721_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3707,tc_HOL_Obool)),U_3708),hAPP(hAPP(c_Set_Oinsert(U_3707),U_3709),c_Orderings_Obot__class_Obot(tc_fun(U_3707,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3707),U_3708)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3707),U_3709),U_3708))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3707),U_3708)) ),
    inference(clausify,[status(thm)],[f_721_2]) ).

fof(f_722_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).

fof(f_722_2,plain,
    ! [U_3712,U_3711,U_3710] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3710),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3710,tc_HOL_Obool)),U_3711),hAPP(hAPP(c_Set_Oinsert(U_3710),U_3712),c_Orderings_Obot__class_Obot(tc_fun(U_3710,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_3710),U_3711)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3710),U_3712),U_3711))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3710),U_3711)) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

cnf(f_722_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3710),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3710,tc_HOL_Obool)),U_3711),hAPP(hAPP(c_Set_Oinsert(U_3710),U_3712),c_Orderings_Obot__class_Obot(tc_fun(U_3710,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_3710),U_3711)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3710),U_3712),U_3711))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3710),U_3711)) ),
    inference(clausify,[status(thm)],[f_722_2]) ).

fof(f_723_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__0]) ).

fof(f_723_2,plain,
    ! [U_3716,U_3715,U_3714,U_3713] : c_Hoare__Mirabelle_Otriple__valid(U_3713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3713),U_3714),hAPP(c_Com_Ocom_OBODY,U_3715)),U_3716)),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

cnf(f_723_3,plain,
    c_Hoare__Mirabelle_Otriple__valid(U_3713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3713),U_3714),hAPP(c_Com_Ocom_OBODY,U_3715)),U_3716)),
    inference(clausify,[status(thm)],[f_723_2]) ).

fof(f_724_1,plain,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
      ( ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
          & hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).

fof(f_724_2,plain,
    ! [U_3723,U_3722,U_3721,U_3720,U_3719] :
      ( ? [U_3718,U_3717] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_3719),U_3718),U_3717))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3719,U_3719,U_3720,U_3718,U_3717),U_3723))
          & hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722) = hAPP(hAPP(c_Set_Oinsert(U_3719),U_3718),U_3717) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ! [U_3723,U_3722,U_3721,U_3720,U_3719] :
      ( ? [U_3717] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),U_3717))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3719,U_3719,U_3720,sK75(U_3723,U_3722,U_3721,U_3720,U_3719),U_3717),U_3723))
          & hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722) = hAPP(hAPP(c_Set_Oinsert(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),U_3717) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3718,sK75(U_3723,U_3722,U_3721,U_3720,U_3719))],[f_724_2]) ).

fof(f_724_4,plain,
    ! [U_3723,U_3722,U_3721,U_3720,U_3719] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),sK76(U_3723,U_3722,U_3721,U_3720,U_3719)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3719,U_3719,U_3720,sK75(U_3723,U_3722,U_3721,U_3720,U_3719),sK76(U_3723,U_3722,U_3721,U_3720,U_3719)),U_3723))
        & hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722) = hAPP(hAPP(c_Set_Oinsert(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),sK76(U_3723,U_3722,U_3721,U_3720,U_3719)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3717,sK76(U_3723,U_3722,U_3721,U_3720,U_3719))],[f_724_3]) ).

cnf(f_724_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722) = hAPP(hAPP(c_Set_Oinsert(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),sK76(U_3723,U_3722,U_3721,U_3720,U_3719))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3719,U_3719,U_3720,sK75(U_3723,U_3722,U_3721,U_3720,U_3719),sK76(U_3723,U_3722,U_3721,U_3720,U_3719)),U_3723))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3719),sK75(U_3723,U_3722,U_3721,U_3720,U_3719)),sK76(U_3723,U_3722,U_3721,U_3720,U_3719)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3719,U_3720,hAPP(hAPP(c_Set_Oinsert(U_3719),U_3721),U_3722)),U_3723)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

fof(f_725_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2))
        | ! [B_a,B_A] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
            | hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) ) )
      & ( ? [B_a,B_A] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
            & hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(f_725_2,plain,
    ! [U_3732,U_3731,U_3730,U_3729,U_3728] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3728,U_3729,hAPP(hAPP(c_Set_Oinsert(U_3728),U_3730),U_3731)),U_3732))
        | ! [U_3727,U_3726] :
            ( hBOOL(hAPP(hAPP(c_member(U_3728),U_3727),U_3726))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3728,U_3728,U_3729,U_3727,U_3726),U_3732))
            | hAPP(hAPP(c_Set_Oinsert(U_3728),U_3730),U_3731) != hAPP(hAPP(c_Set_Oinsert(U_3728),U_3727),U_3726) ) )
      & ( ? [U_3725,U_3724] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_3728),U_3725),U_3724))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3728,U_3728,U_3729,U_3725,U_3724),U_3732))
            & hAPP(hAPP(c_Set_Oinsert(U_3728),U_3730),U_3731) = hAPP(hAPP(c_Set_Oinsert(U_3728),U_3725),U_3724) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3728,U_3729,hAPP(hAPP(c_Set_Oinsert(U_3728),U_3730),U_3731)),U_3732)) ) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ( ! [U_3742,U_3740,U_3738,U_3736,U_3734] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3734,U_3736,hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740)),U_3742))
        | ! [U_3727,U_3726] :
            ( hBOOL(hAPP(hAPP(c_member(U_3734),U_3727),U_3726))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3734,U_3734,U_3736,U_3727,U_3726),U_3742))
            | hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740) != hAPP(hAPP(c_Set_Oinsert(U_3734),U_3727),U_3726) ) )
    & ! [U_3741,U_3739,U_3737,U_3735,U_3733] :
        ( ? [U_3725,U_3724] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_3733),U_3725),U_3724))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3733,U_3733,U_3735,U_3725,U_3724),U_3741))
            & hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739) = hAPP(hAPP(c_Set_Oinsert(U_3733),U_3725),U_3724) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ) ),
    inference(miniscope,[status(thm)],[f_725_2]) ).

fof(f_725_4,plain,
    ( ! [U_3742,U_3740,U_3738,U_3736,U_3734] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3734,U_3736,hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740)),U_3742))
        | ! [U_3727,U_3726] :
            ( hBOOL(hAPP(hAPP(c_member(U_3734),U_3727),U_3726))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3734,U_3734,U_3736,U_3727,U_3726),U_3742))
            | hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740) != hAPP(hAPP(c_Set_Oinsert(U_3734),U_3727),U_3726) ) )
    & ! [U_3741,U_3739,U_3737,U_3735,U_3733] :
        ( ? [U_3724] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),U_3724))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3733,U_3733,U_3735,sK77(U_3741,U_3739,U_3737,U_3735,U_3733),U_3724),U_3741))
            & hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739) = hAPP(hAPP(c_Set_Oinsert(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),U_3724) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3725,sK77(U_3741,U_3739,U_3737,U_3735,U_3733))],[f_725_3]) ).

fof(f_725_5,plain,
    ( ! [U_3742,U_3740,U_3738,U_3736,U_3734] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3734,U_3736,hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740)),U_3742))
        | ! [U_3727,U_3726] :
            ( hBOOL(hAPP(hAPP(c_member(U_3734),U_3727),U_3726))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3734,U_3734,U_3736,U_3727,U_3726),U_3742))
            | hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740) != hAPP(hAPP(c_Set_Oinsert(U_3734),U_3727),U_3726) ) )
    & ! [U_3741,U_3739,U_3737,U_3735,U_3733] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),sK78(U_3741,U_3739,U_3737,U_3735,U_3733)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3733,U_3733,U_3735,sK77(U_3741,U_3739,U_3737,U_3735,U_3733),sK78(U_3741,U_3739,U_3737,U_3735,U_3733)),U_3741))
          & hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739) = hAPP(hAPP(c_Set_Oinsert(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),sK78(U_3741,U_3739,U_3737,U_3735,U_3733)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3724,sK78(U_3741,U_3739,U_3737,U_3735,U_3733))],[f_725_4]) ).

cnf(f_725_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739) = hAPP(hAPP(c_Set_Oinsert(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),sK78(U_3741,U_3739,U_3737,U_3735,U_3733))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ),
    inference(clausify,[status(thm)],[f_725_5]) ).

cnf(f_725_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3733,U_3733,U_3735,sK77(U_3741,U_3739,U_3737,U_3735,U_3733),sK78(U_3741,U_3739,U_3737,U_3735,U_3733)),U_3741))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ),
    inference(clausify,[status(thm)],[f_725_5]) ).

cnf(f_725_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3733),sK77(U_3741,U_3739,U_3737,U_3735,U_3733)),sK78(U_3741,U_3739,U_3737,U_3735,U_3733)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3733,U_3735,hAPP(hAPP(c_Set_Oinsert(U_3733),U_3737),U_3739)),U_3741)) ),
    inference(clausify,[status(thm)],[f_725_5]) ).

cnf(f_725_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_3734,U_3736,hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740)),U_3742))
    | hBOOL(hAPP(hAPP(c_member(U_3734),U_3727),U_3726))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_3734,U_3734,U_3736,U_3727,U_3726),U_3742))
    | hAPP(hAPP(c_Set_Oinsert(U_3734),U_3738),U_3740) != hAPP(hAPP(c_Set_Oinsert(U_3734),U_3727),U_3726) ),
    inference(clausify,[status(thm)],[f_725_5]) ).

fof(f_726_1,plain,
    ! [V_a_2,T_a] :
      ( 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)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).

fof(f_726_2,plain,
    ! [U_3744,U_3743] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3743),c_Groups_Oone__class_Oone(U_3743)),U_3744)),U_3744) != c_Groups_Ozero__class_Ozero(U_3743)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3743),U_3744),c_Int_Oring__1__class_OInts(U_3743)))
      | ~ class_Int_Oring__char__0(U_3743) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

cnf(f_726_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3743),c_Groups_Oone__class_Oone(U_3743)),U_3744)),U_3744) != c_Groups_Ozero__class_Ozero(U_3743)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3743),U_3744),c_Int_Oring__1__class_OInts(U_3743)))
    | ~ class_Int_Oring__char__0(U_3743) ),
    inference(clausify,[status(thm)],[f_726_2]) ).

fof(f_727_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_727_2,plain,
    ! [U_3745] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3745),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

cnf(f_727_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3745),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_727_2]) ).

fof(f_728_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_728_2,plain,
    ! [U_3747,U_3746] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3746)),hAPP(c_Nat_OSuc,U_3747)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3746),U_3747)) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

cnf(f_728_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3746)),hAPP(c_Nat_OSuc,U_3747)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3746),U_3747)) ),
    inference(clausify,[status(thm)],[f_728_2]) ).

fof(f_729_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_729_2,plain,
    ! [U_3748] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3748),hAPP(c_Nat_OSuc,U_3748))),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

cnf(f_729_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3748),hAPP(c_Nat_OSuc,U_3748))),
    inference(clausify,[status(thm)],[f_729_2]) ).

fof(f_730_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_730_2,plain,
    ! [U_3749] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_3749))),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

cnf(f_730_3,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_3749))),
    inference(clausify,[status(thm)],[f_730_2]) ).

fof(f_731_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_731_2,plain,
    ! [U_3753,U_3752,U_3751,U_3750] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),U_3753),U_3752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),U_3753),U_3751)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),U_3753),c_Groups_Ozero__class_Ozero(U_3750)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),U_3751),U_3752))
      | ~ class_Rings_Olinordered__ring__strict(U_3750) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

cnf(f_731_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),U_3753),U_3752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),U_3753),U_3751)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),U_3753),c_Groups_Ozero__class_Ozero(U_3750)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3750),U_3751),U_3752))
    | ~ class_Rings_Olinordered__ring__strict(U_3750) ),
    inference(clausify,[status(thm)],[f_731_2]) ).

fof(f_732_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_732_2,plain,
    ! [U_3757,U_3756,U_3755,U_3754] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3754),U_3756),U_3757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3754),U_3755),U_3757)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),U_3757),c_Groups_Ozero__class_Ozero(U_3754)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),U_3755),U_3756))
      | ~ class_Rings_Olinordered__ring__strict(U_3754) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

cnf(f_732_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3754),U_3756),U_3757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3754),U_3755),U_3757)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),U_3757),c_Groups_Ozero__class_Ozero(U_3754)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3754),U_3755),U_3756))
    | ~ class_Rings_Olinordered__ring__strict(U_3754) ),
    inference(clausify,[status(thm)],[f_732_2]) ).

fof(f_733_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_733_2,plain,
    ! [U_3761,U_3760,U_3759,U_3758] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3761),U_3759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3761),U_3760)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),c_Groups_Ozero__class_Ozero(U_3758)),U_3761))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),U_3759),U_3760))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_3758) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

cnf(f_733_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3761),U_3759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3761),U_3760)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),c_Groups_Ozero__class_Ozero(U_3758)),U_3761))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3758),U_3759),U_3760))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_3758) ),
    inference(clausify,[status(thm)],[f_733_2]) ).

fof(f_734_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_734_2,plain,
    ! [U_3765,U_3764,U_3763,U_3762] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3762),U_3765),U_3763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3762),U_3765),U_3764)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),c_Groups_Ozero__class_Ozero(U_3762)),U_3765))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),U_3763),U_3764))
      | ~ class_Rings_Olinordered__semiring__strict(U_3762) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

cnf(f_734_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3762),U_3765),U_3763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3762),U_3765),U_3764)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),c_Groups_Ozero__class_Ozero(U_3762)),U_3765))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3762),U_3763),U_3764))
    | ~ class_Rings_Olinordered__semiring__strict(U_3762) ),
    inference(clausify,[status(thm)],[f_734_2]) ).

fof(f_735_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_735_2,plain,
    ! [U_3769,U_3768,U_3767,U_3766] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3766),U_3767),U_3769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3766),U_3768),U_3769)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),c_Groups_Ozero__class_Ozero(U_3766)),U_3769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),U_3767),U_3768))
      | ~ class_Rings_Olinordered__semiring__strict(U_3766) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

cnf(f_735_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3766),U_3767),U_3769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3766),U_3768),U_3769)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),c_Groups_Ozero__class_Ozero(U_3766)),U_3769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3766),U_3767),U_3768))
    | ~ class_Rings_Olinordered__semiring__strict(U_3766) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

fof(f_736_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_736_2,plain,
    ! [U_3772,U_3771,U_3770] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),c_Groups_Ozero__class_Ozero(U_3770)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3772),c_Groups_Ozero__class_Ozero(U_3770)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3771),c_Groups_Ozero__class_Ozero(U_3770)))
      | ~ class_Rings_Olinordered__ring__strict(U_3770) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

cnf(f_736_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),c_Groups_Ozero__class_Ozero(U_3770)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3772),c_Groups_Ozero__class_Ozero(U_3770)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3771),c_Groups_Ozero__class_Ozero(U_3770)))
    | ~ class_Rings_Olinordered__ring__strict(U_3770) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

fof(f_737_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_737_2,plain,
    ! [U_3775,U_3774,U_3773] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3773),U_3774),U_3775)),c_Groups_Ozero__class_Ozero(U_3773)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),c_Groups_Ozero__class_Ozero(U_3773)),U_3775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),U_3774),c_Groups_Ozero__class_Ozero(U_3773)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3773) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

cnf(f_737_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3773),U_3774),U_3775)),c_Groups_Ozero__class_Ozero(U_3773)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),c_Groups_Ozero__class_Ozero(U_3773)),U_3775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3773),U_3774),c_Groups_Ozero__class_Ozero(U_3773)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3773) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

fof(f_738_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).

fof(f_738_2,plain,
    ! [U_3779,U_3778,U_3777,U_3776] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3779)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3779),U_3778)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3779),U_3778))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3779))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3777),c_Groups_Ozero__class_Ozero(U_3776)))
      | ~ class_Rings_Olinordered__ring__strict(U_3776) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

cnf(f_738_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3779),U_3778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3777),c_Groups_Ozero__class_Ozero(U_3776)))
    | ~ class_Rings_Olinordered__ring__strict(U_3776) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

cnf(f_738_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3779),U_3778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),U_3777),c_Groups_Ozero__class_Ozero(U_3776)))
    | ~ class_Rings_Olinordered__ring__strict(U_3776) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

fof(f_739_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_739_2,plain,
    ! [U_3782,U_3781,U_3780] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),U_3781))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),U_3782))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3780),U_3781),U_3782)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3780) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),U_3781))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),U_3782))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3780),c_Groups_Ozero__class_Ozero(U_3780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3780),U_3781),U_3782)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3780) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_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_740_2,plain,
    ! [U_3785,U_3784,U_3783] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),U_3785))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),U_3784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3783),U_3784),U_3785)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3783) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),U_3785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),U_3784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3783),c_Groups_Ozero__class_Ozero(U_3783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3783),U_3784),U_3785)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3783) ),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_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_741_2,plain,
    ! [U_3788,U_3787,U_3786] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3786),U_3788),U_3787)),c_Groups_Ozero__class_Ozero(U_3786)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),U_3788),c_Groups_Ozero__class_Ozero(U_3786)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),c_Groups_Ozero__class_Ozero(U_3786)),U_3787))
      | ~ class_Rings_Olinordered__semiring__strict(U_3786) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

cnf(f_741_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3786),U_3788),U_3787)),c_Groups_Ozero__class_Ozero(U_3786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),U_3788),c_Groups_Ozero__class_Ozero(U_3786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3786),c_Groups_Ozero__class_Ozero(U_3786)),U_3787))
    | ~ class_Rings_Olinordered__semiring__strict(U_3786) ),
    inference(clausify,[status(thm)],[f_741_2]) ).

fof(f_742_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_742_2,plain,
    ! [U_3791,U_3790,U_3789] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3789),U_3790),U_3791)),c_Groups_Ozero__class_Ozero(U_3789)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),U_3791),c_Groups_Ozero__class_Ozero(U_3789)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),c_Groups_Ozero__class_Ozero(U_3789)),U_3790))
      | ~ class_Rings_Olinordered__semiring__strict(U_3789) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

cnf(f_742_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3789),U_3790),U_3791)),c_Groups_Ozero__class_Ozero(U_3789)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),U_3791),c_Groups_Ozero__class_Ozero(U_3789)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3789),c_Groups_Ozero__class_Ozero(U_3789)),U_3790))
    | ~ class_Rings_Olinordered__semiring__strict(U_3789) ),
    inference(clausify,[status(thm)],[f_742_2]) ).

fof(f_743_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_743_2,plain,
    ! [U_3794,U_3793,U_3792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3792),U_3793),U_3794)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),U_3793))
      | ~ class_Rings_Olinordered__semiring__strict(U_3792) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

cnf(f_743_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3792),U_3793),U_3794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),U_3794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3792),c_Groups_Ozero__class_Ozero(U_3792)),U_3793))
    | ~ class_Rings_Olinordered__semiring__strict(U_3792) ),
    inference(clausify,[status(thm)],[f_743_2]) ).

fof(f_744_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_744_2,plain,
    ! [U_3798,U_3797,U_3796,U_3795] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3798)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),U_3797),U_3798)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),U_3797),U_3798))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3798))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),c_Groups_Ozero__class_Ozero(U_3795)),U_3796))
      | ~ class_Rings_Olinordered__ring__strict(U_3795) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

cnf(f_744_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),U_3797),U_3798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3798)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),c_Groups_Ozero__class_Ozero(U_3795)),U_3796))
    | ~ class_Rings_Olinordered__ring__strict(U_3795) ),
    inference(clausify,[status(thm)],[f_744_2]) ).

cnf(f_744_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3795),U_3796),U_3798)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),U_3797),U_3798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3795),c_Groups_Ozero__class_Ozero(U_3795)),U_3796))
    | ~ class_Rings_Olinordered__ring__strict(U_3795) ),
    inference(clausify,[status(thm)],[f_744_2]) ).

fof(f_745_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_745_2,plain,
    ! [U_3802,U_3801,U_3800,U_3799] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3802),U_3801))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3801),U_3802))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),c_Groups_Ozero__class_Ozero(U_3799)),U_3800)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3802),U_3801))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3801),U_3802))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),c_Groups_Ozero__class_Ozero(U_3799)),U_3800)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

cnf(f_745_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),c_Groups_Ozero__class_Ozero(U_3799)),U_3800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3802),U_3801))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),c_Groups_Ozero__class_Ozero(U_3799)),U_3800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

cnf(f_745_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3801),U_3802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

cnf(f_745_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3802),U_3801))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3801),U_3802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

cnf(f_745_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3801),U_3802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),c_Groups_Ozero__class_Ozero(U_3799)),U_3800))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

cnf(f_745_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3802),U_3801))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3799),U_3800),U_3802)))
    | ~ class_Rings_Olinordered__ring__strict(U_3799) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

fof(f_746_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_746_2,plain,
    ! [U_3806,U_3805,U_3804,U_3803] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3806),U_3804))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3805),c_Groups_Ozero__class_Ozero(U_3803))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3804),U_3806))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),c_Groups_Ozero__class_Ozero(U_3803)),U_3805)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3806),U_3804))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3805),c_Groups_Ozero__class_Ozero(U_3803))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3804),U_3806))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),c_Groups_Ozero__class_Ozero(U_3803)),U_3805)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3805),c_Groups_Ozero__class_Ozero(U_3803)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),c_Groups_Ozero__class_Ozero(U_3803)),U_3805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3806),U_3804))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),c_Groups_Ozero__class_Ozero(U_3803)),U_3805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

cnf(f_746_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3805),c_Groups_Ozero__class_Ozero(U_3803)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3804),U_3806))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

cnf(f_746_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3806),U_3804))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3804),U_3806))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

cnf(f_746_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3804),U_3806))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),c_Groups_Ozero__class_Ozero(U_3803)),U_3805))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

cnf(f_746_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3806),U_3804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),U_3805),c_Groups_Ozero__class_Ozero(U_3803)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3804),U_3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3803),U_3806),U_3805)))
    | ~ class_Rings_Olinordered__ring__strict(U_3803) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_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_747_2,plain,
    ! [U_3808,U_3807] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3807),U_3808),U_3808)),c_Groups_Ozero__class_Ozero(U_3807)))
      | ~ class_Rings_Olinordered__ring(U_3807) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

cnf(f_747_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3807),U_3808),U_3808)),c_Groups_Ozero__class_Ozero(U_3807)))
    | ~ class_Rings_Olinordered__ring(U_3807) ),
    inference(clausify,[status(thm)],[f_747_2]) ).

fof(f_748_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_748_2,plain,
    ! [U_3811,U_3810,U_3809] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3809),U_3810),U_3811)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),U_3811))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),U_3810))
      | ~ class_Rings_Olinordered__semidom(U_3809) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

cnf(f_748_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3809),U_3810),U_3811)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),U_3811))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3809),c_Groups_Oone__class_Oone(U_3809)),U_3810))
    | ~ class_Rings_Olinordered__semidom(U_3809) ),
    inference(clausify,[status(thm)],[f_748_2]) ).

fof(f_749_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_749_2,plain,
    ! [U_3814,U_3813,U_3812] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3812),U_3814),U_3813))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3812),U_3813),U_3814))
      | U_3813 = U_3814
      | ~ class_Rings_Olinordered__idom(U_3812) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

cnf(f_749_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3812),U_3814),U_3813))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3812),U_3813),U_3814))
    | U_3813 = U_3814
    | ~ class_Rings_Olinordered__idom(U_3812) ),
    inference(clausify,[status(thm)],[f_749_2]) ).

fof(f_750_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_750_2,plain,
    ! [U_3819,U_3818,U_3817,U_3816,U_3815] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3816),U_3817)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3818),U_3819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3816),U_3818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3817),U_3819))
      | ~ class_Rings_Ocomm__semiring__1(U_3815) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

cnf(f_750_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3816),U_3817)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3818),U_3819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3816),U_3818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3815),U_3817),U_3819))
    | ~ class_Rings_Ocomm__semiring__1(U_3815) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

fof(f_751_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_751_2,plain,
    ! [U_3824,U_3823,U_3822,U_3821,U_3820] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3821),U_3822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3821),U_3822)),U_3824))
      | ~ class_Rings_Ocomm__semiring__1(U_3820) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

cnf(f_751_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3821),U_3822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3820),U_3821),U_3822)),U_3824))
    | ~ class_Rings_Ocomm__semiring__1(U_3820) ),
    inference(clausify,[status(thm)],[f_751_2]) ).

fof(f_752_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_752_2,plain,
    ! [U_3829,U_3828,U_3827,U_3826,U_3825] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3826),U_3827)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3828),U_3829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3828),U_3829)))
      | ~ class_Rings_Ocomm__semiring__1(U_3825) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

cnf(f_752_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3826),U_3827)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3828),U_3829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3825),U_3828),U_3829)))
    | ~ class_Rings_Ocomm__semiring__1(U_3825) ),
    inference(clausify,[status(thm)],[f_752_2]) ).

fof(f_753_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_753_2,plain,
    ! [U_3833,U_3832,U_3831,U_3830] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),U_3831),U_3832)),U_3833) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),U_3831),U_3833)),U_3832)
      | ~ class_Rings_Ocomm__semiring__1(U_3830) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

cnf(f_753_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),U_3831),U_3832)),U_3833) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3830),U_3831),U_3833)),U_3832)
    | ~ class_Rings_Ocomm__semiring__1(U_3830) ),
    inference(clausify,[status(thm)],[f_753_2]) ).

fof(f_754_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_754_2,plain,
    ! [U_3837,U_3836,U_3835,U_3834] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3835),U_3836)),U_3837) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3836),U_3837))
      | ~ class_Rings_Ocomm__semiring__1(U_3834) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

cnf(f_754_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3835),U_3836)),U_3837) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3834),U_3836),U_3837))
    | ~ class_Rings_Ocomm__semiring__1(U_3834) ),
    inference(clausify,[status(thm)],[f_754_2]) ).

fof(f_755_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_755_2,plain,
    ! [U_3841,U_3840,U_3839,U_3838] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3840),U_3841)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3839),U_3840)),U_3841)
      | ~ class_Rings_Ocomm__semiring__1(U_3838) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

cnf(f_755_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3840),U_3841)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3838),U_3839),U_3840)),U_3841)
    | ~ class_Rings_Ocomm__semiring__1(U_3838) ),
    inference(clausify,[status(thm)],[f_755_2]) ).

fof(f_756_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_756_2,plain,
    ! [U_3845,U_3844,U_3843,U_3842] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3844),U_3845)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3843),U_3845))
      | ~ class_Rings_Ocomm__semiring__1(U_3842) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

cnf(f_756_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3844),U_3845)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3842),U_3843),U_3845))
    | ~ class_Rings_Ocomm__semiring__1(U_3842) ),
    inference(clausify,[status(thm)],[f_756_2]) ).

fof(f_757_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_757_2,plain,
    ! [U_3848,U_3847,U_3846] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3846),U_3847),U_3848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3846),U_3848),U_3847)
      | ~ class_Rings_Ocomm__semiring__1(U_3846) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

cnf(f_757_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3846),U_3847),U_3848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3846),U_3848),U_3847)
    | ~ class_Rings_Ocomm__semiring__1(U_3846) ),
    inference(clausify,[status(thm)],[f_757_2]) ).

fof(f_758_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).

fof(f_758_2,plain,
    ! [U_3851,U_3850,U_3849] :
      ( hBOOL(hAPP(hAPP(c_member(U_3849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3849),U_3850),U_3851)),c_Int_Oring__1__class_OInts(U_3849)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3851),c_Int_Oring__1__class_OInts(U_3849)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3850),c_Int_Oring__1__class_OInts(U_3849)))
      | ~ class_Rings_Oring__1(U_3849) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

cnf(f_758_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3849),U_3850),U_3851)),c_Int_Oring__1__class_OInts(U_3849)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3851),c_Int_Oring__1__class_OInts(U_3849)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3850),c_Int_Oring__1__class_OInts(U_3849)))
    | ~ class_Rings_Oring__1(U_3849) ),
    inference(clausify,[status(thm)],[f_758_2]) ).

fof(f_759_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_759_2,plain,
    ! [U_3854,U_3853,U_3852] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_3852,U_3853,U_3854)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_3852,hAPP(c_Nat_OSuc,U_3853),U_3854) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

cnf(f_759_3,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_3852,U_3853,U_3854)
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_3852,hAPP(c_Nat_OSuc,U_3853),U_3854) ),
    inference(clausify,[status(thm)],[f_759_2]) ).

fof(f_760_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_760_2,plain,
    ! [U_3857,U_3856,U_3855] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3855),U_3857),U_3856))
      | U_3856 = U_3857
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3855),U_3856),U_3857))
      | ~ class_Orderings_Olinorder(U_3855) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

cnf(f_760_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3855),U_3857),U_3856))
    | U_3856 = U_3857
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3855),U_3856),U_3857))
    | ~ class_Orderings_Olinorder(U_3855) ),
    inference(clausify,[status(thm)],[f_760_2]) ).

fof(f_761_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_761_2,plain,
    ! [U_3860,U_3859,U_3858] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3858),U_3860),U_3859))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3858),U_3859),U_3860))
      | ~ class_Orderings_Opreorder(U_3858) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

cnf(f_761_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3858),U_3860),U_3859))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3858),U_3859),U_3860))
    | ~ class_Orderings_Opreorder(U_3858) ),
    inference(clausify,[status(thm)],[f_761_2]) ).

fof(f_762_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_762_2,plain,
    ! [U_3864,U_3863,U_3862,U_3861] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3864),U_3863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3864),U_3862))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3862),U_3863))
      | ~ class_Orderings_Oorder(U_3861) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

cnf(f_762_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3864),U_3863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3864),U_3862))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3861),U_3862),U_3863))
    | ~ class_Orderings_Oorder(U_3861) ),
    inference(clausify,[status(thm)],[f_762_2]) ).

fof(f_763_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_763_2,plain,
    ! [U_3868,U_3867,U_3866,U_3865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3866),U_3868))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3867),U_3868))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3866),U_3867))
      | ~ class_Orderings_Opreorder(U_3865) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

cnf(f_763_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3866),U_3868))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3867),U_3868))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3865),U_3866),U_3867))
    | ~ class_Orderings_Opreorder(U_3865) ),
    inference(clausify,[status(thm)],[f_763_2]) ).

fof(f_764_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_764_2,plain,
    ! [U_3872,U_3871,U_3870,U_3869] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3869),U_3872),U_3871))
      | U_3870 != U_3872
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3869),U_3870),U_3871))
      | ~ class_Orderings_Oorder(U_3869) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

cnf(f_764_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3869),U_3872),U_3871))
    | U_3870 != U_3872
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3869),U_3870),U_3871))
    | ~ class_Orderings_Oorder(U_3869) ),
    inference(clausify,[status(thm)],[f_764_2]) ).

fof(f_765_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_765_2,plain,
    ! [U_3876,U_3875,U_3874,U_3873] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3873),U_3874),U_3876))
      | U_3875 != U_3876
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3873),U_3874),U_3875))
      | ~ class_Orderings_Oord(U_3873) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

cnf(f_765_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3873),U_3874),U_3876))
    | U_3875 != U_3876
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3873),U_3874),U_3875))
    | ~ class_Orderings_Oord(U_3873) ),
    inference(clausify,[status(thm)],[f_765_2]) ).

fof(f_766_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_766_2,plain,
    ! [U_3880,U_3879,U_3878,U_3877] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3877),U_3880),U_3878))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3877),U_3880),U_3879))
      | U_3878 != U_3879
      | ~ class_Orderings_Oorder(U_3877) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

cnf(f_766_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3877),U_3880),U_3878))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3877),U_3880),U_3879))
    | U_3878 != U_3879
    | ~ class_Orderings_Oorder(U_3877) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

fof(f_767_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_767_2,plain,
    ! [U_3884,U_3883,U_3882,U_3881] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3881),U_3882),U_3884))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3881),U_3883),U_3884))
      | U_3882 != U_3883
      | ~ class_Orderings_Oord(U_3881) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

cnf(f_767_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3881),U_3882),U_3884))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3881),U_3883),U_3884))
    | U_3882 != U_3883
    | ~ class_Orderings_Oord(U_3881) ),
    inference(clausify,[status(thm)],[f_767_2]) ).

fof(f_768_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_768_2,plain,
    ! [U_3887,U_3886,U_3885] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3885),U_3887),U_3886))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3885),U_3886),U_3887))
      | ~ class_Orderings_Oorder(U_3885) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

cnf(f_768_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3885),U_3887),U_3886))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3885),U_3886),U_3887))
    | ~ class_Orderings_Oorder(U_3885) ),
    inference(clausify,[status(thm)],[f_768_2]) ).

fof(f_769_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_769_2,plain,
    ! [U_3890,U_3889,U_3888] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3888),U_3890),U_3889))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3888),U_3889),U_3890))
      | ~ class_Orderings_Opreorder(U_3888) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

cnf(f_769_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3888),U_3890),U_3889))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3888),U_3889),U_3890))
    | ~ class_Orderings_Opreorder(U_3888) ),
    inference(clausify,[status(thm)],[f_769_2]) ).

fof(f_770_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_770_2,plain,
    ! [U_3893,U_3892,U_3891] :
      ( U_3893 != U_3892
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3891),U_3892),U_3893))
      | ~ class_Orderings_Oorder(U_3891) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

cnf(f_770_3,plain,
    ( U_3893 != U_3892
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3891),U_3892),U_3893))
    | ~ class_Orderings_Oorder(U_3891) ),
    inference(clausify,[status(thm)],[f_770_2]) ).

fof(f_771_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_771_2,plain,
    ! [U_3896,U_3895,U_3894] :
      ( U_3895 != U_3896
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),U_3895),U_3896))
      | ~ class_Orderings_Oorder(U_3894) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

cnf(f_771_3,plain,
    ( U_3895 != U_3896
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3894),U_3895),U_3896))
    | ~ class_Orderings_Oorder(U_3894) ),
    inference(clausify,[status(thm)],[f_771_2]) ).

fof(f_772_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_772_2,plain,
    ! [U_3899,U_3898,U_3897] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3897),U_3899),U_3898))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3897),U_3898),U_3899))
      | ~ class_Orderings_Opreorder(U_3897) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

cnf(f_772_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3897),U_3899),U_3898))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3897),U_3898),U_3899))
    | ~ class_Orderings_Opreorder(U_3897) ),
    inference(clausify,[status(thm)],[f_772_2]) ).

fof(f_773_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_773_2,plain,
    ! [U_3902,U_3901,U_3900] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3900),U_3902),U_3901))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3900),U_3901),U_3902))
      | ~ class_Orderings_Opreorder(U_3900) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

cnf(f_773_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3900),U_3902),U_3901))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3900),U_3901),U_3902))
    | ~ class_Orderings_Opreorder(U_3900) ),
    inference(clausify,[status(thm)],[f_773_2]) ).

fof(f_774_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_774_2,plain,
    ! [U_3905,U_3904,U_3903] :
      ( U_3904 != U_3905
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3903),U_3904),U_3905))
      | ~ class_Orderings_Oorder(U_3903) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

cnf(f_774_3,plain,
    ( U_3904 != U_3905
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3903),U_3904),U_3905))
    | ~ class_Orderings_Oorder(U_3903) ),
    inference(clausify,[status(thm)],[f_774_2]) ).

fof(f_775_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_775_2,plain,
    ! [U_3908,U_3907,U_3906] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3906),U_3908),U_3907))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3906),U_3907),U_3908))
      | U_3907 = U_3908
      | ~ class_Orderings_Olinorder(U_3906) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

cnf(f_775_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3906),U_3908),U_3907))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3906),U_3907),U_3908))
    | U_3907 = U_3908
    | ~ class_Orderings_Olinorder(U_3906) ),
    inference(clausify,[status(thm)],[f_775_2]) ).

fof(f_776_1,plain,
    ! [V_x_2,V_y_2,T_a] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(f_776_2,plain,
    ! [U_3911,U_3910,U_3909] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3911),U_3910))
          | U_3911 != U_3910 )
        & ( U_3911 = U_3910
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3911),U_3910)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3910),U_3911))
      | ~ class_Orderings_Olinorder(U_3909) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

cnf(f_776_3,plain,
    ( U_3911 = U_3910
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3911),U_3910))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3910),U_3911))
    | ~ class_Orderings_Olinorder(U_3909) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

cnf(f_776_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3911),U_3910))
    | U_3911 != U_3910
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3909),U_3910),U_3911))
    | ~ class_Orderings_Olinorder(U_3909) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

fof(f_777_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_777_2,plain,
    ! [U_3914,U_3913,U_3912] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),U_3914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),U_3914)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3912) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

cnf(f_777_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),U_3914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3912),U_3913),U_3914)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3912) ),
    inference(clausify,[status(thm)],[f_777_2]) ).

fof(f_778_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_778_2,plain,
    ! [U_3917,U_3916,U_3915] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3915),U_3917),U_3916))
      | U_3916 = U_3917
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3915),U_3916),U_3917))
      | ~ class_Orderings_Olinorder(U_3915) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

cnf(f_778_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3915),U_3917),U_3916))
    | U_3916 = U_3917
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3915),U_3916),U_3917))
    | ~ class_Orderings_Olinorder(U_3915) ),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_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_779_2,plain,
    ! [U_3919,U_3918] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3919) = U_3919
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3918) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

cnf(f_779_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3919) = U_3919
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3918) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

fof(f_780_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_780_2,plain,
    ! [U_3921,U_3920] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3920),U_3921),U_3921) = U_3921
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3920) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

cnf(f_780_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3920),U_3921),U_3921) = U_3921
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3920) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

fof(f_781_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(f_781_2,plain,
    ! [U_3924,U_3923,U_3922] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3923),U_3924))
          | ( U_3923 != U_3924
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3924),U_3923)) ) )
        & ( U_3923 = U_3924
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3924),U_3923))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3923),U_3924)) ) )
      | ~ class_Orderings_Olinorder(U_3922) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

cnf(f_781_3,plain,
    ( U_3923 = U_3924
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3924),U_3923))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3923),U_3924))
    | ~ class_Orderings_Olinorder(U_3922) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3924),U_3923))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3923),U_3924))
    | ~ class_Orderings_Olinorder(U_3922) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

cnf(f_781_5,plain,
    ( U_3923 != U_3924
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3922),U_3923),U_3924))
    | ~ class_Orderings_Olinorder(U_3922) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

fof(f_782_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( V_x_2 != V_y_2
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | V_x_2 = V_y_2 ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).

fof(f_782_2,plain,
    ! [U_3927,U_3926,U_3925] :
      ( ( ( U_3926 != U_3927
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3927),U_3926))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3926),U_3927)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3927),U_3926))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3926),U_3927))
          | U_3926 = U_3927 ) )
      | ~ class_Orderings_Olinorder(U_3925) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

cnf(f_782_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3927),U_3926))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3926),U_3927))
    | U_3926 = U_3927
    | ~ class_Orderings_Olinorder(U_3925) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3926),U_3927))
    | U_3926 != U_3927
    | ~ class_Orderings_Olinorder(U_3925) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

cnf(f_782_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3925),U_3927),U_3926))
    | U_3926 != U_3927
    | ~ class_Orderings_Olinorder(U_3925) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

fof(f_783_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_783_2,plain,
    ! [U_3929,U_3928] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3928),U_3929),U_3929))
      | ~ class_Orderings_Opreorder(U_3928) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

cnf(f_783_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3928),U_3929),U_3929))
    | ~ class_Orderings_Opreorder(U_3928) ),
    inference(clausify,[status(thm)],[f_783_2]) ).

fof(f_784_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_784_2,plain,
    ! [U_3933,U_3932,U_3931,U_3930] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3931),U_3932)),U_3933) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3932),U_3933))
      | ~ class_Groups_Oab__semigroup__mult(U_3930) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

cnf(f_784_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3931),U_3932)),U_3933) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3930),U_3932),U_3933))
    | ~ class_Groups_Oab__semigroup__mult(U_3930) ),
    inference(clausify,[status(thm)],[f_784_2]) ).

fof(f_785_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_785_2,plain,
    ! [U_3935,U_3934] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3934)),U_3935) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3934),U_3935)),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

cnf(f_785_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3934)),U_3935) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3934),U_3935)),
    inference(clausify,[status(thm)],[f_785_2]) ).

fof(f_786_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_786_2,plain,
    ! [U_3937,U_3936] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3936),hAPP(c_Nat_OSuc,U_3937)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3936),U_3937)),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

cnf(f_786_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3936),hAPP(c_Nat_OSuc,U_3937)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3936),U_3937)),
    inference(clausify,[status(thm)],[f_786_2]) ).

fof(f_787_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_787_2,plain,
    ! [U_3941,U_3940] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3940),U_3941))
        | ! [U_3939] : U_3941 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),U_3939)) )
      & ( ? [U_3938] : U_3941 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),U_3938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3940),U_3941)) ) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ( ! [U_3945,U_3943] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3943),U_3945))
        | ! [U_3939] : U_3945 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3943),U_3939)) )
    & ! [U_3944,U_3942] :
        ( ? [U_3938] : U_3944 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3942),U_3938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3942),U_3944)) ) ),
    inference(miniscope,[status(thm)],[f_787_2]) ).

fof(f_787_4,plain,
    ( ! [U_3945,U_3943] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3943),U_3945))
        | ! [U_3939] : U_3945 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3943),U_3939)) )
    & ! [U_3944,U_3942] :
        ( U_3944 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3942),sK79(U_3944,U_3942)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3942),U_3944)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_3938,sK79(U_3944,U_3942))],[f_787_3]) ).

cnf(f_787_5,plain,
    ( U_3944 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3942),sK79(U_3944,U_3942)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3942),U_3944)) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

cnf(f_787_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3943),U_3945))
    | U_3945 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3943),U_3939)) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

fof(f_788_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_788_2,plain,
    ! [U_3947,U_3946] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3946),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3947),U_3946)))),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

cnf(f_788_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3946),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3947),U_3946)))),
    inference(clausify,[status(thm)],[f_788_2]) ).

fof(f_789_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_789_2,plain,
    ! [U_3949,U_3948] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3948),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3948),U_3949)))),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

cnf(f_789_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3948),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3948),U_3949)))),
    inference(clausify,[status(thm)],[f_789_2]) ).

fof(f_790_1,plain,
    ! [V_P_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).

fof(f_790_2,plain,
    ! [U_3952,U_3951,U_3950] :
      ( hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
      | ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3950)) )
      | ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
        & U_3950 = U_3951 )
      | ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3950),U_3951)) ) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

cnf(f_790_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | U_3950 = U_3951
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3950),U_3951)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | U_3950 = U_3951
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3950),U_3951)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3950),U_3951)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3950),U_3951)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | U_3950 = U_3951
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | U_3950 = U_3951
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

cnf(f_790_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950))
    | ~ hBOOL(hAPP(hAPP(U_3952,U_3951),U_3950)) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

fof(f_791_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_791_2,plain,
    ! [U_3954,U_3953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3953)),hAPP(c_Nat_OSuc,U_3954))) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

cnf(f_791_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3953)),hAPP(c_Nat_OSuc,U_3954))) ),
    inference(clausify,[status(thm)],[f_791_2]) ).

fof(f_792_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_792_2,plain,
    ! [U_3956,U_3955] :
      ( U_3955 = U_3956
      | hAPP(c_Nat_OSuc,U_3955) != hAPP(c_Nat_OSuc,U_3956) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

cnf(f_792_3,plain,
    ( U_3955 = U_3956
    | hAPP(c_Nat_OSuc,U_3955) != hAPP(c_Nat_OSuc,U_3956) ),
    inference(clausify,[status(thm)],[f_792_2]) ).

fof(f_793_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_793_2,plain,
    ! [U_3958,U_3957] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3957),U_3958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3957)),U_3958)) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

cnf(f_793_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3957),U_3958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3957)),U_3958)) ),
    inference(clausify,[status(thm)],[f_793_2]) ).

fof(f_794_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_794_2,plain,
    ! [U_3960,U_3959] :
      ( U_3959 = U_3960
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3959),U_3960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3959),hAPP(c_Nat_OSuc,U_3960))) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

cnf(f_794_3,plain,
    ( U_3959 = U_3960
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3959),U_3960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3959),hAPP(c_Nat_OSuc,U_3960))) ),
    inference(clausify,[status(thm)],[f_794_2]) ).

fof(f_795_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_795_2,plain,
    ! [U_3963,U_3962,U_3961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3961)),U_3963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3961),U_3962)) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

cnf(f_795_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3961)),U_3963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3961),U_3962)) ),
    inference(clausify,[status(thm)],[f_795_2]) ).

fof(f_796_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_796_2,plain,
    ! [U_3965,U_3964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3964)),U_3965))
      | hAPP(c_Nat_OSuc,U_3964) = U_3965
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3964),U_3965)) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

cnf(f_796_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3964)),U_3965))
    | hAPP(c_Nat_OSuc,U_3964) = U_3965
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3964),U_3965)) ),
    inference(clausify,[status(thm)],[f_796_2]) ).

fof(f_797_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_797_2,plain,
    ! [U_3967,U_3966] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3966),hAPP(c_Nat_OSuc,U_3967)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3966),U_3967)) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

cnf(f_797_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3966),hAPP(c_Nat_OSuc,U_3967)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3966),U_3967)) ),
    inference(clausify,[status(thm)],[f_797_2]) ).

fof(f_798_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_798_2,plain,
    ! [U_3969,U_3968] :
      ( U_3968 != U_3969
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3968),U_3969)) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

cnf(f_798_3,plain,
    ( U_3968 != U_3969
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3968),U_3969)) ),
    inference(clausify,[status(thm)],[f_798_2]) ).

fof(f_799_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_799_2,plain,
    ! [U_3971,U_3970] :
      ( U_3971 != U_3970
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3970),U_3971)) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

cnf(f_799_3,plain,
    ( U_3971 != U_3970
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3970),U_3971)) ),
    inference(clausify,[status(thm)],[f_799_2]) ).

fof(f_800_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_800_2,plain,
    ! [U_3972] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3972),U_3972)),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

cnf(f_800_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3972),U_3972)),
    inference(clausify,[status(thm)],[f_800_2]) ).

fof(f_801_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_801_2,plain,
    ! [U_3974,U_3973] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3974),U_3973))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3973),U_3974))
      | U_3973 = U_3974 ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

cnf(f_801_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3974),U_3973))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3973),U_3974))
    | U_3973 = U_3974 ),
    inference(clausify,[status(thm)],[f_801_2]) ).

fof(f_802_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_802_2,plain,
    ! [U_3976,U_3975] :
      ( U_3976 = U_3975
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),hAPP(c_Nat_OSuc,U_3976)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),U_3976)) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

cnf(f_802_3,plain,
    ( U_3976 = U_3975
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),hAPP(c_Nat_OSuc,U_3976)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),U_3976)) ),
    inference(clausify,[status(thm)],[f_802_2]) ).

fof(f_803_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_803_2,plain,
    ! [U_3978,U_3977] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),hAPP(c_Nat_OSuc,U_3978)))
          | U_3977 != U_3978 )
        & ( U_3977 = U_3978
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),hAPP(c_Nat_OSuc,U_3978))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),U_3978)) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

cnf(f_803_3,plain,
    ( U_3977 = U_3978
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),hAPP(c_Nat_OSuc,U_3978)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),U_3978)) ),
    inference(clausify,[status(thm)],[f_803_2]) ).

cnf(f_803_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),hAPP(c_Nat_OSuc,U_3978)))
    | U_3977 != U_3978
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3977),U_3978)) ),
    inference(clausify,[status(thm)],[f_803_2]) ).

fof(f_804_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_804_2,plain,
    ! [U_3981,U_3980,U_3979] :
      ( ( 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_3979)),U_3980)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3979)),U_3981)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3980),U_3981)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3980),U_3981))
        | ~ 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_3979)),U_3980)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3979)),U_3981))) ) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ( ! [U_3987,U_3985] :
        ( ! [U_3983] : 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_3983)),U_3985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3983)),U_3987)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3985),U_3987)) )
    & ! [U_3986,U_3984] :
        ( ! [U_3982] : ~ 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_3982)),U_3984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3982)),U_3986)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3984),U_3986)) ) ),
    inference(miniscope,[status(thm)],[f_804_2]) ).

cnf(f_804_4,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_3982)),U_3984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3982)),U_3986)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3984),U_3986)) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_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_3983)),U_3985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3983)),U_3987)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3985),U_3987)) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_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_805_2,plain,
    ! [U_3990,U_3989,U_3988] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3988)),U_3989) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3988)),U_3990)
        | U_3989 != U_3990 )
      & ( U_3989 = U_3990
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3988)),U_3989) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3988)),U_3990) ) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ( ! [U_3996,U_3994] :
        ( ! [U_3992] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3992)),U_3994) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3992)),U_3996)
        | U_3994 != U_3996 )
    & ! [U_3995,U_3993] :
        ( ! [U_3991] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3991)),U_3993) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3991)),U_3995)
        | U_3993 = U_3995 ) ),
    inference(miniscope,[status(thm)],[f_805_2]) ).

cnf(f_805_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3991)),U_3993) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3991)),U_3995)
    | U_3993 = U_3995 ),
    inference(clausify,[status(thm)],[f_805_3]) ).

cnf(f_805_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3992)),U_3994) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3992)),U_3996)
    | U_3994 != U_3996 ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_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_806_2,plain,
    ! [U_3998,U_3997] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3997)),hAPP(c_Nat_OSuc,U_3998)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3997),U_3998)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3997),U_3998))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3997)),hAPP(c_Nat_OSuc,U_3998))) ) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ( ! [U_4002,U_4000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4000)),hAPP(c_Nat_OSuc,U_4002)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4000),U_4002)) )
    & ! [U_4001,U_3999] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3999),U_4001))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3999)),hAPP(c_Nat_OSuc,U_4001))) ) ),
    inference(miniscope,[status(thm)],[f_806_2]) ).

cnf(f_806_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3999),U_4001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3999)),hAPP(c_Nat_OSuc,U_4001))) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4000)),hAPP(c_Nat_OSuc,U_4002)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4000),U_4002)) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_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_807_2,plain,
    ! [U_4004,U_4003] :
      ( ( hAPP(c_Nat_OSuc,U_4003) = hAPP(c_Nat_OSuc,U_4004)
        | U_4003 != U_4004 )
      & ( U_4003 = U_4004
        | hAPP(c_Nat_OSuc,U_4003) != hAPP(c_Nat_OSuc,U_4004) ) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ( ! [U_4008,U_4006] :
        ( hAPP(c_Nat_OSuc,U_4006) = hAPP(c_Nat_OSuc,U_4008)
        | U_4006 != U_4008 )
    & ! [U_4007,U_4005] :
        ( U_4005 = U_4007
        | hAPP(c_Nat_OSuc,U_4005) != hAPP(c_Nat_OSuc,U_4007) ) ),
    inference(miniscope,[status(thm)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( U_4005 = U_4007
    | hAPP(c_Nat_OSuc,U_4005) != hAPP(c_Nat_OSuc,U_4007) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

cnf(f_807_5,plain,
    ( hAPP(c_Nat_OSuc,U_4006) = hAPP(c_Nat_OSuc,U_4008)
    | U_4006 != U_4008 ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_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_808_2,plain,
    ! [U_4010,U_4009] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4009),hAPP(c_Nat_OSuc,U_4010)))
        | ( U_4009 != U_4010
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4009),U_4010)) ) )
      & ( U_4009 = U_4010
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4009),U_4010))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4009),hAPP(c_Nat_OSuc,U_4010))) ) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ( ! [U_4014,U_4012] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4012),hAPP(c_Nat_OSuc,U_4014)))
        | ( U_4012 != U_4014
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4012),U_4014)) ) )
    & ! [U_4013,U_4011] :
        ( U_4011 = U_4013
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4011),U_4013))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4011),hAPP(c_Nat_OSuc,U_4013))) ) ),
    inference(miniscope,[status(thm)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( U_4011 = U_4013
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4011),U_4013))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4011),hAPP(c_Nat_OSuc,U_4013))) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

cnf(f_808_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4012),U_4014))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4012),hAPP(c_Nat_OSuc,U_4014))) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

cnf(f_808_6,plain,
    ( U_4012 != U_4014
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4012),hAPP(c_Nat_OSuc,U_4014))) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_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_809_2,plain,
    ! [U_4016,U_4015] :
      ( ( U_4015 != U_4016
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4016),U_4015))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4015),U_4016)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4016),U_4015))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4015),U_4016))
        | U_4015 = U_4016 ) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ( ! [U_4020,U_4018] :
        ( U_4018 != U_4020
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4020),U_4018))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4018),U_4020)) ) )
    & ! [U_4019,U_4017] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4019),U_4017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4017),U_4019))
        | U_4017 = U_4019 ) ),
    inference(miniscope,[status(thm)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4019),U_4017))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4017),U_4019))
    | U_4017 = U_4019 ),
    inference(clausify,[status(thm)],[f_809_3]) ).

cnf(f_809_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4018),U_4020))
    | U_4018 != U_4020 ),
    inference(clausify,[status(thm)],[f_809_3]) ).

cnf(f_809_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4020),U_4018))
    | U_4018 != U_4020 ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_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_810_2,plain,
    ! [U_4022,U_4021] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4021),U_4022))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4022),hAPP(c_Nat_OSuc,U_4021))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4022),hAPP(c_Nat_OSuc,U_4021)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4021),U_4022)) ) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ( ! [U_4026,U_4024] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4024),U_4026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4026),hAPP(c_Nat_OSuc,U_4024))) )
    & ! [U_4025,U_4023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4025),hAPP(c_Nat_OSuc,U_4023)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4023),U_4025)) ) ),
    inference(miniscope,[status(thm)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4025),hAPP(c_Nat_OSuc,U_4023)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4023),U_4025)) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

cnf(f_810_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4024),U_4026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4026),hAPP(c_Nat_OSuc,U_4024))) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_811_2,plain,
    ! [U_4027] : hAPP(c_Nat_OSuc,U_4027) != U_4027,
    inference(variable_rename,[status(thm)],[f_811_1]) ).

cnf(f_811_3,plain,
    hAPP(c_Nat_OSuc,U_4027) != U_4027,
    inference(clausify,[status(thm)],[f_811_2]) ).

fof(f_812_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_812_2,plain,
    ! [U_4028] : U_4028 != hAPP(c_Nat_OSuc,U_4028),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

cnf(f_812_3,plain,
    U_4028 != hAPP(c_Nat_OSuc,U_4028),
    inference(clausify,[status(thm)],[f_812_2]) ).

fof(f_813_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_813_2,plain,
    ! [U_4029] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4029),U_4029)),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

cnf(f_813_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4029),U_4029)),
    inference(clausify,[status(thm)],[f_813_2]) ).

fof(f_814_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_814_2,plain,
    ! [U_4031,U_4030] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4030),U_4031)),hAPP(c_Nat_OSuc,U_4030))),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

cnf(f_814_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4030),U_4031)),hAPP(c_Nat_OSuc,U_4030))),
    inference(clausify,[status(thm)],[f_814_2]) ).

fof(f_815_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_815_2,plain,
    ! [U_4033,U_4032] :
      ( 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_4033),U_4032)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4033))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4032)) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

cnf(f_815_3,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_4033),U_4032)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4032)) ),
    inference(clausify,[status(thm)],[f_815_2]) ).

fof(f_816_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_816_2,plain,
    ! [U_4035,U_4034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4034),U_4035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4034)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

cnf(f_816_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4034),U_4035)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4035))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4034)) ),
    inference(clausify,[status(thm)],[f_816_2]) ).

fof(f_817_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_817_2,plain,
    ! [U_4037,U_4036] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4037),U_4036)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4037))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4036)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

cnf(f_817_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4037),U_4036)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4037))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4036)) ),
    inference(clausify,[status(thm)],[f_817_2]) ).

fof(f_818_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_818_2,plain,
    ! [U_4040,U_4039,U_4038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4039)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4040))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4038),U_4039)) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

cnf(f_818_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4039)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4040))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4038),U_4039)) ),
    inference(clausify,[status(thm)],[f_818_2]) ).

fof(f_819_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_819_2,plain,
    ! [U_4043,U_4042,U_4041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4041),U_4043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4042),U_4043)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4041),U_4042)) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

cnf(f_819_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4041),U_4043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4042),U_4043)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4041),U_4042)) ),
    inference(clausify,[status(thm)],[f_819_2]) ).

fof(f_820_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_820_2,plain,
    ! [U_4046,U_4045,U_4044] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4044),U_4045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4046),U_4045)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4044),U_4046))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4045)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4044),U_4046))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4045)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4044),U_4045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4046),U_4045))) ) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ( ! [U_4052,U_4050,U_4048] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4048),U_4050)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4052),U_4050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4048),U_4052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4050)) )
    & ! [U_4051,U_4049,U_4047] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4047),U_4051))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4049)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4047),U_4049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4051),U_4049))) ) ),
    inference(miniscope,[status(thm)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4049))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4047),U_4049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4051),U_4049))) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

cnf(f_820_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4047),U_4051))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4047),U_4049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4051),U_4049))) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

cnf(f_820_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4048),U_4050)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4052),U_4050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4048),U_4052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4050)) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_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_821_2,plain,
    ! [U_4055,U_4054,U_4053] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4054)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4055)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4054),U_4055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4053)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4054),U_4055))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4053)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4054)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4055))) ) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ( ! [U_4061,U_4059,U_4057] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4057),U_4059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4057),U_4061)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4059),U_4061))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4057)) )
    & ! [U_4060,U_4058,U_4056] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4058),U_4060))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4056)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4060))) ) ),
    inference(miniscope,[status(thm)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4056))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4060))) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

cnf(f_821_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4058),U_4060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4056),U_4060))) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

cnf(f_821_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4057),U_4059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4057),U_4061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4059),U_4061))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4057)) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_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_822_2,plain,
    ! [U_4063,U_4062] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4062),U_4063) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4063 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4062 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_4063 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4062 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4062),U_4063) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ( ! [U_4067,U_4065] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4065),U_4067) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4067 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4065 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_4066,U_4064] :
        ( ( U_4066 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4064 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4064),U_4066) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( U_4064 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4064),U_4066) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

cnf(f_822_5,plain,
    ( U_4066 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4064),U_4066) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

cnf(f_822_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4065),U_4067) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4067 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4065 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_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_823_2,plain,
    ! [U_4071,U_4070] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4070),hAPP(c_Nat_OSuc,U_4071)))
        | ( ! [U_4069] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4069),U_4071))
              | U_4070 != hAPP(c_Nat_OSuc,U_4069) )
          & U_4070 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_4068] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4068),U_4071))
            & U_4070 = hAPP(c_Nat_OSuc,U_4068) )
        | U_4070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4070),hAPP(c_Nat_OSuc,U_4071))) ) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ( ! [U_4075,U_4073] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4073),hAPP(c_Nat_OSuc,U_4075)))
        | ( ! [U_4069] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4069),U_4075))
              | U_4073 != hAPP(c_Nat_OSuc,U_4069) )
          & U_4073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4074,U_4072] :
        ( ? [U_4068] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4068),U_4074))
            & U_4072 = hAPP(c_Nat_OSuc,U_4068) )
        | U_4072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4072),hAPP(c_Nat_OSuc,U_4074))) ) ),
    inference(miniscope,[status(thm)],[f_823_2]) ).

fof(f_823_4,plain,
    ( ! [U_4075,U_4073] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4073),hAPP(c_Nat_OSuc,U_4075)))
        | ( ! [U_4069] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4069),U_4075))
              | U_4073 != hAPP(c_Nat_OSuc,U_4069) )
          & U_4073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4074,U_4072] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK80(U_4074,U_4072)),U_4074))
          & U_4072 = hAPP(c_Nat_OSuc,sK80(U_4074,U_4072)) )
        | U_4072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4072),hAPP(c_Nat_OSuc,U_4074))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_4068,sK80(U_4074,U_4072))],[f_823_3]) ).

cnf(f_823_5,plain,
    ( U_4072 = hAPP(c_Nat_OSuc,sK80(U_4074,U_4072))
    | U_4072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4072),hAPP(c_Nat_OSuc,U_4074))) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK80(U_4074,U_4072)),U_4074))
    | U_4072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4072),hAPP(c_Nat_OSuc,U_4074))) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_7,plain,
    ( U_4073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4073),hAPP(c_Nat_OSuc,U_4075))) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4069),U_4075))
    | U_4073 != hAPP(c_Nat_OSuc,U_4069)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4073),hAPP(c_Nat_OSuc,U_4075))) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

fof(f_824_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_824_2,plain,
    ! [U_4076] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4076),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_4076 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_4076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4076),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ( ! [U_4078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4078),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_4078 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4077] :
        ( U_4077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4077),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_824_2]) ).

cnf(f_824_4,plain,
    ( U_4077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4077),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_824_3]) ).

cnf(f_824_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4078),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_4078 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_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_825_2,plain,
    ! [U_4080,U_4079] :
      ( ( 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_4079),U_4080)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4080))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4079)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4080))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4079)) )
        | ~ 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_4079),U_4080))) ) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ( ! [U_4084,U_4082] :
        ( 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_4082),U_4084)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4084))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4082)) )
    & ! [U_4083,U_4081] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4083))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4081)) )
        | ~ 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_4081),U_4083))) ) ),
    inference(miniscope,[status(thm)],[f_825_2]) ).

cnf(f_825_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4081))
    | ~ 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_4081),U_4083))) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

cnf(f_825_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4083))
    | ~ 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_4081),U_4083))) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

cnf(f_825_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_4082),U_4084)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4082)) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_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_826_2,plain,
    ! [U_4087] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4087))
        | ! [U_4086] : U_4087 != hAPP(c_Nat_OSuc,U_4086) )
      & ( ? [U_4085] : U_4087 = hAPP(c_Nat_OSuc,U_4085)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4087)) ) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ( ! [U_4089] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4089))
        | ! [U_4086] : U_4089 != hAPP(c_Nat_OSuc,U_4086) )
    & ! [U_4088] :
        ( ? [U_4085] : U_4088 = hAPP(c_Nat_OSuc,U_4085)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4088)) ) ),
    inference(miniscope,[status(thm)],[f_826_2]) ).

fof(f_826_4,plain,
    ( ! [U_4089] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4089))
        | ! [U_4086] : U_4089 != hAPP(c_Nat_OSuc,U_4086) )
    & ! [U_4088] :
        ( U_4088 = hAPP(c_Nat_OSuc,sK81(U_4088))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4088)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_4085,sK81(U_4088))],[f_826_3]) ).

cnf(f_826_5,plain,
    ( U_4088 = hAPP(c_Nat_OSuc,sK81(U_4088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4088)) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

cnf(f_826_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4089))
    | U_4089 != hAPP(c_Nat_OSuc,U_4086) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

fof(f_827_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).

fof(f_827_2,plain,
    ! [U_4095,U_4094,U_4093,U_4092,U_4091,U_4090] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4091),U_4092)),U_4093)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4094),U_4092)),U_4095)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4090),U_4094),U_4091)),U_4092)),U_4095))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4090),U_4094),U_4091)),U_4092)),U_4095)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4091),U_4092)),U_4093)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4094),U_4092)),U_4095))) ) )
      | ~ class_Rings_Oordered__ring(U_4090) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

cnf(f_827_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4090),U_4094),U_4091)),U_4092)),U_4095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4091),U_4092)),U_4093)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4094),U_4092)),U_4095)))
    | ~ class_Rings_Oordered__ring(U_4090) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

cnf(f_827_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4091),U_4092)),U_4093)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4094),U_4092)),U_4095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4090),U_4094),U_4091)),U_4092)),U_4095)))
    | ~ class_Rings_Oordered__ring(U_4090) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

fof(f_828_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
          | ~ 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
        & ( 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
          | ~ 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).

fof(f_828_2,plain,
    ! [U_4101,U_4100,U_4099,U_4098,U_4097,U_4096] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4097),U_4098)),U_4099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4100),U_4098)),U_4101)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4096),U_4097),U_4100)),U_4098)),U_4099)),U_4101)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4096),U_4097),U_4100)),U_4098)),U_4099)),U_4101))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4097),U_4098)),U_4099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4100),U_4098)),U_4101))) ) )
      | ~ class_Rings_Oordered__ring(U_4096) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

cnf(f_828_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4096),U_4097),U_4100)),U_4098)),U_4099)),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4097),U_4098)),U_4099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4100),U_4098)),U_4101)))
    | ~ class_Rings_Oordered__ring(U_4096) ),
    inference(clausify,[status(thm)],[f_828_2]) ).

cnf(f_828_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4097),U_4098)),U_4099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),U_4100),U_4098)),U_4101)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4096),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4096),U_4097),U_4100)),U_4098)),U_4099)),U_4101))
    | ~ class_Rings_Oordered__ring(U_4096) ),
    inference(clausify,[status(thm)],[f_828_2]) ).

fof(f_829_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_829_2,plain,
    ! [U_4103,U_4102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4102),hAPP(c_Nat_OSuc,U_4103))),U_4102))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4102)) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

cnf(f_829_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4102),hAPP(c_Nat_OSuc,U_4103))),U_4102))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4102)) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

fof(f_830_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_830_2,plain,
    ! [U_4104] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4104),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4104
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4104)) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

cnf(f_830_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4104),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4104
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4104)) ),
    inference(clausify,[status(thm)],[f_830_2]) ).

fof(f_831_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_831_2,plain,
    ! [U_4106,U_4105] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4105),c_Groups_Ozero__class_Ozero(U_4105)),U_4106) = c_Groups_Ozero__class_Ozero(U_4105)
      | ~ class_Rings_Omult__zero(U_4105) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

cnf(f_831_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4105),c_Groups_Ozero__class_Ozero(U_4105)),U_4106) = c_Groups_Ozero__class_Ozero(U_4105)
    | ~ class_Rings_Omult__zero(U_4105) ),
    inference(clausify,[status(thm)],[f_831_2]) ).

fof(f_832_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_832_2,plain,
    ! [U_4108,U_4107] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4107),c_Groups_Ozero__class_Ozero(U_4107)),U_4108) = c_Groups_Ozero__class_Ozero(U_4107)
      | ~ class_Rings_Ocomm__semiring__1(U_4107) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

cnf(f_832_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4107),c_Groups_Ozero__class_Ozero(U_4107)),U_4108) = c_Groups_Ozero__class_Ozero(U_4107)
    | ~ class_Rings_Ocomm__semiring__1(U_4107) ),
    inference(clausify,[status(thm)],[f_832_2]) ).

fof(f_833_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_833_2,plain,
    ! [U_4110,U_4109] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109)) = c_Groups_Ozero__class_Ozero(U_4109)
      | ~ class_Rings_Omult__zero(U_4109) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

cnf(f_833_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109)) = c_Groups_Ozero__class_Ozero(U_4109)
    | ~ class_Rings_Omult__zero(U_4109) ),
    inference(clausify,[status(thm)],[f_833_2]) ).

fof(f_834_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_834_2,plain,
    ! [U_4112,U_4111] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4111),U_4112),c_Groups_Ozero__class_Ozero(U_4111)) = c_Groups_Ozero__class_Ozero(U_4111)
      | ~ class_Rings_Ocomm__semiring__1(U_4111) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

cnf(f_834_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4111),U_4112),c_Groups_Ozero__class_Ozero(U_4111)) = c_Groups_Ozero__class_Ozero(U_4111)
    | ~ class_Rings_Ocomm__semiring__1(U_4111) ),
    inference(clausify,[status(thm)],[f_834_2]) ).

fof(f_835_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
            & V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Oring__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).

fof(f_835_2,plain,
    ! [U_4115,U_4114,U_4113] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),U_4115) = c_Groups_Ozero__class_Ozero(U_4113)
          | ( U_4115 != c_Groups_Ozero__class_Ozero(U_4113)
            & U_4114 != c_Groups_Ozero__class_Ozero(U_4113) ) )
        & ( U_4115 = c_Groups_Ozero__class_Ozero(U_4113)
          | U_4114 = c_Groups_Ozero__class_Ozero(U_4113)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),U_4115) != c_Groups_Ozero__class_Ozero(U_4113) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_4113) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

cnf(f_835_3,plain,
    ( U_4115 = c_Groups_Ozero__class_Ozero(U_4113)
    | U_4114 = c_Groups_Ozero__class_Ozero(U_4113)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),U_4115) != c_Groups_Ozero__class_Ozero(U_4113)
    | ~ class_Rings_Oring__no__zero__divisors(U_4113) ),
    inference(clausify,[status(thm)],[f_835_2]) ).

cnf(f_835_4,plain,
    ( U_4114 != c_Groups_Ozero__class_Ozero(U_4113)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),U_4115) = c_Groups_Ozero__class_Ozero(U_4113)
    | ~ class_Rings_Oring__no__zero__divisors(U_4113) ),
    inference(clausify,[status(thm)],[f_835_2]) ).

cnf(f_835_5,plain,
    ( U_4115 != c_Groups_Ozero__class_Ozero(U_4113)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),U_4115) = c_Groups_Ozero__class_Ozero(U_4113)
    | ~ class_Rings_Oring__no__zero__divisors(U_4113) ),
    inference(clausify,[status(thm)],[f_835_2]) ).

fof(f_836_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_836_2,plain,
    ! [U_4118,U_4117,U_4116] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118) != c_Groups_Ozero__class_Ozero(U_4116)
      | U_4118 = c_Groups_Ozero__class_Ozero(U_4116)
      | U_4117 = c_Groups_Ozero__class_Ozero(U_4116)
      | ~ class_Rings_Ono__zero__divisors(U_4116) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

cnf(f_836_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118) != c_Groups_Ozero__class_Ozero(U_4116)
    | U_4118 = c_Groups_Ozero__class_Ozero(U_4116)
    | U_4117 = c_Groups_Ozero__class_Ozero(U_4116)
    | ~ class_Rings_Ono__zero__divisors(U_4116) ),
    inference(clausify,[status(thm)],[f_836_2]) ).

fof(f_837_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_837_2,plain,
    ! [U_4121,U_4120,U_4119] :
      ( U_4121 = c_Groups_Ozero__class_Ozero(U_4119)
      | U_4120 = c_Groups_Ozero__class_Ozero(U_4119)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4119),U_4120),U_4121) != c_Groups_Ozero__class_Ozero(U_4119)
      | ~ class_Rings_Ono__zero__divisors(U_4119) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

cnf(f_837_3,plain,
    ( U_4121 = c_Groups_Ozero__class_Ozero(U_4119)
    | U_4120 = c_Groups_Ozero__class_Ozero(U_4119)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4119),U_4120),U_4121) != c_Groups_Ozero__class_Ozero(U_4119)
    | ~ class_Rings_Ono__zero__divisors(U_4119) ),
    inference(clausify,[status(thm)],[f_837_2]) ).

fof(f_838_1,plain,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).

fof(f_838_2,plain,
    ! [U_4126,U_4125,U_4124,U_4123,U_4122] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4124))
          | ( U_4124 != U_4126
            & U_4123 != U_4125 ) )
        & ( U_4124 = U_4126
          | U_4123 = U_4125
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4126)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4124)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4122) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

cnf(f_838_3,plain,
    ( U_4124 = U_4126
    | U_4123 = U_4125
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4126)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4124))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4122) ),
    inference(clausify,[status(thm)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( U_4123 != U_4125
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4124))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4122) ),
    inference(clausify,[status(thm)],[f_838_2]) ).

cnf(f_838_5,plain,
    ( U_4124 != U_4126
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4125),U_4124))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4122) ),
    inference(clausify,[status(thm)],[f_838_2]) ).

fof(f_839_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_839_2,plain,
    ! [U_4131,U_4130,U_4129,U_4128,U_4127] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),U_4128),U_4129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),U_4130),U_4129)),U_4131)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),U_4128),U_4130)),U_4129)),U_4131)
      | ~ class_Rings_Osemiring(U_4127) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

cnf(f_839_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),U_4128),U_4129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),U_4130),U_4129)),U_4131)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4127),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4127),U_4128),U_4130)),U_4129)),U_4131)
    | ~ class_Rings_Osemiring(U_4127) ),
    inference(clausify,[status(thm)],[f_839_2]) ).

fof(f_840_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_840_2,plain,
    ! [U_4135,U_4134,U_4133,U_4132] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),U_4133),U_4134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),U_4135),U_4134)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4132),U_4133),U_4135)),U_4134)
      | ~ class_Rings_Ocomm__semiring__1(U_4132) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

cnf(f_840_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),U_4133),U_4134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),U_4135),U_4134)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4132),U_4133),U_4135)),U_4134)
    | ~ class_Rings_Ocomm__semiring__1(U_4132) ),
    inference(clausify,[status(thm)],[f_840_2]) ).

fof(f_841_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_841_2,plain,
    ! [U_4139,U_4138,U_4137,U_4136] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4136),U_4137),U_4138)),U_4139) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),U_4137),U_4139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),U_4138),U_4139))
      | ~ class_Rings_Ocomm__semiring__1(U_4136) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

cnf(f_841_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4136),U_4137),U_4138)),U_4139) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),U_4137),U_4139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4136),U_4138),U_4139))
    | ~ class_Rings_Ocomm__semiring__1(U_4136) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

fof(f_842_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_842_2,plain,
    ! [U_4143,U_4142,U_4141,U_4140] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4140),U_4141),U_4142)),U_4143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),U_4141),U_4143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),U_4142),U_4143))
      | ~ class_Rings_Ocomm__semiring(U_4140) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

cnf(f_842_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4140),U_4141),U_4142)),U_4143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),U_4141),U_4143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4140),U_4142),U_4143))
    | ~ class_Rings_Ocomm__semiring(U_4140) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

fof(f_843_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( ( V_c_2 != V_d_2
            & V_a_2 != V_b_2 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).

fof(f_843_2,plain,
    ! [U_4148,U_4147,U_4146,U_4145,U_4144] :
      ( ( ( ( U_4147 != U_4148
            & U_4145 != U_4146 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4148)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4147)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4148)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4147))
          | U_4147 = U_4148
          | U_4145 = U_4146 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4144) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

cnf(f_843_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4148)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4147))
    | U_4147 = U_4148
    | U_4145 = U_4146
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4144) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

cnf(f_843_4,plain,
    ( U_4145 != U_4146
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4148)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4147))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4144) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

cnf(f_843_5,plain,
    ( U_4147 != U_4148
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4148)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4146),U_4147))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4144) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

fof(f_844_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_844_2,plain,
    ! [U_4152,U_4151,U_4150,U_4149] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4149),U_4151),U_4152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),U_4151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),U_4152))
      | ~ class_Rings_Ocomm__semiring__1(U_4149) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

cnf(f_844_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4149),U_4151),U_4152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),U_4151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4150),U_4152))
    | ~ class_Rings_Ocomm__semiring__1(U_4149) ),
    inference(clausify,[status(thm)],[f_844_2]) ).

fof(f_845_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_845_2,plain,
    ! [U_4156,U_4155,U_4154,U_4153] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4154),U_4155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4156),U_4155)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),U_4156)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),U_4156))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4154),U_4155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4156),U_4155))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4153) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

cnf(f_845_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),U_4156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4154),U_4155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4156),U_4155)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4153) ),
    inference(clausify,[status(thm)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4154),U_4155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),U_4156),U_4155)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4153),U_4154),U_4156))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4153) ),
    inference(clausify,[status(thm)],[f_845_2]) ).

fof(f_846_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).

fof(f_846_2,plain,
    ! [U_4160,U_4159,U_4158,U_4157] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4160)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),U_4159),U_4160)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),U_4159),U_4160))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4160))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4157) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

cnf(f_846_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),U_4159),U_4160))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4160)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4157) ),
    inference(clausify,[status(thm)],[f_846_2]) ).

cnf(f_846_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4157),U_4158),U_4160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4157),U_4159),U_4160))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4157) ),
    inference(clausify,[status(thm)],[f_846_2]) ).

fof(f_847_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_847_2,plain,
    ! [U_4164,U_4163,U_4162,U_4161] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4161),U_4162),U_4164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4161),U_4163),U_4164)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4161),U_4162),U_4163))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4161) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

cnf(f_847_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4161),U_4162),U_4164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4161),U_4163),U_4164)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4161),U_4162),U_4163))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4161) ),
    inference(clausify,[status(thm)],[f_847_2]) ).

fof(f_848_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_848_2,plain,
    ! [U_4168,U_4167,U_4166,U_4165] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4165),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4165),U_4168),U_4166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4165),U_4168),U_4167)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4165),U_4166),U_4167))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4165) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

cnf(f_848_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4165),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4165),U_4168),U_4166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4165),U_4168),U_4167)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4165),U_4166),U_4167))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4165) ),
    inference(clausify,[status(thm)],[f_848_2]) ).

fof(f_849_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_849_2,plain,
    ! [U_4173,U_4172,U_4171,U_4170,U_4169] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4169),U_4170),U_4172)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4169),U_4171),U_4173)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),U_4172),U_4173))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),U_4170),U_4171))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4169) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

cnf(f_849_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4169),U_4170),U_4172)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4169),U_4171),U_4173)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),U_4172),U_4173))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4169),U_4170),U_4171))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4169) ),
    inference(clausify,[status(thm)],[f_849_2]) ).

fof(f_850_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_850_2,plain,
    ! [U_4177,U_4176,U_4175,U_4174] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4174),U_4175),U_4177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4174),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4174),U_4175),U_4176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4174),U_4177),U_4176)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4174) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

cnf(f_850_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4174),U_4175),U_4177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4174),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4174),U_4175),U_4176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4174),U_4177),U_4176)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4174) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

fof(f_851_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_851_2,plain,
    ! [U_4181,U_4180,U_4179,U_4178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4178),U_4180),U_4181))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4178),U_4179),U_4180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4178),U_4179),U_4181)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4178) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

cnf(f_851_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4178),U_4180),U_4181))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4178),U_4179),U_4180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4178),U_4179),U_4181)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4178) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

fof(f_852_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_852_2,plain,
    ! [U_4182] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4182),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

cnf(f_852_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4182),
    inference(clausify,[status(thm)],[f_852_2]) ).

fof(f_853_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_853_2,plain,
    ! [U_4183] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4183),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

cnf(f_853_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4183),
    inference(clausify,[status(thm)],[f_853_2]) ).

fof(f_854_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_854_2,plain,
    ! [U_4184] : hAPP(c_Nat_OSuc,U_4184) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

cnf(f_854_3,plain,
    hAPP(c_Nat_OSuc,U_4184) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_854_2]) ).

fof(f_855_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_855_2,plain,
    ! [U_4185] : hAPP(c_Nat_OSuc,U_4185) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

cnf(f_855_3,plain,
    hAPP(c_Nat_OSuc,U_4185) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_855_2]) ).

fof(f_856_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_856_2,plain,
    ! [U_4186] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4186),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4186),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_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_857_2,plain,
    ! [U_4187] : hAPP(c_Nat_OSuc,U_4187) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

cnf(f_857_3,plain,
    hAPP(c_Nat_OSuc,U_4187) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_857_2]) ).

fof(f_858_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_858_2,plain,
    ! [U_4192,U_4191,U_4190,U_4189,U_4188] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4189),U_4190))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4191),U_4192)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4191),U_4192))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4189),U_4190)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4189),U_4190) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4191),U_4192)
      | ~ class_Groups_Oordered__ab__group__add(U_4188) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4191),U_4192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4189),U_4190))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4189),U_4190) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4191),U_4192)
    | ~ class_Groups_Oordered__ab__group__add(U_4188) ),
    inference(clausify,[status(thm)],[f_858_2]) ).

cnf(f_858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4189),U_4190))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4188),U_4191),U_4192))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4189),U_4190) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4188),U_4191),U_4192)
    | ~ class_Groups_Oordered__ab__group__add(U_4188) ),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_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_859_2,plain,
    ! [U_4194,U_4193] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4193),U_4194),c_Groups_Oone__class_Oone(U_4193)) = U_4194
      | ~ class_Groups_Ocomm__monoid__mult(U_4193) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

cnf(f_859_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4193),U_4194),c_Groups_Oone__class_Oone(U_4193)) = U_4194
    | ~ class_Groups_Ocomm__monoid__mult(U_4193) ),
    inference(clausify,[status(thm)],[f_859_2]) ).

fof(f_860_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_860_2,plain,
    ! [U_4196,U_4195] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4195),U_4196),c_Groups_Oone__class_Oone(U_4195)) = U_4196
      | ~ class_Groups_Omonoid__mult(U_4195) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

cnf(f_860_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4195),U_4196),c_Groups_Oone__class_Oone(U_4195)) = U_4196
    | ~ class_Groups_Omonoid__mult(U_4195) ),
    inference(clausify,[status(thm)],[f_860_2]) ).

fof(f_861_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_861_2,plain,
    ! [U_4198,U_4197] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4197),c_Groups_Oone__class_Oone(U_4197)),U_4198) = U_4198
      | ~ class_Groups_Ocomm__monoid__mult(U_4197) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

cnf(f_861_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4197),c_Groups_Oone__class_Oone(U_4197)),U_4198) = U_4198
    | ~ class_Groups_Ocomm__monoid__mult(U_4197) ),
    inference(clausify,[status(thm)],[f_861_2]) ).

fof(f_862_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_862_2,plain,
    ! [U_4200,U_4199] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4199),c_Groups_Oone__class_Oone(U_4199)),U_4200) = U_4200
      | ~ class_Groups_Omonoid__mult(U_4199) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

cnf(f_862_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4199),c_Groups_Oone__class_Oone(U_4199)),U_4200) = U_4200
    | ~ class_Groups_Omonoid__mult(U_4199) ),
    inference(clausify,[status(thm)],[f_862_2]) ).

fof(f_863_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_863_2,plain,
    ! [U_4202,U_4201] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4201),U_4202),c_Groups_Oone__class_Oone(U_4201)) = U_4202
      | ~ class_Rings_Ocomm__semiring__1(U_4201) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

cnf(f_863_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4201),U_4202),c_Groups_Oone__class_Oone(U_4201)) = U_4202
    | ~ class_Rings_Ocomm__semiring__1(U_4201) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

fof(f_864_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_864_2,plain,
    ! [U_4204,U_4203] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4203),c_Groups_Oone__class_Oone(U_4203)),U_4204) = U_4204
      | ~ class_Rings_Ocomm__semiring__1(U_4203) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

cnf(f_864_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4203),c_Groups_Oone__class_Oone(U_4203)),U_4204) = U_4204
    | ~ class_Rings_Ocomm__semiring__1(U_4203) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

fof(f_865_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_865_2,plain,
    ! [U_4206,U_4205] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4205)),U_4206) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4205),hAPP(c_Nat_OSuc,U_4206)),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4205)),U_4206) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4205),hAPP(c_Nat_OSuc,U_4206)),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_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_866_2,plain,
    ! [U_4208,U_4207] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4207)),U_4208) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4207),U_4208)),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4207)),U_4208) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4207),U_4208)),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_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_867_2,plain,
    ! [U_4210,U_4209] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4209),hAPP(c_Nat_OSuc,U_4210)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4209),U_4210)),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4209),hAPP(c_Nat_OSuc,U_4210)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4209),U_4210)),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_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_868_2,plain,
    ! [U_4214,U_4213,U_4212,U_4211] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4211),U_4212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4211),U_4214),U_4213)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4211),U_4212),U_4213))
      | ~ class_Lattices_Osemilattice__sup(U_4211) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

cnf(f_868_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4211),U_4212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4211),U_4214),U_4213)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4211),U_4212),U_4213))
    | ~ class_Lattices_Osemilattice__sup(U_4211) ),
    inference(clausify,[status(thm)],[f_868_2]) ).

fof(f_869_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_869_2,plain,
    ! [U_4218,U_4217,U_4216,U_4215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4215),U_4216),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4215),U_4217),U_4218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4215),U_4216),U_4217))
      | ~ class_Lattices_Osemilattice__sup(U_4215) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

cnf(f_869_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4215),U_4216),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4215),U_4217),U_4218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4215),U_4216),U_4217))
    | ~ class_Lattices_Osemilattice__sup(U_4215) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

fof(f_870_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_870_2,plain,
    ! [U_4219] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_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_871_2,plain,
    ! [U_4220] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4220),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

cnf(f_871_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4220),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_871_2]) ).

fof(f_872_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_872_2,plain,
    ! [U_4222,U_4221] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4221),U_4222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_4222 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4221 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_4222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4221),U_4222) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ( ! [U_4226,U_4224] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4224),U_4226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_4226 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4224 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4225,U_4223] :
        ( U_4225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4223),U_4225) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( U_4225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4223),U_4225) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

cnf(f_872_5,plain,
    ( U_4224 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4224),U_4226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

cnf(f_872_6,plain,
    ( U_4226 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4224),U_4226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_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_873_2,plain,
    ! [U_4229,U_4228,U_4227] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4227),U_4228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4227),U_4229)
        | ( U_4227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4228 != U_4229 ) )
      & ( U_4227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4228 = U_4229
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4227),U_4228) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4227),U_4229) ) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ( ! [U_4235,U_4233,U_4231] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4235)
        | ( U_4231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4233 != U_4235 ) )
    & ! [U_4234,U_4232,U_4230] :
        ( U_4230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4232 = U_4234
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4230),U_4232) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4230),U_4234) ) ),
    inference(miniscope,[status(thm)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( U_4230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4232 = U_4234
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4230),U_4232) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4230),U_4234) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

cnf(f_873_5,plain,
    ( U_4233 != U_4235
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4235) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

cnf(f_873_6,plain,
    ( U_4231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4235) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_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_874_2,plain,
    ! [U_4238,U_4237,U_4236] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4236),U_4237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4238),U_4237)
        | ( U_4237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4236 != U_4238 ) )
      & ( U_4237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4236 = U_4238
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4236),U_4237) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4238),U_4237) ) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ( ! [U_4244,U_4242,U_4240] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4240),U_4242) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4244),U_4242)
        | ( U_4242 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4240 != U_4244 ) )
    & ! [U_4243,U_4241,U_4239] :
        ( U_4241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4239 = U_4243
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4239),U_4241) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4243),U_4241) ) ),
    inference(miniscope,[status(thm)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( U_4241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4239 = U_4243
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4239),U_4241) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4243),U_4241) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

cnf(f_874_5,plain,
    ( U_4240 != U_4244
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4240),U_4242) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4244),U_4242) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

cnf(f_874_6,plain,
    ( U_4242 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4240),U_4242) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4244),U_4242) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_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_875_2,plain,
    ! [U_4248,U_4247,U_4246,U_4245] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4245),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4245),U_4248),U_4246)),U_4247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4245),U_4246),U_4247))
      | ~ class_Lattices_Osemilattice__inf(U_4245) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

cnf(f_875_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4245),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4245),U_4248),U_4246)),U_4247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4245),U_4246),U_4247))
    | ~ class_Lattices_Osemilattice__inf(U_4245) ),
    inference(clausify,[status(thm)],[f_875_2]) ).

fof(f_876_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_876_2,plain,
    ! [U_4252,U_4251,U_4250,U_4249] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4249),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4249),U_4250),U_4252)),U_4251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4249),U_4250),U_4251))
      | ~ class_Lattices_Osemilattice__inf(U_4249) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4249),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4249),U_4250),U_4252)),U_4251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4249),U_4250),U_4251))
    | ~ class_Lattices_Osemilattice__inf(U_4249) ),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_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_877_2,plain,
    ! [U_4253] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4253),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

cnf(f_877_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4253),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_877_2]) ).

fof(f_878_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_878_2,plain,
    ! [U_4254] :
      ( ( U_4254 != 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_4254)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4254))
        | U_4254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ( ! [U_4256] :
        ( U_4256 != 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_4256)) )
    & ! [U_4255] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4255))
        | U_4255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_878_2]) ).

cnf(f_878_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4255))
    | U_4255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

cnf(f_878_5,plain,
    ( U_4256 != 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_4256)) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_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_879_2,plain,
    ! [U_4257] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4257),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4257),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_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_880_2,plain,
    ! [U_4259,U_4258] :
      ( U_4259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4258),U_4259)) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_4259] :
      ( ! [U_4258] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4258),U_4259))
      | U_4259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_880_2]) ).

cnf(f_880_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4258),U_4259))
    | U_4259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_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_881_2,plain,
    ! [U_4260] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4260))
      | U_4260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

cnf(f_881_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4260))
    | U_4260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_881_2]) ).

fof(f_882_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_882_2,plain,
    ! [U_4262,U_4261] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4261)),hAPP(c_Nat_OSuc,U_4262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4261),U_4262),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

cnf(f_882_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4261)),hAPP(c_Nat_OSuc,U_4262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4261),U_4262),
    inference(clausify,[status(thm)],[f_882_2]) ).

fof(f_883_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_883_2,plain,
    ! [U_4265,U_4264,U_4263] : 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_4263)),U_4264)),hAPP(c_Nat_OSuc,U_4265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4263),U_4264)),U_4265),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

cnf(f_883_3,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_4263)),U_4264)),hAPP(c_Nat_OSuc,U_4265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4263),U_4264)),U_4265),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_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_884_2,plain,
    ! [U_4268,U_4267,U_4266] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4266),U_4267)),U_4268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),U_4268)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4267),U_4268)),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

cnf(f_884_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4266),U_4267)),U_4268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),U_4268)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4267),U_4268)),
    inference(clausify,[status(thm)],[f_884_2]) ).

fof(f_885_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_885_2,plain,
    ! [U_4271,U_4270,U_4269] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4270),U_4271)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),U_4270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),U_4271)),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

cnf(f_885_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4270),U_4271)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),U_4270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4269),U_4271)),
    inference(clausify,[status(thm)],[f_885_2]) ).

fof(f_886_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_886_2,plain,
    ! [U_4274,U_4273,U_4272] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),U_4274))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4272),U_4273)),U_4274)) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

cnf(f_886_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),U_4274))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4272),U_4273)),U_4274)) ),
    inference(clausify,[status(thm)],[f_886_2]) ).

fof(f_887_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_887_2,plain,
    ! [U_4278,U_4277,U_4276,U_4275] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4277),U_4278))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4277),U_4276) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4275),U_4278)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),U_4276)) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

cnf(f_887_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4277),U_4278))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4277),U_4276) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4275),U_4278)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),U_4276)) ),
    inference(clausify,[status(thm)],[f_887_2]) ).

fof(f_888_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_888_2,plain,
    ! [U_4282,U_4281,U_4280,U_4279] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4279),U_4281)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4280),U_4282)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4281),U_4282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4279),U_4280)) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

cnf(f_888_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4279),U_4281)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4280),U_4282)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4281),U_4282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4279),U_4280)) ),
    inference(clausify,[status(thm)],[f_888_2]) ).

fof(f_889_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_889_2,plain,
    ! [U_4285,U_4284,U_4283] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4283),U_4285)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4284),U_4285)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4283),U_4284)) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

cnf(f_889_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4283),U_4285)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4284),U_4285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4283),U_4284)) ),
    inference(clausify,[status(thm)],[f_889_2]) ).

fof(f_890_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_890_2,plain,
    ! [U_4288,U_4287,U_4286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4288),U_4287)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4286),U_4287)) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

cnf(f_890_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4288),U_4287)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4286),U_4287)) ),
    inference(clausify,[status(thm)],[f_890_2]) ).

fof(f_891_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_891_2,plain,
    ! [U_4291,U_4290,U_4289] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4290),U_4291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4289),U_4290)) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

cnf(f_891_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4290),U_4291)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4289),U_4290)) ),
    inference(clausify,[status(thm)],[f_891_2]) ).

fof(f_892_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_892_2,plain,
    ! [U_4294,U_4293,U_4292] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4292),U_4293)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4292),U_4294)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4293),U_4294)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4293),U_4294))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4292),U_4293)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4292),U_4294))) ) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ( ! [U_4300,U_4298] :
        ( ! [U_4296] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4296),U_4298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4296),U_4300)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4298),U_4300)) )
    & ! [U_4299,U_4297] :
        ( ! [U_4295] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4295),U_4297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4295),U_4299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4297),U_4299)) ) ),
    inference(miniscope,[status(thm)],[f_892_2]) ).

cnf(f_892_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4295),U_4297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4295),U_4299)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4297),U_4299)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

cnf(f_892_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4296),U_4298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4296),U_4300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4298),U_4300)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_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_893_2,plain,
    ! [U_4302,U_4301] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4301),U_4302)),U_4302)),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

cnf(f_893_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4301),U_4302)),U_4302)),
    inference(clausify,[status(thm)],[f_893_2]) ).

fof(f_894_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_894_2,plain,
    ! [U_4304,U_4303] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4303),U_4304)),U_4303)),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

cnf(f_894_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4303),U_4304)),U_4303)),
    inference(clausify,[status(thm)],[f_894_2]) ).

fof(f_895_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_895_2,plain,
    ! [U_4307,U_4306,U_4305] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4306),U_4307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),U_4306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),U_4307)),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

cnf(f_895_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4306),U_4307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),U_4306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4305),U_4307)),
    inference(clausify,[status(thm)],[f_895_2]) ).

fof(f_896_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_896_2,plain,
    ! [U_4310,U_4309,U_4308] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4308),U_4309)),U_4310) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4308),U_4310)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4309),U_4310)),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

cnf(f_896_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4308),U_4309)),U_4310) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4308),U_4310)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4309),U_4310)),
    inference(clausify,[status(thm)],[f_896_2]) ).

fof(f_897_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_897_2,plain,
    ! [U_4313,U_4312,U_4311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4311),U_4313)),U_4312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4311),U_4312)) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

cnf(f_897_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4311),U_4313)),U_4312))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4311),U_4312)) ),
    inference(clausify,[status(thm)],[f_897_2]) ).

fof(f_898_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_898_2,plain,
    ! [U_4316,U_4315,U_4314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4316),U_4315)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4316),U_4314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4316))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315)) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

cnf(f_898_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4316),U_4315)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4316),U_4314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4316))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4314),U_4315)) ),
    inference(clausify,[status(thm)],[f_898_2]) ).

fof(f_899_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_899_2,plain,
    ! [U_4318,U_4317] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4317),U_4318) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4318 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4317 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_4318 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4317 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4317),U_4318) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ( ! [U_4322,U_4320] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4320),U_4322) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4322 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4320 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4321,U_4319] :
        ( ( U_4321 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4319 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_899_2]) ).

cnf(f_899_4,plain,
    ( U_4319 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_5,plain,
    ( U_4321 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4320),U_4322) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4322 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4320 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_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_900_2,plain,
    ! [U_4323] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4323),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4323,
    inference(variable_rename,[status(thm)],[f_900_1]) ).

cnf(f_900_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4323),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4323,
    inference(clausify,[status(thm)],[f_900_2]) ).

fof(f_901_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_901_2,plain,
    ! [U_4325,U_4324] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4324),U_4325)
        | U_4325 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4324 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_4325 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4324 = 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_4324),U_4325) ) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ( ! [U_4329,U_4327] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4327),U_4329)
        | U_4329 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4327 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4328,U_4326] :
        ( ( U_4328 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4326 = 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_4326),U_4328) ) ),
    inference(miniscope,[status(thm)],[f_901_2]) ).

cnf(f_901_4,plain,
    ( U_4326 = 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_4326),U_4328) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

cnf(f_901_5,plain,
    ( U_4328 = 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_4326),U_4328) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

cnf(f_901_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4327),U_4329)
    | U_4329 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4327 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_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_902_2,plain,
    ! [U_4330] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4330) = U_4330,
    inference(variable_rename,[status(thm)],[f_902_1]) ).

cnf(f_902_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4330) = U_4330,
    inference(clausify,[status(thm)],[f_902_2]) ).

fof(f_903_1,plain,
    ! [V_S_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).

fof(f_903_2,plain,
    ! [U_4335,U_4334,U_4333] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335)))
          | ! [U_4332] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),U_4332))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4333),U_4332),U_4335)) ) )
        & ( ? [U_4331] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),U_4331))
              & hBOOL(hAPP(hAPP(c_member(U_4333),U_4331),U_4335)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335))) ) )
      | ~ class_Orderings_Olinorder(U_4333)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4333) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_4335,U_4334,U_4333] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335)))
          | ! [U_4332] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),U_4332))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4333),U_4332),U_4335)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),sK82(U_4335,U_4334,U_4333)))
            & hBOOL(hAPP(hAPP(c_member(U_4333),sK82(U_4335,U_4334,U_4333)),U_4335)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335))) ) )
      | ~ class_Orderings_Olinorder(U_4333)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4333) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_4331,sK82(U_4335,U_4334,U_4333))],[f_903_2]) ).

cnf(f_903_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4333),sK82(U_4335,U_4334,U_4333)),U_4335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335)))
    | ~ class_Orderings_Olinorder(U_4333)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4333) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

cnf(f_903_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),sK82(U_4335,U_4334,U_4333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335)))
    | ~ class_Orderings_Olinorder(U_4333)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4333) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

cnf(f_903_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),c_Complete__Lattice_OSup__class_OSup(U_4333,U_4335)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),U_4334),U_4332))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4333),U_4332),U_4335))
    | ~ class_Orderings_Olinorder(U_4333)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4333) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [V_a_2,V_S_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).

fof(f_904_2,plain,
    ! [U_4340,U_4339,U_4338] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340))
          | ! [U_4337] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),U_4337),U_4340))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4338),U_4337),U_4339)) ) )
        & ( ? [U_4336] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),U_4336),U_4340))
              & hBOOL(hAPP(hAPP(c_member(U_4338),U_4336),U_4339)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340)) ) )
      | ~ class_Orderings_Olinorder(U_4338)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4338) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_4340,U_4339,U_4338] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340))
          | ! [U_4337] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),U_4337),U_4340))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4338),U_4337),U_4339)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),sK83(U_4340,U_4339,U_4338)),U_4340))
            & hBOOL(hAPP(hAPP(c_member(U_4338),sK83(U_4340,U_4339,U_4338)),U_4339)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340)) ) )
      | ~ class_Orderings_Olinorder(U_4338)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4338) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_4336,sK83(U_4340,U_4339,U_4338))],[f_904_2]) ).

cnf(f_904_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4338),sK83(U_4340,U_4339,U_4338)),U_4339))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340))
    | ~ class_Orderings_Olinorder(U_4338)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4338) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

cnf(f_904_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),sK83(U_4340,U_4339,U_4338)),U_4340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340))
    | ~ class_Orderings_Olinorder(U_4338)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4338) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

cnf(f_904_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),c_Complete__Lattice_OInf__class_OInf(U_4338,U_4339)),U_4340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4338),U_4337),U_4340))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4338),U_4337),U_4339))
    | ~ class_Orderings_Olinorder(U_4338)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4338) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).

fof(f_905_2,plain,
    ! [U_4341] :
      ( c_Finite__Set_Ofun__left__comm(U_4341,U_4341,c_Groups_Otimes__class_Otimes(U_4341))
      | ~ class_Groups_Oab__semigroup__mult(U_4341) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

cnf(f_905_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_4341,U_4341,c_Groups_Otimes__class_Otimes(U_4341))
    | ~ class_Groups_Oab__semigroup__mult(U_4341) ),
    inference(clausify,[status(thm)],[f_905_2]) ).

fof(f_906_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).

fof(f_906_2,plain,
    ! [U_4342] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_4342,U_4342,c_Groups_Otimes__class_Otimes(U_4342))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_4342) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

cnf(f_906_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_4342,U_4342,c_Groups_Otimes__class_Otimes(U_4342))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_4342) ),
    inference(clausify,[status(thm)],[f_906_2]) ).

fof(f_907_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_907_2,plain,
    ! [U_4343] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4343),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4343
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4343)) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

cnf(f_907_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4343),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4343
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4343)) ),
    inference(clausify,[status(thm)],[f_907_2]) ).

fof(f_908_1,plain,
    ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).

fof(f_908_2,plain,
    ! [U_4350,U_4349,U_4348,U_4347,U_4346,U_4345,U_4344] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4345,U_4344),U_4346),U_4347)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4348,U_4344),U_4349),U_4350)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4345,U_4344),hAPP(hAPP(c_COMBC(U_4345,tc_fun(U_4348,tc_HOL_Obool),U_4344),hAPP(hAPP(c_COMBB(tc_fun(U_4348,U_4344),tc_fun(tc_fun(U_4348,tc_HOL_Obool),U_4344),U_4345),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4348,U_4344)),hAPP(hAPP(c_COMBC(U_4345,tc_fun(U_4348,U_4344),tc_fun(U_4348,U_4344)),hAPP(hAPP(c_COMBB(tc_fun(U_4344,U_4344),tc_fun(tc_fun(U_4348,U_4344),tc_fun(U_4348,U_4344)),U_4345),c_COMBB(U_4344,U_4344,U_4348)),hAPP(hAPP(c_COMBB(U_4344,tc_fun(U_4344,U_4344),U_4345),c_Groups_Otimes__class_Otimes(U_4344)),U_4346))),U_4349))),U_4350)),U_4347)
      | ~ class_Rings_Osemiring__0(U_4344) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

cnf(f_908_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4345,U_4344),U_4346),U_4347)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4348,U_4344),U_4349),U_4350)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4345,U_4344),hAPP(hAPP(c_COMBC(U_4345,tc_fun(U_4348,tc_HOL_Obool),U_4344),hAPP(hAPP(c_COMBB(tc_fun(U_4348,U_4344),tc_fun(tc_fun(U_4348,tc_HOL_Obool),U_4344),U_4345),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4348,U_4344)),hAPP(hAPP(c_COMBC(U_4345,tc_fun(U_4348,U_4344),tc_fun(U_4348,U_4344)),hAPP(hAPP(c_COMBB(tc_fun(U_4344,U_4344),tc_fun(tc_fun(U_4348,U_4344),tc_fun(U_4348,U_4344)),U_4345),c_COMBB(U_4344,U_4344,U_4348)),hAPP(hAPP(c_COMBB(U_4344,tc_fun(U_4344,U_4344),U_4345),c_Groups_Otimes__class_Otimes(U_4344)),U_4346))),U_4349))),U_4350)),U_4347)
    | ~ class_Rings_Osemiring__0(U_4344) ),
    inference(clausify,[status(thm)],[f_908_2]) ).

fof(f_909_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).

fof(f_909_2,plain,
    ! [U_4355,U_4354,U_4353,U_4352,U_4351] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4351),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4352,U_4351),U_4353),U_4354)),U_4355) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4352,U_4351),hAPP(hAPP(c_COMBC(U_4352,U_4351,U_4351),hAPP(hAPP(c_COMBB(U_4351,tc_fun(U_4351,U_4351),U_4352),c_Groups_Otimes__class_Otimes(U_4351)),U_4353)),U_4355)),U_4354)
      | ~ class_Rings_Osemiring__0(U_4351) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

cnf(f_909_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4351),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4352,U_4351),U_4353),U_4354)),U_4355) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4352,U_4351),hAPP(hAPP(c_COMBC(U_4352,U_4351,U_4351),hAPP(hAPP(c_COMBB(U_4351,tc_fun(U_4351,U_4351),U_4352),c_Groups_Otimes__class_Otimes(U_4351)),U_4353)),U_4355)),U_4354)
    | ~ class_Rings_Osemiring__0(U_4351) ),
    inference(clausify,[status(thm)],[f_909_2]) ).

fof(f_910_1,plain,
    ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).

fof(f_910_2,plain,
    ! [U_4360,U_4359,U_4358,U_4357,U_4356] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4358,U_4356),U_4359),U_4360)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4358,U_4356),hAPP(hAPP(c_COMBB(U_4356,U_4356,U_4358),hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357)),U_4359)),U_4360)
      | ~ class_Rings_Osemiring__0(U_4356) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

cnf(f_910_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4358,U_4356),U_4359),U_4360)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4358,U_4356),hAPP(hAPP(c_COMBB(U_4356,U_4356,U_4358),hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357)),U_4359)),U_4360)
    | ~ class_Rings_Osemiring__0(U_4356) ),
    inference(clausify,[status(thm)],[f_910_2]) ).

fof(f_911_1,plain,
    ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_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_a),V_a_2),hAPP(V_f_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2))) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).

fof(f_911_2,plain,
    ! [U_4367,U_4366,U_4365,U_4364,U_4363] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367)))
          | ! [U_4362] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,U_4362)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4365),U_4362),U_4366)) ) )
        & ( ? [U_4361] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,U_4361)))
              & hBOOL(hAPP(hAPP(c_member(U_4365),U_4361),U_4366)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367))) ) )
      | ~ class_Orderings_Olinorder(U_4363)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4363) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_4367,U_4366,U_4365,U_4364,U_4363] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367)))
          | ! [U_4362] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,U_4362)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4365),U_4362),U_4366)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,sK84(U_4367,U_4366,U_4365,U_4364,U_4363))))
            & hBOOL(hAPP(hAPP(c_member(U_4365),sK84(U_4367,U_4366,U_4365,U_4364,U_4363)),U_4366)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367))) ) )
      | ~ class_Orderings_Olinorder(U_4363)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4363) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4361,sK84(U_4367,U_4366,U_4365,U_4364,U_4363))],[f_911_2]) ).

cnf(f_911_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4365),sK84(U_4367,U_4366,U_4365,U_4364,U_4363)),U_4366))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367)))
    | ~ class_Orderings_Olinorder(U_4363)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4363) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

cnf(f_911_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,sK84(U_4367,U_4366,U_4365,U_4364,U_4363))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367)))
    | ~ class_Orderings_Olinorder(U_4363)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4363) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

cnf(f_911_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4365,U_4363),U_4366),U_4367)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4363),U_4364),hAPP(U_4367,U_4362)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4365),U_4362),U_4366))
    | ~ class_Orderings_Olinorder(U_4363)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4363) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).

fof(f_912_2,plain,
    ! [U_4374,U_4373,U_4372,U_4371,U_4370] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374))
          | ! [U_4369] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,U_4369)),U_4374))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4371),U_4369),U_4372)) ) )
        & ( ? [U_4368] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,U_4368)),U_4374))
              & hBOOL(hAPP(hAPP(c_member(U_4371),U_4368),U_4372)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374)) ) )
      | ~ class_Orderings_Olinorder(U_4370)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4370) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_4374,U_4373,U_4372,U_4371,U_4370] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374))
          | ! [U_4369] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,U_4369)),U_4374))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4371),U_4369),U_4372)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,sK85(U_4374,U_4373,U_4372,U_4371,U_4370))),U_4374))
            & hBOOL(hAPP(hAPP(c_member(U_4371),sK85(U_4374,U_4373,U_4372,U_4371,U_4370)),U_4372)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374)) ) )
      | ~ class_Orderings_Olinorder(U_4370)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4370) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_4368,sK85(U_4374,U_4373,U_4372,U_4371,U_4370))],[f_912_2]) ).

cnf(f_912_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4371),sK85(U_4374,U_4373,U_4372,U_4371,U_4370)),U_4372))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374))
    | ~ class_Orderings_Olinorder(U_4370)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4370) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

cnf(f_912_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,sK85(U_4374,U_4373,U_4372,U_4371,U_4370))),U_4374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374))
    | ~ class_Orderings_Olinorder(U_4370)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4370) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

cnf(f_912_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4371,U_4370),U_4372),U_4373)),U_4374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4370),hAPP(U_4373,U_4369)),U_4374))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4371),U_4369),U_4372))
    | ~ class_Orderings_Olinorder(U_4370)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4370) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

fof(f_913_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_913_2,plain,
    ! [U_4380,U_4379,U_4378,U_4377,U_4376,U_4375] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4375),U_4377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4375),U_4376),U_4379)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4375),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4375),U_4376),U_4380))
      | U_4379 = U_4380
      | U_4377 != U_4378
      | U_4376 = c_Groups_Ozero__class_Ozero(U_4375)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4375) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

cnf(f_913_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4375),U_4377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4375),U_4376),U_4379)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4375),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4375),U_4376),U_4380))
    | U_4379 = U_4380
    | U_4377 != U_4378
    | U_4376 = c_Groups_Ozero__class_Ozero(U_4375)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4375) ),
    inference(clausify,[status(thm)],[f_913_2]) ).

fof(f_914_1,plain,
    ! [V_a_2,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_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ 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_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_914_2,plain,
    ! [U_4382,U_4381] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4381),U_4382),U_4382)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),U_4382)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),U_4382))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4381),U_4382),U_4382))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_4381) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

cnf(f_914_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),U_4382))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4381),U_4382),U_4382)))
    | ~ class_Groups_Olinordered__ab__group__add(U_4381) ),
    inference(clausify,[status(thm)],[f_914_2]) ).

cnf(f_914_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4381),U_4382),U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),c_Groups_Ozero__class_Ozero(U_4381)),U_4382))
    | ~ class_Groups_Olinordered__ab__group__add(U_4381) ),
    inference(clausify,[status(thm)],[f_914_2]) ).

fof(f_915_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_915_2,plain,
    ! [U_4384,U_4383] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4383),U_4384),U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4383),U_4384),U_4384)),c_Groups_Ozero__class_Ozero(U_4383))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_4383) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

cnf(f_915_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4383),U_4384),U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
    | ~ class_Groups_Olinordered__ab__group__add(U_4383) ),
    inference(clausify,[status(thm)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4383),U_4384),U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
    | ~ class_Groups_Olinordered__ab__group__add(U_4383) ),
    inference(clausify,[status(thm)],[f_915_2]) ).

fof(f_916_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_916_2,plain,
    ! [U_4387,U_4386,U_4385] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4385),U_4386),U_4387)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386))
      | ~ class_Groups_Oordered__comm__monoid__add(U_4385) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

cnf(f_916_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4385),U_4386),U_4387)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4387))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386))
    | ~ class_Groups_Oordered__comm__monoid__add(U_4385) ),
    inference(clausify,[status(thm)],[f_916_2]) ).

fof(f_917_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_917_2,plain,
    ! [U_4390,U_4389,U_4388] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4388),U_4389),U_4390)),c_Groups_Ozero__class_Ozero(U_4388)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),c_Groups_Ozero__class_Ozero(U_4388)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_4388) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

cnf(f_917_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4388),U_4389),U_4390)),c_Groups_Ozero__class_Ozero(U_4388)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),c_Groups_Ozero__class_Ozero(U_4388)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_4388) ),
    inference(clausify,[status(thm)],[f_917_2]) ).

fof(f_918_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).

fof(f_918_2,plain,
    ! [U_4392,U_4391] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4392),U_4392)),c_Groups_Ozero__class_Ozero(U_4391)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),U_4392),c_Groups_Ozero__class_Ozero(U_4391))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),U_4392),c_Groups_Ozero__class_Ozero(U_4391)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4392),U_4392)),c_Groups_Ozero__class_Ozero(U_4391))) ) )
      | ~ class_Rings_Olinordered__idom(U_4391) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

cnf(f_918_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),U_4392),c_Groups_Ozero__class_Ozero(U_4391)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4392),U_4392)),c_Groups_Ozero__class_Ozero(U_4391)))
    | ~ class_Rings_Olinordered__idom(U_4391) ),
    inference(clausify,[status(thm)],[f_918_2]) ).

cnf(f_918_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4392),U_4392)),c_Groups_Ozero__class_Ozero(U_4391)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4391),U_4392),c_Groups_Ozero__class_Ozero(U_4391)))
    | ~ class_Rings_Olinordered__idom(U_4391) ),
    inference(clausify,[status(thm)],[f_918_2]) ).

fof(f_919_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_919_2,plain,
    ! [U_4396,U_4395,U_4394,U_4393] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),U_4395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4393),U_4394),U_4396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),U_4395),U_4396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),c_Groups_Ozero__class_Ozero(U_4393)),U_4394))
      | ~ class_Rings_Olinordered__semidom(U_4393) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

cnf(f_919_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),U_4395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4393),U_4394),U_4396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),U_4395),U_4396))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4393),c_Groups_Ozero__class_Ozero(U_4393)),U_4394))
    | ~ class_Rings_Olinordered__semidom(U_4393) ),
    inference(clausify,[status(thm)],[f_919_2]) ).

fof(f_920_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).

fof(f_920_2,plain,
    ! [U_4399,U_4398,U_4397] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),U_4398),U_4399))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4397),U_4398),U_4399)),c_Groups_Ozero__class_Ozero(U_4397))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4397),U_4398),U_4399)),c_Groups_Ozero__class_Ozero(U_4397)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),U_4398),U_4399)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_4397) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

cnf(f_920_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4397),U_4398),U_4399)),c_Groups_Ozero__class_Ozero(U_4397)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),U_4398),U_4399))
    | ~ class_Groups_Oordered__ab__group__add(U_4397) ),
    inference(clausify,[status(thm)],[f_920_2]) ).

cnf(f_920_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),U_4398),U_4399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4397),U_4398),U_4399)),c_Groups_Ozero__class_Ozero(U_4397)))
    | ~ class_Groups_Oordered__ab__group__add(U_4397) ),
    inference(clausify,[status(thm)],[f_920_2]) ).

fof(f_921_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
          | V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) )
        & ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).

fof(f_921_2,plain,
    ! [U_4405,U_4404,U_4403,U_4402,U_4401,U_4400] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4401),U_4402)),U_4403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4404),U_4402)),U_4405)
          | U_4403 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4400),U_4404),U_4401)),U_4402)),U_4405) )
        & ( U_4403 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4400),U_4404),U_4401)),U_4402)),U_4405)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4401),U_4402)),U_4403) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4404),U_4402)),U_4405) ) )
      | ~ class_Rings_Oring(U_4400) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

cnf(f_921_3,plain,
    ( U_4403 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4400),U_4404),U_4401)),U_4402)),U_4405)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4401),U_4402)),U_4403) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4404),U_4402)),U_4405)
    | ~ class_Rings_Oring(U_4400) ),
    inference(clausify,[status(thm)],[f_921_2]) ).

cnf(f_921_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4401),U_4402)),U_4403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),U_4404),U_4402)),U_4405)
    | U_4403 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4400),U_4404),U_4401)),U_4402)),U_4405)
    | ~ class_Rings_Oring(U_4400) ),
    inference(clausify,[status(thm)],[f_921_2]) ).

fof(f_922_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).

fof(f_922_2,plain,
    ! [U_4411,U_4410,U_4409,U_4408,U_4407,U_4406] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4407),U_4408)),U_4409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4410),U_4408)),U_4411)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4406),U_4407),U_4410)),U_4408)),U_4409) != U_4411 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4406),U_4407),U_4410)),U_4408)),U_4409) = U_4411
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4407),U_4408)),U_4409) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4410),U_4408)),U_4411) ) )
      | ~ class_Rings_Oring(U_4406) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

cnf(f_922_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4406),U_4407),U_4410)),U_4408)),U_4409) = U_4411
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4407),U_4408)),U_4409) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4410),U_4408)),U_4411)
    | ~ class_Rings_Oring(U_4406) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

cnf(f_922_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4407),U_4408)),U_4409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),U_4410),U_4408)),U_4411)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4406),U_4407),U_4410)),U_4408)),U_4409) != U_4411
    | ~ class_Rings_Oring(U_4406) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

fof(f_923_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_923_2,plain,
    ! [U_4412] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4412),c_Groups_Ozero__class_Ozero(U_4412)),c_Groups_Oone__class_Oone(U_4412)))
      | ~ class_Rings_Olinordered__semidom(U_4412) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

cnf(f_923_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4412),c_Groups_Ozero__class_Ozero(U_4412)),c_Groups_Oone__class_Oone(U_4412)))
    | ~ class_Rings_Olinordered__semidom(U_4412) ),
    inference(clausify,[status(thm)],[f_923_2]) ).

fof(f_924_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_924_2,plain,
    ! [U_4413] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4413),c_Groups_Oone__class_Oone(U_4413)),c_Groups_Ozero__class_Ozero(U_4413)))
      | ~ class_Rings_Olinordered__semidom(U_4413) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

cnf(f_924_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4413),c_Groups_Oone__class_Oone(U_4413)),c_Groups_Ozero__class_Ozero(U_4413)))
    | ~ class_Rings_Olinordered__semidom(U_4413) ),
    inference(clausify,[status(thm)],[f_924_2]) ).

fof(f_925_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_925_2,plain,
    ! [U_4415,U_4414] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4414),U_4415),U_4415) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4414),c_Groups_Oone__class_Oone(U_4414)),c_Groups_Oone__class_Oone(U_4414))),U_4415)
      | ~ class_Rings_Ocomm__semiring__1(U_4414) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

cnf(f_925_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4414),U_4415),U_4415) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4414),c_Groups_Oone__class_Oone(U_4414)),c_Groups_Oone__class_Oone(U_4414))),U_4415)
    | ~ class_Rings_Ocomm__semiring__1(U_4414) ),
    inference(clausify,[status(thm)],[f_925_2]) ).

fof(f_926_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_926_2,plain,
    ! [U_4418,U_4417,U_4416] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4416),U_4417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4416),U_4418),U_4417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4416),U_4418),c_Groups_Oone__class_Oone(U_4416))),U_4417)
      | ~ class_Rings_Ocomm__semiring__1(U_4416) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

cnf(f_926_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4416),U_4417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4416),U_4418),U_4417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4416),U_4418),c_Groups_Oone__class_Oone(U_4416))),U_4417)
    | ~ class_Rings_Ocomm__semiring__1(U_4416) ),
    inference(clausify,[status(thm)],[f_926_2]) ).

fof(f_927_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_927_2,plain,
    ! [U_4421,U_4420,U_4419] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4419),U_4420),U_4421)),U_4421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4419),U_4420),c_Groups_Oone__class_Oone(U_4419))),U_4421)
      | ~ class_Rings_Ocomm__semiring__1(U_4419) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

cnf(f_927_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4419),U_4420),U_4421)),U_4421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4419),U_4420),c_Groups_Oone__class_Oone(U_4419))),U_4421)
    | ~ class_Rings_Ocomm__semiring__1(U_4419) ),
    inference(clausify,[status(thm)],[f_927_2]) ).

fof(f_928_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_928_2,plain,
    ! [U_4423,U_4422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4422),U_4423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4422),U_4423),c_Groups_Oone__class_Oone(U_4422))))
      | ~ class_Rings_Olinordered__semidom(U_4422) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

cnf(f_928_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4422),U_4423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4422),U_4423),c_Groups_Oone__class_Oone(U_4422))))
    | ~ class_Rings_Olinordered__semidom(U_4422) ),
    inference(clausify,[status(thm)],[f_928_2]) ).

fof(f_929_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_929_2,plain,
    ! [U_4425,U_4424] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4424),U_4425) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_4425 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_4424 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_4425 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4424 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_4425 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_4425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4424 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4424),U_4425) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ( ! [U_4429,U_4427] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4427),U_4429) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_4429 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_4427 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_4429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4427 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_4428,U_4426] :
        ( ( U_4428 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_4428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4426 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4426),U_4428) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_929_2]) ).

cnf(f_929_4,plain,
    ( U_4426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4426 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4426),U_4428) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_5,plain,
    ( U_4428 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4426 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4426),U_4428) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_6,plain,
    ( U_4426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4426),U_4428) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_7,plain,
    ( U_4428 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4426),U_4428) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_8,plain,
    ( U_4429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4427 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4427),U_4429) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_9,plain,
    ( U_4429 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4427 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4427),U_4429) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_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_930_2,plain,
    ! [U_4431,U_4430] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4430),U_4431)
        | ( ( U_4431 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_4430 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_4431 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4430 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_4431 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_4431 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4430 = 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_4430),U_4431) ) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ( ! [U_4435,U_4433] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4433),U_4435)
        | ( ( U_4435 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_4433 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_4435 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4433 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_4434,U_4432] :
        ( ( U_4434 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_4434 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4432 = 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_4432),U_4434) ) ),
    inference(miniscope,[status(thm)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( U_4432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4432 = 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_4432),U_4434) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_5,plain,
    ( U_4434 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4432 = 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_4432),U_4434) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_6,plain,
    ( U_4432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4434 = 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_4432),U_4434) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_7,plain,
    ( U_4434 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4434 = 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_4432),U_4434) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_8,plain,
    ( U_4435 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4433 != 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_4433),U_4435) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_9,plain,
    ( U_4435 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4433 != 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_4433),U_4435) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_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]) ).

cnf(f_931_2,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_931_1]) ).

fof(f_932_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_932_2,plain,
    ! [U_4437,U_4436] :
      ( ( 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_4436),U_4437)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4437))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4436)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4437))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4436))
        | ~ 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_4436),U_4437))) ) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ( ! [U_4441,U_4439] :
        ( 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_4439),U_4441)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4441))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4439)) ) )
    & ! [U_4440,U_4438] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4440))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4438))
        | ~ 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_4438),U_4440))) ) ),
    inference(miniscope,[status(thm)],[f_932_2]) ).

cnf(f_932_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4440))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4438))
    | ~ 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_4438),U_4440))) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

cnf(f_932_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4439))
    | 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_4439),U_4441))) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

cnf(f_932_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4441))
    | 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_4439),U_4441))) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

fof(f_933_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_933_2,plain,
    ! [U_4443,U_4442] :
      ( ( 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_4442),U_4443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4443),U_4442)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4443),U_4442))
        | ~ 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_4442),U_4443))) ) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ( ! [U_4447,U_4445] :
        ( 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_4445),U_4447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4447),U_4445)) )
    & ! [U_4446,U_4444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4446),U_4444))
        | ~ 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_4444),U_4446))) ) ),
    inference(miniscope,[status(thm)],[f_933_2]) ).

cnf(f_933_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4446),U_4444))
    | ~ 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_4444),U_4446))) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

cnf(f_933_5,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_4445),U_4447)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4447),U_4445)) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_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_934_2,plain,
    ! [U_4449,U_4448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4449),U_4448)),U_4449))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4449))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4448)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

cnf(f_934_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4449),U_4448)),U_4449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4448)) ),
    inference(clausify,[status(thm)],[f_934_2]) ).

fof(f_935_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_935_2,plain,
    ! [U_4451,U_4450] :
      ( U_4450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_4451 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_4450 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4450),U_4451) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

cnf(f_935_3,plain,
    ( U_4450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4451 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4450 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4450),U_4451) ),
    inference(clausify,[status(thm)],[f_935_2]) ).

fof(f_936_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_936_2,plain,
    ! [U_4452] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4452)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4452,
    inference(variable_rename,[status(thm)],[f_936_1]) ).

cnf(f_936_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4452)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4452,
    inference(clausify,[status(thm)],[f_936_2]) ).

fof(f_937_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_937_2,plain,
    ! [U_4455,U_4454,U_4453] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4454),U_4455)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4453),U_4455)),U_4454)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4453),U_4455)),U_4454))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4454),U_4455))) ) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ( ! [U_4461,U_4459,U_4457] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4459),U_4461)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4457),U_4461)),U_4459)) )
    & ! [U_4460,U_4458,U_4456] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4456),U_4460)),U_4458))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4458),U_4460))) ) ),
    inference(miniscope,[status(thm)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4456),U_4460)),U_4458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4458),U_4460))) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

cnf(f_937_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4459),U_4461)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4457),U_4461)),U_4459)) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_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_938_2,plain,
    ! [U_4463,U_4462] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4462),U_4463)) = U_4462
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),U_4463)) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

cnf(f_938_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4462),U_4463)) = U_4462
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),U_4463)) ),
    inference(clausify,[status(thm)],[f_938_2]) ).

fof(f_939_1,plain,
    ! [V_a_2,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_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).

fof(f_939_2,plain,
    ! [U_4465,U_4464] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465)),U_4465)),c_Groups_Ozero__class_Ozero(U_4464)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),U_4465),c_Groups_Ozero__class_Ozero(U_4464))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),U_4465),c_Groups_Ozero__class_Ozero(U_4464)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465)),U_4465)),c_Groups_Ozero__class_Ozero(U_4464))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4464),U_4465),c_Int_Oring__1__class_OInts(U_4464)))
      | ~ class_Rings_Olinordered__idom(U_4464) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

cnf(f_939_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),U_4465),c_Groups_Ozero__class_Ozero(U_4464)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465)),U_4465)),c_Groups_Ozero__class_Ozero(U_4464)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4464),U_4465),c_Int_Oring__1__class_OInts(U_4464)))
    | ~ class_Rings_Olinordered__idom(U_4464) ),
    inference(clausify,[status(thm)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465)),U_4465)),c_Groups_Ozero__class_Ozero(U_4464)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),U_4465),c_Groups_Ozero__class_Ozero(U_4464)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4464),U_4465),c_Int_Oring__1__class_OInts(U_4464)))
    | ~ class_Rings_Olinordered__idom(U_4464) ),
    inference(clausify,[status(thm)],[f_939_2]) ).

fof(f_940_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).

fof(f_940_2,plain,
    ! [U_4466] :
      ( hBOOL(hAPP(hAPP(c_member(U_4466),c_Groups_Ozero__class_Ozero(U_4466)),c_Int_Oring__1__class_OInts(U_4466)))
      | ~ class_Rings_Oring__1(U_4466) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

cnf(f_940_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4466),c_Groups_Ozero__class_Ozero(U_4466)),c_Int_Oring__1__class_OInts(U_4466)))
    | ~ class_Rings_Oring__1(U_4466) ),
    inference(clausify,[status(thm)],[f_940_2]) ).

fof(f_941_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).

fof(f_941_2,plain,
    ! [U_4469,U_4468,U_4467] :
      ( hBOOL(hAPP(hAPP(c_member(U_4467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4467),U_4468),U_4469)),c_Int_Oring__1__class_OInts(U_4467)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4467),U_4469),c_Int_Oring__1__class_OInts(U_4467)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4467),U_4468),c_Int_Oring__1__class_OInts(U_4467)))
      | ~ class_Rings_Oring__1(U_4467) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

cnf(f_941_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4467),U_4468),U_4469)),c_Int_Oring__1__class_OInts(U_4467)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4467),U_4469),c_Int_Oring__1__class_OInts(U_4467)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4467),U_4468),c_Int_Oring__1__class_OInts(U_4467)))
    | ~ class_Rings_Oring__1(U_4467) ),
    inference(clausify,[status(thm)],[f_941_2]) ).

fof(f_942_1,plain,
    ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__Suc]) ).

fof(f_942_2,plain,
    ! [U_4474,U_4473,U_4472,U_4471,U_4470] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_4470,U_4471,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4470),U_4472),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4473))),U_4474))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_4470,hAPP(c_Nat_OSuc,U_4471),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4470),U_4472),hAPP(c_Com_Ocom_OBODY,U_4473)),U_4474)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(U_4470,hAPP(c_Nat_OSuc,U_4471),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4470),U_4472),hAPP(c_Com_Ocom_OBODY,U_4473)),U_4474))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_4470,U_4471,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4470),U_4472),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4473))),U_4474)) ) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ( ! [U_4484,U_4482,U_4480,U_4478,U_4476] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_4476,U_4478,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4476),U_4480),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4482))),U_4484))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_4476,hAPP(c_Nat_OSuc,U_4478),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4476),U_4480),hAPP(c_Com_Ocom_OBODY,U_4482)),U_4484)) )
    & ! [U_4483,U_4481,U_4479,U_4477,U_4475] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_4475,hAPP(c_Nat_OSuc,U_4477),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4475),U_4479),hAPP(c_Com_Ocom_OBODY,U_4481)),U_4483))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_4475,U_4477,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4475),U_4479),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4481))),U_4483)) ) ),
    inference(miniscope,[status(thm)],[f_942_2]) ).

cnf(f_942_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_4475,hAPP(c_Nat_OSuc,U_4477),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4475),U_4479),hAPP(c_Com_Ocom_OBODY,U_4481)),U_4483))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_4475,U_4477,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4475),U_4479),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4481))),U_4483)) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

cnf(f_942_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_4476,U_4478,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4476),U_4480),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4482))),U_4484))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_4476,hAPP(c_Nat_OSuc,U_4478),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_4476),U_4480),hAPP(c_Com_Ocom_OBODY,U_4482)),U_4484)) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).

fof(f_943_2,plain,
    ! [U_4487,U_4486,U_4485] :
      ( hBOOL(hAPP(hAPP(c_member(U_4485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4485),U_4486),U_4487)),c_Int_Oring__1__class_OInts(U_4485)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4485),U_4487),c_Int_Oring__1__class_OInts(U_4485)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4485),U_4486),c_Int_Oring__1__class_OInts(U_4485)))
      | ~ class_Rings_Oring__1(U_4485) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

cnf(f_943_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4485),U_4486),U_4487)),c_Int_Oring__1__class_OInts(U_4485)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4485),U_4487),c_Int_Oring__1__class_OInts(U_4485)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4485),U_4486),c_Int_Oring__1__class_OInts(U_4485)))
    | ~ class_Rings_Oring__1(U_4485) ),
    inference(clausify,[status(thm)],[f_943_2]) ).

fof(f_944_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).

fof(f_944_2,plain,
    ! [U_4488] :
      ( hBOOL(hAPP(hAPP(c_member(U_4488),c_Groups_Oone__class_Oone(U_4488)),c_Int_Oring__1__class_OInts(U_4488)))
      | ~ class_Rings_Oring__1(U_4488) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

cnf(f_944_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4488),c_Groups_Oone__class_Oone(U_4488)),c_Int_Oring__1__class_OInts(U_4488)))
    | ~ class_Rings_Oring__1(U_4488) ),
    inference(clausify,[status(thm)],[f_944_2]) ).

fof(f_945_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_945_2,plain,
    ! [U_4489] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4489),c_Groups_Ozero__class_Ozero(U_4489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4489),c_Groups_Oone__class_Oone(U_4489)),c_Groups_Oone__class_Oone(U_4489))))
      | ~ class_Rings_Olinordered__semidom(U_4489) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

cnf(f_945_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4489),c_Groups_Ozero__class_Ozero(U_4489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4489),c_Groups_Oone__class_Oone(U_4489)),c_Groups_Oone__class_Oone(U_4489))))
    | ~ class_Rings_Olinordered__semidom(U_4489) ),
    inference(clausify,[status(thm)],[f_945_2]) ).

fof(f_946_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),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_a),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).

fof(f_946_2,plain,
    ! [U_4491,U_4490] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4491))
      | ~ 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_4490),U_4491))) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

cnf(f_946_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4491))
    | ~ 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_4490),U_4491))) ),
    inference(clausify,[status(thm)],[f_946_2]) ).

fof(f_947_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).

fof(f_947_2,plain,
    ! [U_4496,U_4495,U_4494] :
      ( ( hBOOL(hAPP(U_4494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4495),U_4496)))
        | ? [U_4493] :
            ( ~ hBOOL(hAPP(U_4494,U_4493))
            & U_4495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4496),U_4493) )
        | ( ~ hBOOL(hAPP(U_4494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4495),U_4496)) ) )
      & ( ( ! [U_4492] :
              ( hBOOL(hAPP(U_4494,U_4492))
              | U_4495 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4496),U_4492) )
          & ( hBOOL(hAPP(U_4494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4495),U_4496)) ) )
        | ~ hBOOL(hAPP(U_4494,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4495),U_4496))) ) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ( ! [U_4502,U_4500,U_4498] :
        ( hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502)))
        | ? [U_4493] :
            ( ~ hBOOL(hAPP(U_4498,U_4493))
            & U_4500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4502),U_4493) )
        | ( ~ hBOOL(hAPP(U_4498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4500),U_4502)) ) )
    & ! [U_4501,U_4499,U_4497] :
        ( ( ! [U_4492] :
              ( hBOOL(hAPP(U_4497,U_4492))
              | U_4499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4501),U_4492) )
          & ( hBOOL(hAPP(U_4497,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4499),U_4501)) ) )
        | ~ hBOOL(hAPP(U_4497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4499),U_4501))) ) ),
    inference(miniscope,[status(thm)],[f_947_2]) ).

fof(f_947_4,plain,
    ( ! [U_4502,U_4500,U_4498] :
        ( hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502)))
        | ( ~ hBOOL(hAPP(U_4498,sK86(U_4502,U_4500,U_4498)))
          & U_4500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4502),sK86(U_4502,U_4500,U_4498)) )
        | ( ~ hBOOL(hAPP(U_4498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4500),U_4502)) ) )
    & ! [U_4501,U_4499,U_4497] :
        ( ( ! [U_4492] :
              ( hBOOL(hAPP(U_4497,U_4492))
              | U_4499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4501),U_4492) )
          & ( hBOOL(hAPP(U_4497,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4499),U_4501)) ) )
        | ~ hBOOL(hAPP(U_4497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4499),U_4501))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_4493,sK86(U_4502,U_4500,U_4498))],[f_947_3]) ).

cnf(f_947_5,plain,
    ( hBOOL(hAPP(U_4497,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4499),U_4501))
    | ~ hBOOL(hAPP(U_4497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4499),U_4501))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_6,plain,
    ( hBOOL(hAPP(U_4497,U_4492))
    | U_4499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4501),U_4492)
    | ~ hBOOL(hAPP(U_4497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4499),U_4501))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_7,plain,
    ( U_4500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4502),sK86(U_4502,U_4500,U_4498))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4500),U_4502))
    | hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_8,plain,
    ( ~ hBOOL(hAPP(U_4498,sK86(U_4502,U_4500,U_4498)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4500),U_4502))
    | hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_9,plain,
    ( U_4500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4502),sK86(U_4502,U_4500,U_4498))
    | ~ hBOOL(hAPP(U_4498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_10,plain,
    ( ~ hBOOL(hAPP(U_4498,sK86(U_4502,U_4500,U_4498)))
    | ~ hBOOL(hAPP(U_4498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_4498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4500),U_4502))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

fof(f_948_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(f_948_2,plain,
    ! [U_4507,U_4506,U_4505] :
      ( ( hBOOL(hAPP(U_4505,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4506),U_4507)))
        | ? [U_4504] :
            ( ~ hBOOL(hAPP(U_4505,U_4504))
            & U_4506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4507),U_4504) )
        | ( ~ hBOOL(hAPP(U_4505,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4506),U_4507)) ) )
      & ( ( ! [U_4503] :
              ( hBOOL(hAPP(U_4505,U_4503))
              | U_4506 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4507),U_4503) )
          & ( hBOOL(hAPP(U_4505,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4506),U_4507)) ) )
        | ~ hBOOL(hAPP(U_4505,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4506),U_4507))) ) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ( ! [U_4513,U_4511,U_4509] :
        ( hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513)))
        | ? [U_4504] :
            ( ~ hBOOL(hAPP(U_4509,U_4504))
            & U_4511 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4513),U_4504) )
        | ( ~ hBOOL(hAPP(U_4509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4511),U_4513)) ) )
    & ! [U_4512,U_4510,U_4508] :
        ( ( ! [U_4503] :
              ( hBOOL(hAPP(U_4508,U_4503))
              | U_4510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4512),U_4503) )
          & ( hBOOL(hAPP(U_4508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4510),U_4512)) ) )
        | ~ hBOOL(hAPP(U_4508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4510),U_4512))) ) ),
    inference(miniscope,[status(thm)],[f_948_2]) ).

fof(f_948_4,plain,
    ( ! [U_4513,U_4511,U_4509] :
        ( hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513)))
        | ( ~ hBOOL(hAPP(U_4509,sK87(U_4513,U_4511,U_4509)))
          & U_4511 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4513),sK87(U_4513,U_4511,U_4509)) )
        | ( ~ hBOOL(hAPP(U_4509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4511),U_4513)) ) )
    & ! [U_4512,U_4510,U_4508] :
        ( ( ! [U_4503] :
              ( hBOOL(hAPP(U_4508,U_4503))
              | U_4510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4512),U_4503) )
          & ( hBOOL(hAPP(U_4508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4510),U_4512)) ) )
        | ~ hBOOL(hAPP(U_4508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4510),U_4512))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_4504,sK87(U_4513,U_4511,U_4509))],[f_948_3]) ).

cnf(f_948_5,plain,
    ( hBOOL(hAPP(U_4508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4510),U_4512))
    | ~ hBOOL(hAPP(U_4508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4510),U_4512))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_6,plain,
    ( hBOOL(hAPP(U_4508,U_4503))
    | U_4510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4512),U_4503)
    | ~ hBOOL(hAPP(U_4508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4510),U_4512))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_7,plain,
    ( U_4511 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4513),sK87(U_4513,U_4511,U_4509))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4511),U_4513))
    | hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_8,plain,
    ( ~ hBOOL(hAPP(U_4509,sK87(U_4513,U_4511,U_4509)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4511),U_4513))
    | hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_9,plain,
    ( U_4511 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4513),sK87(U_4513,U_4511,U_4509))
    | ~ hBOOL(hAPP(U_4509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_10,plain,
    ( ~ hBOOL(hAPP(U_4509,sK87(U_4513,U_4511,U_4509)))
    | ~ hBOOL(hAPP(U_4509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_4509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4511),U_4513))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

fof(f_949_1,plain,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2)))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(f_949_2,plain,
    ! [U_4518,U_4517,U_4516,U_4515,U_4514] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4514,U_4514,c_Groups_Otimes__class_Otimes(U_4514),U_4518,hAPP(hAPP(c_Set_Oinsert(U_4514),U_4515),U_4516)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4514),U_4518),U_4517)))
      | hBOOL(hAPP(hAPP(c_member(U_4514),U_4515),U_4516))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4514,U_4514,c_Groups_Otimes__class_Otimes(U_4514),U_4515,U_4516),U_4517))
      | ~ class_Groups_Oab__semigroup__mult(U_4514) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

cnf(f_949_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4514,U_4514,c_Groups_Otimes__class_Otimes(U_4514),U_4518,hAPP(hAPP(c_Set_Oinsert(U_4514),U_4515),U_4516)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4514),U_4518),U_4517)))
    | hBOOL(hAPP(hAPP(c_member(U_4514),U_4515),U_4516))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4514,U_4514,c_Groups_Otimes__class_Otimes(U_4514),U_4515,U_4516),U_4517))
    | ~ class_Groups_Oab__semigroup__mult(U_4514) ),
    inference(clausify,[status(thm)],[f_949_2]) ).

fof(f_950_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),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_a),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_a),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_a),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).

fof(f_950_2,plain,
    ! [U_4525,U_4524,U_4523] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_4522] :
              ( ? [U_4521] :
                  ( hAPP(U_4525,U_4521) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_4522 != U_4521
                  & hBOOL(hAPP(hAPP(c_member(U_4523),U_4521),U_4524)) )
              | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524)) ) )
        & ( ? [U_4520] :
              ( ! [U_4519] :
                  ( hAPP(U_4525,U_4519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_4520 = U_4519
                  | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4519),U_4524)) )
              & hAPP(U_4525,U_4520) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_4523),U_4520),U_4524)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_4525,U_4524,U_4523] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_4522] :
              ( ? [U_4521] :
                  ( hAPP(U_4525,U_4521) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_4522 != U_4521
                  & hBOOL(hAPP(hAPP(c_member(U_4523),U_4521),U_4524)) )
              | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524)) ) )
        & ( ( ! [U_4519] :
                ( hAPP(U_4525,U_4519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK88(U_4525,U_4524,U_4523) = U_4519
                | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4519),U_4524)) )
            & hAPP(U_4525,sK88(U_4525,U_4524,U_4523)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_4523),sK88(U_4525,U_4524,U_4523)),U_4524)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4520,sK88(U_4525,U_4524,U_4523))],[f_950_2]) ).

fof(f_950_4,plain,
    ! [U_4525,U_4524,U_4523] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_4522] :
              ( ( hAPP(U_4525,sK89(U_4525,U_4524,U_4523,U_4522)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_4522 != sK89(U_4525,U_4524,U_4523,U_4522)
                & hBOOL(hAPP(hAPP(c_member(U_4523),sK89(U_4525,U_4524,U_4523,U_4522)),U_4524)) )
              | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524)) ) )
        & ( ( ! [U_4519] :
                ( hAPP(U_4525,U_4519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK88(U_4525,U_4524,U_4523) = U_4519
                | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4519),U_4524)) )
            & hAPP(U_4525,sK88(U_4525,U_4524,U_4523)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_4523),sK88(U_4525,U_4524,U_4523)),U_4524)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4521,sK89(U_4525,U_4524,U_4523,U_4522))],[f_950_3]) ).

cnf(f_950_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4523),sK88(U_4525,U_4524,U_4523)),U_4524))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_6,plain,
    ( hAPP(U_4525,sK88(U_4525,U_4524,U_4523)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_7,plain,
    ( hAPP(U_4525,U_4519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK88(U_4525,U_4524,U_4523) = U_4519
    | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4519),U_4524))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4523),sK89(U_4525,U_4524,U_4523,U_4522)),U_4524))
    | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_9,plain,
    ( U_4522 != sK89(U_4525,U_4524,U_4523,U_4522)
    | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_10,plain,
    ( hAPP(U_4525,sK89(U_4525,U_4524,U_4523,U_4522)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_4525,U_4522) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4523),U_4522),U_4524))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4523,tc_Nat_Onat),U_4525),U_4524) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4523),U_4524)) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

fof(f_951_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).

fof(f_951_2,plain,
    ! [U_4530,U_4529,U_4528,U_4527,U_4526] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),hAPP(hAPP(c_COMBS(U_4527,U_4526,U_4526),hAPP(hAPP(c_COMBB(U_4526,tc_fun(U_4526,U_4526),U_4527),c_Groups_Otimes__class_Otimes(U_4526)),U_4529)),U_4530)),c_Groups_Oone__class_Oone(U_4526)),U_4528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4526),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),U_4529),c_Groups_Oone__class_Oone(U_4526)),U_4528)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),U_4530),c_Groups_Oone__class_Oone(U_4526)),U_4528))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4527),U_4528))
      | ~ class_Groups_Ocomm__monoid__mult(U_4526) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

cnf(f_951_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),hAPP(hAPP(c_COMBS(U_4527,U_4526,U_4526),hAPP(hAPP(c_COMBB(U_4526,tc_fun(U_4526,U_4526),U_4527),c_Groups_Otimes__class_Otimes(U_4526)),U_4529)),U_4530)),c_Groups_Oone__class_Oone(U_4526)),U_4528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4526),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),U_4529),c_Groups_Oone__class_Oone(U_4526)),U_4528)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4526,U_4527,c_Groups_Otimes__class_Otimes(U_4526)),U_4530),c_Groups_Oone__class_Oone(U_4526)),U_4528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4527),U_4528))
    | ~ class_Groups_Ocomm__monoid__mult(U_4526) ),
    inference(clausify,[status(thm)],[f_951_2]) ).

fof(f_952_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).

fof(f_952_2,plain,
    ! [U_4533,U_4532,U_4531] :
      ( hAPP(c_Finite__Set_Ocard(U_4531),hAPP(hAPP(c_Set_Oinsert(U_4531),U_4533),U_4532)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4531),U_4532))
      | hBOOL(hAPP(hAPP(c_member(U_4531),U_4533),U_4532))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4531),U_4532)) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

cnf(f_952_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4531),hAPP(hAPP(c_Set_Oinsert(U_4531),U_4533),U_4532)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4531),U_4532))
    | hBOOL(hAPP(hAPP(c_member(U_4531),U_4533),U_4532))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4531),U_4532)) ),
    inference(clausify,[status(thm)],[f_952_2]) ).

fof(f_953_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2))
          | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).

fof(f_953_2,plain,
    ! [U_4536,U_4535,U_4534] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_4534),hAPP(hAPP(c_Set_Oinsert(U_4534),U_4536),U_4535)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4534),U_4535))
          | hBOOL(hAPP(hAPP(c_member(U_4534),U_4536),U_4535)) )
        & ( hAPP(c_Finite__Set_Ocard(U_4534),hAPP(hAPP(c_Set_Oinsert(U_4534),U_4536),U_4535)) = hAPP(c_Finite__Set_Ocard(U_4534),U_4535)
          | ~ hBOOL(hAPP(hAPP(c_member(U_4534),U_4536),U_4535)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4534),U_4535)) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

cnf(f_953_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4534),hAPP(hAPP(c_Set_Oinsert(U_4534),U_4536),U_4535)) = hAPP(c_Finite__Set_Ocard(U_4534),U_4535)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4534),U_4536),U_4535))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4534),U_4535)) ),
    inference(clausify,[status(thm)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4534),hAPP(hAPP(c_Set_Oinsert(U_4534),U_4536),U_4535)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4534),U_4535))
    | hBOOL(hAPP(hAPP(c_member(U_4534),U_4536),U_4535))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4534),U_4535)) ),
    inference(clausify,[status(thm)],[f_953_2]) ).

fof(f_954_1,plain,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).

fof(f_954_2,plain,
    ! [U_4542,U_4541,U_4540,U_4539,U_4538,U_4537] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4537,U_4538,c_Groups_Otimes__class_Otimes(U_4537)),U_4541),U_4542),hAPP(hAPP(c_Set_Oinsert(U_4538),U_4540),U_4539)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),hAPP(U_4541,U_4540)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4537,U_4538,c_Groups_Otimes__class_Otimes(U_4537)),U_4541),U_4542),U_4539))
      | hBOOL(hAPP(hAPP(c_member(U_4538),U_4540),U_4539))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4538),U_4539))
      | ~ class_Groups_Oab__semigroup__mult(U_4537) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

cnf(f_954_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4537,U_4538,c_Groups_Otimes__class_Otimes(U_4537)),U_4541),U_4542),hAPP(hAPP(c_Set_Oinsert(U_4538),U_4540),U_4539)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4537),hAPP(U_4541,U_4540)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4537,U_4538,c_Groups_Otimes__class_Otimes(U_4537)),U_4541),U_4542),U_4539))
    | hBOOL(hAPP(hAPP(c_member(U_4538),U_4540),U_4539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4538),U_4539))
    | ~ class_Groups_Oab__semigroup__mult(U_4537) ),
    inference(clausify,[status(thm)],[f_954_2]) ).

fof(f_955_1,plain,
    ! [V_A_2,T_a] :
      ( ( 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_a),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).

fof(f_955_2,plain,
    ! [U_4544,U_4543] :
      ( ( 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_4543),U_4544)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4543),U_4544))
        | U_4544 = c_Orderings_Obot__class_Obot(tc_fun(U_4543,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4543),U_4544))
          & U_4544 != c_Orderings_Obot__class_Obot(tc_fun(U_4543,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_4543),U_4544))) ) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ( ! [U_4548,U_4546] :
        ( 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_4546),U_4548)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4546),U_4548))
        | U_4548 = c_Orderings_Obot__class_Obot(tc_fun(U_4546,tc_HOL_Obool)) )
    & ! [U_4547,U_4545] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4545),U_4547))
          & U_4547 != c_Orderings_Obot__class_Obot(tc_fun(U_4545,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_4545),U_4547))) ) ),
    inference(miniscope,[status(thm)],[f_955_2]) ).

cnf(f_955_4,plain,
    ( U_4547 != c_Orderings_Obot__class_Obot(tc_fun(U_4545,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_4545),U_4547))) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

cnf(f_955_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4545),U_4547))
    | ~ 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_4545),U_4547))) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

cnf(f_955_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_4546),U_4548)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4546),U_4548))
    | U_4548 = c_Orderings_Obot__class_Obot(tc_fun(U_4546,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_1,plain,
    ! [T_a] :
      ( 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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).

fof(f_956_2,plain,
    ! [U_4549] :
      ( 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_4549),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4549),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

cnf(f_956_3,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_4549),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4549),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_956_2]) ).

fof(f_957_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).

fof(f_957_2,plain,
    ! [U_4551,U_4550] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4550),U_4551),U_4551) = c_Groups_Ozero__class_Ozero(U_4550)
          | U_4551 != c_Groups_Ozero__class_Ozero(U_4550) )
        & ( U_4551 = c_Groups_Ozero__class_Ozero(U_4550)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4550),U_4551),U_4551) != c_Groups_Ozero__class_Ozero(U_4550) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4550),U_4551),c_Int_Oring__1__class_OInts(U_4550)))
      | ~ class_Int_Oring__char__0(U_4550) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

cnf(f_957_3,plain,
    ( U_4551 = c_Groups_Ozero__class_Ozero(U_4550)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4550),U_4551),U_4551) != c_Groups_Ozero__class_Ozero(U_4550)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4550),U_4551),c_Int_Oring__1__class_OInts(U_4550)))
    | ~ class_Int_Oring__char__0(U_4550) ),
    inference(clausify,[status(thm)],[f_957_2]) ).

cnf(f_957_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4550),U_4551),U_4551) = c_Groups_Ozero__class_Ozero(U_4550)
    | U_4551 != c_Groups_Ozero__class_Ozero(U_4550)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4550),U_4551),c_Int_Oring__1__class_OInts(U_4550)))
    | ~ class_Int_Oring__char__0(U_4550) ),
    inference(clausify,[status(thm)],[f_957_2]) ).

fof(f_958_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).

fof(f_958_2,plain,
    ! [U_4555,U_4554,U_4553,U_4552] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4552,U_4553)),c_Sum__Type_OPlus(U_4552,U_4553,U_4554,U_4555)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4553),U_4555))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4554)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4553),U_4555))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4554)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4552,U_4553)),c_Sum__Type_OPlus(U_4552,U_4553,U_4554,U_4555))) ) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ( ! [U_4563,U_4561,U_4559,U_4557] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4557,U_4559)),c_Sum__Type_OPlus(U_4557,U_4559,U_4561,U_4563)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4559),U_4563))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4557),U_4561)) )
    & ! [U_4562,U_4560,U_4558,U_4556] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4558),U_4562))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_4556),U_4560)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4556,U_4558)),c_Sum__Type_OPlus(U_4556,U_4558,U_4560,U_4562))) ) ),
    inference(miniscope,[status(thm)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4556),U_4560))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4556,U_4558)),c_Sum__Type_OPlus(U_4556,U_4558,U_4560,U_4562))) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

cnf(f_958_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4558),U_4562))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4556,U_4558)),c_Sum__Type_OPlus(U_4556,U_4558,U_4560,U_4562))) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

cnf(f_958_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4557,U_4559)),c_Sum__Type_OPlus(U_4557,U_4559,U_4561,U_4563)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4559),U_4563))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4557),U_4561)) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).

fof(f_959_2,plain,
    ! [U_4567,U_4566,U_4565,U_4564] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4564,U_4566)),c_Sum__Type_OPlus(U_4564,U_4566,U_4565,U_4567)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4566),U_4567))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4564),U_4565)) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

cnf(f_959_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4564,U_4566)),c_Sum__Type_OPlus(U_4564,U_4566,U_4565,U_4567)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4566),U_4567))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4564),U_4565)) ),
    inference(clausify,[status(thm)],[f_959_2]) ).

fof(f_960_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).

fof(f_960_2,plain,
    ! [U_4571,U_4570,U_4569,U_4568] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4568),U_4570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4568,U_4569)),c_Sum__Type_OPlus(U_4568,U_4569,U_4570,U_4571))) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

cnf(f_960_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4568),U_4570))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4568,U_4569)),c_Sum__Type_OPlus(U_4568,U_4569,U_4570,U_4571))) ),
    inference(clausify,[status(thm)],[f_960_2]) ).

fof(f_961_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).

fof(f_961_2,plain,
    ! [U_4575,U_4574,U_4573,U_4572] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4573),U_4575))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4572,U_4573)),c_Sum__Type_OPlus(U_4572,U_4573,U_4574,U_4575))) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_4575,U_4574,U_4573] :
      ( ! [U_4572] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4572,U_4573)),c_Sum__Type_OPlus(U_4572,U_4573,U_4574,U_4575)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4573),U_4575)) ),
    inference(miniscope,[status(thm)],[f_961_2]) ).

cnf(f_961_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4572,U_4573)),c_Sum__Type_OPlus(U_4572,U_4573,U_4574,U_4575)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4573),U_4575)) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert]) ).

fof(f_962_2,plain,
    ! [U_4578,U_4577,U_4576] :
      ( hAPP(c_Finite__Set_Ocard(U_4576),hAPP(hAPP(c_Set_Oinsert(U_4576),U_4578),U_4577)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4576,tc_HOL_Obool)),U_4577),hAPP(hAPP(c_Set_Oinsert(U_4576),U_4578),c_Orderings_Obot__class_Obot(tc_fun(U_4576,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4576),U_4577)) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

cnf(f_962_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4576),hAPP(hAPP(c_Set_Oinsert(U_4576),U_4578),U_4577)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4576,tc_HOL_Obool)),U_4577),hAPP(hAPP(c_Set_Oinsert(U_4576),U_4578),c_Orderings_Obot__class_Obot(tc_fun(U_4576,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4576),U_4577)) ),
    inference(clausify,[status(thm)],[f_962_2]) ).

fof(f_963_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),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_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).

fof(f_963_2,plain,
    ! [U_4582,U_4581,U_4580,U_4579] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_4579,U_4581)),c_Sum__Type_OPlus(U_4579,U_4581,U_4580,U_4582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4579),U_4580)),hAPP(c_Finite__Set_Ocard(U_4581),U_4582))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4581),U_4582))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4579),U_4580)) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

cnf(f_963_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_4579,U_4581)),c_Sum__Type_OPlus(U_4579,U_4581,U_4580,U_4582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4579),U_4580)),hAPP(c_Finite__Set_Ocard(U_4581),U_4582))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4581),U_4582))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4579),U_4580)) ),
    inference(clausify,[status(thm)],[f_963_2]) ).

fof(f_964_1,plain,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(f_964_2,plain,
    ! [U_4587,U_4586,U_4585,U_4584,U_4583] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4583,U_4583,c_Groups_Otimes__class_Otimes(U_4583),U_4587,hAPP(hAPP(c_Set_Oinsert(U_4583),U_4584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4583,tc_HOL_Obool)),U_4585),hAPP(hAPP(c_Set_Oinsert(U_4583),U_4587),c_Orderings_Obot__class_Obot(tc_fun(U_4583,tc_HOL_Obool)))))),U_4586))
      | hBOOL(hAPP(hAPP(c_member(U_4583),U_4584),U_4585))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4583),U_4587),U_4585))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4583,U_4583,c_Groups_Otimes__class_Otimes(U_4583),U_4584,U_4585),U_4586))
      | ~ class_Groups_Oab__semigroup__mult(U_4583) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

cnf(f_964_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4583,U_4583,c_Groups_Otimes__class_Otimes(U_4583),U_4587,hAPP(hAPP(c_Set_Oinsert(U_4583),U_4584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4583,tc_HOL_Obool)),U_4585),hAPP(hAPP(c_Set_Oinsert(U_4583),U_4587),c_Orderings_Obot__class_Obot(tc_fun(U_4583,tc_HOL_Obool)))))),U_4586))
    | hBOOL(hAPP(hAPP(c_member(U_4583),U_4584),U_4585))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4583),U_4587),U_4585))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4583,U_4583,c_Groups_Otimes__class_Otimes(U_4583),U_4584,U_4585),U_4586))
    | ~ class_Groups_Oab__semigroup__mult(U_4583) ),
    inference(clausify,[status(thm)],[f_964_2]) ).

fof(f_965_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).

fof(f_965_2,plain,
    ! [U_4592,U_4591,U_4590,U_4589,U_4588] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),U_4590)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),U_4591)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4589,tc_HOL_Obool)),U_4590),U_4591))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4589,tc_HOL_Obool)),U_4590),U_4591)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4589),U_4591))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4589),U_4590))
      | ~ class_Groups_Ocomm__monoid__mult(U_4588) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

cnf(f_965_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),U_4590)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),U_4591)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4588),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4589,tc_HOL_Obool)),U_4590),U_4591))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4588,U_4589,c_Groups_Otimes__class_Otimes(U_4588)),U_4592),c_Groups_Oone__class_Oone(U_4588)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4589,tc_HOL_Obool)),U_4590),U_4591)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4589),U_4591))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4589),U_4590))
    | ~ class_Groups_Ocomm__monoid__mult(U_4588) ),
    inference(clausify,[status(thm)],[f_965_2]) ).

fof(f_966_1,plain,
    ! [T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).

fof(f_966_2,plain,
    ! [U_4594,U_4593] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4593),c_Orderings_Otop__class_Otop(tc_fun(U_4593,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_4594),c_Orderings_Otop__class_Otop(tc_fun(U_4594,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_4593,U_4594)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_4593,U_4594),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

cnf(f_966_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4593),c_Orderings_Otop__class_Otop(tc_fun(U_4593,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_4594),c_Orderings_Otop__class_Otop(tc_fun(U_4594,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_4593,U_4594)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_4593,U_4594),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_966_2]) ).

fof(f_967_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_967_2,plain,
    ! [U_4596,U_4595] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4595),U_4596) = 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_4595),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4596))
        | U_4595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4595),U_4596) = U_4596
        | U_4595 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ( ! [U_4600,U_4598] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4598),U_4600) = 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_4598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4600))
        | U_4598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4599,U_4597] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4597),U_4599) = U_4599
        | U_4597 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_967_2]) ).

cnf(f_967_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4597),U_4599) = U_4599
    | U_4597 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

cnf(f_967_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4598),U_4600) = 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_4598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4600))
    | U_4598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_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_968_2,plain,
    ! [U_4601] :
      ( U_4601 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4601),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_4601)) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

cnf(f_968_3,plain,
    ( U_4601 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4601),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_4601)) ),
    inference(clausify,[status(thm)],[f_968_2]) ).

fof(f_969_1,plain,
    ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(f_969_2,plain,
    ! [U_4603,U_4602] : c_Sum__Type_OPlus(U_4602,U_4603,c_Orderings_Otop__class_Otop(tc_fun(U_4602,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4603,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_4602,U_4603),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

cnf(f_969_3,plain,
    c_Sum__Type_OPlus(U_4602,U_4603,c_Orderings_Otop__class_Otop(tc_fun(U_4602,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4603,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_4602,U_4603),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_969_2]) ).

fof(f_970_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_970_2,plain,
    ! [U_4605,U_4604] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4604),U_4605) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4604),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4605))
        | U_4604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4604),U_4605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ( ! [U_4609,U_4607] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4607),U_4609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4607),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4609))
        | U_4607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4608,U_4606] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4606),U_4608) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_970_2]) ).

cnf(f_970_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4606),U_4608) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4607),U_4609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4607),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4609))
    | U_4607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_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_971_2,plain,
    ! [U_4612,U_4611,U_4610] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4610),U_4611),U_4611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4610),U_4612),U_4612))),c_Groups_Ozero__class_Ozero(U_4610)))
      | ~ class_Rings_Olinordered__ring(U_4610) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

cnf(f_971_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4610),U_4611),U_4611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4610),U_4612),U_4612))),c_Groups_Ozero__class_Ozero(U_4610)))
    | ~ class_Rings_Olinordered__ring(U_4610) ),
    inference(clausify,[status(thm)],[f_971_2]) ).

fof(f_972_1,plain,
    ! [V_y_2,V_x_2,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != 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_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).

fof(f_972_2,plain,
    ! [U_4615,U_4614,U_4613] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4613),c_Groups_Ozero__class_Ozero(U_4613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4614),U_4614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4615),U_4615))))
          | ( U_4615 = c_Groups_Ozero__class_Ozero(U_4613)
            & U_4614 = c_Groups_Ozero__class_Ozero(U_4613) ) )
        & ( U_4615 != c_Groups_Ozero__class_Ozero(U_4613)
          | U_4614 != c_Groups_Ozero__class_Ozero(U_4613)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4613),c_Groups_Ozero__class_Ozero(U_4613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4614),U_4614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4615),U_4615)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_4613) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

cnf(f_972_3,plain,
    ( U_4615 != c_Groups_Ozero__class_Ozero(U_4613)
    | U_4614 != c_Groups_Ozero__class_Ozero(U_4613)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4613),c_Groups_Ozero__class_Ozero(U_4613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4614),U_4614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4615),U_4615))))
    | ~ class_Rings_Olinordered__ring__strict(U_4613) ),
    inference(clausify,[status(thm)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( U_4614 = c_Groups_Ozero__class_Ozero(U_4613)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4613),c_Groups_Ozero__class_Ozero(U_4613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4614),U_4614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4615),U_4615))))
    | ~ class_Rings_Olinordered__ring__strict(U_4613) ),
    inference(clausify,[status(thm)],[f_972_2]) ).

cnf(f_972_5,plain,
    ( U_4615 = c_Groups_Ozero__class_Ozero(U_4613)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4613),c_Groups_Ozero__class_Ozero(U_4613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4614),U_4614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4613),U_4615),U_4615))))
    | ~ class_Rings_Olinordered__ring__strict(U_4613) ),
    inference(clausify,[status(thm)],[f_972_2]) ).

fof(f_973_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_973_2,plain,
    ! [U_4617,U_4616] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4616),hAPP(c_Nat_OSuc,U_4617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4616),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4617),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

cnf(f_973_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4616),hAPP(c_Nat_OSuc,U_4617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4616),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4617),
    inference(clausify,[status(thm)],[f_973_2]) ).

fof(f_974_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_974_2,plain,
    ! [U_4618] : hAPP(c_Nat_OSuc,U_4618) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4618),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

cnf(f_974_3,plain,
    hAPP(c_Nat_OSuc,U_4618) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4618),
    inference(clausify,[status(thm)],[f_974_2]) ).

fof(f_975_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_975_2,plain,
    ! [U_4621,U_4620,U_4619] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4619),U_4620)),U_4621) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4620),U_4621)),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

cnf(f_975_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4619),U_4620)),U_4621) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4620),U_4621)),
    inference(clausify,[status(thm)],[f_975_2]) ).

fof(f_976_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_976_2,plain,
    ! [U_4623,U_4622] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4622),U_4623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4623),U_4622),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

cnf(f_976_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4622),U_4623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4623),U_4622),
    inference(clausify,[status(thm)],[f_976_2]) ).

fof(f_977_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).

fof(f_977_2,plain,
    ! [U_4627,U_4626,U_4625,U_4624] :
      ( hBOOL(hAPP(hAPP(c_member(U_4624),U_4627),U_4626))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4624),U_4627),U_4625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4624,tc_HOL_Obool)),U_4625),U_4626)) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

cnf(f_977_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4624),U_4627),U_4626))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4624),U_4627),U_4625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4624,tc_HOL_Obool)),U_4625),U_4626)) ),
    inference(clausify,[status(thm)],[f_977_2]) ).

fof(f_978_1,plain,
    ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).

fof(f_978_2,plain,
    ! [U_4629,U_4628] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4628,tc_HOL_Obool)),U_4629),c_Orderings_Obot__class_Obot(tc_fun(U_4628,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

cnf(f_978_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4628,tc_HOL_Obool)),U_4629),c_Orderings_Obot__class_Obot(tc_fun(U_4628,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_978_2]) ).

fof(f_979_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).

fof(f_979_2,plain,
    ! [U_4632,U_4631,U_4630] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4630),U_4632)),hAPP(c_Finite__Set_Ocard(U_4630),U_4631)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4630,tc_HOL_Obool)),U_4632),U_4631))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4630),U_4631)) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

cnf(f_979_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4630),U_4632)),hAPP(c_Finite__Set_Ocard(U_4630),U_4631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4630,tc_HOL_Obool)),U_4632),U_4631))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4630),U_4631)) ),
    inference(clausify,[status(thm)],[f_979_2]) ).

fof(f_980_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,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_a,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_a,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).

fof(f_980_2,plain,
    ! [U_4636,U_4635,U_4634,U_4633] :
      ( ( c_Sum__Type_OPlus(U_4633,U_4634,U_4635,U_4636) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4633,U_4634),tc_HOL_Obool))
        | U_4636 != c_Orderings_Obot__class_Obot(tc_fun(U_4634,tc_HOL_Obool))
        | U_4635 != c_Orderings_Obot__class_Obot(tc_fun(U_4633,tc_HOL_Obool)) )
      & ( ( U_4636 = c_Orderings_Obot__class_Obot(tc_fun(U_4634,tc_HOL_Obool))
          & U_4635 = c_Orderings_Obot__class_Obot(tc_fun(U_4633,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_4633,U_4634,U_4635,U_4636) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4633,U_4634),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ( ! [U_4644,U_4642,U_4640,U_4638] :
        ( c_Sum__Type_OPlus(U_4638,U_4640,U_4642,U_4644) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4638,U_4640),tc_HOL_Obool))
        | U_4644 != c_Orderings_Obot__class_Obot(tc_fun(U_4640,tc_HOL_Obool))
        | U_4642 != c_Orderings_Obot__class_Obot(tc_fun(U_4638,tc_HOL_Obool)) )
    & ! [U_4643,U_4641,U_4639,U_4637] :
        ( ( U_4643 = c_Orderings_Obot__class_Obot(tc_fun(U_4639,tc_HOL_Obool))
          & U_4641 = c_Orderings_Obot__class_Obot(tc_fun(U_4637,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_4637,U_4639,U_4641,U_4643) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4637,U_4639),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( U_4641 = c_Orderings_Obot__class_Obot(tc_fun(U_4637,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_4637,U_4639,U_4641,U_4643) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4637,U_4639),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

cnf(f_980_5,plain,
    ( U_4643 = c_Orderings_Obot__class_Obot(tc_fun(U_4639,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_4637,U_4639,U_4641,U_4643) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4637,U_4639),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

cnf(f_980_6,plain,
    ( c_Sum__Type_OPlus(U_4638,U_4640,U_4642,U_4644) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4638,U_4640),tc_HOL_Obool))
    | U_4644 != c_Orderings_Obot__class_Obot(tc_fun(U_4640,tc_HOL_Obool))
    | U_4642 != c_Orderings_Obot__class_Obot(tc_fun(U_4638,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = 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_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).

fof(f_981_2,plain,
    ! [U_4647,U_4646,U_4645] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4646),U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4647),U_4647)) = c_Groups_Ozero__class_Ozero(U_4645)
          | U_4647 != c_Groups_Ozero__class_Ozero(U_4645)
          | U_4646 != c_Groups_Ozero__class_Ozero(U_4645) )
        & ( ( U_4647 = c_Groups_Ozero__class_Ozero(U_4645)
            & U_4646 = c_Groups_Ozero__class_Ozero(U_4645) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4646),U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4647),U_4647)) != c_Groups_Ozero__class_Ozero(U_4645) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_4645) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

cnf(f_981_3,plain,
    ( U_4646 = c_Groups_Ozero__class_Ozero(U_4645)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4646),U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4647),U_4647)) != c_Groups_Ozero__class_Ozero(U_4645)
    | ~ class_Rings_Olinordered__ring__strict(U_4645) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( U_4647 = c_Groups_Ozero__class_Ozero(U_4645)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4646),U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4647),U_4647)) != c_Groups_Ozero__class_Ozero(U_4645)
    | ~ class_Rings_Olinordered__ring__strict(U_4645) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

cnf(f_981_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4646),U_4646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),U_4647),U_4647)) = c_Groups_Ozero__class_Ozero(U_4645)
    | U_4647 != c_Groups_Ozero__class_Ozero(U_4645)
    | U_4646 != c_Groups_Ozero__class_Ozero(U_4645)
    | ~ class_Rings_Olinordered__ring__strict(U_4645) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

fof(f_982_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_982_2,plain,
    ! [U_4648] : hAPP(c_Nat_OSuc,U_4648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4648),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

cnf(f_982_3,plain,
    hAPP(c_Nat_OSuc,U_4648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4648),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_982_2]) ).

fof(f_983_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_983_2,plain,
    ! [U_4651,U_4650,U_4649] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4651)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4651))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4649)) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

cnf(f_983_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4651)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4649)) ),
    inference(clausify,[status(thm)],[f_983_2]) ).

cnf(f_983_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4649),U_4651)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4649)) ),
    inference(clausify,[status(thm)],[f_983_2]) ).

fof(f_984_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_984_2,plain,
    ! [U_4654,U_4653,U_4652] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4654)
          | U_4653 != U_4654 )
        & ( U_4653 = U_4654
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4653) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4654) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4652)) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

cnf(f_984_3,plain,
    ( U_4653 = U_4654
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4653) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4654)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4652)) ),
    inference(clausify,[status(thm)],[f_984_2]) ).

cnf(f_984_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4652),U_4654)
    | U_4653 != U_4654
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4652)) ),
    inference(clausify,[status(thm)],[f_984_2]) ).

fof(f_985_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).

fof(f_985_2,plain,
    ! [U_4660,U_4659,U_4658,U_4657,U_4656] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4656),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4658)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4659))
      | ? [U_4655] :
          ( hAPP(U_4660,U_4655) != c_Groups_Oone__class_Oone(U_4656)
          & hBOOL(hAPP(hAPP(c_member(U_4657),U_4655),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4659))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4658))
      | ~ class_Groups_Ocomm__monoid__mult(U_4656) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ! [U_4660,U_4659,U_4658,U_4657,U_4656] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4656),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4658)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4659))
      | ( hAPP(U_4660,sK90(U_4660,U_4659,U_4658,U_4657,U_4656)) != c_Groups_Oone__class_Oone(U_4656)
        & hBOOL(hAPP(hAPP(c_member(U_4657),sK90(U_4660,U_4659,U_4658,U_4657,U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4659))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4658))
      | ~ class_Groups_Ocomm__monoid__mult(U_4656) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4655,sK90(U_4660,U_4659,U_4658,U_4657,U_4656))],[f_985_2]) ).

cnf(f_985_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4657),sK90(U_4660,U_4659,U_4658,U_4657,U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659)))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4656),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4658)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4659))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4659))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4658))
    | ~ class_Groups_Ocomm__monoid__mult(U_4656) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_5,plain,
    ( hAPP(U_4660,sK90(U_4660,U_4659,U_4658,U_4657,U_4656)) != c_Groups_Oone__class_Oone(U_4656)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4657,tc_HOL_Obool)),U_4658),U_4659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4656),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4658)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4656,U_4657,c_Groups_Otimes__class_Otimes(U_4656)),U_4660),c_Groups_Oone__class_Oone(U_4656)),U_4659))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4659))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4657),U_4658))
    | ~ class_Groups_Ocomm__monoid__mult(U_4656) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_1,plain,
    ! [V_k_2,V_A_2,T_a] :
      ( ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
        | ! [B_b,B_B] :
            ( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
              & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(T_a),B_B) != V_k_2
            | hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
            | V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) ) )
      & ( ? [B_b,B_B] :
            ( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
              | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
            & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
            & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) )
        | hAPP(c_Finite__Set_Ocard(T_a),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).

fof(f_986_2,plain,
    ! [U_4667,U_4666,U_4665] :
      ( ( hAPP(c_Finite__Set_Ocard(U_4665),U_4666) = hAPP(c_Nat_OSuc,U_4667)
        | ! [U_4664,U_4663] :
            ( ( U_4663 != c_Orderings_Obot__class_Obot(tc_fun(U_4665,tc_HOL_Obool))
              & U_4667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_4665),U_4663) != U_4667
            | hBOOL(hAPP(hAPP(c_member(U_4665),U_4664),U_4663))
            | U_4666 != hAPP(hAPP(c_Set_Oinsert(U_4665),U_4664),U_4663) ) )
      & ( ? [U_4662,U_4661] :
            ( ( U_4661 = c_Orderings_Obot__class_Obot(tc_fun(U_4665,tc_HOL_Obool))
              | U_4667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_4665),U_4661) = U_4667
            & ~ hBOOL(hAPP(hAPP(c_member(U_4665),U_4662),U_4661))
            & U_4666 = hAPP(hAPP(c_Set_Oinsert(U_4665),U_4662),U_4661) )
        | hAPP(c_Finite__Set_Ocard(U_4665),U_4666) != hAPP(c_Nat_OSuc,U_4667) ) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ( ! [U_4673,U_4671,U_4669] :
        ( hAPP(c_Finite__Set_Ocard(U_4669),U_4671) = hAPP(c_Nat_OSuc,U_4673)
        | ! [U_4664,U_4663] :
            ( ( U_4663 != c_Orderings_Obot__class_Obot(tc_fun(U_4669,tc_HOL_Obool))
              & U_4673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_4669),U_4663) != U_4673
            | hBOOL(hAPP(hAPP(c_member(U_4669),U_4664),U_4663))
            | U_4671 != hAPP(hAPP(c_Set_Oinsert(U_4669),U_4664),U_4663) ) )
    & ! [U_4672,U_4670,U_4668] :
        ( ? [U_4662,U_4661] :
            ( ( U_4661 = c_Orderings_Obot__class_Obot(tc_fun(U_4668,tc_HOL_Obool))
              | U_4672 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_4668),U_4661) = U_4672
            & ~ hBOOL(hAPP(hAPP(c_member(U_4668),U_4662),U_4661))
            & U_4670 = hAPP(hAPP(c_Set_Oinsert(U_4668),U_4662),U_4661) )
        | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ) ),
    inference(miniscope,[status(thm)],[f_986_2]) ).

fof(f_986_4,plain,
    ( ! [U_4673,U_4671,U_4669] :
        ( hAPP(c_Finite__Set_Ocard(U_4669),U_4671) = hAPP(c_Nat_OSuc,U_4673)
        | ! [U_4664,U_4663] :
            ( ( U_4663 != c_Orderings_Obot__class_Obot(tc_fun(U_4669,tc_HOL_Obool))
              & U_4673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_4669),U_4663) != U_4673
            | hBOOL(hAPP(hAPP(c_member(U_4669),U_4664),U_4663))
            | U_4671 != hAPP(hAPP(c_Set_Oinsert(U_4669),U_4664),U_4663) ) )
    & ! [U_4672,U_4670,U_4668] :
        ( ? [U_4661] :
            ( ( U_4661 = c_Orderings_Obot__class_Obot(tc_fun(U_4668,tc_HOL_Obool))
              | U_4672 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_4668),U_4661) = U_4672
            & ~ hBOOL(hAPP(hAPP(c_member(U_4668),sK91(U_4672,U_4670,U_4668)),U_4661))
            & U_4670 = hAPP(hAPP(c_Set_Oinsert(U_4668),sK91(U_4672,U_4670,U_4668)),U_4661) )
        | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4662,sK91(U_4672,U_4670,U_4668))],[f_986_3]) ).

fof(f_986_5,plain,
    ( ! [U_4673,U_4671,U_4669] :
        ( hAPP(c_Finite__Set_Ocard(U_4669),U_4671) = hAPP(c_Nat_OSuc,U_4673)
        | ! [U_4664,U_4663] :
            ( ( U_4663 != c_Orderings_Obot__class_Obot(tc_fun(U_4669,tc_HOL_Obool))
              & U_4673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_4669),U_4663) != U_4673
            | hBOOL(hAPP(hAPP(c_member(U_4669),U_4664),U_4663))
            | U_4671 != hAPP(hAPP(c_Set_Oinsert(U_4669),U_4664),U_4663) ) )
    & ! [U_4672,U_4670,U_4668] :
        ( ( ( sK92(U_4672,U_4670,U_4668) = c_Orderings_Obot__class_Obot(tc_fun(U_4668,tc_HOL_Obool))
            | U_4672 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_4668),sK92(U_4672,U_4670,U_4668)) = U_4672
          & ~ hBOOL(hAPP(hAPP(c_member(U_4668),sK91(U_4672,U_4670,U_4668)),sK92(U_4672,U_4670,U_4668)))
          & U_4670 = hAPP(hAPP(c_Set_Oinsert(U_4668),sK91(U_4672,U_4670,U_4668)),sK92(U_4672,U_4670,U_4668)) )
        | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4661,sK92(U_4672,U_4670,U_4668))],[f_986_4]) ).

cnf(f_986_6,plain,
    ( U_4670 = hAPP(hAPP(c_Set_Oinsert(U_4668),sK91(U_4672,U_4670,U_4668)),sK92(U_4672,U_4670,U_4668))
    | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

cnf(f_986_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4668),sK91(U_4672,U_4670,U_4668)),sK92(U_4672,U_4670,U_4668)))
    | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

cnf(f_986_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4668),sK92(U_4672,U_4670,U_4668)) = U_4672
    | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

cnf(f_986_9,plain,
    ( sK92(U_4672,U_4670,U_4668) = c_Orderings_Obot__class_Obot(tc_fun(U_4668,tc_HOL_Obool))
    | U_4672 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_4668),U_4670) != hAPP(c_Nat_OSuc,U_4672) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

cnf(f_986_10,plain,
    ( U_4673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_4669),U_4663) != U_4673
    | hBOOL(hAPP(hAPP(c_member(U_4669),U_4664),U_4663))
    | U_4671 != hAPP(hAPP(c_Set_Oinsert(U_4669),U_4664),U_4663)
    | hAPP(c_Finite__Set_Ocard(U_4669),U_4671) = hAPP(c_Nat_OSuc,U_4673) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

cnf(f_986_11,plain,
    ( U_4663 != c_Orderings_Obot__class_Obot(tc_fun(U_4669,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_4669),U_4663) != U_4673
    | hBOOL(hAPP(hAPP(c_member(U_4669),U_4664),U_4663))
    | U_4671 != hAPP(hAPP(c_Set_Oinsert(U_4669),U_4664),U_4663)
    | hAPP(c_Finite__Set_Ocard(U_4669),U_4671) = hAPP(c_Nat_OSuc,U_4673) ),
    inference(clausify,[status(thm)],[f_986_5]) ).

fof(f_987_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_987_2,plain,
    ! [U_4677,U_4676,U_4675,U_4674] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4674),U_4675)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4676),U_4675)),U_4677)) = 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_4674),U_4676)),U_4675)),U_4677),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

cnf(f_987_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4674),U_4675)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4676),U_4675)),U_4677)) = 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_4674),U_4676)),U_4675)),U_4677),
    inference(clausify,[status(thm)],[f_987_2]) ).

fof(f_988_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_988_2,plain,
    ! [U_4680,U_4679,U_4678] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4678),U_4679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4678),U_4680)
        | ( U_4679 != U_4680
          & U_4678 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_4679 = U_4680
        | U_4678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4678),U_4679) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4678),U_4680) ) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ( ! [U_4686,U_4684,U_4682] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4686)
        | ( U_4684 != U_4686
          & U_4682 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4685,U_4683,U_4681] :
        ( U_4683 = U_4685
        | U_4681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4681),U_4683) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4681),U_4685) ) ),
    inference(miniscope,[status(thm)],[f_988_2]) ).

cnf(f_988_4,plain,
    ( U_4683 = U_4685
    | U_4681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4681),U_4683) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4681),U_4685) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_5,plain,
    ( U_4682 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4686) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_6,plain,
    ( U_4684 != U_4686
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4682),U_4686) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_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_989_2,plain,
    ! [U_4689,U_4688,U_4687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4689),U_4688)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4687),U_4688)) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

cnf(f_989_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4689),U_4688)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4687),U_4688)) ),
    inference(clausify,[status(thm)],[f_989_2]) ).

fof(f_990_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_990_2,plain,
    ! [U_4692,U_4691,U_4690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4691),U_4692)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691)) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

cnf(f_990_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4691),U_4692)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691)) ),
    inference(clausify,[status(thm)],[f_990_2]) ).

fof(f_991_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).

fof(f_991_2,plain,
    ! [U_4696,U_4695,U_4694,U_4693] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4694),U_4696))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4695),U_4696))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4694),U_4695)) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

cnf(f_991_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4694),U_4696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4695),U_4696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4693,tc_HOL_Obool)),U_4694),U_4695)) ),
    inference(clausify,[status(thm)],[f_991_2]) ).

fof(f_992_1,plain,
    ! [T_e,T_d,T_c,T_a,T_b,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_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,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_992_2,plain,
    ! [U_4707,U_4706,U_4705,U_4704,U_4703,U_4702,U_4701,U_4700,U_4699,U_4698,U_4697] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_4703,U_4704,U_4705,U_4697),U_4698),U_4699) = hAPP(hAPP(c_Fun_Ocomp(U_4706,U_4704,U_4707,U_4700),U_4701),U_4702)
      | hAPP(U_4697,hAPP(U_4698,U_4699)) != hAPP(U_4700,hAPP(U_4701,U_4702)) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

cnf(f_992_3,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_4703,U_4704,U_4705,U_4697),U_4698),U_4699) = hAPP(hAPP(c_Fun_Ocomp(U_4706,U_4704,U_4707,U_4700),U_4701),U_4702)
    | hAPP(U_4697,hAPP(U_4698,U_4699)) != hAPP(U_4700,hAPP(U_4701,U_4702)) ),
    inference(clausify,[status(thm)],[f_992_2]) ).

fof(f_993_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_993_2,plain,
    ! [U_4709,U_4708] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_4708,U_4709)) = 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_4708)),c_Com_Ocom_Ocom__size(U_4709))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

cnf(f_993_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_4708,U_4709)) = 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_4708)),c_Com_Ocom_Ocom__size(U_4709))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_993_2]) ).

fof(f_994_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_994_2,plain,
    ! [U_4712,U_4711,U_4710] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_4710,U_4711,U_4712)) = 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_4711)),c_Com_Ocom_Ocom__size(U_4712))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

cnf(f_994_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_4710,U_4711,U_4712)) = 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_4711)),c_Com_Ocom_Ocom__size(U_4712))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_994_2]) ).

fof(f_995_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_995_2,plain,
    ! [U_4714,U_4713] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_4713,U_4714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4714)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

cnf(f_995_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_4713,U_4714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4714)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_995_2]) ).

fof(f_996_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_996_2,plain,
    ! [U_4716,U_4715] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_4715,U_4716)) = 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_4715)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4716))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

cnf(f_996_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_4715,U_4716)) = 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_4715)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4716))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_996_2]) ).

fof(f_997_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_997_2,plain,
    ! [U_4719,U_4718,U_4717] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_4717,U_4718,U_4719)) = 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_4718)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4719))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

cnf(f_997_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_4717,U_4718,U_4719)) = 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_4718)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4719))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_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_998_2,plain,
    ! [U_4721,U_4720] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_4720,U_4721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4721)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

cnf(f_998_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_4720,U_4721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4721)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_998_2]) ).

fof(f_999_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).

fof(f_999_2,plain,
    ! [U_4727,U_4726,U_4725,U_4724,U_4723] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4726),U_4725)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4727),U_4725)))
      | ? [U_4722] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(U_4726,U_4722)),hAPP(U_4727,U_4722)))
          & hBOOL(hAPP(hAPP(c_member(U_4724),U_4722),U_4725)) )
      | U_4725 = c_Orderings_Obot__class_Obot(tc_fun(U_4724,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4724),U_4725))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4723)
      | ~ class_Groups_Ocomm__monoid__add(U_4723) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_4727,U_4726,U_4725,U_4724,U_4723] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4726),U_4725)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4727),U_4725)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(U_4726,sK93(U_4727,U_4726,U_4725,U_4724,U_4723))),hAPP(U_4727,sK93(U_4727,U_4726,U_4725,U_4724,U_4723))))
        & hBOOL(hAPP(hAPP(c_member(U_4724),sK93(U_4727,U_4726,U_4725,U_4724,U_4723)),U_4725)) )
      | U_4725 = c_Orderings_Obot__class_Obot(tc_fun(U_4724,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4724),U_4725))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4723)
      | ~ class_Groups_Ocomm__monoid__add(U_4723) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_4722,sK93(U_4727,U_4726,U_4725,U_4724,U_4723))],[f_999_2]) ).

cnf(f_999_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4724),sK93(U_4727,U_4726,U_4725,U_4724,U_4723)),U_4725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4726),U_4725)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4727),U_4725)))
    | U_4725 = c_Orderings_Obot__class_Obot(tc_fun(U_4724,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4724),U_4725))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4723)
    | ~ class_Groups_Ocomm__monoid__add(U_4723) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

cnf(f_999_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(U_4726,sK93(U_4727,U_4726,U_4725,U_4724,U_4723))),hAPP(U_4727,sK93(U_4727,U_4726,U_4725,U_4724,U_4723))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4723),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4726),U_4725)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4724,U_4723),U_4727),U_4725)))
    | U_4725 = c_Orderings_Obot__class_Obot(tc_fun(U_4724,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4724),U_4725))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4723)
    | ~ class_Groups_Ocomm__monoid__add(U_4723) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_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_1000_2,plain,
    ! [U_4729,U_4728] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4728),hAPP(c_Nat_OSuc,U_4729)) = 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_4728),U_4729)),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4728),hAPP(c_Nat_OSuc,U_4729)) = 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_4728),U_4729)),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_1,plain,
    ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_1001_2,plain,
    ! [U_4732,U_4731,U_4730] : c_Nat_Onat_Onat__case(U_4730,U_4731,U_4732,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4731,
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

cnf(f_1001_3,plain,
    c_Nat_Onat_Onat__case(U_4730,U_4731,U_4732,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4731,
    inference(clausify,[status(thm)],[f_1001_2]) ).

fof(f_1002_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_1002_2,plain,
    ! [U_4736,U_4735,U_4734,U_4733] : c_Nat_Onat_Onat__case(U_4733,U_4734,U_4735,hAPP(c_Nat_OSuc,U_4736)) = hAPP(U_4735,U_4736),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

cnf(f_1002_3,plain,
    c_Nat_Onat_Onat__case(U_4733,U_4734,U_4735,hAPP(c_Nat_OSuc,U_4736)) = hAPP(U_4735,U_4736),
    inference(clausify,[status(thm)],[f_1002_2]) ).

fof(f_1003_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_1003_2,plain,
    ! [U_4737] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_4737)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

cnf(f_1003_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_4737)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1003_2]) ).

fof(f_1004_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_1004_2,plain,
    ! [U_4738] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_4738)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_4738)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_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]) ).

cnf(f_1005_2,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_1005_1]) ).

fof(f_1006_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]) ).

cnf(f_1006_2,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1006_1]) ).

fof(f_1007_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).

fof(f_1007_2,plain,
    ! [U_4741,U_4740,U_4739] :
      ( hAPP(c_Finite__Set_Ofold1(U_4739,c_Groups_Otimes__class_Otimes(U_4739)),hAPP(hAPP(c_Set_Oinsert(U_4739),U_4741),U_4740)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4739,U_4739,c_Groups_Otimes__class_Otimes(U_4739)),U_4741),U_4740)
      | hBOOL(hAPP(hAPP(c_member(U_4739),U_4741),U_4740))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4739),U_4740))
      | ~ class_Groups_Oab__semigroup__mult(U_4739) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_4739,c_Groups_Otimes__class_Otimes(U_4739)),hAPP(hAPP(c_Set_Oinsert(U_4739),U_4741),U_4740)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4739,U_4739,c_Groups_Otimes__class_Otimes(U_4739)),U_4741),U_4740)
    | hBOOL(hAPP(hAPP(c_member(U_4739),U_4741),U_4740))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4739),U_4740))
    | ~ class_Groups_Oab__semigroup__mult(U_4739) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).

fof(f_1008_2,plain,
    ! [U_4744,U_4743,U_4742] :
      ( hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4742),hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),U_4743)),hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),U_4744))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744) != c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
      | U_4744 = c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4744))
      | U_4743 = c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4743))
      | ~ class_Groups_Oab__semigroup__mult(U_4742) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4742),hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),U_4743)),hAPP(c_Finite__Set_Ofold1(U_4742,c_Groups_Otimes__class_Otimes(U_4742)),U_4744))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744) != c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
    | U_4744 = c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4744))
    | U_4743 = c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4743))
    | ~ class_Groups_Oab__semigroup__mult(U_4742) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_1,plain,
    ! [V_s1,V_n,V_s0,V_pn] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1009_2,plain,
    ! [U_4748,U_4747,U_4746,U_4745] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_4745)),U_4746),hAPP(c_Nat_OSuc,U_4747)),U_4748))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4745))),U_4746),U_4747),U_4748)) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_4745)),U_4746),hAPP(c_Nat_OSuc,U_4747)),U_4748))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_4745))),U_4746),U_4747),U_4748)) ),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).

fof(f_1010_2,plain,
    ! [U_4751,U_4750,U_4749] :
      ( hAPP(c_Finite__Set_Ofold1(U_4749,c_Groups_Otimes__class_Otimes(U_4749)),hAPP(hAPP(c_Set_Oinsert(U_4749),U_4751),U_4750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4749),U_4751),hAPP(c_Finite__Set_Ofold1(U_4749,c_Groups_Otimes__class_Otimes(U_4749)),U_4750))
      | hBOOL(hAPP(hAPP(c_member(U_4749),U_4751),U_4750))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4749),U_4750))
      | U_4750 = c_Orderings_Obot__class_Obot(tc_fun(U_4749,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_4749) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_4749,c_Groups_Otimes__class_Otimes(U_4749)),hAPP(hAPP(c_Set_Oinsert(U_4749),U_4751),U_4750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4749),U_4751),hAPP(c_Finite__Set_Ofold1(U_4749,c_Groups_Otimes__class_Otimes(U_4749)),U_4750))
    | hBOOL(hAPP(hAPP(c_member(U_4749),U_4751),U_4750))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4749),U_4750))
    | U_4750 = c_Orderings_Obot__class_Obot(tc_fun(U_4749,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_4749) ),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_1,plain,
    ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] :
      ( ? [B_y] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,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_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(f_1011_2,plain,
    ! [U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753] :
      ( ? [U_4752] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,U_4758),U_4752))
          & U_4759 = hAPP(hAPP(U_4755,U_4757),U_4752) )
      | hBOOL(hAPP(hAPP(c_member(U_4753),U_4757),U_4758))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,hAPP(hAPP(c_Set_Oinsert(U_4753),U_4757),U_4758)),U_4759))
      | ~ c_Finite__Set_Ofun__left__comm(U_4753,U_4754,U_4755) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,U_4758),sK94(U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753)))
        & U_4759 = hAPP(hAPP(U_4755,U_4757),sK94(U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753)) )
      | hBOOL(hAPP(hAPP(c_member(U_4753),U_4757),U_4758))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,hAPP(hAPP(c_Set_Oinsert(U_4753),U_4757),U_4758)),U_4759))
      | ~ c_Finite__Set_Ofun__left__comm(U_4753,U_4754,U_4755) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_4752,sK94(U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753))],[f_1011_2]) ).

cnf(f_1011_4,plain,
    ( U_4759 = hAPP(hAPP(U_4755,U_4757),sK94(U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753))
    | hBOOL(hAPP(hAPP(c_member(U_4753),U_4757),U_4758))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,hAPP(hAPP(c_Set_Oinsert(U_4753),U_4757),U_4758)),U_4759))
    | ~ c_Finite__Set_Ofun__left__comm(U_4753,U_4754,U_4755) ),
    inference(clausify,[status(thm)],[f_1011_3]) ).

cnf(f_1011_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,U_4758),sK94(U_4759,U_4758,U_4757,U_4756,U_4755,U_4754,U_4753)))
    | hBOOL(hAPP(hAPP(c_member(U_4753),U_4757),U_4758))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4753,U_4754,U_4755,U_4756,hAPP(hAPP(c_Set_Oinsert(U_4753),U_4757),U_4758)),U_4759))
    | ~ c_Finite__Set_Ofun__left__comm(U_4753,U_4754,U_4755) ),
    inference(clausify,[status(thm)],[f_1011_3]) ).

fof(f_1012_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_1012_2,plain,
    ! [U_4762,U_4761,U_4760] : 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_4760)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_4761))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4762))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4762),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4761)))),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

cnf(f_1012_3,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_4760)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_4761))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4762))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4762),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4761)))),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
              & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
                | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
            | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).

fof(f_1013_2,plain,
    ! [U_4766,U_4765,U_4764,U_4763] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),U_4764),hAPP(hAPP(c_Set_Oinsert(U_4763),U_4765),U_4766)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4763,tc_HOL_Obool)),U_4764),U_4766))
              & ~ hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4764)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4763,tc_HOL_Obool)),U_4764),hAPP(hAPP(c_Set_Oinsert(U_4763),U_4765),c_Orderings_Obot__class_Obot(tc_fun(U_4763,tc_HOL_Obool))))),U_4766))
              & hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4764)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4766)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),U_4764),U_4766))
          & hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4766)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4763,tc_HOL_Obool)),U_4764),U_4766))
                | hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4764)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4763,tc_HOL_Obool)),U_4764),hAPP(hAPP(c_Set_Oinsert(U_4763),U_4765),c_Orderings_Obot__class_Obot(tc_fun(U_4763,tc_HOL_Obool))))),U_4766))
                | ~ hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4764)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4766)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),U_4764),U_4766))
            | ~ hBOOL(hAPP(hAPP(c_member(U_4763),U_4765),U_4766)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4763,tc_HOL_Obool)),U_4764),hAPP(hAPP(c_Set_Oinsert(U_4763),U_4765),U_4766))) ) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ( ! [U_4774,U_4772,U_4770,U_4768] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
              & ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),c_Orderings_Obot__class_Obot(tc_fun(U_4768,tc_HOL_Obool))))),U_4774))
              & hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
          & hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774)) ) )
    & ! [U_4773,U_4771,U_4769,U_4767] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4767,tc_HOL_Obool)),U_4769),U_4773))
                | hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4769)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),c_Orderings_Obot__class_Obot(tc_fun(U_4767,tc_HOL_Obool))))),U_4773))
                | ~ hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4769)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4773)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),U_4773))
            | ~ hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4773)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),U_4773))) ) ),
    inference(miniscope,[status(thm)],[f_1013_2]) ).

cnf(f_1013_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),U_4773))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),c_Orderings_Obot__class_Obot(tc_fun(U_4767,tc_HOL_Obool))))),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4769))
    | hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),U_4773))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4767,tc_HOL_Obool)),U_4769),U_4773))
    | hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4769))
    | hBOOL(hAPP(hAPP(c_member(U_4767),U_4771),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4767,tc_HOL_Obool)),U_4769),hAPP(hAPP(c_Set_Oinsert(U_4767),U_4771),U_4773))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),c_Orderings_Obot__class_Obot(tc_fun(U_4768,tc_HOL_Obool))))),U_4774))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),c_Orderings_Obot__class_Obot(tc_fun(U_4768,tc_HOL_Obool))))),U_4774))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4768),U_4772),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),c_Orderings_Obot__class_Obot(tc_fun(U_4768,tc_HOL_Obool))))),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),c_Orderings_Obot__class_Obot(tc_fun(U_4768,tc_HOL_Obool))))),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),U_4774))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4768,tc_HOL_Obool)),U_4770),hAPP(hAPP(c_Set_Oinsert(U_4768),U_4772),U_4774))) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

fof(f_1014_1,plain,
    ! [V_n_2,V_A_2,V_f_2,T_a] :
      ( ? [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_a),B_x),V_A_2)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_1014_2,plain,
    ! [U_4779,U_4778,U_4777,U_4776] :
      ( ? [U_4775] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4777,U_4775)))
          & hBOOL(hAPP(hAPP(c_member(U_4776),U_4775),U_4778)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4776,tc_Nat_Onat),U_4777),U_4778) != hAPP(c_Nat_OSuc,U_4779) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_4779,U_4778,U_4777,U_4776] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4777,sK95(U_4779,U_4778,U_4777,U_4776))))
        & hBOOL(hAPP(hAPP(c_member(U_4776),sK95(U_4779,U_4778,U_4777,U_4776)),U_4778)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4776,tc_Nat_Onat),U_4777),U_4778) != hAPP(c_Nat_OSuc,U_4779) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_4775,sK95(U_4779,U_4778,U_4777,U_4776))],[f_1014_2]) ).

cnf(f_1014_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4776),sK95(U_4779,U_4778,U_4777,U_4776)),U_4778))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4776,tc_Nat_Onat),U_4777),U_4778) != hAPP(c_Nat_OSuc,U_4779) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

cnf(f_1014_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4777,sK95(U_4779,U_4778,U_4777,U_4776))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4776,tc_Nat_Onat),U_4777),U_4778) != hAPP(c_Nat_OSuc,U_4779) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

fof(f_1015_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_1015_2,plain,
    ! [U_4781,U_4780] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4780),U_4781),U_4781))
      | ~ class_Orderings_Opreorder(U_4780) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

cnf(f_1015_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4780),U_4781),U_4781))
    | ~ class_Orderings_Opreorder(U_4780) ),
    inference(clausify,[status(thm)],[f_1015_2]) ).

fof(f_1016_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_equalityI]) ).

fof(f_1016_2,plain,
    ! [U_4784,U_4783,U_4782] :
      ( U_4783 = U_4784
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4782,tc_HOL_Obool)),U_4784),U_4783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4782,tc_HOL_Obool)),U_4783),U_4784)) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

cnf(f_1016_3,plain,
    ( U_4783 = U_4784
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4782,tc_HOL_Obool)),U_4784),U_4783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4782,tc_HOL_Obool)),U_4783),U_4784)) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

fof(f_1017_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_1017_2,plain,
    ! [U_4785] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4785))),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4785))),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subsetD]) ).

fof(f_1018_2,plain,
    ! [U_4789,U_4788,U_4787,U_4786] :
      ( hBOOL(hAPP(hAPP(c_member(U_4786),U_4789),U_4788))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4786),U_4789),U_4787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4786,tc_HOL_Obool)),U_4787),U_4788)) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

cnf(f_1018_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4786),U_4789),U_4788))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4786),U_4789),U_4787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4786,tc_HOL_Obool)),U_4787),U_4788)) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

fof(f_1019_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).

fof(f_1019_2,plain,
    ! [U_4791,U_4790] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4790,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_4790,tc_HOL_Obool))),U_4791)),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

cnf(f_1019_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4790,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_4790,tc_HOL_Obool))),U_4791)),
    inference(clausify,[status(thm)],[f_1019_2]) ).

fof(f_1020_1,plain,
    ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1020_2,plain,
    ! [U_4797,U_4796,U_4795,U_4794,U_4793,U_4792] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4792,U_4794)),U_4793),U_4795),U_4797))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4792,U_4794)),U_4796),U_4795),U_4797))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4794),U_4793),U_4795),U_4796))
      | ~ hBOOL(hAPP(U_4792,U_4793)) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4792,U_4794)),U_4793),U_4795),U_4797))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4792,U_4794)),U_4796),U_4795),U_4797))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4794),U_4793),U_4795),U_4796))
    | ~ hBOOL(hAPP(U_4792,U_4793)) ),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_1,plain,
    ! [V_n_2,V_c_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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_1021_2,plain,
    ! [U_4801,U_4800,U_4799,U_4798] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4798,U_4800)),U_4799),U_4801),U_4799))
      | hBOOL(hAPP(U_4798,U_4799)) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_4798,U_4800)),U_4799),U_4801),U_4799))
    | hBOOL(hAPP(U_4798,U_4799)) ),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_1,plain,
    ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2))
        & ~ hBOOL(hAPP(V_b_2,V_s_2)) )
      | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2))
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1022_2,plain,
    ! [U_4807,U_4806,U_4805,U_4804,U_4803,U_4802] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4804),U_4805),U_4806),U_4807))
        & ~ hBOOL(hAPP(U_4802,U_4805)) )
      | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4803),U_4805),U_4806),U_4807))
        & hBOOL(hAPP(U_4802,U_4805)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4802,U_4803,U_4804)),U_4805),U_4806),U_4807)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    ( ~ hBOOL(hAPP(U_4802,U_4805))
    | hBOOL(hAPP(U_4802,U_4805))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4802,U_4803,U_4804)),U_4805),U_4806),U_4807)) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

cnf(f_1022_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4804),U_4805),U_4806),U_4807))
    | hBOOL(hAPP(U_4802,U_4805))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4802,U_4803,U_4804)),U_4805),U_4806),U_4807)) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

cnf(f_1022_5,plain,
    ( ~ hBOOL(hAPP(U_4802,U_4805))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4803),U_4805),U_4806),U_4807))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4802,U_4803,U_4804)),U_4805),U_4806),U_4807)) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

cnf(f_1022_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4804),U_4805),U_4806),U_4807))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4803),U_4805),U_4806),U_4807))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4802,U_4803,U_4804)),U_4805),U_4806),U_4807)) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_1,plain,
    ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1023_2,plain,
    ! [U_4813,U_4812,U_4811,U_4810,U_4809,U_4808] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4808,U_4810,U_4813)),U_4809),U_4811),U_4812))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4810),U_4809),U_4811),U_4812))
      | ~ hBOOL(hAPP(U_4808,U_4809)) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4808,U_4810,U_4813)),U_4809),U_4811),U_4812))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4810),U_4809),U_4811),U_4812))
    | ~ hBOOL(hAPP(U_4808,U_4809)) ),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_1,plain,
    ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1024_2,plain,
    ! [U_4819,U_4818,U_4817,U_4816,U_4815,U_4814] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4814,U_4819,U_4816)),U_4815),U_4817),U_4818))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4816),U_4815),U_4817),U_4818))
      | hBOOL(hAPP(U_4814,U_4815)) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

cnf(f_1024_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_4814,U_4819,U_4816)),U_4815),U_4817),U_4818))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4816),U_4815),U_4817),U_4818))
    | hBOOL(hAPP(U_4814,U_4815)) ),
    inference(clausify,[status(thm)],[f_1024_2]) ).

fof(f_1025_1,plain,
    ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln_OSemi]) ).

fof(f_1025_2,plain,
    ! [U_4825,U_4824,U_4823,U_4822,U_4821,U_4820] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_4820,U_4824)),U_4821),U_4822),U_4825))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4824),U_4823),U_4822),U_4825))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4820),U_4821),U_4822),U_4823)) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_4820,U_4824)),U_4821),U_4822),U_4825))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4824),U_4823),U_4822),U_4825))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4820),U_4821),U_4822),U_4823)) ),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_1,plain,
    ! [V_t,V_n,V_s] :
      ( V_t = V_s
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1026_2,plain,
    ! [U_4828,U_4827,U_4826] :
      ( U_4828 = U_4826
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_4826),U_4827),U_4828)) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    ( U_4828 = U_4826
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_4826),U_4827),U_4828)) ),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_1,plain,
    ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)),
    inference(fof_nnf,[status(thm)],[fact_evaln_OSkip]) ).

fof(f_1027_2,plain,
    ! [U_4830,U_4829] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_4829),U_4830),U_4829)),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_4829),U_4830),U_4829)),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_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_1028_2,plain,
    ! [U_4831] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4831)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4831),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4831)),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4831)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4831),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4831)),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_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]) ).

cnf(f_1029_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(clausify,[status(thm)],[f_1029_1]) ).

fof(f_1030_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).

fof(f_1030_2,plain,
    ! [U_4836,U_4835,U_4834,U_4833,U_4832] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4833,U_4832),U_4835),U_4836)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4833,U_4832),U_4834),U_4836)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4833,tc_HOL_Obool)),U_4834),U_4835))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4832) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4833,U_4832),U_4835),U_4836)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4833,U_4832),U_4834),U_4836)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4833,tc_HOL_Obool)),U_4834),U_4835))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4832) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).

fof(f_1031_2,plain,
    ! [U_4839,U_4838,U_4837] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4838) = hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4839)
          | U_4838 != U_4839 )
        & ( U_4838 = U_4839
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4838) != hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4839) ) )
      | ~ class_Orderings_Olinorder(U_4837) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    ( U_4838 = U_4839
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4838) != hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4839)
    | ~ class_Orderings_Olinorder(U_4837) ),
    inference(clausify,[status(thm)],[f_1031_2]) ).

cnf(f_1031_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4838) = hAPP(c_SetInterval_Oord__class_OlessThan(U_4837),U_4839)
    | U_4838 != U_4839
    | ~ class_Orderings_Olinorder(U_4837) ),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).

fof(f_1032_2,plain,
    ! [U_4842,U_4841,U_4840] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4841)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4842)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),U_4841),U_4842)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),U_4841),U_4842))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4841)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4842))) ) )
      | ~ class_Orderings_Olinorder(U_4840) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),U_4841),U_4842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4841)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4842)))
    | ~ class_Orderings_Olinorder(U_4840) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4840,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4841)),hAPP(c_SetInterval_Oord__class_OlessThan(U_4840),U_4842)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),U_4841),U_4842))
    | ~ class_Orderings_Olinorder(U_4840) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_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_1033_2,plain,
    ! [U_4845,U_4844,U_4843] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4843),U_4845),U_4844))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4843),U_4844),U_4845))
      | ~ class_Orderings_Olinorder(U_4843) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4843),U_4845),U_4844))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4843),U_4844),U_4845))
    | ~ class_Orderings_Olinorder(U_4843) ),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),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_a,T_b)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funE]) ).

fof(f_1034_2,plain,
    ! [U_4850,U_4849,U_4848,U_4847,U_4846] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4846),hAPP(U_4848,U_4850)),hAPP(U_4849,U_4850)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4847,U_4846)),U_4848),U_4849))
      | ~ class_Orderings_Oord(U_4846) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4846),hAPP(U_4848,U_4850)),hAPP(U_4849,U_4850)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4847,U_4846)),U_4848),U_4849))
    | ~ class_Orderings_Oord(U_4846) ),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    ! [T_a,V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityE]) ).

fof(f_1035_2,plain,
    ! [U_4853,U_4852,U_4851] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4853,tc_HOL_Obool)),U_4852),U_4851))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4853,tc_HOL_Obool)),U_4851),U_4852)) )
      | U_4851 != U_4852 ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4853,tc_HOL_Obool)),U_4851),U_4852))
    | U_4851 != U_4852 ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4853,tc_HOL_Obool)),U_4852),U_4851))
    | U_4851 != U_4852 ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_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_1036_2,plain,
    ! [U_4857,U_4856,U_4855,U_4854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4857),U_4856))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4857),U_4855))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4855),U_4856))
      | ~ class_Orderings_Oorder(U_4854) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4857),U_4856))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4857),U_4855))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4854),U_4855),U_4856))
    | ~ class_Orderings_Oorder(U_4854) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_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_1037_2,plain,
    ! [U_4860,U_4859,U_4858] :
      ( U_4860 = U_4859
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),U_4860),U_4859))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),U_4859),U_4860))
      | ~ class_Orderings_Oorder(U_4858) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    ( U_4860 = U_4859
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),U_4860),U_4859))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4858),U_4859),U_4860))
    | ~ class_Orderings_Oorder(U_4858) ),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_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_1038_2,plain,
    ! [U_4864,U_4863,U_4862,U_4861] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4862),U_4864))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4863),U_4864))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4862),U_4863))
      | ~ class_Orderings_Opreorder(U_4861) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4862),U_4864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4863),U_4864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4861),U_4862),U_4863))
    | ~ class_Orderings_Opreorder(U_4861) ),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_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_1039_2,plain,
    ! [U_4867,U_4866,U_4865] :
      ( U_4866 = U_4867
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4865),U_4867),U_4866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4865),U_4866),U_4867))
      | ~ class_Orderings_Oorder(U_4865) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    ( U_4866 = U_4867
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4865),U_4867),U_4866))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4865),U_4866),U_4867))
    | ~ class_Orderings_Oorder(U_4865) ),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_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_1040_2,plain,
    ! [U_4871,U_4870,U_4869,U_4868] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4871),U_4870))
      | U_4869 != U_4871
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4869),U_4870))
      | ~ class_Orderings_Oorder(U_4868) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4871),U_4870))
    | U_4869 != U_4871
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4868),U_4869),U_4870))
    | ~ class_Orderings_Oorder(U_4868) ),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_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_1041_2,plain,
    ! [U_4875,U_4874,U_4873,U_4872] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),U_4873),U_4875))
      | U_4874 != U_4875
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),U_4873),U_4874))
      | ~ class_Orderings_Oord(U_4872) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),U_4873),U_4875))
    | U_4874 != U_4875
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4872),U_4873),U_4874))
    | ~ class_Orderings_Oord(U_4872) ),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).

fof(f_1042_2,plain,
    ! [U_4879,U_4878,U_4877,U_4876] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4877),U_4879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4878),U_4879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4877),U_4878)) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4877),U_4879))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4878),U_4879))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4876,tc_HOL_Obool)),U_4877),U_4878)) ),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_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_1043_2,plain,
    ! [U_4883,U_4882,U_4881,U_4880] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),U_4883),U_4881))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),U_4883),U_4882))
      | U_4881 != U_4882
      | ~ class_Orderings_Oorder(U_4880) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),U_4883),U_4881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4880),U_4883),U_4882))
    | U_4881 != U_4882
    | ~ class_Orderings_Oorder(U_4880) ),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_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_1044_2,plain,
    ! [U_4887,U_4886,U_4885,U_4884] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),U_4885),U_4887))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),U_4886),U_4887))
      | U_4885 != U_4886
      | ~ class_Orderings_Oord(U_4884) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),U_4885),U_4887))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4884),U_4886),U_4887))
    | U_4885 != U_4886
    | ~ class_Orderings_Oord(U_4884) ),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_1,plain,
    ! [V_x_2,V_Q_2,V_P_2,T_a] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).

fof(f_1045_2,plain,
    ! [U_4891,U_4890,U_4889,U_4888] :
      ( hBOOL(hAPP(U_4890,U_4891))
      | ~ hBOOL(hAPP(U_4889,U_4891))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4888,tc_HOL_Obool)),U_4889),U_4890)) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

fof(f_1045_3,plain,
    ! [U_4891,U_4890,U_4889] :
      ( ! [U_4888] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4888,tc_HOL_Obool)),U_4889),U_4890))
      | hBOOL(hAPP(U_4890,U_4891))
      | ~ hBOOL(hAPP(U_4889,U_4891)) ),
    inference(miniscope,[status(thm)],[f_1045_2]) ).

cnf(f_1045_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4888,tc_HOL_Obool)),U_4889),U_4890))
    | hBOOL(hAPP(U_4890,U_4891))
    | ~ hBOOL(hAPP(U_4889,U_4891)) ),
    inference(clausify,[status(thm)],[f_1045_3]) ).

fof(f_1046_1,plain,
    ! [V_x_2,V_y_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).

fof(f_1046_2,plain,
    ! [U_4894,U_4893,U_4892] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4894),U_4893))
          | U_4894 != U_4893 )
        & ( U_4894 = U_4893
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4894),U_4893)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4893),U_4894))
      | ~ class_Orderings_Oorder(U_4892) ),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    ( U_4894 = U_4893
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4894),U_4893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4893),U_4894))
    | ~ class_Orderings_Oorder(U_4892) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

cnf(f_1046_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4894),U_4893))
    | U_4894 != U_4893
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4892),U_4893),U_4894))
    | ~ class_Orderings_Oorder(U_4892) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),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_a,T_b)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funD]) ).

fof(f_1047_2,plain,
    ! [U_4899,U_4898,U_4897,U_4896,U_4895] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4895),hAPP(U_4897,U_4899)),hAPP(U_4898,U_4899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4896,U_4895)),U_4897),U_4898))
      | ~ class_Orderings_Oord(U_4895) ),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4895),hAPP(U_4897,U_4899)),hAPP(U_4898,U_4899)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4896,U_4895)),U_4897),U_4898))
    | ~ class_Orderings_Oord(U_4895) ),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_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_1048_2,plain,
    ! [U_4902,U_4901,U_4900] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4900),U_4901),U_4902))
      | U_4901 != U_4902
      | ~ class_Orderings_Opreorder(U_4900) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4900),U_4901),U_4902))
    | U_4901 != U_4902
    | ~ class_Orderings_Opreorder(U_4900) ),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    ! [T_a,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).

fof(f_1049_2,plain,
    ! [U_4905,U_4904,U_4903] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4905,tc_HOL_Obool)),U_4904),U_4903))
      | U_4903 != U_4904 ),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

cnf(f_1049_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4905,tc_HOL_Obool)),U_4904),U_4903))
    | U_4903 != U_4904 ),
    inference(clausify,[status(thm)],[f_1049_2]) ).

fof(f_1050_1,plain,
    ! [T_a,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).

fof(f_1050_2,plain,
    ! [U_4908,U_4907,U_4906] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4908,tc_HOL_Obool)),U_4906),U_4907))
      | U_4906 != U_4907 ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4908,tc_HOL_Obool)),U_4906),U_4907))
    | U_4906 != U_4907 ),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_1,plain,
    ! [V_Q_2,T_a,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).

fof(f_1051_2,plain,
    ! [U_4912,U_4911,U_4910,U_4909] :
      ( hBOOL(hAPP(U_4912,U_4910))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4911,tc_HOL_Obool)),U_4909),U_4912))
      | ~ hBOOL(hAPP(U_4909,U_4910)) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    ( hBOOL(hAPP(U_4912,U_4910))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4911,tc_HOL_Obool)),U_4909),U_4912))
    | ~ hBOOL(hAPP(U_4909,U_4910)) ),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | V_x_2 != V_y_2 ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).

fof(f_1052_2,plain,
    ! [U_4915,U_4914,U_4913] :
      ( ( ( U_4914 = U_4915
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4915),U_4914))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4914),U_4915)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4915),U_4914))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4914),U_4915)) )
          | U_4914 != U_4915 ) )
      | ~ class_Orderings_Oorder(U_4913) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4914),U_4915))
    | U_4914 != U_4915
    | ~ class_Orderings_Oorder(U_4913) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

cnf(f_1052_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4915),U_4914))
    | U_4914 != U_4915
    | ~ class_Orderings_Oorder(U_4913) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

cnf(f_1052_5,plain,
    ( U_4914 = U_4915
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4915),U_4914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4913),U_4914),U_4915))
    | ~ class_Orderings_Oorder(U_4913) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    ! [T_a,V_B_2,V_A_2] :
      ( ( V_A_2 = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_1053_2,plain,
    ! [U_4918,U_4917,U_4916] :
      ( ( U_4916 = U_4917
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4918,tc_HOL_Obool)),U_4917),U_4916))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4918,tc_HOL_Obool)),U_4916),U_4917)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4918,tc_HOL_Obool)),U_4917),U_4916))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4918,tc_HOL_Obool)),U_4916),U_4917)) )
        | U_4916 != U_4917 ) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ( ! [U_4924,U_4922,U_4920] :
        ( U_4920 = U_4922
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4924,tc_HOL_Obool)),U_4922),U_4920))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4924,tc_HOL_Obool)),U_4920),U_4922)) )
    & ! [U_4923,U_4921,U_4919] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4923,tc_HOL_Obool)),U_4921),U_4919))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4923,tc_HOL_Obool)),U_4919),U_4921)) )
        | U_4919 != U_4921 ) ),
    inference(miniscope,[status(thm)],[f_1053_2]) ).

cnf(f_1053_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4923,tc_HOL_Obool)),U_4919),U_4921))
    | U_4919 != U_4921 ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

cnf(f_1053_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4923,tc_HOL_Obool)),U_4921),U_4919))
    | U_4919 != U_4921 ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

cnf(f_1053_6,plain,
    ( U_4920 = U_4922
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4924,tc_HOL_Obool)),U_4922),U_4920))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4924,tc_HOL_Obool)),U_4920),U_4922)) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_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_1054_2,plain,
    ! [U_4927,U_4926,U_4925] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4925),U_4927),U_4926))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4925),U_4926),U_4927))
      | ~ class_Orderings_Olinorder(U_4925) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4925),U_4927),U_4926))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4925),U_4926),U_4927))
    | ~ class_Orderings_Olinorder(U_4925) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
          | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
        & ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).

fof(f_1055_2,plain,
    ! [U_4933,U_4932,U_4931,U_4930] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933))
          | ? [U_4929] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,U_4929)),hAPP(U_4933,U_4929))) )
        & ( ! [U_4928] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,U_4928)),hAPP(U_4933,U_4928)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933)) ) )
      | ~ class_Orderings_Oord(U_4930) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ! [U_4933,U_4932,U_4931,U_4930] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,sK96(U_4933,U_4932,U_4931,U_4930))),hAPP(U_4933,sK96(U_4933,U_4932,U_4931,U_4930)))) )
        & ( ! [U_4928] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,U_4928)),hAPP(U_4933,U_4928)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933)) ) )
      | ~ class_Orderings_Oord(U_4930) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_4929,sK96(U_4933,U_4932,U_4931,U_4930))],[f_1055_2]) ).

cnf(f_1055_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,U_4928)),hAPP(U_4933,U_4928)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933))
    | ~ class_Orderings_Oord(U_4930) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

cnf(f_1055_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4931,U_4930)),U_4932),U_4933))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4930),hAPP(U_4932,sK96(U_4933,U_4932,U_4931,U_4930))),hAPP(U_4933,sK96(U_4933,U_4932,U_4931,U_4930))))
    | ~ class_Orderings_Oord(U_4930) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

fof(f_1056_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).

fof(f_1056_2,plain,
    ! [U_4935,U_4934] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4934,tc_HOL_Obool)),U_4935),U_4935)),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4934,tc_HOL_Obool)),U_4935),U_4935)),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).

fof(f_1057_2,plain,
    ! [U_4940,U_4939,U_4938,U_4937,U_4936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4936),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4937,U_4936),U_4938),U_4940)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4937,U_4936),U_4939),U_4940)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4937,tc_HOL_Obool)),U_4938),U_4939))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4936) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

cnf(f_1057_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4936),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4937,U_4936),U_4938),U_4940)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4937,U_4936),U_4939),U_4940)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4937,tc_HOL_Obool)),U_4938),U_4939))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4936) ),
    inference(clausify,[status(thm)],[f_1057_2]) ).

fof(f_1058_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).

fof(f_1058_2,plain,
    ! [U_4943,U_4942,U_4941] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4941,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4941,tc_HOL_Obool),U_4942)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4941,tc_HOL_Obool),U_4943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_4941,tc_HOL_Obool),tc_HOL_Obool)),U_4942),U_4943)) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4941,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4941,tc_HOL_Obool),U_4942)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4941,tc_HOL_Obool),U_4943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_4941,tc_HOL_Obool),tc_HOL_Obool)),U_4942),U_4943)) ),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).

fof(f_1059_2,plain,
    ! [U_4946,U_4945,U_4944] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4944,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4944,tc_HOL_Obool),U_4946)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4944,tc_HOL_Obool),U_4945)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_4944,tc_HOL_Obool),tc_HOL_Obool)),U_4945),U_4946)) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4944,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4944,tc_HOL_Obool),U_4946)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4944,tc_HOL_Obool),U_4945)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_4944,tc_HOL_Obool),tc_HOL_Obool)),U_4945),U_4946)) ),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_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_1060_2,plain,
    ! [U_4947] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4947)) = U_4947,
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4947)) = U_4947,
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_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]) ).

cnf(f_1061_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(clausify,[status(thm)],[f_1061_1]) ).

fof(f_1062_1,plain,
    ! [V_s_H,V_n,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__Suc]) ).

fof(f_1062_2,plain,
    ! [U_4951,U_4950,U_4949,U_4948] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4948),U_4949),hAPP(c_Nat_OSuc,U_4950)),U_4951))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4948),U_4949),U_4950),U_4951)) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4948),U_4949),hAPP(c_Nat_OSuc,U_4950)),U_4951))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_4948),U_4949),U_4950),U_4951)) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_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_1063_2,plain,
    ! [U_4955,U_4954,U_4953,U_4952] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4952),U_4955),U_4954))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4952),U_4955),U_4953))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4952),U_4953),U_4954))
      | ~ class_Orderings_Oorder(U_4952) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4952),U_4955),U_4954))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4952),U_4955),U_4953))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4952),U_4953),U_4954))
    | ~ class_Orderings_Oorder(U_4952) ),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_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_1064_2,plain,
    ! [U_4959,U_4958,U_4957,U_4956] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),U_4957),U_4959))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),U_4958),U_4959))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4956),U_4957),U_4958))
      | ~ class_Orderings_Opreorder(U_4956) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),U_4957),U_4959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4956),U_4958),U_4959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4956),U_4957),U_4958))
    | ~ class_Orderings_Opreorder(U_4956) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_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_1065_2,plain,
    ! [U_4963,U_4962,U_4961,U_4960] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4960),U_4963),U_4962))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4960),U_4963),U_4961))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4960),U_4961),U_4962))
      | ~ class_Orderings_Oorder(U_4960) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4960),U_4963),U_4962))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4960),U_4963),U_4961))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4960),U_4961),U_4962))
    | ~ class_Orderings_Oorder(U_4960) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_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_1066_2,plain,
    ! [U_4967,U_4966,U_4965,U_4964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4964),U_4965),U_4967))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4964),U_4966),U_4967))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4964),U_4965),U_4966))
      | ~ class_Orderings_Opreorder(U_4964) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4964),U_4965),U_4967))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4964),U_4966),U_4967))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4964),U_4965),U_4966))
    | ~ class_Orderings_Opreorder(U_4964) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_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_1067_2,plain,
    ! [U_4970,U_4969,U_4968] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4968),U_4969),U_4970))
      | U_4970 = U_4969
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4968),U_4969),U_4970))
      | ~ class_Orderings_Oorder(U_4968) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4968),U_4969),U_4970))
    | U_4970 = U_4969
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4968),U_4969),U_4970))
    | ~ class_Orderings_Oorder(U_4968) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_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_1068_2,plain,
    ! [U_4973,U_4972,U_4971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4971),U_4972),U_4973))
      | U_4972 = U_4973
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4971),U_4972),U_4973))
      | ~ class_Orderings_Oorder(U_4971) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4971),U_4972),U_4973))
    | U_4972 = U_4973
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4971),U_4972),U_4973))
    | ~ class_Orderings_Oorder(U_4971) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_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_1069_2,plain,
    ! [U_4976,U_4975,U_4974] :
      ( U_4975 = U_4976
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4974),U_4975),U_4976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4974),U_4975),U_4976))
      | ~ class_Orderings_Oorder(U_4974) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    ( U_4975 = U_4976
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4974),U_4975),U_4976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4974),U_4975),U_4976))
    | ~ class_Orderings_Oorder(U_4974) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_a),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(f_1070_2,plain,
    ! [U_4979,U_4978,U_4977] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4977),U_4978),U_4979))
          | U_4978 != U_4979 )
        & ( U_4978 = U_4979
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4977),U_4978),U_4979)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4977),U_4978),U_4979))
      | ~ class_Orderings_Olinorder(U_4977) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    ( U_4978 = U_4979
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4977),U_4978),U_4979))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4977),U_4978),U_4979))
    | ~ class_Orderings_Olinorder(U_4977) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4977),U_4978),U_4979))
    | U_4978 != U_4979
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4977),U_4978),U_4979))
    | ~ class_Orderings_Olinorder(U_4977) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_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_1071_2,plain,
    ! [U_4982,U_4981,U_4980] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4980),U_4981),U_4982))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4980),U_4981),U_4982))
      | ~ class_Orderings_Opreorder(U_4980) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4980),U_4981),U_4982))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4980),U_4981),U_4982))
    | ~ class_Orderings_Opreorder(U_4980) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_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_1072_2,plain,
    ! [U_4985,U_4984,U_4983] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4983),U_4985),U_4984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4983),U_4984),U_4985))
      | ~ class_Orderings_Olinorder(U_4983) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4983),U_4985),U_4984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4983),U_4984),U_4985))
    | ~ class_Orderings_Olinorder(U_4983) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_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_1073_2,plain,
    ! [U_4988,U_4987,U_4986] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4986),U_4988),U_4987))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4986),U_4988),U_4987))
      | U_4987 = U_4988
      | ~ class_Orderings_Oorder(U_4986) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4986),U_4988),U_4987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4986),U_4988),U_4987))
    | U_4987 = U_4988
    | ~ class_Orderings_Oorder(U_4986) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_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_1074_2,plain,
    ! [U_4991,U_4990,U_4989] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4989),U_4990),U_4991))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),U_4990),U_4991))
      | U_4990 = U_4991
      | ~ class_Orderings_Oorder(U_4989) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4989),U_4990),U_4991))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),U_4990),U_4991))
    | U_4990 = U_4991
    | ~ class_Orderings_Oorder(U_4989) ),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),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_a),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(f_1075_2,plain,
    ! [U_4994,U_4993,U_4992] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4992),U_4993),U_4994))
          | U_4993 != U_4994 )
        & ( U_4993 = U_4994
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4992),U_4993),U_4994)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4992),U_4993),U_4994))
      | ~ class_Orderings_Olinorder(U_4992) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    ( U_4993 = U_4994
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4992),U_4993),U_4994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4992),U_4993),U_4994))
    | ~ class_Orderings_Olinorder(U_4992) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

cnf(f_1075_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4992),U_4993),U_4994))
    | U_4993 != U_4994
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4992),U_4993),U_4994))
    | ~ class_Orderings_Olinorder(U_4992) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_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_1076_2,plain,
    ! [U_4997,U_4996,U_4995] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4995),U_4997),U_4996))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4995),U_4996),U_4997))
      | ~ class_Orderings_Olinorder(U_4995) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4995),U_4997),U_4996))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4995),U_4996),U_4997))
    | ~ class_Orderings_Olinorder(U_4995) ),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_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_1077_2,plain,
    ! [U_5000,U_4999,U_4998] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4998),U_5000),U_4999))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4998),U_4999),U_5000))
      | ~ class_Orderings_Olinorder(U_4998) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4998),U_5000),U_4999))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4998),U_4999),U_5000))
    | ~ class_Orderings_Olinorder(U_4998) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).

fof(f_1078_2,plain,
    ! [U_5003,U_5002,U_5001] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5001),U_5002),U_5003))
          | ( U_5002 != U_5003
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),U_5002),U_5003)) ) )
        & ( U_5002 = U_5003
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),U_5002),U_5003))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5001),U_5002),U_5003)) ) )
      | ~ class_Orderings_Oorder(U_5001) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ( U_5002 = U_5003
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),U_5002),U_5003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5001),U_5002),U_5003))
    | ~ class_Orderings_Oorder(U_5001) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

cnf(f_1078_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),U_5002),U_5003))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5001),U_5002),U_5003))
    | ~ class_Orderings_Oorder(U_5001) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

cnf(f_1078_5,plain,
    ( U_5002 != U_5003
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5001),U_5002),U_5003))
    | ~ class_Orderings_Oorder(U_5001) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).

fof(f_1079_2,plain,
    ! [U_5006,U_5005,U_5004] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5004),U_5005),U_5006))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5006),U_5005))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5005),U_5006)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5006),U_5005))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5005),U_5006)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5004),U_5005),U_5006)) ) )
      | ~ class_Orderings_Opreorder(U_5004) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5005),U_5006))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5004),U_5005),U_5006))
    | ~ class_Orderings_Opreorder(U_5004) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

cnf(f_1079_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5006),U_5005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5004),U_5005),U_5006))
    | ~ class_Orderings_Opreorder(U_5004) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

cnf(f_1079_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5004),U_5005),U_5006))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5006),U_5005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5004),U_5005),U_5006))
    | ~ class_Orderings_Opreorder(U_5004) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( V_x_2 != V_y_2
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).

fof(f_1080_2,plain,
    ! [U_5009,U_5008,U_5007] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5007),U_5008),U_5009))
          | U_5008 = U_5009
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5007),U_5008),U_5009)) )
        & ( ( U_5008 != U_5009
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5007),U_5008),U_5009)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5007),U_5008),U_5009)) ) )
      | ~ class_Orderings_Oorder(U_5007) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5007),U_5008),U_5009))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5007),U_5008),U_5009))
    | ~ class_Orderings_Oorder(U_5007) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

cnf(f_1080_4,plain,
    ( U_5008 != U_5009
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5007),U_5008),U_5009))
    | ~ class_Orderings_Oorder(U_5007) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

cnf(f_1080_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5007),U_5008),U_5009))
    | U_5008 = U_5009
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5007),U_5008),U_5009))
    | ~ class_Orderings_Oorder(U_5007) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_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_1081_2,plain,
    ! [U_5012,U_5011,U_5010] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5010),U_5012),U_5011))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5010),U_5011),U_5012))
      | ~ class_Orderings_Olinorder(U_5010) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5010),U_5012),U_5011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5010),U_5011),U_5012))
    | ~ class_Orderings_Olinorder(U_5010) ),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).

fof(f_1082_2,plain,
    ! [U_5015,U_5014,U_5013] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5013),U_5014),U_5015))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5013),U_5015),U_5014)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5013),U_5015),U_5014))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5013),U_5014),U_5015)) ) )
      | ~ class_Orderings_Olinorder(U_5013) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5013),U_5015),U_5014))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5013),U_5014),U_5015))
    | ~ class_Orderings_Olinorder(U_5013) ),
    inference(clausify,[status(thm)],[f_1082_2]) ).

cnf(f_1082_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5013),U_5014),U_5015))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5013),U_5015),U_5014))
    | ~ class_Orderings_Olinorder(U_5013) ),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).

fof(f_1083_2,plain,
    ! [U_5018,U_5017,U_5016] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5016),U_5017),U_5018))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5018),U_5017)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5018),U_5017))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5016),U_5017),U_5018)) ) )
      | ~ class_Orderings_Olinorder(U_5016) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5018),U_5017))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5016),U_5017),U_5018))
    | ~ class_Orderings_Olinorder(U_5016) ),
    inference(clausify,[status(thm)],[f_1083_2]) ).

cnf(f_1083_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5016),U_5017),U_5018))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5016),U_5018),U_5017))
    | ~ class_Orderings_Olinorder(U_5016) ),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_in__mono]) ).

fof(f_1084_2,plain,
    ! [U_5022,U_5021,U_5020,U_5019] :
      ( hBOOL(hAPP(hAPP(c_member(U_5019),U_5022),U_5021))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5019),U_5022),U_5020))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5019,tc_HOL_Obool)),U_5020),U_5021)) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5019),U_5022),U_5021))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5019),U_5022),U_5020))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5019,tc_HOL_Obool)),U_5020),U_5021)) ),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).

fof(f_1085_2,plain,
    ! [U_5026,U_5025,U_5024,U_5023] :
      ( hBOOL(hAPP(hAPP(c_member(U_5023),U_5024),U_5026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5023,tc_HOL_Obool)),U_5025),U_5026))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5023),U_5024),U_5025)) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5023),U_5024),U_5026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5023,tc_HOL_Obool)),U_5025),U_5026))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5023),U_5024),U_5025)) ),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__mp]) ).

fof(f_1086_2,plain,
    ! [U_5030,U_5029,U_5028,U_5027] :
      ( hBOOL(hAPP(hAPP(c_member(U_5027),U_5030),U_5029))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5027),U_5030),U_5028))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5027,tc_HOL_Obool)),U_5028),U_5029)) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5027),U_5030),U_5029))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5027),U_5030),U_5028))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5027,tc_HOL_Obool)),U_5028),U_5029)) ),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_1087_2,plain,
    ! [U_5034,U_5033,U_5032,U_5031] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5032),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5034),U_5033)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),U_5032),U_5034)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),U_5032),U_5034))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5032),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5034),U_5033))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5031) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),U_5032),U_5034))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5032),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5034),U_5033)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5031) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

cnf(f_1087_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5032),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5031),U_5034),U_5033)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5031),U_5032),U_5034))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5031) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).

fof(f_1088_2,plain,
    ! [U_5038,U_5037,U_5036,U_5035] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5038)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),U_5037),U_5038)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),U_5037),U_5038))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5038))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5035) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),U_5037),U_5038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5038)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5035) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

cnf(f_1088_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5035),U_5036),U_5038)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),U_5037),U_5038))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5035) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_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_1089_2,plain,
    ! [U_5042,U_5041,U_5040,U_5039] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5039),U_5040),U_5042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5039),U_5041),U_5042)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5039),U_5040),U_5041))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5039) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5039),U_5040),U_5042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5039),U_5041),U_5042)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5039),U_5040),U_5041))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5039) ),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_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_1090_2,plain,
    ! [U_5046,U_5045,U_5044,U_5043] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),U_5046),U_5044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),U_5046),U_5045)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5043),U_5044),U_5045))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5043) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),U_5046),U_5044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),U_5046),U_5045)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5043),U_5044),U_5045))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5043) ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_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_1091_2,plain,
    ! [U_5051,U_5050,U_5049,U_5048,U_5047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5047),U_5048),U_5050)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5047),U_5049),U_5051)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),U_5050),U_5051))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),U_5048),U_5049))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5047) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5047),U_5048),U_5050)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5047),U_5049),U_5051)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),U_5050),U_5051))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5047),U_5048),U_5049))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5047) ),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_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_1092_2,plain,
    ! [U_5055,U_5054,U_5053,U_5052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5053),U_5055))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5053),U_5054)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5055),U_5054)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5052) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5053),U_5055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5053),U_5054)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5055),U_5054)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5052) ),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_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_1093_2,plain,
    ! [U_5059,U_5058,U_5057,U_5056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),U_5059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5058)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5059)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5056) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),U_5059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5058)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5059)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5056) ),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_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_1094_2,plain,
    ! [U_5061,U_5060] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Orderings_Obot__class_Obot(U_5060)),U_5061))
      | ~ class_Orderings_Obot(U_5060) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Orderings_Obot__class_Obot(U_5060)),U_5061))
    | ~ class_Orderings_Obot(U_5060) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).

fof(f_1095_2,plain,
    ! [U_5066,U_5065,U_5064,U_5063,U_5062] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5063),U_5064))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5065),U_5066)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5065),U_5066))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5063),U_5064)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5063),U_5064) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5065),U_5066)
      | ~ class_Groups_Oordered__ab__group__add(U_5062) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5065),U_5066))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5063),U_5064))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5063),U_5064) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5065),U_5066)
    | ~ class_Groups_Oordered__ab__group__add(U_5062) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5063),U_5064))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5062),U_5065),U_5066))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5063),U_5064) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5062),U_5065),U_5066)
    | ~ class_Groups_Oordered__ab__group__add(U_5062) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ! [V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).

fof(f_1096_2,plain,
    ! [U_5068,U_5067] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5067,tc_HOL_Obool)),U_5068),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))))
        | U_5068 != c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)) )
      & ( U_5068 = c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5067,tc_HOL_Obool)),U_5068),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

fof(f_1096_3,plain,
    ( ! [U_5072,U_5070] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5070,tc_HOL_Obool)),U_5072),c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool))))
        | U_5072 != c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool)) )
    & ! [U_5071,U_5069] :
        ( U_5071 = c_Orderings_Obot__class_Obot(tc_fun(U_5069,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5069,tc_HOL_Obool)),U_5071),c_Orderings_Obot__class_Obot(tc_fun(U_5069,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_1096_2]) ).

cnf(f_1096_4,plain,
    ( U_5071 = c_Orderings_Obot__class_Obot(tc_fun(U_5069,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5069,tc_HOL_Obool)),U_5071),c_Orderings_Obot__class_Obot(tc_fun(U_5069,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

cnf(f_1096_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5070,tc_HOL_Obool)),U_5072),c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool))))
    | U_5072 != c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

fof(f_1097_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_1097_2,plain,
    ! [U_5076,U_5075,U_5074,U_5073] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5075),U_5076))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5074),U_5076)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5073),U_5074),U_5075)),U_5076))
      | ~ class_Lattices_Osemilattice__sup(U_5073) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5074),U_5076))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5073),U_5074),U_5075)),U_5076))
    | ~ class_Lattices_Osemilattice__sup(U_5073) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5075),U_5076))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5073),U_5074),U_5075)),U_5076))
    | ~ class_Lattices_Osemilattice__sup(U_5073) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_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_1098_2,plain,
    ! [U_5081,U_5080,U_5079,U_5078,U_5077] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5077),U_5078),U_5080)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5077),U_5079),U_5081)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),U_5080),U_5081))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),U_5078),U_5079))
      | ~ class_Lattices_Osemilattice__sup(U_5077) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5077),U_5078),U_5080)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5077),U_5079),U_5081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),U_5080),U_5081))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5077),U_5078),U_5079))
    | ~ class_Lattices_Osemilattice__sup(U_5077) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_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_1099_2,plain,
    ! [U_5085,U_5084,U_5083,U_5082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5082),U_5083),U_5085)),U_5084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),U_5085),U_5084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),U_5083),U_5084))
      | ~ class_Lattices_Osemilattice__sup(U_5082) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5082),U_5083),U_5085)),U_5084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),U_5085),U_5084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5082),U_5083),U_5084))
    | ~ class_Lattices_Osemilattice__sup(U_5082) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_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_1100_2,plain,
    ! [U_5089,U_5088,U_5087,U_5086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5086),U_5087),U_5089)),U_5088))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5089),U_5088))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5087),U_5088))
      | ~ class_Lattices_Osemilattice__sup(U_5086) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5086),U_5087),U_5089)),U_5088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5089),U_5088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5087),U_5088))
    | ~ class_Lattices_Osemilattice__sup(U_5086) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_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_1101_2,plain,
    ! [U_5092,U_5091,U_5090] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5090),U_5092),U_5091) = U_5092
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5091),U_5092))
      | ~ class_Lattices_Osemilattice__sup(U_5090) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5090),U_5092),U_5091) = U_5092
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5091),U_5092))
    | ~ class_Lattices_Osemilattice__sup(U_5090) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_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_1102_2,plain,
    ! [U_5095,U_5094,U_5093] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5093),U_5094),U_5095) = U_5095
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5093),U_5094),U_5095))
      | ~ class_Lattices_Osemilattice__sup(U_5093) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5093),U_5094),U_5095) = U_5095
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5093),U_5094),U_5095))
    | ~ class_Lattices_Osemilattice__sup(U_5093) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_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_1103_2,plain,
    ! [U_5099,U_5098,U_5097,U_5096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5096),U_5097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5096),U_5099),U_5098)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5096),U_5097),U_5098))
      | ~ class_Lattices_Osemilattice__sup(U_5096) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5096),U_5097),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5096),U_5099),U_5098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5096),U_5097),U_5098))
    | ~ class_Lattices_Osemilattice__sup(U_5096) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_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_1104_2,plain,
    ! [U_5103,U_5102,U_5101,U_5100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5100),U_5101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5100),U_5102),U_5103)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5100),U_5101),U_5102))
      | ~ class_Lattices_Osemilattice__sup(U_5100) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5100),U_5101),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5100),U_5102),U_5103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5100),U_5101),U_5102))
    | ~ class_Lattices_Osemilattice__sup(U_5100) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    ! [V_z_2,V_y_2,V_x_2,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_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).

fof(f_1105_2,plain,
    ! [U_5107,U_5106,U_5105,U_5104] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5104),U_5105),U_5106)),U_5107))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5106),U_5107))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5105),U_5107)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5106),U_5107))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5105),U_5107)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5104),U_5105),U_5106)),U_5107)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_5104) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5105),U_5107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5104),U_5105),U_5106)),U_5107))
    | ~ class_Lattices_Osemilattice__sup(U_5104) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5106),U_5107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5104),U_5105),U_5106)),U_5107))
    | ~ class_Lattices_Osemilattice__sup(U_5104) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5104),U_5105),U_5106)),U_5107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5106),U_5107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5104),U_5105),U_5107))
    | ~ class_Lattices_Osemilattice__sup(U_5104) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).

fof(f_1106_2,plain,
    ! [U_5110,U_5109,U_5108] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5108),U_5109),U_5110))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5108),U_5109),U_5110) != U_5110 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5108),U_5109),U_5110) = U_5110
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5108),U_5109),U_5110)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_5108) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5108),U_5109),U_5110) = U_5110
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5108),U_5109),U_5110))
    | ~ class_Lattices_Osemilattice__sup(U_5108) ),
    inference(clausify,[status(thm)],[f_1106_2]) ).

cnf(f_1106_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5108),U_5109),U_5110))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5108),U_5109),U_5110) != U_5110
    | ~ class_Lattices_Osemilattice__sup(U_5108) ),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_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_1107_2,plain,
    ! [U_5113,U_5112,U_5111] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5111),U_5112),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5111),U_5113),U_5112)))
      | ~ class_Lattices_Osemilattice__sup(U_5111) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5111),U_5112),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5111),U_5113),U_5112)))
    | ~ class_Lattices_Osemilattice__sup(U_5111) ),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_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_1108_2,plain,
    ! [U_5116,U_5115,U_5114] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5114),U_5115),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5114),U_5116),U_5115)))
      | ~ class_Lattices_Olattice(U_5114) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5114),U_5115),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5114),U_5116),U_5115)))
    | ~ class_Lattices_Olattice(U_5114) ),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_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_1109_2,plain,
    ! [U_5119,U_5118,U_5117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5117),U_5118),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5117),U_5118),U_5119)))
      | ~ class_Lattices_Osemilattice__sup(U_5117) ),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5117),U_5118),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5117),U_5118),U_5119)))
    | ~ class_Lattices_Osemilattice__sup(U_5117) ),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_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_1110_2,plain,
    ! [U_5122,U_5121,U_5120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5120),U_5121),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5120),U_5121),U_5122)))
      | ~ class_Lattices_Olattice(U_5120) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5120),U_5121),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5120),U_5121),U_5122)))
    | ~ class_Lattices_Olattice(U_5120) ),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).

fof(f_1111_2,plain,
    ! [U_5125,U_5124,U_5123] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5125))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124)) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

cnf(f_1111_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5123,tc_HOL_Obool)),U_5125),U_5124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5123),U_5124)) ),
    inference(clausify,[status(thm)],[f_1111_2]) ).

fof(f_1112_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).

fof(f_1112_2,plain,
    ! [U_5128,U_5127,U_5126] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5126),U_5127))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5126),U_5128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5126,tc_HOL_Obool)),U_5127),U_5128)) ),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5126),U_5127))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5126),U_5128))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5126,tc_HOL_Obool)),U_5127),U_5128)) ),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_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_1113_2,plain,
    ! [U_5132,U_5131,U_5130,U_5129] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),U_5132))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),U_5131)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5129),U_5131),U_5132)))
      | ~ class_Lattices_Osemilattice__inf(U_5129) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),U_5131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5129),U_5131),U_5132)))
    | ~ class_Lattices_Osemilattice__inf(U_5129) ),
    inference(clausify,[status(thm)],[f_1113_2]) ).

cnf(f_1113_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),U_5132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5129),U_5130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5129),U_5131),U_5132)))
    | ~ class_Lattices_Osemilattice__inf(U_5129) ),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_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_1114_2,plain,
    ! [U_5137,U_5136,U_5135,U_5134,U_5133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5133),U_5134),U_5136)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5133),U_5135),U_5137)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),U_5136),U_5137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),U_5134),U_5135))
      | ~ class_Lattices_Osemilattice__inf(U_5133) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5133),U_5134),U_5136)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5133),U_5135),U_5137)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),U_5136),U_5137))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5133),U_5134),U_5135))
    | ~ class_Lattices_Osemilattice__inf(U_5133) ),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_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_1115_2,plain,
    ! [U_5141,U_5140,U_5139,U_5138] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5138),U_5140),U_5141)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),U_5141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),U_5140))
      | ~ class_Lattices_Osemilattice__inf(U_5138) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

cnf(f_1115_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5138),U_5140),U_5141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),U_5141))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5138),U_5139),U_5140))
    | ~ class_Lattices_Osemilattice__inf(U_5138) ),
    inference(clausify,[status(thm)],[f_1115_2]) ).

fof(f_1116_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_1116_2,plain,
    ! [U_5145,U_5144,U_5143,U_5142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5142),U_5144),U_5145)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),U_5145))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),U_5144))
      | ~ class_Lattices_Osemilattice__inf(U_5142) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

cnf(f_1116_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5142),U_5144),U_5145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),U_5145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5142),U_5143),U_5144))
    | ~ class_Lattices_Osemilattice__inf(U_5142) ),
    inference(clausify,[status(thm)],[f_1116_2]) ).

fof(f_1117_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_1117_2,plain,
    ! [U_5148,U_5147,U_5146] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5146),U_5148),U_5147) = U_5147
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5146),U_5147),U_5148))
      | ~ class_Lattices_Osemilattice__inf(U_5146) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5146),U_5148),U_5147) = U_5147
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5146),U_5147),U_5148))
    | ~ class_Lattices_Osemilattice__inf(U_5146) ),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_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_1118_2,plain,
    ! [U_5151,U_5150,U_5149] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5149),U_5150),U_5151) = U_5150
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5149),U_5150),U_5151))
      | ~ class_Lattices_Osemilattice__inf(U_5149) ),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5149),U_5150),U_5151) = U_5150
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5149),U_5150),U_5151))
    | ~ class_Lattices_Osemilattice__inf(U_5149) ),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_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_1119_2,plain,
    ! [U_5155,U_5154,U_5153,U_5152] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5152),U_5155),U_5153)),U_5154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5152),U_5153),U_5154))
      | ~ class_Lattices_Osemilattice__inf(U_5152) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

cnf(f_1119_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5152),U_5155),U_5153)),U_5154))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5152),U_5153),U_5154))
    | ~ class_Lattices_Osemilattice__inf(U_5152) ),
    inference(clausify,[status(thm)],[f_1119_2]) ).

fof(f_1120_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_1120_2,plain,
    ! [U_5159,U_5158,U_5157,U_5156] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5156),U_5157),U_5159)),U_5158))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5156),U_5157),U_5158))
      | ~ class_Lattices_Osemilattice__inf(U_5156) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5156),U_5157),U_5159)),U_5158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5156),U_5157),U_5158))
    | ~ class_Lattices_Osemilattice__inf(U_5156) ),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) ) )
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).

fof(f_1121_2,plain,
    ! [U_5163,U_5162,U_5161,U_5160] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5160),U_5162),U_5163)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5163))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5162)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5163))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5162)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5160),U_5162),U_5163))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_5160) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5162))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5160),U_5162),U_5163)))
    | ~ class_Lattices_Osemilattice__inf(U_5160) ),
    inference(clausify,[status(thm)],[f_1121_2]) ).

cnf(f_1121_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5160),U_5162),U_5163)))
    | ~ class_Lattices_Osemilattice__inf(U_5160) ),
    inference(clausify,[status(thm)],[f_1121_2]) ).

cnf(f_1121_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5160),U_5162),U_5163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5160),U_5161),U_5162))
    | ~ class_Lattices_Osemilattice__inf(U_5160) ),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).

fof(f_1122_2,plain,
    ! [U_5166,U_5165,U_5164] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5164),U_5165),U_5166))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5164),U_5165),U_5166) != U_5165 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5164),U_5165),U_5166) = U_5165
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5164),U_5165),U_5166)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_5164) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5164),U_5165),U_5166) = U_5165
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5164),U_5165),U_5166))
    | ~ class_Lattices_Osemilattice__inf(U_5164) ),
    inference(clausify,[status(thm)],[f_1122_2]) ).

cnf(f_1122_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5164),U_5165),U_5166))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5164),U_5165),U_5166) != U_5165
    | ~ class_Lattices_Osemilattice__inf(U_5164) ),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_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_1123_2,plain,
    ! [U_5169,U_5168,U_5167] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5167),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5167),U_5168),U_5169)),U_5169))
      | ~ class_Lattices_Osemilattice__inf(U_5167) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5167),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5167),U_5168),U_5169)),U_5169))
    | ~ class_Lattices_Osemilattice__inf(U_5167) ),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_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_1124_2,plain,
    ! [U_5172,U_5171,U_5170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5170),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5170),U_5171),U_5172)),U_5172))
      | ~ class_Lattices_Olattice(U_5170) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5170),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5170),U_5171),U_5172)),U_5172))
    | ~ class_Lattices_Olattice(U_5170) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_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_1125_2,plain,
    ! [U_5175,U_5174,U_5173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5173),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5173),U_5174),U_5175)),U_5174))
      | ~ class_Lattices_Osemilattice__inf(U_5173) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5173),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5173),U_5174),U_5175)),U_5174))
    | ~ class_Lattices_Osemilattice__inf(U_5173) ),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_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_1126_2,plain,
    ! [U_5178,U_5177,U_5176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5176),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5176),U_5177),U_5178)),U_5177))
      | ~ class_Lattices_Olattice(U_5176) ),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5176),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5176),U_5177),U_5178)),U_5177))
    | ~ class_Lattices_Olattice(U_5176) ),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_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_1127_2,plain,
    ! [U_5180,U_5179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5179),U_5180),c_Orderings_Otop__class_Otop(U_5179)))
      | ~ class_Orderings_Otop(U_5179) ),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

cnf(f_1127_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5179),U_5180),c_Orderings_Otop__class_Otop(U_5179)))
    | ~ class_Orderings_Otop(U_5179) ),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_1,plain,
    ! [V_a_2,V_D_2,V_C_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).

fof(f_1128_2,plain,
    ! [U_5184,U_5183,U_5182,U_5181] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5181,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5181),U_5184),U_5182)),hAPP(hAPP(c_Set_Oinsert(U_5181),U_5184),U_5183)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5181,tc_HOL_Obool)),U_5182),U_5183)) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5181,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5181),U_5184),U_5182)),hAPP(hAPP(c_Set_Oinsert(U_5181),U_5184),U_5183)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5181,tc_HOL_Obool)),U_5182),U_5183)) ),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).

fof(f_1129_2,plain,
    ! [U_5188,U_5187,U_5186,U_5185] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5185,tc_HOL_Obool)),U_5186),hAPP(hAPP(c_Set_Oinsert(U_5185),U_5188),U_5187)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5185,tc_HOL_Obool)),U_5186),U_5187)) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

cnf(f_1129_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5185,tc_HOL_Obool)),U_5186),hAPP(hAPP(c_Set_Oinsert(U_5185),U_5188),U_5187)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5185,tc_HOL_Obool)),U_5186),U_5187)) ),
    inference(clausify,[status(thm)],[f_1129_2]) ).

fof(f_1130_1,plain,
    ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).

fof(f_1130_2,plain,
    ! [U_5191,U_5190,U_5189] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5189,tc_HOL_Obool)),U_5190),hAPP(hAPP(c_Set_Oinsert(U_5189),U_5191),U_5190))),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5189,tc_HOL_Obool)),U_5190),hAPP(hAPP(c_Set_Oinsert(U_5189),U_5191),U_5190))),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).

fof(f_1131_2,plain,
    ! [U_5193,U_5192] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5192,tc_HOL_Obool)),U_5193),c_Orderings_Otop__class_Otop(tc_fun(U_5192,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5192,tc_HOL_Obool)),U_5193),c_Orderings_Otop__class_Otop(tc_fun(U_5192,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__mono]) ).

fof(f_1132_2,plain,
    ! [U_5198,U_5197,U_5196,U_5195,U_5194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5197,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5194,U_5197,U_5198),U_5195)),hAPP(c_Set_Oimage(U_5194,U_5197,U_5198),U_5196)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5194,tc_HOL_Obool)),U_5195),U_5196)) ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5197,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5194,U_5197,U_5198),U_5195)),hAPP(c_Set_Oimage(U_5194,U_5197,U_5198),U_5196)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5194,tc_HOL_Obool)),U_5195),U_5196)) ),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_1,plain,
    ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
        | ! [B_AA] :
            ( V_B_2 != hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) ) )
      & ( ? [B_AA] :
            ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).

fof(f_1133_2,plain,
    ! [U_5205,U_5204,U_5203,U_5202,U_5201] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5201,tc_HOL_Obool)),U_5202),hAPP(c_Set_Oimage(U_5203,U_5201,U_5204),U_5205)))
        | ! [U_5200] :
            ( U_5202 != hAPP(c_Set_Oimage(U_5203,U_5201,U_5204),U_5200)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5203,tc_HOL_Obool)),U_5200),U_5205)) ) )
      & ( ? [U_5199] :
            ( U_5202 = hAPP(c_Set_Oimage(U_5203,U_5201,U_5204),U_5199)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5203,tc_HOL_Obool)),U_5199),U_5205)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5201,tc_HOL_Obool)),U_5202),hAPP(c_Set_Oimage(U_5203,U_5201,U_5204),U_5205))) ) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

fof(f_1133_3,plain,
    ( ! [U_5215,U_5213,U_5211,U_5209,U_5207] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5207,tc_HOL_Obool)),U_5209),hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5215)))
        | ! [U_5200] :
            ( U_5209 != hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5200)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5211,tc_HOL_Obool)),U_5200),U_5215)) ) )
    & ! [U_5214,U_5212,U_5210,U_5208,U_5206] :
        ( ? [U_5199] :
            ( U_5208 = hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),U_5199)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5210,tc_HOL_Obool)),U_5199),U_5214)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),U_5214))) ) ),
    inference(miniscope,[status(thm)],[f_1133_2]) ).

fof(f_1133_4,plain,
    ( ! [U_5215,U_5213,U_5211,U_5209,U_5207] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5207,tc_HOL_Obool)),U_5209),hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5215)))
        | ! [U_5200] :
            ( U_5209 != hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5200)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5211,tc_HOL_Obool)),U_5200),U_5215)) ) )
    & ! [U_5214,U_5212,U_5210,U_5208,U_5206] :
        ( ( U_5208 = hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),sK97(U_5214,U_5212,U_5210,U_5208,U_5206))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5210,tc_HOL_Obool)),sK97(U_5214,U_5212,U_5210,U_5208,U_5206)),U_5214)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),U_5214))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_5199,sK97(U_5214,U_5212,U_5210,U_5208,U_5206))],[f_1133_3]) ).

cnf(f_1133_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5210,tc_HOL_Obool)),sK97(U_5214,U_5212,U_5210,U_5208,U_5206)),U_5214))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),U_5214))) ),
    inference(clausify,[status(thm)],[f_1133_4]) ).

cnf(f_1133_6,plain,
    ( U_5208 = hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),sK97(U_5214,U_5212,U_5210,U_5208,U_5206))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5206,tc_HOL_Obool)),U_5208),hAPP(c_Set_Oimage(U_5210,U_5206,U_5212),U_5214))) ),
    inference(clausify,[status(thm)],[f_1133_4]) ).

cnf(f_1133_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5207,tc_HOL_Obool)),U_5209),hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5215)))
    | U_5209 != hAPP(c_Set_Oimage(U_5211,U_5207,U_5213),U_5200)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5211,tc_HOL_Obool)),U_5200),U_5215)) ),
    inference(clausify,[status(thm)],[f_1133_4]) ).

fof(f_1134_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).

fof(f_1134_2,plain,
    ! [U_5220,U_5219,U_5218,U_5217,U_5216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5216,tc_HOL_Obool)),U_5217),U_5219)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5216,tc_HOL_Obool)),U_5218),U_5220)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),U_5219),U_5220))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),U_5217),U_5218)) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5216,tc_HOL_Obool)),U_5217),U_5219)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5216,tc_HOL_Obool)),U_5218),U_5220)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),U_5219),U_5220))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5216,tc_HOL_Obool)),U_5217),U_5218)) ),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__least]) ).

fof(f_1135_2,plain,
    ! [U_5224,U_5223,U_5222,U_5221] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5221,tc_HOL_Obool)),U_5222),U_5224)),U_5223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),U_5224),U_5223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),U_5222),U_5223)) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

cnf(f_1135_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5221,tc_HOL_Obool)),U_5222),U_5224)),U_5223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),U_5224),U_5223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5221,tc_HOL_Obool)),U_5222),U_5223)) ),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).

fof(f_1136_2,plain,
    ! [U_5227,U_5226,U_5225] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5225,tc_HOL_Obool)),U_5227),U_5226) = U_5227
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5225,tc_HOL_Obool)),U_5226),U_5227)) ),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5225,tc_HOL_Obool)),U_5227),U_5226) = U_5227
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5225,tc_HOL_Obool)),U_5226),U_5227)) ),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).

fof(f_1137_2,plain,
    ! [U_5230,U_5229,U_5228] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5228,tc_HOL_Obool)),U_5229),U_5230) = U_5230
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5228,tc_HOL_Obool)),U_5229),U_5230)) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5228,tc_HOL_Obool)),U_5229),U_5230) = U_5230
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5228,tc_HOL_Obool)),U_5229),U_5230)) ),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).

fof(f_1138_2,plain,
    ! [U_5233,U_5232,U_5231] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5231,tc_HOL_Obool)),U_5232),U_5233))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5231,tc_HOL_Obool)),U_5232),U_5233) != U_5233 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5231,tc_HOL_Obool)),U_5232),U_5233) = U_5233
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5231,tc_HOL_Obool)),U_5232),U_5233)) ) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ( ! [U_5239,U_5237,U_5235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5235,tc_HOL_Obool)),U_5237),U_5239))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5235,tc_HOL_Obool)),U_5237),U_5239) != U_5239 )
    & ! [U_5238,U_5236,U_5234] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5234,tc_HOL_Obool)),U_5236),U_5238) = U_5238
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5234,tc_HOL_Obool)),U_5236),U_5238)) ) ),
    inference(miniscope,[status(thm)],[f_1138_2]) ).

cnf(f_1138_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5234,tc_HOL_Obool)),U_5236),U_5238) = U_5238
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5234,tc_HOL_Obool)),U_5236),U_5238)) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5235,tc_HOL_Obool)),U_5237),U_5239))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5235,tc_HOL_Obool)),U_5237),U_5239) != U_5239 ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

fof(f_1139_1,plain,
    ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).

fof(f_1139_2,plain,
    ! [U_5242,U_5241,U_5240] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5240,tc_HOL_Obool)),U_5241),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5240,tc_HOL_Obool)),U_5242),U_5241))),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5240,tc_HOL_Obool)),U_5241),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5240,tc_HOL_Obool)),U_5242),U_5241))),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).

fof(f_1140_2,plain,
    ! [U_5245,U_5244,U_5243] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5243,tc_HOL_Obool)),U_5244),U_5245))),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5243,tc_HOL_Obool)),U_5244),U_5245))),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).

fof(f_1141_2,plain,
    ! [U_5250,U_5249,U_5248,U_5247,U_5246] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5246,tc_HOL_Obool)),U_5247),U_5249)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5246,tc_HOL_Obool)),U_5248),U_5250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),U_5249),U_5250))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),U_5247),U_5248)) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5246,tc_HOL_Obool)),U_5247),U_5249)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5246,tc_HOL_Obool)),U_5248),U_5250)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),U_5249),U_5250))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5246,tc_HOL_Obool)),U_5247),U_5248)) ),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).

fof(f_1142_2,plain,
    ! [U_5254,U_5253,U_5252,U_5251] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5251,tc_HOL_Obool)),U_5253),U_5254)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),U_5254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),U_5253)) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5251,tc_HOL_Obool)),U_5253),U_5254)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),U_5254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5251,tc_HOL_Obool)),U_5252),U_5253)) ),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).

fof(f_1143_2,plain,
    ! [U_5257,U_5256,U_5255] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5255,tc_HOL_Obool)),U_5257),U_5256) = U_5256
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5255,tc_HOL_Obool)),U_5256),U_5257)) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5255,tc_HOL_Obool)),U_5257),U_5256) = U_5256
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5255,tc_HOL_Obool)),U_5256),U_5257)) ),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).

fof(f_1144_2,plain,
    ! [U_5260,U_5259,U_5258] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5258,tc_HOL_Obool)),U_5259),U_5260) = U_5259
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5258,tc_HOL_Obool)),U_5259),U_5260)) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5258,tc_HOL_Obool)),U_5259),U_5260) = U_5259
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5258,tc_HOL_Obool)),U_5259),U_5260)) ),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).

fof(f_1145_2,plain,
    ! [U_5263,U_5262,U_5261] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5261,tc_HOL_Obool)),U_5262),U_5263)),U_5263)),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

cnf(f_1145_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5261,tc_HOL_Obool)),U_5262),U_5263)),U_5263)),
    inference(clausify,[status(thm)],[f_1145_2]) ).

fof(f_1146_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).

fof(f_1146_2,plain,
    ! [U_5266,U_5265,U_5264] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5264,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5264,tc_HOL_Obool)),U_5265),U_5266)),U_5265)),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5264,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5264,tc_HOL_Obool)),U_5265),U_5266)),U_5265)),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_double__diff]) ).

fof(f_1147_2,plain,
    ! [U_5270,U_5269,U_5268,U_5267] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5267,tc_HOL_Obool)),U_5269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5267,tc_HOL_Obool)),U_5270),U_5268)) = U_5268
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5267,tc_HOL_Obool)),U_5269),U_5270))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5267,tc_HOL_Obool)),U_5268),U_5269)) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5267,tc_HOL_Obool)),U_5269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5267,tc_HOL_Obool)),U_5270),U_5268)) = U_5268
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5267,tc_HOL_Obool)),U_5269),U_5270))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5267,tc_HOL_Obool)),U_5268),U_5269)) ),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).

fof(f_1148_2,plain,
    ! [U_5275,U_5274,U_5273,U_5272,U_5271] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5271,tc_HOL_Obool)),U_5272),U_5275)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5271,tc_HOL_Obool)),U_5273),U_5274)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),U_5274),U_5275))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),U_5272),U_5273)) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5271,tc_HOL_Obool)),U_5272),U_5275)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5271,tc_HOL_Obool)),U_5273),U_5274)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),U_5274),U_5275))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5271,tc_HOL_Obool)),U_5272),U_5273)) ),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).

fof(f_1149_2,plain,
    ! [U_5278,U_5277,U_5276] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5276,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5276,tc_HOL_Obool)),U_5277),U_5278)),U_5277)),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5276,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5276,tc_HOL_Obool)),U_5277),U_5278)),U_5277)),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    ! [V_t,V_n,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__evalc]) ).

fof(f_1150_2,plain,
    ! [U_5282,U_5281,U_5280,U_5279] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5279),U_5280),U_5282))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5279),U_5280),U_5281),U_5282)) ),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5279),U_5280),U_5282))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5279),U_5280),U_5281),U_5282)) ),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    ! [V_t_2,V_s_2,V_c_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s_2),V_t_2))
        | ! [B_n] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) )
      & ( ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s_2),V_t_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_eval__eq]) ).

fof(f_1151_2,plain,
    ! [U_5287,U_5286,U_5285] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5285),U_5286),U_5287))
        | ! [U_5284] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5285),U_5286),U_5284),U_5287)) )
      & ( ? [U_5283] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5285),U_5286),U_5283),U_5287))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5285),U_5286),U_5287)) ) ),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

fof(f_1151_3,plain,
    ( ! [U_5293,U_5291,U_5289] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5289),U_5291),U_5293))
        | ! [U_5284] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5289),U_5291),U_5284),U_5293)) )
    & ! [U_5292,U_5290,U_5288] :
        ( ? [U_5283] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5288),U_5290),U_5283),U_5292))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5288),U_5290),U_5292)) ) ),
    inference(miniscope,[status(thm)],[f_1151_2]) ).

fof(f_1151_4,plain,
    ( ! [U_5293,U_5291,U_5289] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5289),U_5291),U_5293))
        | ! [U_5284] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5289),U_5291),U_5284),U_5293)) )
    & ! [U_5292,U_5290,U_5288] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5288),U_5290),sK98(U_5292,U_5290,U_5288)),U_5292))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5288),U_5290),U_5292)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_5283,sK98(U_5292,U_5290,U_5288))],[f_1151_3]) ).

cnf(f_1151_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5288),U_5290),sK98(U_5292,U_5290,U_5288)),U_5292))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5288),U_5290),U_5292)) ),
    inference(clausify,[status(thm)],[f_1151_4]) ).

cnf(f_1151_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,U_5289),U_5291),U_5293))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5289),U_5291),U_5284),U_5293)) ),
    inference(clausify,[status(thm)],[f_1151_4]) ).

fof(f_1152_1,plain,
    ! [V_b_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).

fof(f_1152_2,plain,
    ! [U_5298,U_5297,U_5296] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298))
          | ? [U_5295] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5295),U_5298))
              & hBOOL(hAPP(hAPP(c_member(U_5296),U_5295),U_5297)) ) )
        & ( ! [U_5294] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5294),U_5298))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5296),U_5294),U_5297)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5296) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ! [U_5298,U_5297,U_5296] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),sK99(U_5298,U_5297,U_5296)),U_5298))
            & hBOOL(hAPP(hAPP(c_member(U_5296),sK99(U_5298,U_5297,U_5296)),U_5297)) ) )
        & ( ! [U_5294] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5294),U_5298))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5296),U_5294),U_5297)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5296) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_5295,sK99(U_5298,U_5297,U_5296))],[f_1152_2]) ).

cnf(f_1152_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5294),U_5298))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5296),U_5294),U_5297))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5296) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

cnf(f_1152_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5296),sK99(U_5298,U_5297,U_5296)),U_5297))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5296) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

cnf(f_1152_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),sK99(U_5298,U_5297,U_5296)),U_5298))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),c_Complete__Lattice_OSup__class_OSup(U_5296,U_5297)),U_5298))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5296) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

fof(f_1153_1,plain,
    ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2))
        | ( ( ! [B_s1] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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] :
              ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2))
              & hBOOL(hAPP(hAPP(hAPP(hAPP(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 )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1153_2,plain,
    ! [U_5305,U_5304,U_5303,U_5302,U_5301] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5301,U_5302)),U_5303),U_5304),U_5305))
        | ( ( ! [U_5300] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5301,U_5302)),U_5300),U_5304),U_5305))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5302),U_5303),U_5304),U_5300)) )
            | ~ hBOOL(hAPP(U_5301,U_5303)) )
          & ( hBOOL(hAPP(U_5301,U_5303))
            | U_5305 != U_5303 ) ) )
      & ( ( ? [U_5299] :
              ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5301,U_5302)),U_5299),U_5304),U_5305))
              & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5302),U_5303),U_5304),U_5299)) )
          & hBOOL(hAPP(U_5301,U_5303)) )
        | ( ~ hBOOL(hAPP(U_5301,U_5303))
          & U_5305 = U_5303 )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5301,U_5302)),U_5303),U_5304),U_5305)) ) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ( ! [U_5315,U_5313,U_5311,U_5309,U_5307] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5311),U_5313),U_5315))
        | ( ( ! [U_5300] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5300),U_5313),U_5315))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5309),U_5311),U_5313),U_5300)) )
            | ~ hBOOL(hAPP(U_5307,U_5311)) )
          & ( hBOOL(hAPP(U_5307,U_5311))
            | U_5315 != U_5311 ) ) )
    & ! [U_5314,U_5312,U_5310,U_5308,U_5306] :
        ( ( ? [U_5299] :
              ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5299),U_5312),U_5314))
              & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5308),U_5310),U_5312),U_5299)) )
          & hBOOL(hAPP(U_5306,U_5310)) )
        | ( ~ hBOOL(hAPP(U_5306,U_5310))
          & U_5314 = U_5310 )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ) ),
    inference(miniscope,[status(thm)],[f_1153_2]) ).

fof(f_1153_4,plain,
    ( ! [U_5315,U_5313,U_5311,U_5309,U_5307] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5311),U_5313),U_5315))
        | ( ( ! [U_5300] :
                ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5300),U_5313),U_5315))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5309),U_5311),U_5313),U_5300)) )
            | ~ hBOOL(hAPP(U_5307,U_5311)) )
          & ( hBOOL(hAPP(U_5307,U_5311))
            | U_5315 != U_5311 ) ) )
    & ! [U_5314,U_5312,U_5310,U_5308,U_5306] :
        ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)),U_5312),U_5314))
          & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5308),U_5310),U_5312),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)))
          & hBOOL(hAPP(U_5306,U_5310)) )
        | ( ~ hBOOL(hAPP(U_5306,U_5310))
          & U_5314 = U_5310 )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_5299,sK100(U_5314,U_5312,U_5310,U_5308,U_5306))],[f_1153_3]) ).

cnf(f_1153_5,plain,
    ( hBOOL(hAPP(U_5306,U_5310))
    | U_5314 = U_5310
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5308),U_5310),U_5312),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)))
    | U_5314 = U_5310
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)),U_5312),U_5314))
    | U_5314 = U_5310
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_8,plain,
    ( hBOOL(hAPP(U_5306,U_5310))
    | ~ hBOOL(hAPP(U_5306,U_5310))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5308),U_5310),U_5312),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)))
    | ~ hBOOL(hAPP(U_5306,U_5310))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_10,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),sK100(U_5314,U_5312,U_5310,U_5308,U_5306)),U_5312),U_5314))
    | ~ hBOOL(hAPP(U_5306,U_5310))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5306,U_5308)),U_5310),U_5312),U_5314)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_11,plain,
    ( hBOOL(hAPP(U_5307,U_5311))
    | U_5315 != U_5311
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5311),U_5313),U_5315)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

cnf(f_1153_12,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5300),U_5313),U_5315))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5309),U_5311),U_5313),U_5300))
    | ~ hBOOL(hAPP(U_5307,U_5311))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5307,U_5309)),U_5311),U_5313),U_5315)) ),
    inference(clausify,[status(thm)],[f_1153_4]) ).

fof(f_1154_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2))
        | ( ! [B_s1] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2))
              | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) )
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) )
        | ~ hBOOL(hAPP(V_a1_2,V_a2_2))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1154_2,plain,
    ! [U_5321,U_5320,U_5319,U_5318] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5318,U_5319)),U_5320),U_5321),U_5320))
        | ( ! [U_5317] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5318,U_5319)),U_5317),U_5321),U_5320))
              | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5319),U_5320),U_5321),U_5317)) )
          & hBOOL(hAPP(U_5318,U_5320)) ) )
      & ( ? [U_5316] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5318,U_5319)),U_5316),U_5321),U_5320))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5319),U_5320),U_5321),U_5316)) )
        | ~ hBOOL(hAPP(U_5318,U_5320))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5318,U_5319)),U_5320),U_5321),U_5320)) ) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

fof(f_1154_3,plain,
    ( ! [U_5329,U_5327,U_5325,U_5323] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5327),U_5329),U_5327))
        | ( ! [U_5317] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5317),U_5329),U_5327))
              | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5325),U_5327),U_5329),U_5317)) )
          & hBOOL(hAPP(U_5323,U_5327)) ) )
    & ! [U_5328,U_5326,U_5324,U_5322] :
        ( ? [U_5316] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),U_5316),U_5328),U_5326))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5324),U_5326),U_5328),U_5316)) )
        | ~ hBOOL(hAPP(U_5322,U_5326))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),U_5326),U_5328),U_5326)) ) ),
    inference(miniscope,[status(thm)],[f_1154_2]) ).

fof(f_1154_4,plain,
    ( ! [U_5329,U_5327,U_5325,U_5323] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5327),U_5329),U_5327))
        | ( ! [U_5317] :
              ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5317),U_5329),U_5327))
              | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5325),U_5327),U_5329),U_5317)) )
          & hBOOL(hAPP(U_5323,U_5327)) ) )
    & ! [U_5328,U_5326,U_5324,U_5322] :
        ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),sK101(U_5328,U_5326,U_5324,U_5322)),U_5328),U_5326))
          & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5324),U_5326),U_5328),sK101(U_5328,U_5326,U_5324,U_5322))) )
        | ~ hBOOL(hAPP(U_5322,U_5326))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),U_5326),U_5328),U_5326)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_5316,sK101(U_5328,U_5326,U_5324,U_5322))],[f_1154_3]) ).

cnf(f_1154_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5324),U_5326),U_5328),sK101(U_5328,U_5326,U_5324,U_5322)))
    | ~ hBOOL(hAPP(U_5322,U_5326))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),U_5326),U_5328),U_5326)) ),
    inference(clausify,[status(thm)],[f_1154_4]) ).

cnf(f_1154_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),sK101(U_5328,U_5326,U_5324,U_5322)),U_5328),U_5326))
    | ~ hBOOL(hAPP(U_5322,U_5326))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5322,U_5324)),U_5326),U_5328),U_5326)) ),
    inference(clausify,[status(thm)],[f_1154_4]) ).

cnf(f_1154_7,plain,
    ( hBOOL(hAPP(U_5323,U_5327))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5327),U_5329),U_5327)) ),
    inference(clausify,[status(thm)],[f_1154_4]) ).

cnf(f_1154_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5317),U_5329),U_5327))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5325),U_5327),U_5329),U_5317))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(U_5323,U_5325)),U_5327),U_5329),U_5327)) ),
    inference(clausify,[status(thm)],[f_1154_4]) ).

fof(f_1155_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).

fof(f_1155_2,plain,
    ! [U_5333,U_5332,U_5331,U_5330] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5331,U_5330)),U_5332),U_5333))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5333),U_5332))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5332),U_5333)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5333),U_5332))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5332),U_5333)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5331,U_5330)),U_5332),U_5333)) ) )
      | ~ class_Orderings_Oord(U_5330) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5332),U_5333))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5331,U_5330)),U_5332),U_5333))
    | ~ class_Orderings_Oord(U_5330) ),
    inference(clausify,[status(thm)],[f_1155_2]) ).

cnf(f_1155_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5333),U_5332))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5331,U_5330)),U_5332),U_5333))
    | ~ class_Orderings_Oord(U_5330) ),
    inference(clausify,[status(thm)],[f_1155_2]) ).

cnf(f_1155_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5331,U_5330)),U_5332),U_5333))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5333),U_5332))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5331,U_5330)),U_5332),U_5333))
    | ~ class_Orderings_Oord(U_5330) ),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_thin]) ).

fof(f_1156_2,plain,
    ! [U_5337,U_5336,U_5335,U_5334] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_5334,U_5337,U_5336)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5334),tc_HOL_Obool)),U_5335),U_5337))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_5334,U_5335,U_5336) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_5334,U_5337,U_5336)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5334),tc_HOL_Obool)),U_5335),U_5337))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_5334,U_5335,U_5336) ),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_weaken]) ).

fof(f_1157_2,plain,
    ! [U_5341,U_5340,U_5339,U_5338] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_5338,U_5339,U_5341)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5338),tc_HOL_Obool)),U_5341),U_5340))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_5338,U_5339,U_5340) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_5338,U_5339,U_5341)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5338),tc_HOL_Obool)),U_5341),U_5340))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_5338,U_5339,U_5340) ),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    ! [V_Ga_2,V_ts_2,T_a] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2)) ),
    inference(fof_nnf,[status(thm)],[fact_asm]) ).

fof(f_1158_2,plain,
    ! [U_5344,U_5343,U_5342] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_5342,U_5344,U_5343)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5342),tc_HOL_Obool)),U_5343),U_5344)) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_5342,U_5344,U_5343)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5342),tc_HOL_Obool)),U_5343),U_5344)) ),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2))
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1159_2,plain,
    ! [U_5350,U_5349,U_5348,U_5347,U_5346,U_5345] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5345,U_5346,U_5347)),U_5348),U_5349),U_5350))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5347),U_5348),U_5349),U_5350))
            | hBOOL(hAPP(U_5345,U_5348)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5346),U_5348),U_5349),U_5350))
            | ~ hBOOL(hAPP(U_5345,U_5348)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5347),U_5348),U_5349),U_5350))
          & ~ hBOOL(hAPP(U_5345,U_5348)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5346),U_5348),U_5349),U_5350))
          & hBOOL(hAPP(U_5345,U_5348)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5345,U_5346,U_5347)),U_5348),U_5349),U_5350)) ) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

fof(f_1159_3,plain,
    ( ! [U_5362,U_5360,U_5358,U_5356,U_5354,U_5352] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5352,U_5354,U_5356)),U_5358),U_5360),U_5362))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5356),U_5358),U_5360),U_5362))
            | hBOOL(hAPP(U_5352,U_5358)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5354),U_5358),U_5360),U_5362))
            | ~ hBOOL(hAPP(U_5352,U_5358)) ) ) )
    & ! [U_5361,U_5359,U_5357,U_5355,U_5353,U_5351] :
        ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5355),U_5357),U_5359),U_5361))
          & ~ hBOOL(hAPP(U_5351,U_5357)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5353),U_5357),U_5359),U_5361))
          & hBOOL(hAPP(U_5351,U_5357)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5351,U_5353,U_5355)),U_5357),U_5359),U_5361)) ) ),
    inference(miniscope,[status(thm)],[f_1159_2]) ).

cnf(f_1159_4,plain,
    ( ~ hBOOL(hAPP(U_5351,U_5357))
    | hBOOL(hAPP(U_5351,U_5357))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5351,U_5353,U_5355)),U_5357),U_5359),U_5361)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

cnf(f_1159_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5355),U_5357),U_5359),U_5361))
    | hBOOL(hAPP(U_5351,U_5357))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5351,U_5353,U_5355)),U_5357),U_5359),U_5361)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

cnf(f_1159_6,plain,
    ( ~ hBOOL(hAPP(U_5351,U_5357))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5353),U_5357),U_5359),U_5361))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5351,U_5353,U_5355)),U_5357),U_5359),U_5361)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

cnf(f_1159_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5355),U_5357),U_5359),U_5361))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5353),U_5357),U_5359),U_5361))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5351,U_5353,U_5355)),U_5357),U_5359),U_5361)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

cnf(f_1159_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5354),U_5358),U_5360),U_5362))
    | ~ hBOOL(hAPP(U_5352,U_5358))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5352,U_5354,U_5356)),U_5358),U_5360),U_5362)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

cnf(f_1159_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5356),U_5358),U_5360),U_5362))
    | hBOOL(hAPP(U_5352,U_5358))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5352,U_5354,U_5356)),U_5358),U_5360),U_5362)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

fof(f_1160_1,plain,
    ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2))
            | hBOOL(hAPP(V_a1_2,V_a2_2)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2))
            | ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1160_2,plain,
    ! [U_5368,U_5367,U_5366,U_5365,U_5364,U_5363] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5363,U_5364,U_5365)),U_5366),U_5367),U_5368))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5365),U_5366),U_5367),U_5368))
            | hBOOL(hAPP(U_5363,U_5366)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5364),U_5366),U_5367),U_5368))
            | ~ hBOOL(hAPP(U_5363,U_5366)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5365),U_5366),U_5367),U_5368))
          & ~ hBOOL(hAPP(U_5363,U_5366)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5364),U_5366),U_5367),U_5368))
          & hBOOL(hAPP(U_5363,U_5366)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5363,U_5364,U_5365)),U_5366),U_5367),U_5368)) ) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ( ! [U_5380,U_5378,U_5376,U_5374,U_5372,U_5370] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5370,U_5372,U_5374)),U_5376),U_5378),U_5380))
        | ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5374),U_5376),U_5378),U_5380))
            | hBOOL(hAPP(U_5370,U_5376)) )
          & ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5372),U_5376),U_5378),U_5380))
            | ~ hBOOL(hAPP(U_5370,U_5376)) ) ) )
    & ! [U_5379,U_5377,U_5375,U_5373,U_5371,U_5369] :
        ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5373),U_5375),U_5377),U_5379))
          & ~ hBOOL(hAPP(U_5369,U_5375)) )
        | ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5371),U_5375),U_5377),U_5379))
          & hBOOL(hAPP(U_5369,U_5375)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5369,U_5371,U_5373)),U_5375),U_5377),U_5379)) ) ),
    inference(miniscope,[status(thm)],[f_1160_2]) ).

cnf(f_1160_4,plain,
    ( ~ hBOOL(hAPP(U_5369,U_5375))
    | hBOOL(hAPP(U_5369,U_5375))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5369,U_5371,U_5373)),U_5375),U_5377),U_5379)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5373),U_5375),U_5377),U_5379))
    | hBOOL(hAPP(U_5369,U_5375))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5369,U_5371,U_5373)),U_5375),U_5377),U_5379)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_6,plain,
    ( ~ hBOOL(hAPP(U_5369,U_5375))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5371),U_5375),U_5377),U_5379))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5369,U_5371,U_5373)),U_5375),U_5377),U_5379)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5373),U_5375),U_5377),U_5379))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5371),U_5375),U_5377),U_5379))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5369,U_5371,U_5373)),U_5375),U_5377),U_5379)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5372),U_5376),U_5378),U_5380))
    | ~ hBOOL(hAPP(U_5370,U_5376))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5370,U_5372,U_5374)),U_5376),U_5378),U_5380)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5374),U_5376),U_5378),U_5380))
    | hBOOL(hAPP(U_5370,U_5376))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(U_5370,U_5372,U_5374)),U_5376),U_5378),U_5380)) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

fof(f_1161_1,plain,
    ! [V_A_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).

fof(f_1161_2,plain,
    ! [U_5385,U_5384,U_5383] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385)))
          | ? [U_5382] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),U_5382))
              & hBOOL(hAPP(hAPP(c_member(U_5383),U_5382),U_5385)) ) )
        & ( ! [U_5381] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),U_5381))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5383),U_5381),U_5385)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5383) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ! [U_5385,U_5384,U_5383] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),sK102(U_5385,U_5384,U_5383)))
            & hBOOL(hAPP(hAPP(c_member(U_5383),sK102(U_5385,U_5384,U_5383)),U_5385)) ) )
        & ( ! [U_5381] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),U_5381))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5383),U_5381),U_5385)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5383) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_5382,sK102(U_5385,U_5384,U_5383))],[f_1161_2]) ).

cnf(f_1161_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),U_5381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5383),U_5381),U_5385))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5383) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5383),sK102(U_5385,U_5384,U_5383)),U_5385))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5383) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

cnf(f_1161_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),sK102(U_5385,U_5384,U_5383)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5383),U_5384),c_Complete__Lattice_OInf__class_OInf(U_5383,U_5385)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5383) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

fof(f_1162_1,plain,
    ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__mono]) ).

fof(f_1162_2,plain,
    ! [U_5390,U_5389,U_5388,U_5387,U_5386] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5389,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_5389,U_5386,U_5390),U_5387)),hAPP(c_Set_Ovimage(U_5389,U_5386,U_5390),U_5388)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5386,tc_HOL_Obool)),U_5387),U_5388)) ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5389,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_5389,U_5386,U_5390),U_5387)),hAPP(c_Set_Ovimage(U_5389,U_5386,U_5390),U_5388)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5386,tc_HOL_Obool)),U_5387),U_5388)) ),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2))
        | ! [B_s1] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2))
            | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) ) )
      & ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1163_2,plain,
    ! [U_5397,U_5396,U_5395,U_5394,U_5393] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5393,U_5394)),U_5395),U_5396),U_5397))
        | ! [U_5392] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5394),U_5392),U_5396),U_5397))
            | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5393),U_5395),U_5396),U_5392)) ) )
      & ( ? [U_5391] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5394),U_5391),U_5396),U_5397))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5393),U_5395),U_5396),U_5391)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5393,U_5394)),U_5395),U_5396),U_5397)) ) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ( ! [U_5407,U_5405,U_5403,U_5401,U_5399] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5399,U_5401)),U_5403),U_5405),U_5407))
        | ! [U_5392] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5401),U_5392),U_5405),U_5407))
            | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5399),U_5403),U_5405),U_5392)) ) )
    & ! [U_5406,U_5404,U_5402,U_5400,U_5398] :
        ( ? [U_5391] :
            ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5400),U_5391),U_5404),U_5406))
            & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5398),U_5402),U_5404),U_5391)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5398,U_5400)),U_5402),U_5404),U_5406)) ) ),
    inference(miniscope,[status(thm)],[f_1163_2]) ).

fof(f_1163_4,plain,
    ( ! [U_5407,U_5405,U_5403,U_5401,U_5399] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5399,U_5401)),U_5403),U_5405),U_5407))
        | ! [U_5392] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5401),U_5392),U_5405),U_5407))
            | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5399),U_5403),U_5405),U_5392)) ) )
    & ! [U_5406,U_5404,U_5402,U_5400,U_5398] :
        ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5400),sK103(U_5406,U_5404,U_5402,U_5400,U_5398)),U_5404),U_5406))
          & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5398),U_5402),U_5404),sK103(U_5406,U_5404,U_5402,U_5400,U_5398))) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5398,U_5400)),U_5402),U_5404),U_5406)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_5391,sK103(U_5406,U_5404,U_5402,U_5400,U_5398))],[f_1163_3]) ).

cnf(f_1163_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5398),U_5402),U_5404),sK103(U_5406,U_5404,U_5402,U_5400,U_5398)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5398,U_5400)),U_5402),U_5404),U_5406)) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

cnf(f_1163_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5400),sK103(U_5406,U_5404,U_5402,U_5400,U_5398)),U_5404),U_5406))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5398,U_5400)),U_5402),U_5404),U_5406)) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

cnf(f_1163_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(U_5399,U_5401)),U_5403),U_5405),U_5407))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5401),U_5392),U_5405),U_5407))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5399),U_5403),U_5405),U_5392)) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

fof(f_1164_1,plain,
    ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(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_1164_2,plain,
    ! [U_5409,U_5408] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_5408),U_5409),U_5408)),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),U_5408),U_5409),U_5408)),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).

fof(f_1165_2,plain,
    ! [U_5413,U_5412,U_5411,U_5410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5410,tc_HOL_Obool)),U_5411),U_5413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5410,tc_HOL_Obool)),U_5412),U_5413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5410,tc_HOL_Obool)),U_5411),U_5412)) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5410,tc_HOL_Obool)),U_5411),U_5413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5410,tc_HOL_Obool)),U_5412),U_5413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5410,tc_HOL_Obool)),U_5411),U_5412)) ),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).

fof(f_1166_2,plain,
    ! [U_5417,U_5416,U_5415,U_5414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5414,tc_HOL_Obool)),U_5415),U_5417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5414,tc_HOL_Obool)),U_5416),U_5417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5414,tc_HOL_Obool)),U_5415),U_5416)) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5414,tc_HOL_Obool)),U_5415),U_5417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5414,tc_HOL_Obool)),U_5416),U_5417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5414,tc_HOL_Obool)),U_5415),U_5416)) ),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).

fof(f_1167_2,plain,
    ! [U_5420,U_5419,U_5418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5418,tc_HOL_Obool)),U_5419),U_5420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5418,tc_HOL_Obool)),U_5419),U_5420)) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5418,tc_HOL_Obool)),U_5419),U_5420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5418,tc_HOL_Obool)),U_5419),U_5420)) ),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).

fof(f_1168_2,plain,
    ! [U_5423,U_5422,U_5421] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5421,tc_HOL_Obool)),U_5422),U_5423))
        | ( U_5422 != U_5423
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5421,tc_HOL_Obool)),U_5422),U_5423)) ) )
      & ( U_5422 = U_5423
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5421,tc_HOL_Obool)),U_5422),U_5423))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5421,tc_HOL_Obool)),U_5422),U_5423)) ) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ( ! [U_5429,U_5427,U_5425] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5425,tc_HOL_Obool)),U_5427),U_5429))
        | ( U_5427 != U_5429
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5425,tc_HOL_Obool)),U_5427),U_5429)) ) )
    & ! [U_5428,U_5426,U_5424] :
        ( U_5426 = U_5428
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5424,tc_HOL_Obool)),U_5426),U_5428))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5424,tc_HOL_Obool)),U_5426),U_5428)) ) ),
    inference(miniscope,[status(thm)],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( U_5426 = U_5428
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5424,tc_HOL_Obool)),U_5426),U_5428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5424,tc_HOL_Obool)),U_5426),U_5428)) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

cnf(f_1168_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5425,tc_HOL_Obool)),U_5427),U_5429))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5425,tc_HOL_Obool)),U_5427),U_5429)) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

cnf(f_1168_6,plain,
    ( U_5427 != U_5429
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5425,tc_HOL_Obool)),U_5427),U_5429)) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

fof(f_1169_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a,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_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).

fof(f_1169_2,plain,
    ! [U_5432,U_5431,U_5430] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432))
        | U_5431 = U_5432
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) )
      & ( ( U_5431 != U_5432
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) ) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

fof(f_1169_3,plain,
    ( ! [U_5438,U_5436,U_5434] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5434,tc_HOL_Obool)),U_5436),U_5438))
        | U_5436 = U_5438
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5434,tc_HOL_Obool)),U_5436),U_5438)) )
    & ! [U_5437,U_5435,U_5433] :
        ( ( U_5435 != U_5437
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5433,tc_HOL_Obool)),U_5435),U_5437)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5433,tc_HOL_Obool)),U_5435),U_5437)) ) ),
    inference(miniscope,[status(thm)],[f_1169_2]) ).

cnf(f_1169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5433,tc_HOL_Obool)),U_5435),U_5437))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5433,tc_HOL_Obool)),U_5435),U_5437)) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_5,plain,
    ( U_5435 != U_5437
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5433,tc_HOL_Obool)),U_5435),U_5437)) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5434,tc_HOL_Obool)),U_5436),U_5438))
    | U_5436 = U_5438
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5434,tc_HOL_Obool)),U_5436),U_5438)) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

fof(f_1170_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_1170_2,plain,
    ! [U_5439] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5439)) = 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_5439))),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5439)) = 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_5439))),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).

fof(f_1171_2,plain,
    ! [U_5442,U_5441,U_5440] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5440,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5440,tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5440)),U_5441)),hAPP(hAPP(c_COMBC(U_5440,tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5440)),U_5442)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5440,tc_HOL_Obool)),U_5441),U_5442)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5440,tc_HOL_Obool)),U_5441),U_5442))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5440,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5440,tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5440)),U_5441)),hAPP(hAPP(c_COMBC(U_5440,tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5440)),U_5442))) ) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ( ! [U_5448,U_5446,U_5444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5444,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5446)),hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5448)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5444,tc_HOL_Obool)),U_5446),U_5448)) )
    & ! [U_5447,U_5445,U_5443] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5443,tc_HOL_Obool)),U_5445),U_5447))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5443,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5443,tc_fun(U_5443,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5443)),U_5445)),hAPP(hAPP(c_COMBC(U_5443,tc_fun(U_5443,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5443)),U_5447))) ) ),
    inference(miniscope,[status(thm)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5443,tc_HOL_Obool)),U_5445),U_5447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5443,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5443,tc_fun(U_5443,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5443)),U_5445)),hAPP(hAPP(c_COMBC(U_5443,tc_fun(U_5443,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5443)),U_5447))) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

cnf(f_1171_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5444,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5446)),hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5448)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5444,tc_HOL_Obool)),U_5446),U_5448)) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).

fof(f_1172_2,plain,
    ! [U_5451,U_5450,U_5449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5449),hAPP(c_Finite__Set_Ofold1(U_5449,c_Lattices_Osemilattice__inf__class_Oinf(U_5449)),U_5450)),U_5451))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5449),U_5451),U_5450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5449),U_5450))
      | ~ class_Lattices_Osemilattice__inf(U_5449) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

cnf(f_1172_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5449),hAPP(c_Finite__Set_Ofold1(U_5449,c_Lattices_Osemilattice__inf__class_Oinf(U_5449)),U_5450)),U_5451))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5449),U_5451),U_5450))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5449),U_5450))
    | ~ class_Lattices_Osemilattice__inf(U_5449) ),
    inference(clausify,[status(thm)],[f_1172_2]) ).

fof(f_1173_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).

fof(f_1173_2,plain,
    ! [U_5456,U_5455,U_5454] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455)))
          | ? [U_5453] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),U_5453))
              & hBOOL(hAPP(hAPP(c_member(U_5454),U_5453),U_5455)) ) )
        & ( ! [U_5452] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),U_5452))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5452),U_5455)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455))) ) )
      | U_5455 = c_Orderings_Obot__class_Obot(tc_fun(U_5454,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5454),U_5455))
      | ~ class_Lattices_Osemilattice__inf(U_5454) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_5456,U_5455,U_5454] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),sK104(U_5456,U_5455,U_5454)))
            & hBOOL(hAPP(hAPP(c_member(U_5454),sK104(U_5456,U_5455,U_5454)),U_5455)) ) )
        & ( ! [U_5452] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),U_5452))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5452),U_5455)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455))) ) )
      | U_5455 = c_Orderings_Obot__class_Obot(tc_fun(U_5454,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5454),U_5455))
      | ~ class_Lattices_Osemilattice__inf(U_5454) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_5453,sK104(U_5456,U_5455,U_5454))],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),U_5452))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5452),U_5455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455)))
    | U_5455 = c_Orderings_Obot__class_Obot(tc_fun(U_5454,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5454),U_5455))
    | ~ class_Lattices_Osemilattice__inf(U_5454) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

cnf(f_1173_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5454),sK104(U_5456,U_5455,U_5454)),U_5455))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455)))
    | U_5455 = c_Orderings_Obot__class_Obot(tc_fun(U_5454,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5454),U_5455))
    | ~ class_Lattices_Osemilattice__inf(U_5454) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

cnf(f_1173_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),sK104(U_5456,U_5455,U_5454)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),U_5456),hAPP(c_Finite__Set_Ofold1(U_5454,c_Lattices_Osemilattice__inf__class_Oinf(U_5454)),U_5455)))
    | U_5455 = c_Orderings_Obot__class_Obot(tc_fun(U_5454,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5454),U_5455))
    | ~ class_Lattices_Osemilattice__inf(U_5454) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_1,plain,
    ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_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_a),hAPP(V_M_2,B_x)),V_u_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).

fof(f_1174_2,plain,
    ! [U_5463,U_5462,U_5461,U_5460,U_5459] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463))
          | ? [U_5458] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,U_5458)),U_5463))
              & hBOOL(hAPP(hAPP(c_member(U_5460),U_5458),U_5461)) ) )
        & ( ! [U_5457] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,U_5457)),U_5463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5460),U_5457),U_5461)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5459) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ! [U_5463,U_5462,U_5461,U_5460,U_5459] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,sK105(U_5463,U_5462,U_5461,U_5460,U_5459))),U_5463))
            & hBOOL(hAPP(hAPP(c_member(U_5460),sK105(U_5463,U_5462,U_5461,U_5460,U_5459)),U_5461)) ) )
        & ( ! [U_5457] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,U_5457)),U_5463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5460),U_5457),U_5461)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5459) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_5458,sK105(U_5463,U_5462,U_5461,U_5460,U_5459))],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,U_5457)),U_5463))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5460),U_5457),U_5461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5459) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

cnf(f_1174_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5460),sK105(U_5463,U_5462,U_5461,U_5460,U_5459)),U_5461))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5459) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

cnf(f_1174_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(U_5462,sK105(U_5463,U_5462,U_5461,U_5460,U_5459))),U_5463))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5459),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5460,U_5459),U_5461),U_5462)),U_5463))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5459) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).

fof(f_1175_2,plain,
    ! [U_5470,U_5469,U_5468,U_5467,U_5466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5467,tc_fun(U_5466,tc_HOL_Obool)),U_5468),U_5469)),U_5470))
        | ? [U_5465] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5466,tc_HOL_Obool)),hAPP(U_5469,U_5465)),U_5470))
            & hBOOL(hAPP(hAPP(c_member(U_5467),U_5465),U_5468)) ) )
      & ( ! [U_5464] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5466,tc_HOL_Obool)),hAPP(U_5469,U_5464)),U_5470))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5467),U_5464),U_5468)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5467,tc_fun(U_5466,tc_HOL_Obool)),U_5468),U_5469)),U_5470)) ) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ( ! [U_5480,U_5478,U_5476,U_5474,U_5472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5476),U_5478)),U_5480))
        | ? [U_5465] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(U_5478,U_5465)),U_5480))
            & hBOOL(hAPP(hAPP(c_member(U_5474),U_5465),U_5476)) ) )
    & ! [U_5479,U_5477,U_5475,U_5473,U_5471] :
        ( ! [U_5464] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(U_5477,U_5464)),U_5479))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5473),U_5464),U_5475)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5473,tc_fun(U_5471,tc_HOL_Obool)),U_5475),U_5477)),U_5479)) ) ),
    inference(miniscope,[status(thm)],[f_1175_2]) ).

fof(f_1175_4,plain,
    ( ! [U_5480,U_5478,U_5476,U_5474,U_5472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5476),U_5478)),U_5480))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(U_5478,sK106(U_5480,U_5478,U_5476,U_5474,U_5472))),U_5480))
          & hBOOL(hAPP(hAPP(c_member(U_5474),sK106(U_5480,U_5478,U_5476,U_5474,U_5472)),U_5476)) ) )
    & ! [U_5479,U_5477,U_5475,U_5473,U_5471] :
        ( ! [U_5464] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(U_5477,U_5464)),U_5479))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5473),U_5464),U_5475)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5473,tc_fun(U_5471,tc_HOL_Obool)),U_5475),U_5477)),U_5479)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_5465,sK106(U_5480,U_5478,U_5476,U_5474,U_5472))],[f_1175_3]) ).

cnf(f_1175_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(U_5477,U_5464)),U_5479))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5473),U_5464),U_5475))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5473,tc_fun(U_5471,tc_HOL_Obool)),U_5475),U_5477)),U_5479)) ),
    inference(clausify,[status(thm)],[f_1175_4]) ).

cnf(f_1175_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5474),sK106(U_5480,U_5478,U_5476,U_5474,U_5472)),U_5476))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5476),U_5478)),U_5480)) ),
    inference(clausify,[status(thm)],[f_1175_4]) ).

cnf(f_1175_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(U_5478,sK106(U_5480,U_5478,U_5476,U_5474,U_5472))),U_5480))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5476),U_5478)),U_5480)) ),
    inference(clausify,[status(thm)],[f_1175_4]) ).

fof(f_1176_1,plain,
    ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_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_a),V_u_2),hAPP(V_M_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_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).

fof(f_1176_2,plain,
    ! [U_5487,U_5486,U_5485,U_5484,U_5483] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487)))
          | ? [U_5482] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,U_5482)))
              & hBOOL(hAPP(hAPP(c_member(U_5485),U_5482),U_5486)) ) )
        & ( ! [U_5481] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,U_5481)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5485),U_5481),U_5486)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5483) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ! [U_5487,U_5486,U_5485,U_5484,U_5483] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,sK107(U_5487,U_5486,U_5485,U_5484,U_5483))))
            & hBOOL(hAPP(hAPP(c_member(U_5485),sK107(U_5487,U_5486,U_5485,U_5484,U_5483)),U_5486)) ) )
        & ( ! [U_5481] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,U_5481)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5485),U_5481),U_5486)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5483) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_5482,sK107(U_5487,U_5486,U_5485,U_5484,U_5483))],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,U_5481)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5485),U_5481),U_5486))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5483) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5485),sK107(U_5487,U_5486,U_5485,U_5484,U_5483)),U_5486))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5483) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(U_5487,sK107(U_5487,U_5486,U_5485,U_5484,U_5483))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5483),U_5484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5485,U_5483),U_5486),U_5487)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5483) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_1,plain,
    ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).

fof(f_1177_2,plain,
    ! [U_5494,U_5493,U_5492,U_5491,U_5490] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5490,tc_HOL_Obool)),U_5491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5492,tc_fun(U_5490,tc_HOL_Obool)),U_5493),U_5494)))
        | ? [U_5489] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5490,tc_HOL_Obool)),U_5491),hAPP(U_5494,U_5489)))
            & hBOOL(hAPP(hAPP(c_member(U_5492),U_5489),U_5493)) ) )
      & ( ! [U_5488] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5490,tc_HOL_Obool)),U_5491),hAPP(U_5494,U_5488)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5492),U_5488),U_5493)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5490,tc_HOL_Obool)),U_5491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5492,tc_fun(U_5490,tc_HOL_Obool)),U_5493),U_5494))) ) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ( ! [U_5504,U_5502,U_5500,U_5498,U_5496] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5500,tc_fun(U_5496,tc_HOL_Obool)),U_5502),U_5504)))
        | ? [U_5489] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(U_5504,U_5489)))
            & hBOOL(hAPP(hAPP(c_member(U_5500),U_5489),U_5502)) ) )
    & ! [U_5503,U_5501,U_5499,U_5497,U_5495] :
        ( ! [U_5488] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(U_5503,U_5488)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5499),U_5488),U_5501)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5499,tc_fun(U_5495,tc_HOL_Obool)),U_5501),U_5503))) ) ),
    inference(miniscope,[status(thm)],[f_1177_2]) ).

fof(f_1177_4,plain,
    ( ! [U_5504,U_5502,U_5500,U_5498,U_5496] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5500,tc_fun(U_5496,tc_HOL_Obool)),U_5502),U_5504)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(U_5504,sK108(U_5504,U_5502,U_5500,U_5498,U_5496))))
          & hBOOL(hAPP(hAPP(c_member(U_5500),sK108(U_5504,U_5502,U_5500,U_5498,U_5496)),U_5502)) ) )
    & ! [U_5503,U_5501,U_5499,U_5497,U_5495] :
        ( ! [U_5488] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(U_5503,U_5488)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5499),U_5488),U_5501)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5499,tc_fun(U_5495,tc_HOL_Obool)),U_5501),U_5503))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_5489,sK108(U_5504,U_5502,U_5500,U_5498,U_5496))],[f_1177_3]) ).

cnf(f_1177_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(U_5503,U_5488)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5499),U_5488),U_5501))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5495,tc_HOL_Obool)),U_5497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5499,tc_fun(U_5495,tc_HOL_Obool)),U_5501),U_5503))) ),
    inference(clausify,[status(thm)],[f_1177_4]) ).

cnf(f_1177_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5500),sK108(U_5504,U_5502,U_5500,U_5498,U_5496)),U_5502))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5500,tc_fun(U_5496,tc_HOL_Obool)),U_5502),U_5504))) ),
    inference(clausify,[status(thm)],[f_1177_4]) ).

cnf(f_1177_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(U_5504,sK108(U_5504,U_5502,U_5500,U_5498,U_5496))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5496,tc_HOL_Obool)),U_5498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5500,tc_fun(U_5496,tc_HOL_Obool)),U_5502),U_5504))) ),
    inference(clausify,[status(thm)],[f_1177_4]) ).

fof(f_1178_1,plain,
    ! [V_k_2,V_i_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).

fof(f_1178_2,plain,
    ! [U_5507,U_5506,U_5505] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_5505),U_5506),hAPP(c_SetInterval_Oord__class_OlessThan(U_5505),U_5507)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5505),U_5506),U_5507)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5505),U_5506),U_5507))
          | ~ hBOOL(hAPP(hAPP(c_member(U_5505),U_5506),hAPP(c_SetInterval_Oord__class_OlessThan(U_5505),U_5507))) ) )
      | ~ class_Orderings_Oord(U_5505) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

cnf(f_1178_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5505),U_5506),U_5507))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5505),U_5506),hAPP(c_SetInterval_Oord__class_OlessThan(U_5505),U_5507)))
    | ~ class_Orderings_Oord(U_5505) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5505),U_5506),hAPP(c_SetInterval_Oord__class_OlessThan(U_5505),U_5507)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5505),U_5506),U_5507))
    | ~ class_Orderings_Oord(U_5505) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

fof(f_1179_1,plain,
    ! [V_n_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).

fof(f_1179_2,plain,
    ! [U_5510,U_5509,U_5508] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5508),U_5509),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5510))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5508),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5508),U_5509),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5510))),hAPP(U_5509,U_5510))
      | ~ class_Groups_Ocomm__monoid__add(U_5508) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5508),U_5509),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5510))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5508),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5508),U_5509),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5510))),hAPP(U_5509,U_5510))
    | ~ class_Groups_Ocomm__monoid__add(U_5508) ),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).

fof(f_1180_2,plain,
    ! [U_5513,U_5512,U_5511] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5512)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5513)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5511),U_5512),U_5513)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5511),U_5512),U_5513))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5512)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5513))) ) )
      | ~ class_Orderings_Olinorder(U_5511) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5511),U_5512),U_5513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5512)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5513)))
    | ~ class_Orderings_Olinorder(U_5511) ),
    inference(clausify,[status(thm)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5512)),hAPP(c_SetInterval_Oord__class_OlessThan(U_5511),U_5513)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5511),U_5512),U_5513))
    | ~ class_Orderings_Olinorder(U_5511) ),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_1,plain,
    ! [V_a_2,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_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ 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_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_1181_2,plain,
    ! [U_5515,U_5514] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5514),U_5515),U_5515)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5514),U_5515),U_5515))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5514) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5514),U_5515),U_5515)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5514) ),
    inference(clausify,[status(thm)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5514),U_5515),U_5515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515))
    | ~ class_Groups_Olinordered__ab__group__add(U_5514) ),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_1182_2,plain,
    ! [U_5517,U_5516] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5517)),c_Groups_Ozero__class_Ozero(U_5516)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),U_5517),c_Groups_Ozero__class_Ozero(U_5516))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),U_5517),c_Groups_Ozero__class_Ozero(U_5516)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5517)),c_Groups_Ozero__class_Ozero(U_5516))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5516) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

cnf(f_1182_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),U_5517),c_Groups_Ozero__class_Ozero(U_5516)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5517)),c_Groups_Ozero__class_Ozero(U_5516)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5516) ),
    inference(clausify,[status(thm)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5516),U_5517),U_5517)),c_Groups_Ozero__class_Ozero(U_5516)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5516),U_5517),c_Groups_Ozero__class_Ozero(U_5516)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5516) ),
    inference(clausify,[status(thm)],[f_1182_2]) ).

fof(f_1183_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_1183_2,plain,
    ! [U_5520,U_5519,U_5518] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5518),U_5519),U_5520)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),U_5520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),U_5519))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5518) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5518),U_5519),U_5520)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),U_5520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5518),c_Groups_Ozero__class_Ozero(U_5518)),U_5519))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5518) ),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) != 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_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).

fof(f_1184_2,plain,
    ! [U_5523,U_5522,U_5521] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523) = c_Groups_Ozero__class_Ozero(U_5521)
          | U_5523 != c_Groups_Ozero__class_Ozero(U_5521)
          | U_5522 != c_Groups_Ozero__class_Ozero(U_5521) )
        & ( ( U_5523 = c_Groups_Ozero__class_Ozero(U_5521)
            & U_5522 = c_Groups_Ozero__class_Ozero(U_5521) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523) != c_Groups_Ozero__class_Ozero(U_5521) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5522))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5521) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    ( U_5522 = c_Groups_Ozero__class_Ozero(U_5521)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523) != c_Groups_Ozero__class_Ozero(U_5521)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5522))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5521) ),
    inference(clausify,[status(thm)],[f_1184_2]) ).

cnf(f_1184_4,plain,
    ( U_5523 = c_Groups_Ozero__class_Ozero(U_5521)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523) != c_Groups_Ozero__class_Ozero(U_5521)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5522))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5521) ),
    inference(clausify,[status(thm)],[f_1184_2]) ).

cnf(f_1184_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523) = c_Groups_Ozero__class_Ozero(U_5521)
    | U_5523 != c_Groups_Ozero__class_Ozero(U_5521)
    | U_5522 != c_Groups_Ozero__class_Ozero(U_5521)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5521),c_Groups_Ozero__class_Ozero(U_5521)),U_5522))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5521) ),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_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_1185_2,plain,
    ! [U_5527,U_5526,U_5525,U_5524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),U_5526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5524),U_5525),U_5527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),U_5526),U_5527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),c_Groups_Ozero__class_Ozero(U_5524)),U_5525))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5524) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

cnf(f_1185_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),U_5526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5524),U_5525),U_5527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),U_5526),U_5527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5524),c_Groups_Ozero__class_Ozero(U_5524)),U_5525))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5524) ),
    inference(clausify,[status(thm)],[f_1185_2]) ).

fof(f_1186_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_1186_2,plain,
    ! [U_5531,U_5530,U_5529,U_5528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),U_5530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5528),U_5531),U_5529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),U_5530),U_5531))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),c_Groups_Ozero__class_Ozero(U_5528)),U_5529))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5528) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

cnf(f_1186_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),U_5530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5528),U_5531),U_5529)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),U_5530),U_5531))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5528),c_Groups_Ozero__class_Ozero(U_5528)),U_5529))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5528) ),
    inference(clausify,[status(thm)],[f_1186_2]) ).

fof(f_1187_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_1187_2,plain,
    ! [U_5534,U_5533,U_5532] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5532),U_5533),U_5534)),c_Groups_Ozero__class_Ozero(U_5532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),U_5534),c_Groups_Ozero__class_Ozero(U_5532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),U_5533),c_Groups_Ozero__class_Ozero(U_5532)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5532) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

cnf(f_1187_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5532),U_5533),U_5534)),c_Groups_Ozero__class_Ozero(U_5532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),U_5534),c_Groups_Ozero__class_Ozero(U_5532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),U_5533),c_Groups_Ozero__class_Ozero(U_5532)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5532) ),
    inference(clausify,[status(thm)],[f_1187_2]) ).

fof(f_1188_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_1188_2,plain,
    ! [U_5537,U_5536,U_5535] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5535),U_5536),U_5537)),c_Groups_Ozero__class_Ozero(U_5535)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),c_Groups_Ozero__class_Ozero(U_5535)),U_5537))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),U_5536),c_Groups_Ozero__class_Ozero(U_5535))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),U_5537),c_Groups_Ozero__class_Ozero(U_5535)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),c_Groups_Ozero__class_Ozero(U_5535)),U_5536)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_5535) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),U_5537),c_Groups_Ozero__class_Ozero(U_5535)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),c_Groups_Ozero__class_Ozero(U_5535)),U_5536))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5535),U_5536),U_5537)),c_Groups_Ozero__class_Ozero(U_5535)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5535) ),
    inference(clausify,[status(thm)],[f_1188_2]) ).

cnf(f_1188_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),c_Groups_Ozero__class_Ozero(U_5535)),U_5537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),U_5536),c_Groups_Ozero__class_Ozero(U_5535)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5535),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5535),U_5536),U_5537)),c_Groups_Ozero__class_Ozero(U_5535)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5535) ),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_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_1189_2,plain,
    ! [U_5540,U_5539,U_5538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),U_5539),U_5540)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),U_5540),c_Groups_Ozero__class_Ozero(U_5538)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),U_5539),c_Groups_Ozero__class_Ozero(U_5538))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),U_5540))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),U_5539)) ) )
      | ~ class_Rings_Oordered__ring(U_5538) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),U_5540))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),U_5539))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),U_5539),U_5540)))
    | ~ class_Rings_Oordered__ring(U_5538) ),
    inference(clausify,[status(thm)],[f_1189_2]) ).

cnf(f_1189_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),U_5540),c_Groups_Ozero__class_Ozero(U_5538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),U_5539),c_Groups_Ozero__class_Ozero(U_5538)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5538),c_Groups_Ozero__class_Ozero(U_5538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5538),U_5539),U_5540)))
    | ~ class_Rings_Oordered__ring(U_5538) ),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_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_1190_2,plain,
    ! [U_5545,U_5544,U_5543,U_5542,U_5541] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5542),U_5544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5543),U_5545)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),c_Groups_Ozero__class_Ozero(U_5541)),U_5544))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),c_Groups_Ozero__class_Ozero(U_5541)),U_5543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),U_5544),U_5545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),U_5542),U_5543))
      | ~ class_Rings_Oordered__semiring(U_5541) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

cnf(f_1190_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5542),U_5544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5543),U_5545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),c_Groups_Ozero__class_Ozero(U_5541)),U_5544))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),c_Groups_Ozero__class_Ozero(U_5541)),U_5543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),U_5544),U_5545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5541),U_5542),U_5543))
    | ~ class_Rings_Oordered__semiring(U_5541) ),
    inference(clausify,[status(thm)],[f_1190_2]) ).

fof(f_1191_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_1191_2,plain,
    ! [U_5550,U_5549,U_5548,U_5547,U_5546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5546),U_5547),U_5549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5546),U_5548),U_5550)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),c_Groups_Ozero__class_Ozero(U_5546)),U_5549))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),c_Groups_Ozero__class_Ozero(U_5546)),U_5547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),U_5549),U_5550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),U_5547),U_5548))
      | ~ class_Rings_Oordered__semiring(U_5546) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5546),U_5547),U_5549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5546),U_5548),U_5550)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),c_Groups_Ozero__class_Ozero(U_5546)),U_5549))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),c_Groups_Ozero__class_Ozero(U_5546)),U_5547))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),U_5549),U_5550))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5546),U_5547),U_5548))
    | ~ class_Rings_Oordered__semiring(U_5546) ),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_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_1192_2,plain,
    ! [U_5554,U_5553,U_5552,U_5551] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5551),U_5554),U_5553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5551),U_5554),U_5552)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),U_5554),c_Groups_Ozero__class_Ozero(U_5551)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),U_5552),U_5553))
      | ~ class_Rings_Oordered__ring(U_5551) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

cnf(f_1192_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5551),U_5554),U_5553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5551),U_5554),U_5552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),U_5554),c_Groups_Ozero__class_Ozero(U_5551)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5551),U_5552),U_5553))
    | ~ class_Rings_Oordered__ring(U_5551) ),
    inference(clausify,[status(thm)],[f_1192_2]) ).

fof(f_1193_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_1193_2,plain,
    ! [U_5558,U_5557,U_5556,U_5555] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5555),U_5557),U_5558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5555),U_5556),U_5558)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),U_5558),c_Groups_Ozero__class_Ozero(U_5555)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),U_5556),U_5557))
      | ~ class_Rings_Oordered__ring(U_5555) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5555),U_5557),U_5558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5555),U_5556),U_5558)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),U_5558),c_Groups_Ozero__class_Ozero(U_5555)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5555),U_5556),U_5557))
    | ~ class_Rings_Oordered__ring(U_5555) ),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_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_1194_2,plain,
    ! [U_5562,U_5561,U_5560,U_5559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5562),U_5560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5562),U_5561)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5560),U_5561))
      | ~ class_Rings_Oordered__comm__semiring(U_5559) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

cnf(f_1194_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5562),U_5560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5562),U_5561)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5560),U_5561))
    | ~ class_Rings_Oordered__comm__semiring(U_5559) ),
    inference(clausify,[status(thm)],[f_1194_2]) ).

fof(f_1195_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_1195_2,plain,
    ! [U_5566,U_5565,U_5564,U_5563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5563),U_5566),U_5564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5563),U_5566),U_5565)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),c_Groups_Ozero__class_Ozero(U_5563)),U_5566))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),U_5564),U_5565))
      | ~ class_Rings_Oordered__semiring(U_5563) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

cnf(f_1195_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5563),U_5566),U_5564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5563),U_5566),U_5565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),c_Groups_Ozero__class_Ozero(U_5563)),U_5566))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5563),U_5564),U_5565))
    | ~ class_Rings_Oordered__semiring(U_5563) ),
    inference(clausify,[status(thm)],[f_1195_2]) ).

fof(f_1196_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_1196_2,plain,
    ! [U_5570,U_5569,U_5568,U_5567] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),U_5568),U_5570)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),U_5569),U_5570)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),c_Groups_Ozero__class_Ozero(U_5567)),U_5570))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),U_5568),U_5569))
      | ~ class_Rings_Oordered__semiring(U_5567) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

cnf(f_1196_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),U_5568),U_5570)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),U_5569),U_5570)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),c_Groups_Ozero__class_Ozero(U_5567)),U_5570))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5567),U_5568),U_5569))
    | ~ class_Rings_Oordered__semiring(U_5567) ),
    inference(clausify,[status(thm)],[f_1196_2]) ).

fof(f_1197_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_1197_2,plain,
    ! [U_5573,U_5572,U_5571] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),c_Groups_Ozero__class_Ozero(U_5571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5571),U_5572),U_5573)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),U_5573),c_Groups_Ozero__class_Ozero(U_5571)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),U_5572),c_Groups_Ozero__class_Ozero(U_5571)))
      | ~ class_Rings_Oordered__ring(U_5571) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

cnf(f_1197_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),c_Groups_Ozero__class_Ozero(U_5571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5571),U_5572),U_5573)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),U_5573),c_Groups_Ozero__class_Ozero(U_5571)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5571),U_5572),c_Groups_Ozero__class_Ozero(U_5571)))
    | ~ class_Rings_Oordered__ring(U_5571) ),
    inference(clausify,[status(thm)],[f_1197_2]) ).

fof(f_1198_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_1198_2,plain,
    ! [U_5576,U_5575,U_5574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5574),U_5575),U_5576)),c_Groups_Ozero__class_Ozero(U_5574)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),c_Groups_Ozero__class_Ozero(U_5574)),U_5576))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),U_5575),c_Groups_Ozero__class_Ozero(U_5574)))
      | ~ class_Rings_Oordered__cancel__semiring(U_5574) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

cnf(f_1198_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5574),U_5575),U_5576)),c_Groups_Ozero__class_Ozero(U_5574)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),c_Groups_Ozero__class_Ozero(U_5574)),U_5576))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5574),U_5575),c_Groups_Ozero__class_Ozero(U_5574)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5574) ),
    inference(clausify,[status(thm)],[f_1198_2]) ).

fof(f_1199_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_1199_2,plain,
    ! [U_5579,U_5578,U_5577] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5577),U_5579),U_5578)),c_Groups_Ozero__class_Ozero(U_5577)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),U_5579),c_Groups_Ozero__class_Ozero(U_5577)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),c_Groups_Ozero__class_Ozero(U_5577)),U_5578))
      | ~ class_Rings_Oordered__cancel__semiring(U_5577) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

cnf(f_1199_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5577),U_5579),U_5578)),c_Groups_Ozero__class_Ozero(U_5577)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),U_5579),c_Groups_Ozero__class_Ozero(U_5577)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5577),c_Groups_Ozero__class_Ozero(U_5577)),U_5578))
    | ~ class_Rings_Oordered__cancel__semiring(U_5577) ),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_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_1200_2,plain,
    ! [U_5582,U_5581,U_5580] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),c_Groups_Ozero__class_Ozero(U_5580)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),U_5582),c_Groups_Ozero__class_Ozero(U_5580)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),c_Groups_Ozero__class_Ozero(U_5580)),U_5581))
      | ~ class_Rings_Oordered__cancel__semiring(U_5580) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

cnf(f_1200_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),c_Groups_Ozero__class_Ozero(U_5580)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),U_5582),c_Groups_Ozero__class_Ozero(U_5580)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5580),c_Groups_Ozero__class_Ozero(U_5580)),U_5581))
    | ~ class_Rings_Oordered__cancel__semiring(U_5580) ),
    inference(clausify,[status(thm)],[f_1200_2]) ).

fof(f_1201_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_1201_2,plain,
    ! [U_5585,U_5584,U_5583] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5583),U_5584),U_5585)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),U_5585))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),U_5584))
      | ~ class_Rings_Oordered__cancel__semiring(U_5583) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

cnf(f_1201_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5583),U_5584),U_5585)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),U_5585))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5583),c_Groups_Ozero__class_Ozero(U_5583)),U_5584))
    | ~ class_Rings_Oordered__cancel__semiring(U_5583) ),
    inference(clausify,[status(thm)],[f_1201_2]) ).

fof(f_1202_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).

fof(f_1202_2,plain,
    ! [U_5588,U_5587,U_5586] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5588))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5587),c_Groups_Ozero__class_Ozero(U_5586))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5588),c_Groups_Ozero__class_Ozero(U_5586)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5587)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5588))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5587),c_Groups_Ozero__class_Ozero(U_5586))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5588),c_Groups_Ozero__class_Ozero(U_5586)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5587)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

cnf(f_1202_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5587),c_Groups_Ozero__class_Ozero(U_5586)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

cnf(f_1202_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5588))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

cnf(f_1202_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5587),c_Groups_Ozero__class_Ozero(U_5586)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5588),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

cnf(f_1202_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5588))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5588),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

cnf(f_1202_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5588),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5587))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

cnf(f_1202_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),c_Groups_Ozero__class_Ozero(U_5586)),U_5588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),U_5587),c_Groups_Ozero__class_Ozero(U_5586)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5586),U_5587),U_5588)),c_Groups_Ozero__class_Ozero(U_5586)))
    | ~ class_Rings_Olinordered__ring__strict(U_5586) ),
    inference(clausify,[status(thm)],[f_1202_2]) ).

fof(f_1203_1,plain,
    ! [V_b_2,V_a_2,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_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
          | ~ 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_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).

fof(f_1203_2,plain,
    ! [U_5591,U_5590,U_5589] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5591),c_Groups_Ozero__class_Ozero(U_5589)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5590),c_Groups_Ozero__class_Ozero(U_5589))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5591))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5590)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5591),c_Groups_Ozero__class_Ozero(U_5589)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5590),c_Groups_Ozero__class_Ozero(U_5589))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5591))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5590)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

cnf(f_1203_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5590),c_Groups_Ozero__class_Ozero(U_5589)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5591),c_Groups_Ozero__class_Ozero(U_5589)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

cnf(f_1203_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5590),c_Groups_Ozero__class_Ozero(U_5589)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5591))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

cnf(f_1203_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5591),c_Groups_Ozero__class_Ozero(U_5589)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5591))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

cnf(f_1203_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5591))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),U_5590))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

cnf(f_1203_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5591),c_Groups_Ozero__class_Ozero(U_5589)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),U_5590),c_Groups_Ozero__class_Ozero(U_5589)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5589),c_Groups_Ozero__class_Ozero(U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)))
    | ~ class_Rings_Olinordered__ring__strict(U_5589) ),
    inference(clausify,[status(thm)],[f_1203_2]) ).

fof(f_1204_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_1204_2,plain,
    ! [U_5593,U_5592] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5592),c_Groups_Ozero__class_Ozero(U_5592)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5593),U_5593)))
      | ~ class_Rings_Olinordered__ring(U_5592) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

cnf(f_1204_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5592),c_Groups_Ozero__class_Ozero(U_5592)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5593),U_5593)))
    | ~ class_Rings_Olinordered__ring(U_5592) ),
    inference(clausify,[status(thm)],[f_1204_2]) ).

fof(f_1205_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_1205_2,plain,
    ! [U_5598,U_5597,U_5596,U_5595,U_5594] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5594),U_5595),U_5597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5594),U_5596),U_5598)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5594),U_5597),U_5598))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5594),U_5595),U_5596))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_5594) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

cnf(f_1205_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5594),U_5595),U_5597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5594),U_5596),U_5598)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5594),U_5597),U_5598))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5594),U_5595),U_5596))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_5594) ),
    inference(clausify,[status(thm)],[f_1205_2]) ).

fof(f_1206_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_1206_2,plain,
    ! [U_5603,U_5602,U_5601,U_5600,U_5599] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5599),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5599),U_5600),U_5602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5599),U_5601),U_5603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5599),U_5602),U_5603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5599),U_5600),U_5601))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_5599) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5599),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5599),U_5600),U_5602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5599),U_5601),U_5603)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5599),U_5602),U_5603))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5599),U_5600),U_5601))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_5599) ),
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).

fof(f_1207_2,plain,
    ! [U_5606,U_5605,U_5604] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),U_5605),U_5606))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5604),U_5605),U_5606)),c_Groups_Ozero__class_Ozero(U_5604))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5604),U_5605),U_5606)),c_Groups_Ozero__class_Ozero(U_5604)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),U_5605),U_5606)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5604) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

cnf(f_1207_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5604),U_5605),U_5606)),c_Groups_Ozero__class_Ozero(U_5604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),U_5605),U_5606))
    | ~ class_Groups_Oordered__ab__group__add(U_5604) ),
    inference(clausify,[status(thm)],[f_1207_2]) ).

cnf(f_1207_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),U_5605),U_5606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5604),U_5605),U_5606)),c_Groups_Ozero__class_Ozero(U_5604)))
    | ~ class_Groups_Oordered__ab__group__add(U_5604) ),
    inference(clausify,[status(thm)],[f_1207_2]) ).

fof(f_1208_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_1208_2,plain,
    ! [U_5607] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5607),c_Groups_Ozero__class_Ozero(U_5607)),c_Groups_Oone__class_Oone(U_5607)))
      | ~ class_Rings_Olinordered__semidom(U_5607) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

cnf(f_1208_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5607),c_Groups_Ozero__class_Ozero(U_5607)),c_Groups_Oone__class_Oone(U_5607)))
    | ~ class_Rings_Olinordered__semidom(U_5607) ),
    inference(clausify,[status(thm)],[f_1208_2]) ).

fof(f_1209_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_1209_2,plain,
    ! [U_5608] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5608),c_Groups_Oone__class_Oone(U_5608)),c_Groups_Ozero__class_Ozero(U_5608)))
      | ~ class_Rings_Olinordered__semidom(U_5608) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

cnf(f_1209_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5608),c_Groups_Oone__class_Oone(U_5608)),c_Groups_Ozero__class_Ozero(U_5608)))
    | ~ class_Rings_Olinordered__semidom(U_5608) ),
    inference(clausify,[status(thm)],[f_1209_2]) ).

fof(f_1210_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).

fof(f_1210_2,plain,
    ! [U_5612,U_5611,U_5610,U_5609] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5609,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5609),U_5610),U_5611)),U_5612))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5609,tc_HOL_Obool)),U_5611),U_5612))
        | ~ hBOOL(hAPP(hAPP(c_member(U_5609),U_5610),U_5612)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5609,tc_HOL_Obool)),U_5611),U_5612))
          & hBOOL(hAPP(hAPP(c_member(U_5609),U_5610),U_5612)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5609,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5609),U_5610),U_5611)),U_5612)) ) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ( ! [U_5620,U_5618,U_5616,U_5614] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5614,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5614),U_5616),U_5618)),U_5620))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5614,tc_HOL_Obool)),U_5618),U_5620))
        | ~ hBOOL(hAPP(hAPP(c_member(U_5614),U_5616),U_5620)) )
    & ! [U_5619,U_5617,U_5615,U_5613] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5613,tc_HOL_Obool)),U_5617),U_5619))
          & hBOOL(hAPP(hAPP(c_member(U_5613),U_5615),U_5619)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5613,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5613),U_5615),U_5617)),U_5619)) ) ),
    inference(miniscope,[status(thm)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5613),U_5615),U_5619))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5613,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5613),U_5615),U_5617)),U_5619)) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

cnf(f_1210_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5613,tc_HOL_Obool)),U_5617),U_5619))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5613,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5613),U_5615),U_5617)),U_5619)) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

cnf(f_1210_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5614,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5614),U_5616),U_5618)),U_5620))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5614,tc_HOL_Obool)),U_5618),U_5620))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5614),U_5616),U_5620)) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).

fof(f_1211_2,plain,
    ! [U_5624,U_5623,U_5622,U_5621] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),hAPP(hAPP(c_Set_Oinsert(U_5621),U_5622),U_5624)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),U_5624)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),U_5624))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),hAPP(hAPP(c_Set_Oinsert(U_5621),U_5622),U_5624))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_5621),U_5622),U_5623)) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

cnf(f_1211_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),U_5624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),hAPP(hAPP(c_Set_Oinsert(U_5621),U_5622),U_5624)))
    | hBOOL(hAPP(hAPP(c_member(U_5621),U_5622),U_5623)) ),
    inference(clausify,[status(thm)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),hAPP(hAPP(c_Set_Oinsert(U_5621),U_5622),U_5624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5621,tc_HOL_Obool)),U_5623),U_5624))
    | hBOOL(hAPP(hAPP(c_member(U_5621),U_5622),U_5623)) ),
    inference(clausify,[status(thm)],[f_1211_2]) ).

fof(f_1212_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_1212_2,plain,
    ! [U_5628,U_5627,U_5626,U_5625] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5625),U_5627),U_5628))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),U_5627)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),U_5628))))
      | ~ class_Lattices_Olattice(U_5625) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

cnf(f_1212_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5625),U_5627),U_5628))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),U_5627)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5625),U_5626),U_5628))))
    | ~ class_Lattices_Olattice(U_5625) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

fof(f_1213_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_1213_2,plain,
    ! [U_5632,U_5631,U_5630,U_5629] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),U_5631)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),U_5632))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5629),U_5631),U_5632))))
      | ~ class_Lattices_Olattice(U_5629) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

cnf(f_1213_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),U_5631)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),U_5632))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5629),U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5629),U_5631),U_5632))))
    | ~ class_Lattices_Olattice(U_5629) ),
    inference(clausify,[status(thm)],[f_1213_2]) ).

fof(f_1214_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).

fof(f_1214_2,plain,
    ! [U_5635,U_5634,U_5633] :
      ( U_5634 = hAPP(hAPP(c_Set_Oinsert(U_5633),U_5635),c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool)))
      | U_5634 = c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5633,tc_HOL_Obool)),U_5634),hAPP(hAPP(c_Set_Oinsert(U_5633),U_5635),c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

cnf(f_1214_3,plain,
    ( U_5634 = hAPP(hAPP(c_Set_Oinsert(U_5633),U_5635),c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool)))
    | U_5634 = c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5633,tc_HOL_Obool)),U_5634),hAPP(hAPP(c_Set_Oinsert(U_5633),U_5635),c_Orderings_Obot__class_Obot(tc_fun(U_5633,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_1214_2]) ).

fof(f_1215_1,plain,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
      ( 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),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).

fof(f_1215_2,plain,
    ! [U_5640,U_5639,U_5638,U_5637,U_5636] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5638),U_5639))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5638,tc_HOL_Obool)),U_5639),hAPP(c_Set_Oimage(U_5636,U_5638,U_5640),U_5637)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5636),U_5637)) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

cnf(f_1215_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5638),U_5639))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5638,tc_HOL_Obool)),U_5639),hAPP(c_Set_Oimage(U_5636,U_5638,U_5640),U_5637)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5636),U_5637)) ),
    inference(clausify,[status(thm)],[f_1215_2]) ).

fof(f_1216_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,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_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).

fof(f_1216_2,plain,
    ! [U_5645,U_5644,U_5643,U_5642,U_5641] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5641,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5642,tc_HOL_Obool)),U_5644),U_5645))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5641,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),U_5644)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),U_5645)))),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

cnf(f_1216_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5641,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5642,tc_HOL_Obool)),U_5644),U_5645))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5641,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),U_5644)),hAPP(c_Set_Oimage(U_5642,U_5641,U_5643),U_5645)))),
    inference(clausify,[status(thm)],[f_1216_2]) ).

fof(f_1217_1,plain,
    ! [V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).

fof(f_1217_2,plain,
    ! [U_5648,U_5647,U_5646] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5646),U_5647),c_Complete__Lattice_OSup__class_OSup(U_5646,U_5648)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5646),U_5647),U_5648))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5646) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

cnf(f_1217_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5646),U_5647),c_Complete__Lattice_OSup__class_OSup(U_5646,U_5648)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5646),U_5647),U_5648))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5646) ),
    inference(clausify,[status(thm)],[f_1217_2]) ).

fof(f_1218_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).

fof(f_1218_2,plain,
    ! [U_5652,U_5651,U_5650,U_5649] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)),U_5652) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5651),U_5652))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5649,tc_HOL_Obool)),U_5652),U_5650)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5649,tc_HOL_Obool)),U_5652),U_5650))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)),U_5652) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5651),U_5652)) ) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ( ! [U_5660,U_5658,U_5656,U_5654] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5654,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5654,tc_HOL_Obool)),U_5656),U_5658)),U_5660) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5654,tc_HOL_Obool)),U_5656),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5654,tc_HOL_Obool)),U_5658),U_5660))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5654,tc_HOL_Obool)),U_5660),U_5656)) )
    & ! [U_5659,U_5657,U_5655,U_5653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5653,tc_HOL_Obool)),U_5659),U_5655))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5653,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5653,tc_HOL_Obool)),U_5655),U_5657)),U_5659) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5653,tc_HOL_Obool)),U_5655),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5653,tc_HOL_Obool)),U_5657),U_5659)) ) ),
    inference(miniscope,[status(thm)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5653,tc_HOL_Obool)),U_5659),U_5655))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5653,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5653,tc_HOL_Obool)),U_5655),U_5657)),U_5659) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5653,tc_HOL_Obool)),U_5655),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5653,tc_HOL_Obool)),U_5657),U_5659)) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

cnf(f_1218_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5654,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5654,tc_HOL_Obool)),U_5656),U_5658)),U_5660) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5654,tc_HOL_Obool)),U_5656),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5654,tc_HOL_Obool)),U_5658),U_5660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5654,tc_HOL_Obool)),U_5660),U_5656)) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_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_image__diff__subset]) ).

fof(f_1219_2,plain,
    ! [U_5665,U_5664,U_5663,U_5662,U_5661] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5661,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5661,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),U_5664)),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),U_5665))),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5662,tc_HOL_Obool)),U_5664),U_5665)))),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

cnf(f_1219_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5661,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5661,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),U_5664)),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),U_5665))),hAPP(c_Set_Oimage(U_5662,U_5661,U_5663),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5662,tc_HOL_Obool)),U_5664),U_5665)))),
    inference(clausify,[status(thm)],[f_1219_2]) ).

fof(f_1220_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).

fof(f_1220_2,plain,
    ! [U_5669,U_5668,U_5667,U_5666] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5666,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5666,tc_HOL_Obool)),U_5667),U_5668)),U_5669))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5666,tc_HOL_Obool)),U_5667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5666,tc_HOL_Obool)),U_5668),U_5669))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5666,tc_HOL_Obool)),U_5667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5666,tc_HOL_Obool)),U_5668),U_5669)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5666,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5666,tc_HOL_Obool)),U_5667),U_5668)),U_5669)) ) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ( ! [U_5677,U_5675,U_5673,U_5671] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5671,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5671,tc_HOL_Obool)),U_5673),U_5675)),U_5677))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5671,tc_HOL_Obool)),U_5673),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5671,tc_HOL_Obool)),U_5675),U_5677))) )
    & ! [U_5676,U_5674,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5672),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5670,tc_HOL_Obool)),U_5674),U_5676)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5670,tc_HOL_Obool)),U_5672),U_5674)),U_5676)) ) ),
    inference(miniscope,[status(thm)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),U_5672),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5670,tc_HOL_Obool)),U_5674),U_5676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5670,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5670,tc_HOL_Obool)),U_5672),U_5674)),U_5676)) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

cnf(f_1220_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5671,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5671,tc_HOL_Obool)),U_5673),U_5675)),U_5677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5671,tc_HOL_Obool)),U_5673),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5671,tc_HOL_Obool)),U_5675),U_5677))) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).

fof(f_1221_2,plain,
    ! [U_5680,U_5679,U_5678] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5678,tc_HOL_Obool)),U_5679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5678,tc_HOL_Obool)),U_5680),U_5679)) = U_5680
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5678,tc_HOL_Obool)),U_5679),U_5680)) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

cnf(f_1221_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5678,tc_HOL_Obool)),U_5679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5678,tc_HOL_Obool)),U_5680),U_5679)) = U_5680
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5678,tc_HOL_Obool)),U_5679),U_5680)) ),
    inference(clausify,[status(thm)],[f_1221_2]) ).

fof(f_1222_1,plain,
    ! [V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).

fof(f_1222_2,plain,
    ! [U_5683,U_5682,U_5681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5681),c_Complete__Lattice_OInf__class_OInf(U_5681,U_5683)),U_5682))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5681),U_5682),U_5683))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5681) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

cnf(f_1222_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5681),c_Complete__Lattice_OInf__class_OInf(U_5681,U_5683)),U_5682))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5681),U_5682),U_5683))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5681) ),
    inference(clausify,[status(thm)],[f_1222_2]) ).

fof(f_1223_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__subset]) ).

fof(f_1223_2,plain,
    ! [U_5687,U_5686,U_5685,U_5684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5685,U_5684,U_5686),hAPP(c_Set_Ovimage(U_5685,U_5684,U_5686),U_5687))),U_5687)),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

cnf(f_1223_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5684,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5685,U_5684,U_5686),hAPP(c_Set_Ovimage(U_5685,U_5684,U_5686),U_5687))),U_5687)),
    inference(clausify,[status(thm)],[f_1223_2]) ).

fof(f_1224_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).

fof(f_1224_2,plain,
    ! [U_5690,U_5689,U_5688] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5688,tc_HOL_Obool),tc_HOL_Obool)),U_5689),U_5690))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5688,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),U_5689)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),U_5690)))),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

cnf(f_1224_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5688,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5688,tc_HOL_Obool),tc_HOL_Obool)),U_5689),U_5690))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5688,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),U_5689)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5688,tc_HOL_Obool),U_5690)))),
    inference(clausify,[status(thm)],[f_1224_2]) ).

fof(f_1225_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).

fof(f_1225_2,plain,
    ! [U_5693,U_5692,U_5691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5691,tc_HOL_Obool)),U_5692),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5691,tc_HOL_Obool),U_5693)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5691,tc_HOL_Obool)),U_5692),U_5693)) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

cnf(f_1225_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5691,tc_HOL_Obool)),U_5692),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_5691,tc_HOL_Obool),U_5693)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5691,tc_HOL_Obool)),U_5692),U_5693)) ),
    inference(clausify,[status(thm)],[f_1225_2]) ).

fof(f_1226_1,plain,
    ! [V_a_2,V_f_2,T_a,V_g_2] :
      ( hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2
      | V_g_2 != c_Finite__Set_Ofold1(T_a,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).

fof(f_1226_2,plain,
    ! [U_5697,U_5696,U_5695,U_5694] :
      ( hAPP(U_5694,hAPP(hAPP(c_Set_Oinsert(U_5695),U_5697),c_Orderings_Obot__class_Obot(tc_fun(U_5695,tc_HOL_Obool)))) = U_5697
      | U_5694 != c_Finite__Set_Ofold1(U_5695,U_5696) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

cnf(f_1226_3,plain,
    ( hAPP(U_5694,hAPP(hAPP(c_Set_Oinsert(U_5695),U_5697),c_Orderings_Obot__class_Obot(tc_fun(U_5695,tc_HOL_Obool)))) = U_5697
    | U_5694 != c_Finite__Set_Ofold1(U_5695,U_5696) ),
    inference(clausify,[status(thm)],[f_1226_2]) ).

fof(f_1227_1,plain,
    ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).

fof(f_1227_2,plain,
    ! [U_5700,U_5699,U_5698] : hAPP(c_Finite__Set_Ofold1(U_5698,U_5699),hAPP(hAPP(c_Set_Oinsert(U_5698),U_5700),c_Orderings_Obot__class_Obot(tc_fun(U_5698,tc_HOL_Obool)))) = U_5700,
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

cnf(f_1227_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_5698,U_5699),hAPP(hAPP(c_Set_Oinsert(U_5698),U_5700),c_Orderings_Obot__class_Obot(tc_fun(U_5698,tc_HOL_Obool)))) = U_5700,
    inference(clausify,[status(thm)],[f_1227_2]) ).

fof(f_1228_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).

fof(f_1228_2,plain,
    ! [U_5703,U_5702,U_5701] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5701,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5701,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),U_5702)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),U_5703))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5701,tc_HOL_Obool),tc_HOL_Obool)),U_5702),U_5703)))),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

cnf(f_1228_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5701,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5701,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),U_5702)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),U_5703))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5701,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5701,tc_HOL_Obool),tc_HOL_Obool)),U_5702),U_5703)))),
    inference(clausify,[status(thm)],[f_1228_2]) ).

fof(f_1229_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).

fof(f_1229_2,plain,
    ! [U_5706,U_5705,U_5704] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5704,tc_HOL_Obool),U_5706)),U_5705))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5704,tc_HOL_Obool)),U_5705),U_5706)) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

cnf(f_1229_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5704,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5704,tc_HOL_Obool),U_5706)),U_5705))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5704,tc_HOL_Obool)),U_5705),U_5706)) ),
    inference(clausify,[status(thm)],[f_1229_2]) ).

fof(f_1230_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).

fof(f_1230_2,plain,
    ! [U_5711,U_5710,U_5709,U_5708,U_5707] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5707),hAPP(U_5711,U_5709)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5708,U_5707),U_5710),U_5711)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5708),U_5709),U_5710))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5707) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

cnf(f_1230_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5707),hAPP(U_5711,U_5709)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5708,U_5707),U_5710),U_5711)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5708),U_5709),U_5710))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5707) ),
    inference(clausify,[status(thm)],[f_1230_2]) ).

fof(f_1231_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).

fof(f_1231_2,plain,
    ! [U_5716,U_5715,U_5714,U_5713,U_5712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5712),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5713,U_5712),U_5715),U_5716)),hAPP(U_5716,U_5714)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5713),U_5714),U_5715))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_5712) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

cnf(f_1231_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5712),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5713,U_5712),U_5715),U_5716)),hAPP(U_5716,U_5714)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5713),U_5714),U_5715))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_5712) ),
    inference(clausify,[status(thm)],[f_1231_2]) ).

fof(f_1232_1,plain,
    ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).

fof(f_1232_2,plain,
    ! [U_5721,U_5720,U_5719,U_5718,U_5717] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5720,tc_HOL_Obool)),hAPP(U_5721,U_5718)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5717,tc_fun(U_5720,tc_HOL_Obool)),U_5719),U_5721)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5717),U_5718),U_5719)) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

cnf(f_1232_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5720,tc_HOL_Obool)),hAPP(U_5721,U_5718)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5717,tc_fun(U_5720,tc_HOL_Obool)),U_5719),U_5721)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5717),U_5718),U_5719)) ),
    inference(clausify,[status(thm)],[f_1232_2]) ).

fof(f_1233_1,plain,
    ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2))
        | ? [B_Z,B_s] :
            ( ? [B_s_H] :
                ( ~ hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H))
                & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H)) )
            & hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) ) )
      & ( ! [B_Z,B_s] :
            ( ! [B_s_H] :
                ( hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H)) )
            | ~ hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple__valid__def2]) ).

fof(f_1233_2,plain,
    ! [U_5732,U_5731,U_5730,U_5729,U_5728] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_5728,U_5729,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5728),U_5730),U_5731),U_5732))
        | ? [U_5727,U_5726] :
            ( ? [U_5725] :
                ( ~ hBOOL(hAPP(hAPP(U_5732,U_5727),U_5725))
                & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5731),U_5726),U_5729),U_5725)) )
            & hBOOL(hAPP(hAPP(U_5730,U_5727),U_5726)) ) )
      & ( ! [U_5724,U_5723] :
            ( ! [U_5722] :
                ( hBOOL(hAPP(hAPP(U_5732,U_5724),U_5722))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5731),U_5723),U_5729),U_5722)) )
            | ~ hBOOL(hAPP(hAPP(U_5730,U_5724),U_5723)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_5728,U_5729,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5728),U_5730),U_5731),U_5732)) ) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ( ! [U_5742,U_5740,U_5738,U_5736] :
        ( ! [U_5734] : c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742))
        | ? [U_5727,U_5726] :
            ( ? [U_5725] :
                ( ~ hBOOL(hAPP(hAPP(U_5742,U_5727),U_5725))
                & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5740),U_5726),U_5736),U_5725)) )
            & hBOOL(hAPP(hAPP(U_5738,U_5727),U_5726)) ) )
    & ! [U_5741,U_5739,U_5737,U_5735] :
        ( ! [U_5733] : ~ c_Hoare__Mirabelle_Otriple__valid(U_5733,U_5735,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5733),U_5737),U_5739),U_5741))
        | ! [U_5724,U_5723] :
            ( ! [U_5722] :
                ( hBOOL(hAPP(hAPP(U_5741,U_5724),U_5722))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5739),U_5723),U_5735),U_5722)) )
            | ~ hBOOL(hAPP(hAPP(U_5737,U_5724),U_5723)) ) ) ),
    inference(miniscope,[status(thm)],[f_1233_2]) ).

fof(f_1233_4,plain,
    ( ! [U_5742,U_5740,U_5738,U_5736] :
        ( ! [U_5734] : c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742))
        | ? [U_5726] :
            ( ? [U_5725] :
                ( ~ hBOOL(hAPP(hAPP(U_5742,sK109(U_5742,U_5740,U_5738,U_5736)),U_5725))
                & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5740),U_5726),U_5736),U_5725)) )
            & hBOOL(hAPP(hAPP(U_5738,sK109(U_5742,U_5740,U_5738,U_5736)),U_5726)) ) )
    & ! [U_5741,U_5739,U_5737,U_5735] :
        ( ! [U_5733] : ~ c_Hoare__Mirabelle_Otriple__valid(U_5733,U_5735,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5733),U_5737),U_5739),U_5741))
        | ! [U_5724,U_5723] :
            ( ! [U_5722] :
                ( hBOOL(hAPP(hAPP(U_5741,U_5724),U_5722))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5739),U_5723),U_5735),U_5722)) )
            | ~ hBOOL(hAPP(hAPP(U_5737,U_5724),U_5723)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_5727,sK109(U_5742,U_5740,U_5738,U_5736))],[f_1233_3]) ).

fof(f_1233_5,plain,
    ( ! [U_5742,U_5740,U_5738,U_5736] :
        ( ! [U_5734] : c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742))
        | ( ? [U_5725] :
              ( ~ hBOOL(hAPP(hAPP(U_5742,sK109(U_5742,U_5740,U_5738,U_5736)),U_5725))
              & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5740),sK110(U_5742,U_5740,U_5738,U_5736)),U_5736),U_5725)) )
          & hBOOL(hAPP(hAPP(U_5738,sK109(U_5742,U_5740,U_5738,U_5736)),sK110(U_5742,U_5740,U_5738,U_5736))) ) )
    & ! [U_5741,U_5739,U_5737,U_5735] :
        ( ! [U_5733] : ~ c_Hoare__Mirabelle_Otriple__valid(U_5733,U_5735,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5733),U_5737),U_5739),U_5741))
        | ! [U_5724,U_5723] :
            ( ! [U_5722] :
                ( hBOOL(hAPP(hAPP(U_5741,U_5724),U_5722))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5739),U_5723),U_5735),U_5722)) )
            | ~ hBOOL(hAPP(hAPP(U_5737,U_5724),U_5723)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_5726,sK110(U_5742,U_5740,U_5738,U_5736))],[f_1233_4]) ).

fof(f_1233_6,plain,
    ( ! [U_5742,U_5740,U_5738,U_5736] :
        ( ! [U_5734] : c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742))
        | ( ~ hBOOL(hAPP(hAPP(U_5742,sK109(U_5742,U_5740,U_5738,U_5736)),sK111(U_5742,U_5740,U_5738,U_5736)))
          & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5740),sK110(U_5742,U_5740,U_5738,U_5736)),U_5736),sK111(U_5742,U_5740,U_5738,U_5736)))
          & hBOOL(hAPP(hAPP(U_5738,sK109(U_5742,U_5740,U_5738,U_5736)),sK110(U_5742,U_5740,U_5738,U_5736))) ) )
    & ! [U_5741,U_5739,U_5737,U_5735] :
        ( ! [U_5733] : ~ c_Hoare__Mirabelle_Otriple__valid(U_5733,U_5735,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5733),U_5737),U_5739),U_5741))
        | ! [U_5724,U_5723] :
            ( ! [U_5722] :
                ( hBOOL(hAPP(hAPP(U_5741,U_5724),U_5722))
                | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5739),U_5723),U_5735),U_5722)) )
            | ~ hBOOL(hAPP(hAPP(U_5737,U_5724),U_5723)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_5725,sK111(U_5742,U_5740,U_5738,U_5736))],[f_1233_5]) ).

cnf(f_1233_7,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_5733,U_5735,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5733),U_5737),U_5739),U_5741))
    | hBOOL(hAPP(hAPP(U_5741,U_5724),U_5722))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5739),U_5723),U_5735),U_5722))
    | ~ hBOOL(hAPP(hAPP(U_5737,U_5724),U_5723)) ),
    inference(clausify,[status(thm)],[f_1233_6]) ).

cnf(f_1233_8,plain,
    ( hBOOL(hAPP(hAPP(U_5738,sK109(U_5742,U_5740,U_5738,U_5736)),sK110(U_5742,U_5740,U_5738,U_5736)))
    | c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742)) ),
    inference(clausify,[status(thm)],[f_1233_6]) ).

cnf(f_1233_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_5740),sK110(U_5742,U_5740,U_5738,U_5736)),U_5736),sK111(U_5742,U_5740,U_5738,U_5736)))
    | c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742)) ),
    inference(clausify,[status(thm)],[f_1233_6]) ).

cnf(f_1233_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_5742,sK109(U_5742,U_5740,U_5738,U_5736)),sK111(U_5742,U_5740,U_5738,U_5736)))
    | c_Hoare__Mirabelle_Otriple__valid(U_5734,U_5736,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_5734),U_5738),U_5740),U_5742)) ),
    inference(clausify,[status(thm)],[f_1233_6]) ).

fof(f_1234_1,plain,
    ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).

fof(f_1234_2,plain,
    ! [U_5747,U_5746,U_5745,U_5744,U_5743] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5746,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5743,tc_fun(U_5746,tc_HOL_Obool)),U_5745),U_5747)),hAPP(U_5747,U_5744)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5743),U_5744),U_5745)) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

cnf(f_1234_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5746,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5743,tc_fun(U_5746,tc_HOL_Obool)),U_5745),U_5747)),hAPP(U_5747,U_5744)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5743),U_5744),U_5745)) ),
    inference(clausify,[status(thm)],[f_1234_2]) ).

fof(f_1235_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
      ( 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))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,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_1235_2,plain,
    ! [U_5755,U_5754,U_5753,U_5752,U_5751,U_5750,U_5749,U_5748] :
      ( hAPP(hAPP(U_5750,hAPP(U_5753,U_5755)),hAPP(U_5753,U_5754)) = hAPP(U_5753,U_5754)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5749,tc_HOL_Obool)),U_5755),U_5754))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5749),U_5754))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_5748,U_5749,U_5750,U_5751,U_5752,U_5753) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_5755,U_5754,U_5753,U_5752,U_5751,U_5750,U_5749] :
      ( ! [U_5748] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_5748,U_5749,U_5750,U_5751,U_5752,U_5753)
      | hAPP(hAPP(U_5750,hAPP(U_5753,U_5755)),hAPP(U_5753,U_5754)) = hAPP(U_5753,U_5754)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5749,tc_HOL_Obool)),U_5755),U_5754))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5749),U_5754)) ),
    inference(miniscope,[status(thm)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_5748,U_5749,U_5750,U_5751,U_5752,U_5753)
    | hAPP(hAPP(U_5750,hAPP(U_5753,U_5755)),hAPP(U_5753,U_5754)) = hAPP(U_5753,U_5754)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5749,tc_HOL_Obool)),U_5755),U_5754))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5749),U_5754)) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_1,plain,
    ! [V_k_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).

fof(f_1236_2,plain,
    ! [U_5757,U_5756] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5756,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5756),U_5757),c_Orderings_Obot__class_Obot(tc_fun(U_5756,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_5756),U_5757)) = hAPP(hAPP(c_Set_Oinsert(U_5756),U_5757),c_Orderings_Obot__class_Obot(tc_fun(U_5756,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_5756) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

cnf(f_1236_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5756,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5756),U_5757),c_Orderings_Obot__class_Obot(tc_fun(U_5756,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_5756),U_5757)) = hAPP(hAPP(c_Set_Oinsert(U_5756),U_5757),c_Orderings_Obot__class_Obot(tc_fun(U_5756,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_5756) ),
    inference(clausify,[status(thm)],[f_1236_2]) ).

fof(f_1237_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).

fof(f_1237_2,plain,
    ! [U_5761,U_5760,U_5759,U_5758] :
      ( hAPP(U_5760,U_5761) = hAPP(c_Finite__Set_Ofold1(U_5758,U_5759),U_5761)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5758),U_5761))
      | ~ c_Finite__Set_Ofolding__one(U_5758,U_5759,U_5760) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

cnf(f_1237_3,plain,
    ( hAPP(U_5760,U_5761) = hAPP(c_Finite__Set_Ofold1(U_5758,U_5759),U_5761)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5758),U_5761))
    | ~ c_Finite__Set_Ofolding__one(U_5758,U_5759,U_5760) ),
    inference(clausify,[status(thm)],[f_1237_2]) ).

fof(f_1238_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_1238_2,plain,
    ! [U_5764,U_5763,U_5762] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5762),U_5763),U_5764)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),U_5764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),U_5763))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5762) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

cnf(f_1238_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5762),U_5763),U_5764)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),U_5764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5762),c_Groups_Ozero__class_Ozero(U_5762)),U_5763))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5762) ),
    inference(clausify,[status(thm)],[f_1238_2]) ).

fof(f_1239_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_1239_2,plain,
    ! [U_5767,U_5766,U_5765] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5765),U_5766),U_5767)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5766))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5765) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

cnf(f_1239_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5765),U_5766),U_5767)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5767))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5766))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5765) ),
    inference(clausify,[status(thm)],[f_1239_2]) ).

fof(f_1240_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_1240_2,plain,
    ! [U_5771,U_5770,U_5769,U_5768] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5768),U_5770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5768),U_5769),U_5771)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5770),U_5771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5768),c_Groups_Ozero__class_Ozero(U_5768)),U_5769))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5768) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

cnf(f_1240_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5768),U_5770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5768),U_5769),U_5771)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5770),U_5771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5768),c_Groups_Ozero__class_Ozero(U_5768)),U_5769))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5768) ),
    inference(clausify,[status(thm)],[f_1240_2]) ).

fof(f_1241_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_1241_2,plain,
    ! [U_5775,U_5774,U_5773,U_5772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5772),U_5774),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5772),U_5773),U_5775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_5773))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5772) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

cnf(f_1241_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5772),U_5774),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5772),U_5773),U_5775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_5773))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5772) ),
    inference(clausify,[status(thm)],[f_1241_2]) ).

fof(f_1242_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_1242_2,plain,
    ! [U_5778,U_5777,U_5776] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5776),U_5777),U_5778)),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(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5776) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

cnf(f_1242_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5776),U_5777),U_5778)),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(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5776) ),
    inference(clausify,[status(thm)],[f_1242_2]) ).

fof(f_1243_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_1243_2,plain,
    ! [U_5781,U_5780,U_5779] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5779),U_5780),U_5781)),c_Groups_Ozero__class_Ozero(U_5779)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5779) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

cnf(f_1243_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5779),U_5780),U_5781)),c_Groups_Ozero__class_Ozero(U_5779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5779) ),
    inference(clausify,[status(thm)],[f_1243_2]) ).

fof(f_1244_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_1244_2,plain,
    ! [U_5785,U_5784,U_5783,U_5782] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5782),U_5784),U_5785))
      | ~ 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__eq(U_5782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5782),U_5783),U_5784)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5782),U_5783),U_5785)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5782) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

cnf(f_1244_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5782),U_5784),U_5785))
    | ~ 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__eq(U_5782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5782),U_5783),U_5784)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5782),U_5783),U_5785)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5782) ),
    inference(clausify,[status(thm)],[f_1244_2]) ).

fof(f_1245_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_1245_2,plain,
    ! [U_5789,U_5788,U_5787,U_5786] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5786),U_5787),U_5789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5786),c_Groups_Ozero__class_Ozero(U_5786)),U_5788))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5786),U_5787),U_5788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5786),U_5789),U_5788)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5786) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

cnf(f_1245_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5786),U_5787),U_5789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5786),c_Groups_Ozero__class_Ozero(U_5786)),U_5788))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5786),U_5787),U_5788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5786),U_5789),U_5788)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5786) ),
    inference(clausify,[status(thm)],[f_1245_2]) ).

fof(f_1246_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_1246_2,plain,
    ! [U_5793,U_5792,U_5791,U_5790] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5790),U_5792),U_5793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5790),c_Groups_Ozero__class_Ozero(U_5790)),U_5791))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5790),U_5791),U_5792)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5790),U_5791),U_5793)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5790) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

cnf(f_1246_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5790),U_5792),U_5793))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5790),c_Groups_Ozero__class_Ozero(U_5790)),U_5791))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5790),U_5791),U_5792)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5790),U_5791),U_5793)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5790) ),
    inference(clausify,[status(thm)],[f_1246_2]) ).

fof(f_1247_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_1247_2,plain,
    ! [U_5797,U_5796,U_5795,U_5794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),U_5796),U_5797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5794),c_Groups_Ozero__class_Ozero(U_5794)),U_5795))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5794),U_5795),U_5796)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5794),U_5795),U_5797)))
      | ~ class_Rings_Olinordered__semiring(U_5794) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

cnf(f_1247_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),U_5796),U_5797))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5794),c_Groups_Ozero__class_Ozero(U_5794)),U_5795))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5794),U_5795),U_5796)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5794),U_5795),U_5797)))
    | ~ class_Rings_Olinordered__semiring(U_5794) ),
    inference(clausify,[status(thm)],[f_1247_2]) ).

fof(f_1248_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_1248_2,plain,
    ! [U_5801,U_5800,U_5799,U_5798] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5798),U_5799),U_5801))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5798),c_Groups_Ozero__class_Ozero(U_5798)),U_5800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5798),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5798),U_5799),U_5800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5798),U_5801),U_5800)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5798) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

cnf(f_1248_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5798),U_5799),U_5801))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5798),c_Groups_Ozero__class_Ozero(U_5798)),U_5800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5798),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5798),U_5799),U_5800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5798),U_5801),U_5800)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5798) ),
    inference(clausify,[status(thm)],[f_1248_2]) ).

fof(f_1249_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_1249_2,plain,
    ! [U_5805,U_5804,U_5803,U_5802] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5802),U_5803),U_5805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5802),c_Groups_Ozero__class_Ozero(U_5802)),U_5804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5802),U_5803),U_5804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5802),U_5805),U_5804)))
      | ~ class_Rings_Olinordered__semiring(U_5802) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

cnf(f_1249_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5802),U_5803),U_5805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5802),c_Groups_Ozero__class_Ozero(U_5802)),U_5804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5802),U_5803),U_5804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5802),U_5805),U_5804)))
    | ~ class_Rings_Olinordered__semiring(U_5802) ),
    inference(clausify,[status(thm)],[f_1249_2]) ).

fof(f_1250_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_1250_2,plain,
    ! [U_5810,U_5809,U_5808,U_5807,U_5806] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5806),U_5807),U_5809)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5806),U_5808),U_5810)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5806),c_Groups_Ozero__class_Ozero(U_5806)),U_5809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),c_Groups_Ozero__class_Ozero(U_5806)),U_5807))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),U_5809),U_5810))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5806),U_5807),U_5808))
      | ~ class_Rings_Olinordered__semiring__strict(U_5806) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

cnf(f_1250_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5806),U_5807),U_5809)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5806),U_5808),U_5810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5806),c_Groups_Ozero__class_Ozero(U_5806)),U_5809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),c_Groups_Ozero__class_Ozero(U_5806)),U_5807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5806),U_5809),U_5810))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5806),U_5807),U_5808))
    | ~ class_Rings_Olinordered__semiring__strict(U_5806) ),
    inference(clausify,[status(thm)],[f_1250_2]) ).

fof(f_1251_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_1251_2,plain,
    ! [U_5815,U_5814,U_5813,U_5812,U_5811] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5812),U_5814)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5813),U_5815)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),c_Groups_Ozero__class_Ozero(U_5811)),U_5814))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5811),c_Groups_Ozero__class_Ozero(U_5811)),U_5812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5811),U_5814),U_5815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),U_5812),U_5813))
      | ~ class_Rings_Olinordered__semiring__strict(U_5811) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

cnf(f_1251_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5812),U_5814)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5813),U_5815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),c_Groups_Ozero__class_Ozero(U_5811)),U_5814))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5811),c_Groups_Ozero__class_Ozero(U_5811)),U_5812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5811),U_5814),U_5815))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5811),U_5812),U_5813))
    | ~ class_Rings_Olinordered__semiring__strict(U_5811) ),
    inference(clausify,[status(thm)],[f_1251_2]) ).

fof(f_1252_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_1252_2,plain,
    ! [U_5820,U_5819,U_5818,U_5817,U_5816] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5816),U_5817),U_5819)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5816),U_5818),U_5820)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5816),c_Groups_Ozero__class_Ozero(U_5816)),U_5819))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5816),c_Groups_Ozero__class_Ozero(U_5816)),U_5817))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),U_5819),U_5820))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),U_5817),U_5818))
      | ~ class_Rings_Olinordered__semiring__strict(U_5816) ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

cnf(f_1252_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5816),U_5817),U_5819)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5816),U_5818),U_5820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5816),c_Groups_Ozero__class_Ozero(U_5816)),U_5819))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5816),c_Groups_Ozero__class_Ozero(U_5816)),U_5817))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),U_5819),U_5820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5816),U_5817),U_5818))
    | ~ class_Rings_Olinordered__semiring__strict(U_5816) ),
    inference(clausify,[status(thm)],[f_1252_2]) ).

fof(f_1253_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_1253_2,plain,
    ! [U_5825,U_5824,U_5823,U_5822,U_5821] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5822),U_5824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5823),U_5825)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5821),c_Groups_Ozero__class_Ozero(U_5821)),U_5824))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),c_Groups_Ozero__class_Ozero(U_5821)),U_5823))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),U_5824),U_5825))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),U_5822),U_5823))
      | ~ class_Rings_Olinordered__semiring__strict(U_5821) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

cnf(f_1253_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5822),U_5824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5823),U_5825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5821),c_Groups_Ozero__class_Ozero(U_5821)),U_5824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),c_Groups_Ozero__class_Ozero(U_5821)),U_5823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),U_5824),U_5825))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5821),U_5822),U_5823))
    | ~ class_Rings_Olinordered__semiring__strict(U_5821) ),
    inference(clausify,[status(thm)],[f_1253_2]) ).

fof(f_1254_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).

fof(f_1254_2,plain,
    ! [U_5829,U_5828,U_5827,U_5826] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5828)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5829)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),U_5829),U_5828)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),U_5829),U_5828))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5828)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5829))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5826),U_5827),c_Groups_Ozero__class_Ozero(U_5826)))
      | ~ class_Rings_Olinordered__ring__strict(U_5826) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

cnf(f_1254_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),U_5829),U_5828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5828)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5829)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5826),U_5827),c_Groups_Ozero__class_Ozero(U_5826)))
    | ~ class_Rings_Olinordered__ring__strict(U_5826) ),
    inference(clausify,[status(thm)],[f_1254_2]) ).

cnf(f_1254_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5828)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5826),U_5827),U_5829)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5826),U_5829),U_5828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5826),U_5827),c_Groups_Ozero__class_Ozero(U_5826)))
    | ~ class_Rings_Olinordered__ring__strict(U_5826) ),
    inference(clausify,[status(thm)],[f_1254_2]) ).

fof(f_1255_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_1255_2,plain,
    ! [U_5833,U_5832,U_5831,U_5830] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5833)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),U_5833)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),U_5833))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5833))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
      | ~ class_Rings_Olinordered__ring__strict(U_5830) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

cnf(f_1255_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),U_5833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
    | ~ class_Rings_Olinordered__ring__strict(U_5830) ),
    inference(clausify,[status(thm)],[f_1255_2]) ).

cnf(f_1255_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),U_5833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
    | ~ class_Rings_Olinordered__ring__strict(U_5830) ),
    inference(clausify,[status(thm)],[f_1255_2]) ).

fof(f_1256_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_1256_2,plain,
    ! [U_5836,U_5835,U_5834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),c_Groups_Ozero__class_Ozero(U_5834)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5834),U_5835),U_5835)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5834),U_5836),U_5836))))
      | ~ class_Rings_Olinordered__ring(U_5834) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

cnf(f_1256_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),c_Groups_Ozero__class_Ozero(U_5834)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5834),U_5835),U_5835)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5834),U_5836),U_5836))))
    | ~ class_Rings_Olinordered__ring(U_5834) ),
    inference(clausify,[status(thm)],[f_1256_2]) ).

fof(f_1257_1,plain,
    ! [V_y_2,V_x_2,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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).

fof(f_1257_2,plain,
    ! [U_5839,U_5838,U_5837] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5838),U_5838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5839),U_5839))),c_Groups_Ozero__class_Ozero(U_5837)))
          | U_5839 != c_Groups_Ozero__class_Ozero(U_5837)
          | U_5838 != c_Groups_Ozero__class_Ozero(U_5837) )
        & ( ( U_5839 = c_Groups_Ozero__class_Ozero(U_5837)
            & U_5838 = c_Groups_Ozero__class_Ozero(U_5837) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5838),U_5838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5839),U_5839))),c_Groups_Ozero__class_Ozero(U_5837))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5837) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

cnf(f_1257_3,plain,
    ( U_5838 = c_Groups_Ozero__class_Ozero(U_5837)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5838),U_5838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5839),U_5839))),c_Groups_Ozero__class_Ozero(U_5837)))
    | ~ class_Rings_Olinordered__ring__strict(U_5837) ),
    inference(clausify,[status(thm)],[f_1257_2]) ).

cnf(f_1257_4,plain,
    ( U_5839 = c_Groups_Ozero__class_Ozero(U_5837)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5838),U_5838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5839),U_5839))),c_Groups_Ozero__class_Ozero(U_5837)))
    | ~ class_Rings_Olinordered__ring__strict(U_5837) ),
    inference(clausify,[status(thm)],[f_1257_2]) ).

cnf(f_1257_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5838),U_5838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5837),U_5839),U_5839))),c_Groups_Ozero__class_Ozero(U_5837)))
    | U_5839 != c_Groups_Ozero__class_Ozero(U_5837)
    | U_5838 != c_Groups_Ozero__class_Ozero(U_5837)
    | ~ class_Rings_Olinordered__ring__strict(U_5837) ),
    inference(clausify,[status(thm)],[f_1257_2]) ).

fof(f_1258_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_1258_2,plain,
    ! [U_5842,U_5841,U_5840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5840),U_5842),U_5841)),U_5841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),U_5842),c_Groups_Oone__class_Oone(U_5840)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5842))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841))
      | ~ class_Rings_Olinordered__idom(U_5840) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

cnf(f_1258_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5840),U_5842),U_5841)),U_5841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),U_5842),c_Groups_Oone__class_Oone(U_5840)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841))
    | ~ class_Rings_Olinordered__idom(U_5840) ),
    inference(clausify,[status(thm)],[f_1258_2]) ).

fof(f_1259_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_1259_2,plain,
    ! [U_5845,U_5844,U_5843] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5843),U_5844),U_5845)),U_5844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),U_5845),c_Groups_Oone__class_Oone(U_5843)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5844))
      | ~ class_Rings_Olinordered__idom(U_5843) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

cnf(f_1259_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5843),U_5844),U_5845)),U_5844))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),U_5845),c_Groups_Oone__class_Oone(U_5843)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5844))
    | ~ class_Rings_Olinordered__idom(U_5843) ),
    inference(clausify,[status(thm)],[f_1259_2]) ).

fof(f_1260_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).

fof(f_1260_2,plain,
    ! [U_5851,U_5850,U_5849,U_5848,U_5847,U_5846] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5847),U_5848)),U_5849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5850),U_5848)),U_5851)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5846),U_5850),U_5847)),U_5848)),U_5851))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5846),U_5850),U_5847)),U_5848)),U_5851)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5847),U_5848)),U_5849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5850),U_5848)),U_5851))) ) )
      | ~ class_Rings_Oordered__ring(U_5846) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

cnf(f_1260_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5846),U_5850),U_5847)),U_5848)),U_5851)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5847),U_5848)),U_5849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5850),U_5848)),U_5851)))
    | ~ class_Rings_Oordered__ring(U_5846) ),
    inference(clausify,[status(thm)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5847),U_5848)),U_5849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5850),U_5848)),U_5851)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5846),U_5850),U_5847)),U_5848)),U_5851)))
    | ~ class_Rings_Oordered__ring(U_5846) ),
    inference(clausify,[status(thm)],[f_1260_2]) ).

fof(f_1261_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
          | ~ 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).

fof(f_1261_2,plain,
    ! [U_5857,U_5856,U_5855,U_5854,U_5853,U_5852] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5853),U_5854)),U_5855)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5856),U_5854)),U_5857)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5852),U_5853),U_5856)),U_5854)),U_5855)),U_5857)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5852),U_5853),U_5856)),U_5854)),U_5855)),U_5857))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5853),U_5854)),U_5855)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5856),U_5854)),U_5857))) ) )
      | ~ class_Rings_Oordered__ring(U_5852) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

cnf(f_1261_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5852),U_5853),U_5856)),U_5854)),U_5855)),U_5857))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5853),U_5854)),U_5855)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5856),U_5854)),U_5857)))
    | ~ class_Rings_Oordered__ring(U_5852) ),
    inference(clausify,[status(thm)],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5853),U_5854)),U_5855)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),U_5856),U_5854)),U_5857)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5852),U_5853),U_5856)),U_5854)),U_5855)),U_5857))
    | ~ class_Rings_Oordered__ring(U_5852) ),
    inference(clausify,[status(thm)],[f_1261_2]) ).

fof(f_1262_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,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_a,V_f_2),V_B_2)),V_A_2))
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetD]) ).

fof(f_1262_2,plain,
    ! [U_5862,U_5861,U_5860,U_5859,U_5858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5859,tc_HOL_Obool)),U_5861),hAPP(c_Set_Oimage(U_5858,U_5859,U_5860),U_5862)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5858,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_5858,U_5859,U_5860),U_5861)),U_5862))
      | hAPP(c_Set_Oimage(U_5858,U_5859,U_5860),c_Orderings_Otop__class_Otop(tc_fun(U_5858,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_5859,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

cnf(f_1262_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5859,tc_HOL_Obool)),U_5861),hAPP(c_Set_Oimage(U_5858,U_5859,U_5860),U_5862)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5858,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_5858,U_5859,U_5860),U_5861)),U_5862))
    | hAPP(c_Set_Oimage(U_5858,U_5859,U_5860),c_Orderings_Otop__class_Otop(tc_fun(U_5858,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_5859,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1262_2]) ).

fof(f_1263_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_1263_2,plain,
    ! [U_5867] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5867))
        | ! [U_5866] :
          ? [U_5865] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5865),U_5866))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5865),U_5867)) ) )
      & ( ? [U_5864] :
          ! [U_5863] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5863),U_5864))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5863),U_5867)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5867)) ) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ( ! [U_5869] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5869))
        | ! [U_5866] :
          ? [U_5865] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5865),U_5866))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5865),U_5869)) ) )
    & ! [U_5868] :
        ( ? [U_5864] :
          ! [U_5863] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5863),U_5864))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5863),U_5868)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5868)) ) ),
    inference(miniscope,[status(thm)],[f_1263_2]) ).

fof(f_1263_4,plain,
    ( ! [U_5869] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5869))
        | ! [U_5866] :
          ? [U_5865] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5865),U_5866))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5865),U_5869)) ) )
    & ! [U_5868] :
        ( ! [U_5863] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5863),sK112(U_5868)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5863),U_5868)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5868)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_5864,sK112(U_5868))],[f_1263_3]) ).

fof(f_1263_5,plain,
    ( ! [U_5869] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5869))
        | ! [U_5866] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK113(U_5869,U_5866)),U_5866))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5869,U_5866)),U_5869)) ) )
    & ! [U_5868] :
        ( ! [U_5863] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5863),sK112(U_5868)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5863),U_5868)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5868)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_5865,sK113(U_5869,U_5866))],[f_1263_4]) ).

cnf(f_1263_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5863),sK112(U_5868)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5863),U_5868))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5868)) ),
    inference(clausify,[status(thm)],[f_1263_5]) ).

cnf(f_1263_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK113(U_5869,U_5866)),U_5869))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5869)) ),
    inference(clausify,[status(thm)],[f_1263_5]) ).

cnf(f_1263_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK113(U_5869,U_5866)),U_5866))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5869)) ),
    inference(clausify,[status(thm)],[f_1263_5]) ).

fof(f_1264_1,plain,
    ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold1__def]) ).

fof(f_1264_2,plain,
    ! [U_5872,U_5871,U_5870] : hAPP(c_Finite__Set_Ofold1(U_5870,U_5871),U_5872) = c_HOL_OThe(U_5870,c_Finite__Set_Ofold1Set(U_5870,U_5871,U_5872)),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

cnf(f_1264_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_5870,U_5871),U_5872) = c_HOL_OThe(U_5870,c_Finite__Set_Ofold1Set(U_5870,U_5871,U_5872)),
    inference(clausify,[status(thm)],[f_1264_2]) ).

fof(f_1265_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
      ( 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_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).

fof(f_1265_2,plain,
    ! [U_5877,U_5876,U_5875,U_5874,U_5873] :
      ( hAPP(hAPP(U_5874,hAPP(U_5875,U_5877)),hAPP(U_5875,U_5876)) = hAPP(U_5875,U_5876)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5873,tc_HOL_Obool)),U_5877),U_5876))
      | U_5877 = c_Orderings_Obot__class_Obot(tc_fun(U_5873,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5873),U_5876))
      | ~ c_Finite__Set_Ofolding__one__idem(U_5873,U_5874,U_5875) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

cnf(f_1265_3,plain,
    ( hAPP(hAPP(U_5874,hAPP(U_5875,U_5877)),hAPP(U_5875,U_5876)) = hAPP(U_5875,U_5876)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5873,tc_HOL_Obool)),U_5877),U_5876))
    | U_5877 = c_Orderings_Obot__class_Obot(tc_fun(U_5873,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5873),U_5876))
    | ~ c_Finite__Set_Ofolding__one__idem(U_5873,U_5874,U_5875) ),
    inference(clausify,[status(thm)],[f_1265_2]) ).

fof(f_1266_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).

fof(f_1266_2,plain,
    ! [U_5879,U_5878] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_5878,U_5879) = hAPP(c_Finite__Set_Ofold1(U_5878,c_Lattices_Osemilattice__sup__class_Osup(U_5878)),U_5879)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5878),U_5879))
      | ~ class_Lattices_Olattice(U_5878) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

cnf(f_1266_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_5878,U_5879) = hAPP(c_Finite__Set_Ofold1(U_5878,c_Lattices_Osemilattice__sup__class_Osup(U_5878)),U_5879)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5878),U_5879))
    | ~ class_Lattices_Olattice(U_5878) ),
    inference(clausify,[status(thm)],[f_1266_2]) ).

fof(f_1267_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).

fof(f_1267_2,plain,
    ! [U_5881,U_5880] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_5880,U_5881) = hAPP(c_Finite__Set_Ofold1(U_5880,c_Lattices_Osemilattice__inf__class_Oinf(U_5880)),U_5881)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5880),U_5881))
      | ~ class_Lattices_Olattice(U_5880) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

cnf(f_1267_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_5880,U_5881) = hAPP(c_Finite__Set_Ofold1(U_5880,c_Lattices_Osemilattice__inf__class_Oinf(U_5880)),U_5881)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5880),U_5881))
    | ~ class_Lattices_Olattice(U_5880) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

fof(f_1268_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Ocomp(T_b,T_b,T_b,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_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem]) ).

fof(f_1268_2,plain,
    ! [U_5887,U_5886,U_5885,U_5884,U_5883,U_5882] :
      ( hAPP(c_Fun_Ocomp(U_5883,U_5883,U_5883,hAPP(U_5885,U_5886)),hAPP(U_5885,U_5887)) = hAPP(U_5885,U_5886)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5882,tc_HOL_Obool)),U_5887),U_5886))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5882),U_5886))
      | ~ c_Finite__Set_Ofolding__idem(U_5882,U_5883,U_5884,U_5885) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

cnf(f_1268_3,plain,
    ( hAPP(c_Fun_Ocomp(U_5883,U_5883,U_5883,hAPP(U_5885,U_5886)),hAPP(U_5885,U_5887)) = hAPP(U_5885,U_5886)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5882,tc_HOL_Obool)),U_5887),U_5886))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5882),U_5886))
    | ~ c_Finite__Set_Ofolding__idem(U_5882,U_5883,U_5884,U_5885) ),
    inference(clausify,[status(thm)],[f_1268_2]) ).

fof(f_1269_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_1269_2,plain,
    ! [U_5893,U_5892,U_5891,U_5890,U_5889,U_5888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5888),U_5892),U_5889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5888),U_5893),U_5891))),U_5890))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5888),U_5892),U_5893) != c_Groups_Oone__class_Oone(U_5888)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),c_Groups_Ozero__class_Ozero(U_5888)),U_5893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),c_Groups_Ozero__class_Ozero(U_5888)),U_5892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),U_5891),U_5890))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),U_5889),U_5890))
      | ~ class_Rings_Olinordered__semiring__1(U_5888) ),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

cnf(f_1269_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5888),U_5892),U_5889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5888),U_5893),U_5891))),U_5890))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5888),U_5892),U_5893) != c_Groups_Oone__class_Oone(U_5888)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),c_Groups_Ozero__class_Ozero(U_5888)),U_5893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),c_Groups_Ozero__class_Ozero(U_5888)),U_5892))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),U_5891),U_5890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5888),U_5889),U_5890))
    | ~ class_Rings_Olinordered__semiring__1(U_5888) ),
    inference(clausify,[status(thm)],[f_1269_2]) ).

fof(f_1270_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).

fof(f_1270_2,plain,
    ! [U_5897,U_5896,U_5895,U_5894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5894,tc_HOL_Obool)),U_5895),hAPP(hAPP(c_Set_Oinsert(U_5894),U_5896),U_5897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5894),U_5896),U_5895))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5894,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5894,tc_HOL_Obool)),U_5895),hAPP(hAPP(c_Set_Oinsert(U_5894),U_5896),c_Orderings_Obot__class_Obot(tc_fun(U_5894,tc_HOL_Obool))))),U_5897)) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

cnf(f_1270_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5894,tc_HOL_Obool)),U_5895),hAPP(hAPP(c_Set_Oinsert(U_5894),U_5896),U_5897)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5894),U_5896),U_5895))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5894,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5894,tc_HOL_Obool)),U_5895),hAPP(hAPP(c_Set_Oinsert(U_5894),U_5896),c_Orderings_Obot__class_Obot(tc_fun(U_5894,tc_HOL_Obool))))),U_5897)) ),
    inference(clausify,[status(thm)],[f_1270_2]) ).

fof(f_1271_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
            | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).

fof(f_1271_2,plain,
    ! [U_5901,U_5900,U_5899,U_5898] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),U_5899),hAPP(hAPP(c_Set_Oinsert(U_5898),U_5900),U_5901)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),U_5899),U_5901))
          & ~ hBOOL(hAPP(hAPP(c_member(U_5898),U_5900),U_5899)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5898,tc_HOL_Obool)),U_5899),hAPP(hAPP(c_Set_Oinsert(U_5898),U_5900),c_Orderings_Obot__class_Obot(tc_fun(U_5898,tc_HOL_Obool))))),U_5901))
          & hBOOL(hAPP(hAPP(c_member(U_5898),U_5900),U_5899)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),U_5899),U_5901))
            | hBOOL(hAPP(hAPP(c_member(U_5898),U_5900),U_5899)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5898,tc_HOL_Obool)),U_5899),hAPP(hAPP(c_Set_Oinsert(U_5898),U_5900),c_Orderings_Obot__class_Obot(tc_fun(U_5898,tc_HOL_Obool))))),U_5901))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5898),U_5900),U_5899)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5898,tc_HOL_Obool)),U_5899),hAPP(hAPP(c_Set_Oinsert(U_5898),U_5900),U_5901))) ) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ( ! [U_5909,U_5907,U_5905,U_5903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),U_5909)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),U_5909))
          & ~ hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),c_Orderings_Obot__class_Obot(tc_fun(U_5903,tc_HOL_Obool))))),U_5909))
          & hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905)) ) )
    & ! [U_5908,U_5906,U_5904,U_5902] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),U_5904),U_5908))
            | hBOOL(hAPP(hAPP(c_member(U_5902),U_5906),U_5904)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5902,tc_HOL_Obool)),U_5904),hAPP(hAPP(c_Set_Oinsert(U_5902),U_5906),c_Orderings_Obot__class_Obot(tc_fun(U_5902,tc_HOL_Obool))))),U_5908))
            | ~ hBOOL(hAPP(hAPP(c_member(U_5902),U_5906),U_5904)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),U_5904),hAPP(hAPP(c_Set_Oinsert(U_5902),U_5906),U_5908))) ) ),
    inference(miniscope,[status(thm)],[f_1271_2]) ).

cnf(f_1271_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5902,tc_HOL_Obool)),U_5904),hAPP(hAPP(c_Set_Oinsert(U_5902),U_5906),c_Orderings_Obot__class_Obot(tc_fun(U_5902,tc_HOL_Obool))))),U_5908))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5902),U_5906),U_5904))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),U_5904),hAPP(hAPP(c_Set_Oinsert(U_5902),U_5906),U_5908))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

cnf(f_1271_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),U_5904),U_5908))
    | hBOOL(hAPP(hAPP(c_member(U_5902),U_5906),U_5904))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5902,tc_HOL_Obool)),U_5904),hAPP(hAPP(c_Set_Oinsert(U_5902),U_5906),U_5908))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

cnf(f_1271_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905))
    | hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),U_5909))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

cnf(f_1271_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),U_5909))
    | hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),U_5909))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

cnf(f_1271_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_5903),U_5907),U_5905))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),c_Orderings_Obot__class_Obot(tc_fun(U_5903,tc_HOL_Obool))))),U_5909))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),U_5909))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

cnf(f_1271_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),U_5909))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),c_Orderings_Obot__class_Obot(tc_fun(U_5903,tc_HOL_Obool))))),U_5909))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5903,tc_HOL_Obool)),U_5905),hAPP(hAPP(c_Set_Oinsert(U_5903),U_5907),U_5909))) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

fof(f_1272_1,plain,
    ! [V_b_2,V_a_2,V_A_2,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_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).

fof(f_1272_2,plain,
    ! [U_5913,U_5912,U_5911,U_5910] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5910),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5910),U_5912),U_5913)),hAPP(hAPP(c_Finite__Set_Ofold(U_5910,U_5910,c_Lattices_Osemilattice__sup__class_Osup(U_5910)),U_5913),U_5911)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5910),U_5912),U_5911))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5910),U_5911))
      | ~ class_Lattices_Osemilattice__sup(U_5910) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

cnf(f_1272_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5910),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5910),U_5912),U_5913)),hAPP(hAPP(c_Finite__Set_Ofold(U_5910,U_5910,c_Lattices_Osemilattice__sup__class_Osup(U_5910)),U_5913),U_5911)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5910),U_5912),U_5911))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5910),U_5911))
    | ~ class_Lattices_Osemilattice__sup(U_5910) ),
    inference(clausify,[status(thm)],[f_1272_2]) ).

fof(f_1273_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).

fof(f_1273_2,plain,
    ! [U_5917,U_5916,U_5915,U_5914] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5914),hAPP(hAPP(c_Finite__Set_Ofold(U_5914,U_5914,c_Lattices_Osemilattice__inf__class_Oinf(U_5914)),U_5917),U_5915)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5914),U_5916),U_5917)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5914),U_5916),U_5915))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5914),U_5915))
      | ~ class_Lattices_Osemilattice__inf(U_5914) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

cnf(f_1273_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5914),hAPP(hAPP(c_Finite__Set_Ofold(U_5914,U_5914,c_Lattices_Osemilattice__inf__class_Oinf(U_5914)),U_5917),U_5915)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5914),U_5916),U_5917)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5914),U_5916),U_5915))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5914),U_5915))
    | ~ class_Lattices_Osemilattice__inf(U_5914) ),
    inference(clausify,[status(thm)],[f_1273_2]) ).

fof(f_1274_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).

fof(f_1274_2,plain,
    ! [U_5922,U_5921,U_5920,U_5919,U_5918] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5919,tc_HOL_Obool)),U_5920),U_5921)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5918),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),U_5920)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),U_5921))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5919,tc_HOL_Obool)),U_5921),U_5920))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5919),U_5920))
      | ~ class_Groups_Oab__group__add(U_5918) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

cnf(f_1274_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5919,tc_HOL_Obool)),U_5920),U_5921)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5918),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),U_5920)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5919,U_5918),U_5922),U_5921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5919,tc_HOL_Obool)),U_5921),U_5920))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5919),U_5920))
    | ~ class_Groups_Oab__group__add(U_5918) ),
    inference(clausify,[status(thm)],[f_1274_2]) ).

fof(f_1275_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).

fof(f_1275_2,plain,
    ! [U_5925,U_5924,U_5923] :
      ( hAPP(c_Finite__Set_Ocard(U_5923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5923,tc_HOL_Obool)),U_5925),U_5924)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5923),U_5925)),hAPP(c_Finite__Set_Ocard(U_5923),U_5924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5923,tc_HOL_Obool)),U_5924),U_5925))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5923),U_5924)) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

cnf(f_1275_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_5923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5923,tc_HOL_Obool)),U_5925),U_5924)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5923),U_5925)),hAPP(c_Finite__Set_Ocard(U_5923),U_5924))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5923,tc_HOL_Obool)),U_5924),U_5925))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5923),U_5924)) ),
    inference(clausify,[status(thm)],[f_1275_2]) ).

fof(f_1276_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).

fof(f_1276_2,plain,
    ! [U_5928,U_5927,U_5926] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5926),c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5928)),c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5927)) = c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5927)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5926,tc_HOL_Obool)),U_5928),U_5927))
      | U_5928 = c_Orderings_Obot__class_Obot(tc_fun(U_5926,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5926),U_5927))
      | ~ class_Lattices_Olattice(U_5926) ),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

cnf(f_1276_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5926),c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5928)),c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5927)) = c_Big__Operators_Olattice__class_OSup__fin(U_5926,U_5927)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5926,tc_HOL_Obool)),U_5928),U_5927))
    | U_5928 = c_Orderings_Obot__class_Obot(tc_fun(U_5926,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5926),U_5927))
    | ~ class_Lattices_Olattice(U_5926) ),
    inference(clausify,[status(thm)],[f_1276_2]) ).

fof(f_1277_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).

fof(f_1277_2,plain,
    ! [U_5931,U_5930,U_5929] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5929),c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5931)),c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5930)) = c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5930)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5929,tc_HOL_Obool)),U_5931),U_5930))
      | U_5931 = c_Orderings_Obot__class_Obot(tc_fun(U_5929,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5929),U_5930))
      | ~ class_Lattices_Olattice(U_5929) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

cnf(f_1277_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5929),c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5931)),c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5930)) = c_Big__Operators_Olattice__class_OInf__fin(U_5929,U_5930)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5929,tc_HOL_Obool)),U_5931),U_5930))
    | U_5931 = c_Orderings_Obot__class_Obot(tc_fun(U_5929,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5929),U_5930))
    | ~ class_Lattices_Olattice(U_5929) ),
    inference(clausify,[status(thm)],[f_1277_2]) ).

fof(f_1278_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).

fof(f_1278_2,plain,
    ! [U_5934,U_5933,U_5932] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5932,tc_HOL_Obool)),U_5934),U_5933))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5932),U_5934)),hAPP(c_Finite__Set_Ocard(U_5932),U_5933)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5932,tc_HOL_Obool)),U_5934),U_5933))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5932),U_5933)) ),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

cnf(f_1278_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_5932,tc_HOL_Obool)),U_5934),U_5933))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5932),U_5934)),hAPP(c_Finite__Set_Ocard(U_5932),U_5933)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5932,tc_HOL_Obool)),U_5934),U_5933))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5932),U_5933)) ),
    inference(clausify,[status(thm)],[f_1278_2]) ).

fof(f_1279_1,plain,
    ! [V_t_2,V_n_2,T_a] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
        | ~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) )
      & ( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple__valid__def]) ).

fof(f_1279_2,plain,
    ! [U_5937,U_5936,U_5935] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_5935,U_5936,U_5937)
        | ~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5935,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool)),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5935)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5935),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5935),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5935),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5935),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5935)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5936))))))))),U_5937)) )
      & ( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5935,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool)),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5935)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_HOL_Obool),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5935),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5935),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5935),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5935),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5935,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5935)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5936))))))))),U_5937))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_5935,U_5936,U_5937) ) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

fof(f_1279_3,plain,
    ( ! [U_5943,U_5941,U_5939] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_5939,U_5941,U_5943)
        | ~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5939,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool)),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5939)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5939),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5939),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5939),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5939)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5941))))))))),U_5943)) )
    & ! [U_5942,U_5940,U_5938] :
        ( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5938,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool)),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5938)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5938),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5938),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5938),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5938),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5938)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5940))))))))),U_5942))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_5938,U_5940,U_5942) ) ),
    inference(miniscope,[status(thm)],[f_1279_2]) ).

cnf(f_1279_4,plain,
    ( hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5938,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool)),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5938)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_HOL_Obool),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5938),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5938),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5938),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5938),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5938,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5938)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5940))))))))),U_5942))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_5938,U_5940,U_5942) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

cnf(f_1279_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_5939,U_5941,U_5943)
    | ~ hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(U_5939,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool)),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(U_5939)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_HOL_Obool),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,U_5939),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),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_5939),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),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_5939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_5939),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(U_5939,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_5939)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,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_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),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)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),U_5941))))))))),U_5943)) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

fof(f_1280_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).

fof(f_1280_2,plain,
    ! [U_5947,U_5946,U_5945,U_5944] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5944,tc_HOL_Obool)),U_5946),U_5945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),U_5946)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),U_5945))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5944,tc_HOL_Obool)),U_5945),U_5946))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5944),U_5945)) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

cnf(f_1280_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5944,tc_HOL_Obool)),U_5946),U_5945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),U_5946)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5944,tc_Nat_Onat),U_5947),U_5945))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5944,tc_HOL_Obool)),U_5945),U_5946))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5944),U_5945)) ),
    inference(clausify,[status(thm)],[f_1280_2]) ).

fof(f_1281_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).

fof(f_1281_2,plain,
    ! [U_5949,U_5948] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5948),c_Big__Operators_Olattice__class_OInf__fin(U_5948,U_5949)),c_Big__Operators_Olattice__class_OSup__fin(U_5948,U_5949)))
      | U_5949 = c_Orderings_Obot__class_Obot(tc_fun(U_5948,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5948),U_5949))
      | ~ class_Lattices_Olattice(U_5948) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

cnf(f_1281_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5948),c_Big__Operators_Olattice__class_OInf__fin(U_5948,U_5949)),c_Big__Operators_Olattice__class_OSup__fin(U_5948,U_5949)))
    | U_5949 = c_Orderings_Obot__class_Obot(tc_fun(U_5948,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5948),U_5949))
    | ~ class_Lattices_Olattice(U_5948) ),
    inference(clausify,[status(thm)],[f_1281_2]) ).

fof(f_1282_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).

fof(f_1282_2,plain,
    ! [U_5952,U_5951,U_5950] :
      ( hAPP(c_Finite__Set_Ofold1(U_5950,c_Groups_Otimes__class_Otimes(U_5950)),hAPP(hAPP(c_Set_Oinsert(U_5950),U_5952),U_5951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5952),hAPP(c_Finite__Set_Ofold1(U_5950,c_Groups_Otimes__class_Otimes(U_5950)),U_5951))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5950),U_5951))
      | U_5951 = c_Orderings_Obot__class_Obot(tc_fun(U_5950,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_5950) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

cnf(f_1282_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_5950,c_Groups_Otimes__class_Otimes(U_5950)),hAPP(hAPP(c_Set_Oinsert(U_5950),U_5952),U_5951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5952),hAPP(c_Finite__Set_Ofold1(U_5950,c_Groups_Otimes__class_Otimes(U_5950)),U_5951))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5950),U_5951))
    | U_5951 = c_Orderings_Obot__class_Obot(tc_fun(U_5950,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_5950) ),
    inference(clausify,[status(thm)],[f_1282_2]) ).

fof(f_1283_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).

fof(f_1283_2,plain,
    ! [U_5955,U_5954,U_5953] :
      ( hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5953,tc_HOL_Obool)),U_5954),U_5955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5953),hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),U_5954)),hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),U_5955))
      | U_5955 = c_Orderings_Obot__class_Obot(tc_fun(U_5953,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5953),U_5955))
      | U_5954 = c_Orderings_Obot__class_Obot(tc_fun(U_5953,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5953),U_5954))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_5953) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

cnf(f_1283_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5953,tc_HOL_Obool)),U_5954),U_5955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5953),hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),U_5954)),hAPP(c_Finite__Set_Ofold1(U_5953,c_Groups_Otimes__class_Otimes(U_5953)),U_5955))
    | U_5955 = c_Orderings_Obot__class_Obot(tc_fun(U_5953,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5953),U_5955))
    | U_5954 = c_Orderings_Obot__class_Obot(tc_fun(U_5953,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5953),U_5954))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_5953) ),
    inference(clausify,[status(thm)],[f_1283_2]) ).

fof(f_1284_1,plain,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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)) )
      & ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1284_2,plain,
    ! [U_5959,U_5958,U_5957,U_5956] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5956)),U_5957),hAPP(c_Nat_OSuc,U_5958)),U_5959))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5956))),U_5957),U_5958),U_5959)) )
      & ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5956))),U_5957),U_5958),U_5959))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5956)),U_5957),hAPP(c_Nat_OSuc,U_5958)),U_5959)) ) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ( ! [U_5967,U_5965,U_5963,U_5961] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5961)),U_5963),hAPP(c_Nat_OSuc,U_5965)),U_5967))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5961))),U_5963),U_5965),U_5967)) )
    & ! [U_5966,U_5964,U_5962,U_5960] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5960))),U_5962),U_5964),U_5966))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5960)),U_5962),hAPP(c_Nat_OSuc,U_5964)),U_5966)) ) ),
    inference(miniscope,[status(thm)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5960))),U_5962),U_5964),U_5966))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5960)),U_5962),hAPP(c_Nat_OSuc,U_5964)),U_5966)) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

cnf(f_1284_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5961)),U_5963),hAPP(c_Nat_OSuc,U_5965)),U_5967))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5961))),U_5963),U_5965),U_5967)) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

fof(f_1285_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).

fof(f_1285_2,plain,
    ! [U_5970,U_5969,U_5968] :
      ( hAPP(c_Finite__Set_Ofold1(U_5968,c_Groups_Otimes__class_Otimes(U_5968)),hAPP(hAPP(c_Set_Oinsert(U_5968),U_5970),U_5969)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5968,U_5968,c_Groups_Otimes__class_Otimes(U_5968)),U_5970),U_5969)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5968),U_5969))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_5968) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

cnf(f_1285_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_5968,c_Groups_Otimes__class_Otimes(U_5968)),hAPP(hAPP(c_Set_Oinsert(U_5968),U_5970),U_5969)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5968,U_5968,c_Groups_Otimes__class_Otimes(U_5968)),U_5970),U_5969)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5968),U_5969))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_5968) ),
    inference(clausify,[status(thm)],[f_1285_2]) ).

fof(f_1286_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_1286_2,plain,
    ! [U_5976,U_5975,U_5974,U_5973,U_5972,U_5971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5971),U_5975),U_5972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5971),U_5976),U_5974))),U_5973))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5971),U_5975),U_5976) != c_Groups_Oone__class_Oone(U_5971)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),U_5974),U_5973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),U_5972),U_5973))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_5971) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

cnf(f_1286_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5971),U_5975),U_5972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5971),U_5976),U_5974))),U_5973))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5971),U_5975),U_5976) != c_Groups_Oone__class_Oone(U_5971)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),U_5974),U_5973))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),U_5972),U_5973))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_5971) ),
    inference(clausify,[status(thm)],[f_1286_2]) ).

fof(f_1287_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_a] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).

fof(f_1287_2,plain,
    ! [U_5980,U_5979,U_5978,U_5977] :
      ( hAPP(U_5979,U_5980) = hAPP(c_Finite__Set_Ofold1(U_5977,U_5978),U_5980)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5980))
      | ~ c_Big__Operators_Osemilattice__big(U_5977,U_5978,U_5979) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

cnf(f_1287_3,plain,
    ( hAPP(U_5979,U_5980) = hAPP(c_Finite__Set_Ofold1(U_5977,U_5978),U_5980)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5980))
    | ~ c_Big__Operators_Osemilattice__big(U_5977,U_5978,U_5979) ),
    inference(clausify,[status(thm)],[f_1287_2]) ).

fof(f_1288_1,plain,
    ! [V_s1,V_n,V_s,V_P] :
      ( ? [B_n] :
          ( hBOOL(hAPP(hAPP(hAPP(hAPP(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) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(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_1288_2,plain,
    ! [U_5985,U_5984,U_5983,U_5982] :
      ( ? [U_5981] :
          ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5982))),U_5983),U_5981),U_5985))
          & U_5984 = hAPP(c_Nat_OSuc,U_5981) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5982)),U_5983),U_5984),U_5985)) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

fof(f_1288_3,plain,
    ! [U_5985,U_5984,U_5983,U_5982] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5982))),U_5983),sK114(U_5985,U_5984,U_5983,U_5982)),U_5985))
        & U_5984 = hAPP(c_Nat_OSuc,sK114(U_5985,U_5984,U_5983,U_5982)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5982)),U_5983),U_5984),U_5985)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_5981,sK114(U_5985,U_5984,U_5983,U_5982))],[f_1288_2]) ).

cnf(f_1288_4,plain,
    ( U_5984 = hAPP(c_Nat_OSuc,sK114(U_5985,U_5984,U_5983,U_5982))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5982)),U_5983),U_5984),U_5985)) ),
    inference(clausify,[status(thm)],[f_1288_3]) ).

cnf(f_1288_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_5982))),U_5983),sK114(U_5985,U_5984,U_5983,U_5982)),U_5985))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,U_5982)),U_5983),U_5984),U_5985)) ),
    inference(clausify,[status(thm)],[f_1288_3]) ).

fof(f_1289_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)))
      | ? [B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).

fof(f_1289_2,plain,
    ! [U_5991,U_5990,U_5989,U_5988,U_5987] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5990)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5989)))
      | ? [U_5986] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),c_Groups_Ozero__class_Ozero(U_5987)),hAPP(U_5991,U_5986)))
          & hBOOL(hAPP(hAPP(c_member(U_5988),U_5986),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5988,tc_HOL_Obool)),U_5989),U_5990))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5988,tc_HOL_Obool)),U_5990),U_5989))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5988),U_5989))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5987) ),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

fof(f_1289_3,plain,
    ! [U_5991,U_5990,U_5989,U_5988,U_5987] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5990)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5989)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),c_Groups_Ozero__class_Ozero(U_5987)),hAPP(U_5991,sK115(U_5991,U_5990,U_5989,U_5988,U_5987))))
        & hBOOL(hAPP(hAPP(c_member(U_5988),sK115(U_5991,U_5990,U_5989,U_5988,U_5987)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5988,tc_HOL_Obool)),U_5989),U_5990))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5988,tc_HOL_Obool)),U_5990),U_5989))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5988),U_5989))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5987) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_5986,sK115(U_5991,U_5990,U_5989,U_5988,U_5987))],[f_1289_2]) ).

cnf(f_1289_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5988),sK115(U_5991,U_5990,U_5989,U_5988,U_5987)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5988,tc_HOL_Obool)),U_5989),U_5990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5990)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5989)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5988,tc_HOL_Obool)),U_5990),U_5989))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5988),U_5989))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5987) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

cnf(f_1289_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),c_Groups_Ozero__class_Ozero(U_5987)),hAPP(U_5991,sK115(U_5991,U_5990,U_5989,U_5988,U_5987))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5987),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5990)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5988,U_5987),U_5991),U_5989)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5988,tc_HOL_Obool)),U_5990),U_5989))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5988),U_5989))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5987) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

fof(f_1290_1,plain,
    ! [V_b_2,V_A_2,T_a] :
      ( ( c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_flat__lub__def]) ).

fof(f_1290_2,plain,
    ! [U_5994,U_5993,U_5992] :
      ( ( c_Partial__Function_Oflat__lub(U_5992,U_5994,U_5993) = c_HOL_OThe(U_5992,hAPP(hAPP(c_COMBC(U_5992,tc_fun(U_5992,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5992)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5992,tc_HOL_Obool)),U_5993),hAPP(hAPP(c_Set_Oinsert(U_5992),U_5994),c_Orderings_Obot__class_Obot(tc_fun(U_5992,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5992,tc_HOL_Obool)),U_5993),hAPP(hAPP(c_Set_Oinsert(U_5992),U_5994),c_Orderings_Obot__class_Obot(tc_fun(U_5992,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_5992,U_5994,U_5993) = U_5994
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5992,tc_HOL_Obool)),U_5993),hAPP(hAPP(c_Set_Oinsert(U_5992),U_5994),c_Orderings_Obot__class_Obot(tc_fun(U_5992,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ( ! [U_6000,U_5998,U_5996] :
        ( c_Partial__Function_Oflat__lub(U_5996,U_6000,U_5998) = c_HOL_OThe(U_5996,hAPP(hAPP(c_COMBC(U_5996,tc_fun(U_5996,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5996)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5996,tc_HOL_Obool)),U_5998),hAPP(hAPP(c_Set_Oinsert(U_5996),U_6000),c_Orderings_Obot__class_Obot(tc_fun(U_5996,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5996,tc_HOL_Obool)),U_5998),hAPP(hAPP(c_Set_Oinsert(U_5996),U_6000),c_Orderings_Obot__class_Obot(tc_fun(U_5996,tc_HOL_Obool))))) )
    & ! [U_5999,U_5997,U_5995] :
        ( c_Partial__Function_Oflat__lub(U_5995,U_5999,U_5997) = U_5999
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5995,tc_HOL_Obool)),U_5997),hAPP(hAPP(c_Set_Oinsert(U_5995),U_5999),c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    ( c_Partial__Function_Oflat__lub(U_5995,U_5999,U_5997) = U_5999
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5995,tc_HOL_Obool)),U_5997),hAPP(hAPP(c_Set_Oinsert(U_5995),U_5999),c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

cnf(f_1290_5,plain,
    ( c_Partial__Function_Oflat__lub(U_5996,U_6000,U_5998) = c_HOL_OThe(U_5996,hAPP(hAPP(c_COMBC(U_5996,tc_fun(U_5996,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5996)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5996,tc_HOL_Obool)),U_5998),hAPP(hAPP(c_Set_Oinsert(U_5996),U_6000),c_Orderings_Obot__class_Obot(tc_fun(U_5996,tc_HOL_Obool))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5996,tc_HOL_Obool)),U_5998),hAPP(hAPP(c_Set_Oinsert(U_5996),U_6000),c_Orderings_Obot__class_Obot(tc_fun(U_5996,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_1,plain,
    ! [V_n_2,V_d_2,V_a_2,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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).

fof(f_1291_2,plain,
    ! [U_6004,U_6003,U_6002,U_6001] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),c_Groups_Oone__class_Oone(U_6001)),c_Groups_Oone__class_Oone(U_6001))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6001),hAPP(hAPP(c_COMBB(U_6001,U_6001,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6001,U_6001),hAPP(hAPP(c_COMBB(U_6001,tc_fun(U_6001,U_6001),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6001)),c_Nat_Osemiring__1__class_Oof__nat(U_6001))),U_6003))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6004))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6001),U_6004)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6001),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6004),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6003))))
      | ~ class_Rings_Ocomm__semiring__1(U_6001) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

cnf(f_1291_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),c_Groups_Oone__class_Oone(U_6001)),c_Groups_Oone__class_Oone(U_6001))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6001),hAPP(hAPP(c_COMBB(U_6001,U_6001,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6001,U_6001),hAPP(hAPP(c_COMBB(U_6001,tc_fun(U_6001,U_6001),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6001)),c_Nat_Osemiring__1__class_Oof__nat(U_6001))),U_6003))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6004))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6001),U_6004)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6001),U_6002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6001),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6004),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6003))))
    | ~ class_Rings_Ocomm__semiring__1(U_6001) ),
    inference(clausify,[status(thm)],[f_1291_2]) ).

fof(f_1292_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).

fof(f_1292_2,plain,
    ! [U_6008,U_6007] :
      ( hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(c_Finite__Set_Ofold1(U_6007,c_Groups_Otimes__class_Otimes(U_6007)),U_6008)),U_6008))
      | ? [U_6006,U_6005] : ~ hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6007),U_6006),U_6005)),hAPP(hAPP(c_Set_Oinsert(U_6007),U_6006),hAPP(hAPP(c_Set_Oinsert(U_6007),U_6005),c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))))))
      | U_6008 = c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6007),U_6008))
      | ~ class_Groups_Oab__semigroup__mult(U_6007) ),
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

fof(f_1292_3,plain,
    ! [U_6008,U_6007] :
      ( hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(c_Finite__Set_Ofold1(U_6007,c_Groups_Otimes__class_Otimes(U_6007)),U_6008)),U_6008))
      | ? [U_6005] : ~ hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6007),sK116(U_6008,U_6007)),U_6005)),hAPP(hAPP(c_Set_Oinsert(U_6007),sK116(U_6008,U_6007)),hAPP(hAPP(c_Set_Oinsert(U_6007),U_6005),c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))))))
      | U_6008 = c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6007),U_6008))
      | ~ class_Groups_Oab__semigroup__mult(U_6007) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_6006,sK116(U_6008,U_6007))],[f_1292_2]) ).

fof(f_1292_4,plain,
    ! [U_6008,U_6007] :
      ( hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(c_Finite__Set_Ofold1(U_6007,c_Groups_Otimes__class_Otimes(U_6007)),U_6008)),U_6008))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6007),sK116(U_6008,U_6007)),sK117(U_6008,U_6007))),hAPP(hAPP(c_Set_Oinsert(U_6007),sK116(U_6008,U_6007)),hAPP(hAPP(c_Set_Oinsert(U_6007),sK117(U_6008,U_6007)),c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))))))
      | U_6008 = c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6007),U_6008))
      | ~ class_Groups_Oab__semigroup__mult(U_6007) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_6005,sK117(U_6008,U_6007))],[f_1292_3]) ).

cnf(f_1292_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(c_Finite__Set_Ofold1(U_6007,c_Groups_Otimes__class_Otimes(U_6007)),U_6008)),U_6008))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6007),sK116(U_6008,U_6007)),sK117(U_6008,U_6007))),hAPP(hAPP(c_Set_Oinsert(U_6007),sK116(U_6008,U_6007)),hAPP(hAPP(c_Set_Oinsert(U_6007),sK117(U_6008,U_6007)),c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))))))
    | U_6008 = c_Orderings_Obot__class_Obot(tc_fun(U_6007,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6007),U_6008))
    | ~ class_Groups_Oab__semigroup__mult(U_6007) ),
    inference(clausify,[status(thm)],[f_1292_4]) ).

fof(f_1293_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).

fof(f_1293_2,plain,
    ! [U_6014,U_6013,U_6012,U_6011,U_6010] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6012)))
      | ? [U_6009] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),c_Groups_Ozero__class_Ozero(U_6010)),hAPP(U_6014,U_6009)))
          & hBOOL(hAPP(hAPP(c_member(U_6011),U_6009),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6011,tc_HOL_Obool)),U_6012),U_6013))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6011,tc_HOL_Obool)),U_6013),U_6012))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6011),U_6012))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_6010)
      | ~ class_Groups_Ocomm__monoid__add(U_6010) ),
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

fof(f_1293_3,plain,
    ! [U_6014,U_6013,U_6012,U_6011,U_6010] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6012)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),c_Groups_Ozero__class_Ozero(U_6010)),hAPP(U_6014,sK118(U_6014,U_6013,U_6012,U_6011,U_6010))))
        & hBOOL(hAPP(hAPP(c_member(U_6011),sK118(U_6014,U_6013,U_6012,U_6011,U_6010)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6011,tc_HOL_Obool)),U_6012),U_6013))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6011,tc_HOL_Obool)),U_6013),U_6012))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6011),U_6012))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_6010)
      | ~ class_Groups_Ocomm__monoid__add(U_6010) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_6009,sK118(U_6014,U_6013,U_6012,U_6011,U_6010))],[f_1293_2]) ).

cnf(f_1293_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6011),sK118(U_6014,U_6013,U_6012,U_6011,U_6010)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6011,tc_HOL_Obool)),U_6012),U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6012)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6011,tc_HOL_Obool)),U_6013),U_6012))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6011),U_6012))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_6010)
    | ~ class_Groups_Ocomm__monoid__add(U_6010) ),
    inference(clausify,[status(thm)],[f_1293_3]) ).

cnf(f_1293_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),c_Groups_Ozero__class_Ozero(U_6010)),hAPP(U_6014,sK118(U_6014,U_6013,U_6012,U_6011,U_6010))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6010),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6011,U_6010),U_6014),U_6012)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6011,tc_HOL_Obool)),U_6013),U_6012))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6011),U_6012))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_6010)
    | ~ class_Groups_Ocomm__monoid__add(U_6010) ),
    inference(clausify,[status(thm)],[f_1293_3]) ).

fof(f_1294_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_1294_2,plain,
    ! [U_6015] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6015)),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

cnf(f_1294_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6015)),
    inference(clausify,[status(thm)],[f_1294_2]) ).

fof(f_1295_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_1295_2,plain,
    ! [U_6016] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6016)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_6016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_6016 = 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_6016)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

fof(f_1295_3,plain,
    ( ! [U_6018] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6018)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_6018 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6017] :
        ( U_6017 = 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_6017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1295_2]) ).

cnf(f_1295_4,plain,
    ( U_6017 = 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_6017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1295_3]) ).

cnf(f_1295_5,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_6018)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6018 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1295_3]) ).

fof(f_1296_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_1296_2,plain,
    ! [U_6020,U_6019] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6020)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6019)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6020),U_6019))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6019),U_6020)) ),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

cnf(f_1296_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6020)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6019)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6020),U_6019))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6019),U_6020)) ),
    inference(clausify,[status(thm)],[f_1296_2]) ).

fof(f_1297_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_1297_2,plain,
    ! [U_6025] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6025))
        | ! [U_6024] :
          ? [U_6023] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6023),U_6024))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6023),U_6025)) ) )
      & ( ? [U_6022] :
          ! [U_6021] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6021),U_6022))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6021),U_6025)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6025)) ) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ( ! [U_6027] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6027))
        | ! [U_6024] :
          ? [U_6023] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6023),U_6024))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6023),U_6027)) ) )
    & ! [U_6026] :
        ( ? [U_6022] :
          ! [U_6021] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6021),U_6022))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6021),U_6026)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6026)) ) ),
    inference(miniscope,[status(thm)],[f_1297_2]) ).

fof(f_1297_4,plain,
    ( ! [U_6027] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6027))
        | ! [U_6024] :
          ? [U_6023] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6023),U_6024))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6023),U_6027)) ) )
    & ! [U_6026] :
        ( ! [U_6021] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6021),sK119(U_6026)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6021),U_6026)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6026)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_6022,sK119(U_6026))],[f_1297_3]) ).

fof(f_1297_5,plain,
    ( ! [U_6027] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6027))
        | ! [U_6024] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK120(U_6027,U_6024)),U_6024))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK120(U_6027,U_6024)),U_6027)) ) )
    & ! [U_6026] :
        ( ! [U_6021] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6021),sK119(U_6026)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6021),U_6026)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6026)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_6023,sK120(U_6027,U_6024))],[f_1297_4]) ).

cnf(f_1297_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6021),sK119(U_6026)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6021),U_6026))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6026)) ),
    inference(clausify,[status(thm)],[f_1297_5]) ).

cnf(f_1297_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK120(U_6027,U_6024)),U_6027))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6027)) ),
    inference(clausify,[status(thm)],[f_1297_5]) ).

cnf(f_1297_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK120(U_6027,U_6024)),U_6024))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6027)) ),
    inference(clausify,[status(thm)],[f_1297_5]) ).

fof(f_1298_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) ) )
      | ~ class_Nat_Osemiring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).

fof(f_1298_2,plain,
    ! [U_6030,U_6029,U_6028] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6029) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6030)
          | U_6029 != U_6030 )
        & ( U_6029 = U_6030
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6029) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6030) ) )
      | ~ class_Nat_Osemiring__char__0(U_6028) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

cnf(f_1298_3,plain,
    ( U_6029 = U_6030
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6029) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6030)
    | ~ class_Nat_Osemiring__char__0(U_6028) ),
    inference(clausify,[status(thm)],[f_1298_2]) ).

cnf(f_1298_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6029) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6028),U_6030)
    | U_6029 != U_6030
    | ~ class_Nat_Osemiring__char__0(U_6028) ),
    inference(clausify,[status(thm)],[f_1298_2]) ).

fof(f_1299_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]) ).

cnf(f_1299_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(clausify,[status(thm)],[f_1299_1]) ).

fof(f_1300_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_1300_2,plain,
    ! [U_6033,U_6032,U_6031] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6033),U_6032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6031),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),U_6033)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),U_6032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6032),U_6033))
      | ~ class_Rings_Oring__1(U_6031) ),
    inference(variable_rename,[status(thm)],[f_1300_1]) ).

cnf(f_1300_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6033),U_6032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6031),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),U_6033)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6031),U_6032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6032),U_6033))
    | ~ class_Rings_Oring__1(U_6031) ),
    inference(clausify,[status(thm)],[f_1300_2]) ).

fof(f_1301_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_1301_2,plain,
    ! [U_6034] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6034) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6034 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_6034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6034) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

fof(f_1301_3,plain,
    ( ! [U_6036] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6036) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6035] :
        ( U_6035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1301_2]) ).

cnf(f_1301_4,plain,
    ( U_6035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6036) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

fof(f_1302_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]) ).

cnf(f_1302_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(clausify,[status(thm)],[f_1302_1]) ).

fof(f_1303_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_1303_2,plain,
    ! [U_6040,U_6039] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6039),U_6040))
        | ! [U_6038] : U_6040 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6039),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6038))) )
      & ( ? [U_6037] : U_6040 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6039),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6037)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6039),U_6040)) ) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ( ! [U_6044,U_6042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6042),U_6044))
        | ! [U_6038] : U_6044 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6042),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6038))) )
    & ! [U_6043,U_6041] :
        ( ? [U_6037] : U_6043 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6037)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6041),U_6043)) ) ),
    inference(miniscope,[status(thm)],[f_1303_2]) ).

fof(f_1303_4,plain,
    ( ! [U_6044,U_6042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6042),U_6044))
        | ! [U_6038] : U_6044 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6042),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6038))) )
    & ! [U_6043,U_6041] :
        ( U_6043 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK121(U_6043,U_6041))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6041),U_6043)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_6037,sK121(U_6043,U_6041))],[f_1303_3]) ).

cnf(f_1303_5,plain,
    ( U_6043 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK121(U_6043,U_6041))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6041),U_6043)) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

cnf(f_1303_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6042),U_6044))
    | U_6044 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6042),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6038))) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

fof(f_1304_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_1304_2,plain,
    ! [U_6045] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6045)) = 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_6045)),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

cnf(f_1304_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6045)) = 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_6045)),
    inference(clausify,[status(thm)],[f_1304_2]) ).

fof(f_1305_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_1305_2,plain,
    ! [U_6047,U_6046] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6046)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6047)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6046),U_6047)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6046),U_6047))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6046)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6047))) ) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

fof(f_1305_3,plain,
    ( ! [U_6051,U_6049] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6049)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6051)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6049),U_6051)) )
    & ! [U_6050,U_6048] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6048),U_6050))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6050))) ) ),
    inference(miniscope,[status(thm)],[f_1305_2]) ).

cnf(f_1305_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6048),U_6050))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6050))) ),
    inference(clausify,[status(thm)],[f_1305_3]) ).

cnf(f_1305_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_6049)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6051)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6049),U_6051)) ),
    inference(clausify,[status(thm)],[f_1305_3]) ).

fof(f_1306_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_1306_2,plain,
    ! [U_6054,U_6053,U_6052] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6053)),U_6054)) = 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_6052),U_6053))),U_6054),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

cnf(f_1306_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6053)),U_6054)) = 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_6052),U_6053))),U_6054),
    inference(clausify,[status(thm)],[f_1306_2]) ).

fof(f_1307_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_1307_2,plain,
    ! [U_6056,U_6055] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6055)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6056)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6055),U_6056)),
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

cnf(f_1307_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6055)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6056)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6055),U_6056)),
    inference(clausify,[status(thm)],[f_1307_2]) ).

fof(f_1308_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).

fof(f_1308_2,plain,
    ! [U_6059,U_6058,U_6057] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6058)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6059)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6058),U_6059)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6058),U_6059))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6058)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6059))) ) )
      | ~ class_Rings_Olinordered__semidom(U_6057) ),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

cnf(f_1308_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6058),U_6059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6058)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6059)))
    | ~ class_Rings_Olinordered__semidom(U_6057) ),
    inference(clausify,[status(thm)],[f_1308_2]) ).

cnf(f_1308_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6058)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6057),U_6059)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6058),U_6059))
    | ~ class_Rings_Olinordered__semidom(U_6057) ),
    inference(clausify,[status(thm)],[f_1308_2]) ).

fof(f_1309_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_1309_2,plain,
    ! [U_6061,U_6060] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6060)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6061)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6060),U_6061)),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

cnf(f_1309_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6060)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6061)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6060),U_6061)),
    inference(clausify,[status(thm)],[f_1309_2]) ).

fof(f_1310_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_1310_2,plain,
    ! [U_6063,U_6062] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),U_6063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6062)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6063)),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

cnf(f_1310_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),U_6063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6062)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6063)),
    inference(clausify,[status(thm)],[f_1310_2]) ).

fof(f_1311_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]) ).

cnf(f_1311_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(clausify,[status(thm)],[f_1311_1]) ).

fof(f_1312_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_1312_2,plain,
    ! [U_6064] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6064),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_6064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_6064 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6064),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

fof(f_1312_3,plain,
    ( ! [U_6066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6066),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6065] :
        ( U_6065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6065),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_1312_2]) ).

cnf(f_1312_4,plain,
    ( U_6065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6065),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

cnf(f_1312_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6066),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_6066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

fof(f_1313_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_1313_2,plain,
    ! [U_6067] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6067)),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

cnf(f_1313_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6067)),
    inference(clausify,[status(thm)],[f_1313_2]) ).

fof(f_1314_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_1314_2,plain,
    ! [U_6068] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6068)),U_6068)),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6068)),U_6068)),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_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_1315_2,plain,
    ! [U_6070,U_6069] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6069),U_6070))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6070)),U_6069)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6070)),U_6069))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6069),U_6070)) ) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

fof(f_1315_3,plain,
    ( ! [U_6074,U_6072] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6072),U_6074))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6074)),U_6072)) )
    & ! [U_6073,U_6071] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6073)),U_6071))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6071),U_6073)) ) ),
    inference(miniscope,[status(thm)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6073)),U_6071))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6071),U_6073)) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6072),U_6074))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6074)),U_6072)) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

fof(f_1316_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_1316_2,plain,
    ! [U_6076,U_6075] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6075),hAPP(c_Nat_OSuc,U_6076)))
        | ( U_6075 != hAPP(c_Nat_OSuc,U_6076)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6075),U_6076)) ) )
      & ( U_6075 = hAPP(c_Nat_OSuc,U_6076)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6075),U_6076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6075),hAPP(c_Nat_OSuc,U_6076))) ) ),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ( ! [U_6080,U_6078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),hAPP(c_Nat_OSuc,U_6080)))
        | ( U_6078 != hAPP(c_Nat_OSuc,U_6080)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),U_6080)) ) )
    & ! [U_6079,U_6077] :
        ( U_6077 = hAPP(c_Nat_OSuc,U_6079)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6077),U_6079))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6077),hAPP(c_Nat_OSuc,U_6079))) ) ),
    inference(miniscope,[status(thm)],[f_1316_2]) ).

cnf(f_1316_4,plain,
    ( U_6077 = hAPP(c_Nat_OSuc,U_6079)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6077),U_6079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6077),hAPP(c_Nat_OSuc,U_6079))) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

cnf(f_1316_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),U_6080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),hAPP(c_Nat_OSuc,U_6080))) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

cnf(f_1316_6,plain,
    ( U_6078 != hAPP(c_Nat_OSuc,U_6080)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),hAPP(c_Nat_OSuc,U_6080))) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

fof(f_1317_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_1317_2,plain,
    ! [U_6082,U_6081] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6081)),hAPP(c_Nat_OSuc,U_6082)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6081),U_6082)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6081),U_6082))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6081)),hAPP(c_Nat_OSuc,U_6082))) ) ),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

fof(f_1317_3,plain,
    ( ! [U_6086,U_6084] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6084)),hAPP(c_Nat_OSuc,U_6086)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6084),U_6086)) )
    & ! [U_6085,U_6083] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6083),U_6085))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6083)),hAPP(c_Nat_OSuc,U_6085))) ) ),
    inference(miniscope,[status(thm)],[f_1317_2]) ).

cnf(f_1317_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6083),U_6085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6083)),hAPP(c_Nat_OSuc,U_6085))) ),
    inference(clausify,[status(thm)],[f_1317_3]) ).

cnf(f_1317_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6084)),hAPP(c_Nat_OSuc,U_6086)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6084),U_6086)) ),
    inference(clausify,[status(thm)],[f_1317_3]) ).

fof(f_1318_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_1318_2,plain,
    ! [U_6088,U_6087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6087),hAPP(c_Nat_OSuc,U_6088)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6087),U_6088)) ),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

cnf(f_1318_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6087),hAPP(c_Nat_OSuc,U_6088)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6087),U_6088)) ),
    inference(clausify,[status(thm)],[f_1318_2]) ).

fof(f_1319_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_1319_2,plain,
    ! [U_6090,U_6089] :
      ( U_6089 = hAPP(c_Nat_OSuc,U_6090)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6089),U_6090))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6089),hAPP(c_Nat_OSuc,U_6090))) ),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

cnf(f_1319_3,plain,
    ( U_6089 = hAPP(c_Nat_OSuc,U_6090)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6089),U_6090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6089),hAPP(c_Nat_OSuc,U_6090))) ),
    inference(clausify,[status(thm)],[f_1319_2]) ).

fof(f_1320_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_1320_2,plain,
    ! [U_6092,U_6091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6091),U_6092))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6091)),U_6092)) ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

cnf(f_1320_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6091),U_6092))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6091)),U_6092)) ),
    inference(clausify,[status(thm)],[f_1320_2]) ).

fof(f_1321_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_1321_2,plain,
    ! [U_6094,U_6093] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6093),U_6094))
        | U_6093 = U_6094
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6093),U_6094)) )
      & ( ( U_6093 != U_6094
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6093),U_6094)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6093),U_6094)) ) ),
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ( ! [U_6098,U_6096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6096),U_6098))
        | U_6096 = U_6098
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6096),U_6098)) )
    & ! [U_6097,U_6095] :
        ( ( U_6095 != U_6097
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6095),U_6097)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6095),U_6097)) ) ),
    inference(miniscope,[status(thm)],[f_1321_2]) ).

cnf(f_1321_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6095),U_6097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6095),U_6097)) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

cnf(f_1321_5,plain,
    ( U_6095 != U_6097
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6095),U_6097)) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

cnf(f_1321_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6096),U_6098))
    | U_6096 = U_6098
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6096),U_6098)) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

fof(f_1322_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_1322_2,plain,
    ! [U_6100,U_6099] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6099),U_6100))
        | ( U_6099 != U_6100
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6099),U_6100)) ) )
      & ( U_6099 = U_6100
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6099),U_6100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6099),U_6100)) ) ),
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ( ! [U_6104,U_6102] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6102),U_6104))
        | ( U_6102 != U_6104
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6102),U_6104)) ) )
    & ! [U_6103,U_6101] :
        ( U_6101 = U_6103
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6101),U_6103))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6101),U_6103)) ) ),
    inference(miniscope,[status(thm)],[f_1322_2]) ).

cnf(f_1322_4,plain,
    ( U_6101 = U_6103
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6101),U_6103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6101),U_6103)) ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

cnf(f_1322_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6102),U_6104))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6102),U_6104)) ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

cnf(f_1322_6,plain,
    ( U_6102 != U_6104
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6102),U_6104)) ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

fof(f_1323_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_1323_2,plain,
    ! [U_6106,U_6105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6105),U_6106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6105),U_6106)) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

cnf(f_1323_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6105),U_6106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6105),U_6106)) ),
    inference(clausify,[status(thm)],[f_1323_2]) ).

fof(f_1324_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_1324_2,plain,
    ! [U_6108,U_6107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6107),U_6108))
      | U_6107 = U_6108
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6107),U_6108)) ),
    inference(variable_rename,[status(thm)],[f_1324_1]) ).

cnf(f_1324_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6107),U_6108))
    | U_6107 = U_6108
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6107),U_6108)) ),
    inference(clausify,[status(thm)],[f_1324_2]) ).

fof(f_1325_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_1325_2,plain,
    ! [U_6110,U_6109] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6109),U_6110))
      | ( U_6109 != U_6110
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6109),U_6110)) ) ),
    inference(variable_rename,[status(thm)],[f_1325_1]) ).

cnf(f_1325_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6109),U_6110))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6109),U_6110)) ),
    inference(clausify,[status(thm)],[f_1325_2]) ).

cnf(f_1325_4,plain,
    ( U_6109 != U_6110
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6109),U_6110)) ),
    inference(clausify,[status(thm)],[f_1325_2]) ).

fof(f_1326_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_1326_2,plain,
    ! [U_6112,U_6111] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6111),U_6112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6111),U_6112)) ),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

cnf(f_1326_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6111),U_6112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6111),U_6112)) ),
    inference(clausify,[status(thm)],[f_1326_2]) ).

fof(f_1327_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_1327_2,plain,
    ! [U_6114,U_6113] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6114),U_6113))),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

cnf(f_1327_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6114),U_6113))),
    inference(clausify,[status(thm)],[f_1327_2]) ).

fof(f_1328_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_1328_2,plain,
    ! [U_6116,U_6115] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6115),U_6116))),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

cnf(f_1328_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6115),U_6116))),
    inference(clausify,[status(thm)],[f_1328_2]) ).

fof(f_1329_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_1329_2,plain,
    ! [U_6120,U_6119] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6119),U_6120))
        | ! [U_6118] : U_6120 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6119),U_6118) )
      & ( ? [U_6117] : U_6120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6119),U_6117)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6119),U_6120)) ) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ( ! [U_6124,U_6122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6122),U_6124))
        | ! [U_6118] : U_6124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6122),U_6118) )
    & ! [U_6123,U_6121] :
        ( ? [U_6117] : U_6123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6121),U_6117)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6121),U_6123)) ) ),
    inference(miniscope,[status(thm)],[f_1329_2]) ).

fof(f_1329_4,plain,
    ( ! [U_6124,U_6122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6122),U_6124))
        | ! [U_6118] : U_6124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6122),U_6118) )
    & ! [U_6123,U_6121] :
        ( U_6123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6121),sK122(U_6123,U_6121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6121),U_6123)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_6117,sK122(U_6123,U_6121))],[f_1329_3]) ).

cnf(f_1329_5,plain,
    ( U_6123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6121),sK122(U_6123,U_6121))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6121),U_6123)) ),
    inference(clausify,[status(thm)],[f_1329_4]) ).

cnf(f_1329_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6122),U_6124))
    | U_6124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6122),U_6118) ),
    inference(clausify,[status(thm)],[f_1329_4]) ).

fof(f_1330_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_1330_2,plain,
    ! [U_6127,U_6126,U_6125] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6125),U_6126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6125),U_6127)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6126),U_6127)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6126),U_6127))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6125),U_6126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6125),U_6127))) ) ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

fof(f_1330_3,plain,
    ( ! [U_6133,U_6131] :
        ( ! [U_6129] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6129),U_6131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6129),U_6133)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6131),U_6133)) )
    & ! [U_6132,U_6130] :
        ( ! [U_6128] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6128),U_6130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6128),U_6132)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6130),U_6132)) ) ),
    inference(miniscope,[status(thm)],[f_1330_2]) ).

cnf(f_1330_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_6128),U_6130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6128),U_6132)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6130),U_6132)) ),
    inference(clausify,[status(thm)],[f_1330_3]) ).

cnf(f_1330_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_6129),U_6131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6129),U_6133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6131),U_6133)) ),
    inference(clausify,[status(thm)],[f_1330_3]) ).

fof(f_1331_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_1331_2,plain,
    ! [U_6136,U_6135,U_6134] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6135),U_6136)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6134),U_6135)) ),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

cnf(f_1331_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6135),U_6136)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6134),U_6135)) ),
    inference(clausify,[status(thm)],[f_1331_2]) ).

fof(f_1332_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_1332_2,plain,
    ! [U_6139,U_6138,U_6137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6137),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6139),U_6138)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6137),U_6138)) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

cnf(f_1332_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6137),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6139),U_6138)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6137),U_6138)) ),
    inference(clausify,[status(thm)],[f_1332_2]) ).

fof(f_1333_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_1333_2,plain,
    ! [U_6142,U_6141,U_6140] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6140),U_6142)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6141),U_6142)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6140),U_6141)) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

cnf(f_1333_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6140),U_6142)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6141),U_6142)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6140),U_6141)) ),
    inference(clausify,[status(thm)],[f_1333_2]) ).

fof(f_1334_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_1334_2,plain,
    ! [U_6146,U_6145,U_6144,U_6143] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6143),U_6145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6144),U_6146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6145),U_6146))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6143),U_6144)) ),
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

cnf(f_1334_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6143),U_6145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6144),U_6146)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6145),U_6146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6143),U_6144)) ),
    inference(clausify,[status(thm)],[f_1334_2]) ).

fof(f_1335_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_1335_2,plain,
    ! [U_6149,U_6148,U_6147] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6148),U_6149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6147),U_6148)),U_6149)) ),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

fof(f_1335_3,plain,
    ! [U_6149,U_6148] :
      ( ! [U_6147] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6147),U_6148)),U_6149))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6148),U_6149)) ),
    inference(miniscope,[status(thm)],[f_1335_2]) ).

cnf(f_1335_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_6147),U_6148)),U_6149))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6148),U_6149)) ),
    inference(clausify,[status(thm)],[f_1335_3]) ).

fof(f_1336_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_1336_2,plain,
    ! [U_6152,U_6151,U_6150] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6150),U_6152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6150),U_6151)),U_6152)) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

cnf(f_1336_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6150),U_6152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6150),U_6151)),U_6152)) ),
    inference(clausify,[status(thm)],[f_1336_2]) ).

fof(f_1337_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_1337_2,plain,
    ! [U_6155,U_6154,U_6153] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6154),U_6155))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6153),U_6155)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6153),U_6154)),U_6155)) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

cnf(f_1337_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6153),U_6155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6153),U_6154)),U_6155)) ),
    inference(clausify,[status(thm)],[f_1337_2]) ).

cnf(f_1337_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6154),U_6155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6153),U_6154)),U_6155)) ),
    inference(clausify,[status(thm)],[f_1337_2]) ).

fof(f_1338_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_1338_2,plain,
    ! [U_6158,U_6157,U_6156] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6156),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6158),U_6157)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6156),U_6157)) ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

cnf(f_1338_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6156),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6158),U_6157)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6156),U_6157)) ),
    inference(clausify,[status(thm)],[f_1338_2]) ).

fof(f_1339_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_1339_2,plain,
    ! [U_6161,U_6160,U_6159] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6160),U_6161)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),U_6160)) ),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

cnf(f_1339_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6160),U_6161)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),U_6160)) ),
    inference(clausify,[status(thm)],[f_1339_2]) ).

fof(f_1340_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_1340_2,plain,
    ! [U_6164,U_6163,U_6162] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6162)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6162)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6163),U_6164)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6163),U_6164))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6162)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6162))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6163)) ),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

cnf(f_1340_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6163),U_6164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6162)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6162)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6163)) ),
    inference(clausify,[status(thm)],[f_1340_2]) ).

cnf(f_1340_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_6163),U_6162)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6162)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6163),U_6164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6162),U_6163)) ),
    inference(clausify,[status(thm)],[f_1340_2]) ).

fof(f_1341_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_1341_2,plain,
    ! [U_6167,U_6166,U_6165] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6166),U_6165)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6167),U_6165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6166),U_6167)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6167))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6166)) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

cnf(f_1341_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6166),U_6165)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6167),U_6165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6166),U_6167)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6167))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6166)) ),
    inference(clausify,[status(thm)],[f_1341_2]) ).

fof(f_1342_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_1342_2,plain,
    ! [U_6170,U_6169,U_6168] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6169),U_6168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6170),U_6168)
          | U_6169 != U_6170 )
        & ( U_6169 = U_6170
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6169),U_6168) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6170),U_6168) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6169)) ),
    inference(variable_rename,[status(thm)],[f_1342_1]) ).

cnf(f_1342_3,plain,
    ( U_6169 = U_6170
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6169),U_6168) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6170),U_6168)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6169)) ),
    inference(clausify,[status(thm)],[f_1342_2]) ).

cnf(f_1342_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6169),U_6168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6170),U_6168)
    | U_6169 != U_6170
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6168),U_6169)) ),
    inference(clausify,[status(thm)],[f_1342_2]) ).

fof(f_1343_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_1343_2,plain,
    ! [U_6172,U_6171] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6172),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6172),U_6171)) = U_6171
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6171),U_6172)) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

cnf(f_1343_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6172),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6172),U_6171)) = U_6171
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6171),U_6172)) ),
    inference(clausify,[status(thm)],[f_1343_2]) ).

fof(f_1344_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_1344_2,plain,
    ! [U_6175,U_6174,U_6173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6173),U_6175)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6174),U_6175)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6173),U_6174)) ),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

cnf(f_1344_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6173),U_6175)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6174),U_6175)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6173),U_6174)) ),
    inference(clausify,[status(thm)],[f_1344_2]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_6178,U_6177,U_6176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6178),U_6177)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6178),U_6176)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6176),U_6177)) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

cnf(f_1345_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6178),U_6177)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6178),U_6176)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6176),U_6177)) ),
    inference(clausify,[status(thm)],[f_1345_2]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_6180,U_6179] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6179),U_6180)),U_6179)),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

cnf(f_1346_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6179),U_6180)),U_6179)),
    inference(clausify,[status(thm)],[f_1346_2]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_6184,U_6183,U_6182,U_6181] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6181),U_6183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6184)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6183),U_6184))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6181),U_6182)) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

cnf(f_1347_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6181),U_6183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6184)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6183),U_6184))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6181),U_6182)) ),
    inference(clausify,[status(thm)],[f_1347_2]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_6187,U_6186,U_6185] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6187),U_6185)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6187),U_6186)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6185),U_6186)) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

cnf(f_1348_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6187),U_6185)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6187),U_6186)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6185),U_6186)) ),
    inference(clausify,[status(thm)],[f_1348_2]) ).

fof(f_1349_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_1349_2,plain,
    ! [U_6190,U_6189,U_6188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6188),U_6190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6189),U_6190)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6188),U_6189)) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

cnf(f_1349_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6188),U_6190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6189),U_6190)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6188),U_6189)) ),
    inference(clausify,[status(thm)],[f_1349_2]) ).

fof(f_1350_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_1350_2,plain,
    ! [U_6191] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),U_6191)))),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

cnf(f_1350_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),U_6191)))),
    inference(clausify,[status(thm)],[f_1350_2]) ).

fof(f_1351_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_1351_2,plain,
    ! [U_6192] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6192),U_6192))),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

cnf(f_1351_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6192),U_6192))),
    inference(clausify,[status(thm)],[f_1351_2]) ).

fof(f_1352_1,plain,
    ! [V_m,V_t,V_n,V_s,V_c] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(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))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__nonstrict]) ).

fof(f_1352_2,plain,
    ! [U_6197,U_6196,U_6195,U_6194,U_6193] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_6193),U_6194),U_6197),U_6196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6195),U_6197))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_6193),U_6194),U_6195),U_6196)) ),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

cnf(f_1352_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_6193),U_6194),U_6197),U_6196))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6195),U_6197))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,U_6193),U_6194),U_6195),U_6196)) ),
    inference(clausify,[status(thm)],[f_1352_2]) ).

fof(f_1353_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_1353_2,plain,
    ! [U_6199,U_6198] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6198)),U_6199))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6198),U_6199)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6198),U_6199))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6198)),U_6199)) ) ),
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

fof(f_1353_3,plain,
    ( ! [U_6203,U_6201] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6201)),U_6203))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6201),U_6203)) )
    & ! [U_6202,U_6200] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6200),U_6202))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6200)),U_6202)) ) ),
    inference(miniscope,[status(thm)],[f_1353_2]) ).

cnf(f_1353_4,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6200),U_6202))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6200)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1353_3]) ).

cnf(f_1353_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6201)),U_6203))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6201),U_6203)) ),
    inference(clausify,[status(thm)],[f_1353_3]) ).

fof(f_1354_1,plain,
    ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),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_1354_2,plain,
    ! [U_6206,U_6205,U_6204] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6204,tc_Nat_Onat),U_6205),U_6206)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6204,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6204),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6205)),U_6206),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

cnf(f_1354_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6204,tc_Nat_Onat),U_6205),U_6206)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6204,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6204),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6205)),U_6206),
    inference(clausify,[status(thm)],[f_1354_2]) ).

fof(f_1355_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]) ).

cnf(f_1355_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(clausify,[status(thm)],[f_1355_1]) ).

fof(f_1356_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_1356_2,plain,
    ! [U_6207] :
      ( ( 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_6207)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6207)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6207))
        | ~ 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_6207))) ) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ( ! [U_6209] :
        ( 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_6209)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6209)) )
    & ! [U_6208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6208))
        | ~ 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_6208))) ) ),
    inference(miniscope,[status(thm)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6208))
    | ~ 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_6208))) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

cnf(f_1356_5,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_6209)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6209)) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_6212,U_6211,U_6210] :
      ( 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_6212)),U_6210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6212)),U_6211)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6212))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6210),U_6211)) ),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

cnf(f_1357_3,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_6212)),U_6210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6212)),U_6211)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6212))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6210),U_6211)) ),
    inference(clausify,[status(thm)],[f_1357_2]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_6214,U_6213] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),c_Groups_Ozero__class_Ozero(U_6213)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6213),U_6214)))
      | ~ class_Rings_Olinordered__semidom(U_6213) ),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

cnf(f_1358_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),c_Groups_Ozero__class_Ozero(U_6213)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6213),U_6214)))
    | ~ class_Rings_Olinordered__semidom(U_6213) ),
    inference(clausify,[status(thm)],[f_1358_2]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_6216,U_6215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6215),c_Groups_Ozero__class_Ozero(U_6215)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6215),U_6216)))
      | ~ class_Rings_Olinordered__semidom(U_6215) ),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

cnf(f_1359_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6215),c_Groups_Ozero__class_Ozero(U_6215)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6215),U_6216)))
    | ~ class_Rings_Olinordered__semidom(U_6215) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

fof(f_1360_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_1360_2,plain,
    ! [U_6218,U_6217] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6217),U_6218)),c_Groups_Ozero__class_Ozero(U_6217)))
      | ~ class_Rings_Olinordered__semidom(U_6217) ),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

cnf(f_1360_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6217),U_6218)),c_Groups_Ozero__class_Ozero(U_6217)))
    | ~ class_Rings_Olinordered__semidom(U_6217) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

fof(f_1361_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_1361_2,plain,
    ! [U_6219] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6219),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_6219)
      | ~ class_Rings_Osemiring__1(U_6219) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

cnf(f_1361_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6219),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_6219)
    | ~ class_Rings_Osemiring__1(U_6219) ),
    inference(clausify,[status(thm)],[f_1361_2]) ).

fof(f_1362_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).

fof(f_1362_2,plain,
    ! [U_6222,U_6221,U_6220] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6220),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6221)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6222)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6221),U_6222)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6221),U_6222))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6220),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6221)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6222))) ) )
      | ~ class_Rings_Olinordered__semidom(U_6220) ),
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

cnf(f_1362_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6221),U_6222))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6220),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6221)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6222)))
    | ~ class_Rings_Olinordered__semidom(U_6220) ),
    inference(clausify,[status(thm)],[f_1362_2]) ).

cnf(f_1362_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6220),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6221)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6220),U_6222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6221),U_6222))
    | ~ class_Rings_Olinordered__semidom(U_6220) ),
    inference(clausify,[status(thm)],[f_1362_2]) ).

fof(f_1363_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_1363_2,plain,
    ! [U_6225,U_6224,U_6223] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6223),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6223),U_6224)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6223),U_6225)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6224),U_6225))
      | ~ class_Rings_Olinordered__semidom(U_6223) ),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

cnf(f_1363_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6223),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6223),U_6224)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6223),U_6225)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6224),U_6225))
    | ~ class_Rings_Olinordered__semidom(U_6223) ),
    inference(clausify,[status(thm)],[f_1363_2]) ).

fof(f_1364_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_1364_2,plain,
    ! [U_6228,U_6227,U_6226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6227),U_6228))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6226),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6226),U_6227)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6226),U_6228)))
      | ~ class_Rings_Olinordered__semidom(U_6226) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

cnf(f_1364_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6227),U_6228))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6226),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6226),U_6227)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6226),U_6228)))
    | ~ class_Rings_Olinordered__semidom(U_6226) ),
    inference(clausify,[status(thm)],[f_1364_2]) ).

fof(f_1365_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_1365_2,plain,
    ! [U_6231,U_6230,U_6229] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6230),U_6231)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6229),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),U_6230)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),U_6231))
      | ~ class_Rings_Osemiring__1(U_6229) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

cnf(f_1365_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6230),U_6231)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6229),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),U_6230)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6229),U_6231))
    | ~ class_Rings_Osemiring__1(U_6229) ),
    inference(clausify,[status(thm)],[f_1365_2]) ).

fof(f_1366_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_1366_2,plain,
    ! [U_6233,U_6232] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6232),U_6233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6232)),U_6233)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6232)),U_6233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6232),U_6233)) ) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ( ! [U_6237,U_6235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6235),U_6237))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6235)),U_6237)) )
    & ! [U_6236,U_6234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6234)),U_6236))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6234),U_6236)) ) ),
    inference(miniscope,[status(thm)],[f_1366_2]) ).

cnf(f_1366_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6234)),U_6236))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6234),U_6236)) ),
    inference(clausify,[status(thm)],[f_1366_3]) ).

cnf(f_1366_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6235),U_6237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6235)),U_6237)) ),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_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_1367_2,plain,
    ! [U_6239,U_6238] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6238),hAPP(c_Nat_OSuc,U_6239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6238),U_6239)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6238),U_6239))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6238),hAPP(c_Nat_OSuc,U_6239))) ) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

fof(f_1367_3,plain,
    ( ! [U_6243,U_6241] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6241),hAPP(c_Nat_OSuc,U_6243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6241),U_6243)) )
    & ! [U_6242,U_6240] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6240),U_6242))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6240),hAPP(c_Nat_OSuc,U_6242))) ) ),
    inference(miniscope,[status(thm)],[f_1367_2]) ).

cnf(f_1367_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6240),U_6242))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6240),hAPP(c_Nat_OSuc,U_6242))) ),
    inference(clausify,[status(thm)],[f_1367_3]) ).

cnf(f_1367_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6241),hAPP(c_Nat_OSuc,U_6243)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6241),U_6243)) ),
    inference(clausify,[status(thm)],[f_1367_3]) ).

fof(f_1368_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_1368_2,plain,
    ! [U_6245,U_6244] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6244)),U_6245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6244),U_6245)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6244),U_6245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6244)),U_6245)) ) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

fof(f_1368_3,plain,
    ( ! [U_6249,U_6247] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6247)),U_6249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6247),U_6249)) )
    & ! [U_6248,U_6246] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6246),U_6248))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6246)),U_6248)) ) ),
    inference(miniscope,[status(thm)],[f_1368_2]) ).

cnf(f_1368_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6246),U_6248))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6246)),U_6248)) ),
    inference(clausify,[status(thm)],[f_1368_3]) ).

cnf(f_1368_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6247)),U_6249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6247),U_6249)) ),
    inference(clausify,[status(thm)],[f_1368_3]) ).

fof(f_1369_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_1369_2,plain,
    ! [U_6251,U_6250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6250),hAPP(c_Nat_OSuc,U_6251)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6250),U_6251)) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

cnf(f_1369_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6250),hAPP(c_Nat_OSuc,U_6251)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6250),U_6251)) ),
    inference(clausify,[status(thm)],[f_1369_2]) ).

fof(f_1370_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_1370_2,plain,
    ! [U_6253,U_6252] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6252)),U_6253))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6252),U_6253)) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

cnf(f_1370_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6252)),U_6253))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6252),U_6253)) ),
    inference(clausify,[status(thm)],[f_1370_2]) ).

fof(f_1371_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_1371_2,plain,
    ! [U_6255,U_6254] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6255),hAPP(c_Nat_OSuc,U_6254)))
          | U_6255 != U_6254 )
        & ( U_6255 = U_6254
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6255),hAPP(c_Nat_OSuc,U_6254))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6254),U_6255)) ),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

cnf(f_1371_3,plain,
    ( U_6255 = U_6254
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6255),hAPP(c_Nat_OSuc,U_6254)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6254),U_6255)) ),
    inference(clausify,[status(thm)],[f_1371_2]) ).

cnf(f_1371_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6255),hAPP(c_Nat_OSuc,U_6254)))
    | U_6255 != U_6254
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6254),U_6255)) ),
    inference(clausify,[status(thm)],[f_1371_2]) ).

fof(f_1372_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_1372_2,plain,
    ! [U_6257,U_6256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6256),U_6257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6256)),U_6257)) ),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

cnf(f_1372_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6256),U_6257))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6256)),U_6257)) ),
    inference(clausify,[status(thm)],[f_1372_2]) ).

fof(f_1373_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_1373_2,plain,
    ! [U_6260,U_6259,U_6258] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6259),U_6260)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),U_6259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),U_6260))
      | ~ class_Rings_Osemiring__1(U_6258) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

cnf(f_1373_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6259),U_6260)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),U_6259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6258),U_6260))
    | ~ class_Rings_Osemiring__1(U_6258) ),
    inference(clausify,[status(thm)],[f_1373_2]) ).

fof(f_1374_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_1374_2,plain,
    ! [U_6262,U_6261] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6261),U_6262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6261),U_6262)) ),
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

cnf(f_1374_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6261),U_6262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6261),U_6262)) ),
    inference(clausify,[status(thm)],[f_1374_2]) ).

fof(f_1375_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_1375_2,plain,
    ! [U_6264,U_6263] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6263),U_6264) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6263),U_6264)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6263),U_6264))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6263),U_6264) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ( ! [U_6268,U_6266] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6266),U_6268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6266),U_6268)) )
    & ! [U_6267,U_6265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6265),U_6267))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6265),U_6267) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6265),U_6267))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6265),U_6267) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

cnf(f_1375_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6266),U_6268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6266),U_6268)) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_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_1376_2,plain,
    ! [U_6270,U_6269] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6270)),U_6269) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6270),U_6269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6269),U_6270)) ),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

cnf(f_1376_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6270)),U_6269) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6270),U_6269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6269),U_6270)) ),
    inference(clausify,[status(thm)],[f_1376_2]) ).

fof(f_1377_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_1377_2,plain,
    ! [U_6273,U_6272,U_6271] :
      ( ( 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_6271)),U_6272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6271)),U_6273)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6272),U_6273)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6272),U_6273))
        | ~ 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_6271)),U_6272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6271)),U_6273))) ) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

fof(f_1377_3,plain,
    ( ! [U_6279,U_6277] :
        ( ! [U_6275] : 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_6275)),U_6277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6275)),U_6279)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6277),U_6279)) )
    & ! [U_6278,U_6276] :
        ( ! [U_6274] : ~ 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_6274)),U_6276)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6274)),U_6278)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6276),U_6278)) ) ),
    inference(miniscope,[status(thm)],[f_1377_2]) ).

cnf(f_1377_4,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_6274)),U_6276)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6274)),U_6278)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6276),U_6278)) ),
    inference(clausify,[status(thm)],[f_1377_3]) ).

cnf(f_1377_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_6275)),U_6277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6275)),U_6279)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6277),U_6279)) ),
    inference(clausify,[status(thm)],[f_1377_3]) ).

fof(f_1378_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_1378_2,plain,
    ! [U_6282,U_6281,U_6280] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6281),U_6280)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6282),U_6280)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6281),U_6282)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6281),U_6282))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6281),U_6280)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6282),U_6280))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6281)) ),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

cnf(f_1378_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6281),U_6282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6281),U_6280)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6282),U_6280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6281)) ),
    inference(clausify,[status(thm)],[f_1378_2]) ).

cnf(f_1378_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6281),U_6280)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6282),U_6280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6281),U_6282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6280),U_6281)) ),
    inference(clausify,[status(thm)],[f_1378_2]) ).

fof(f_1379_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_1379_2,plain,
    ! [U_6285,U_6284,U_6283] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6283),U_6285)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6284),U_6285)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6285),U_6283))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6283),U_6284)) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

cnf(f_1379_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6283),U_6285)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6284),U_6285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6285),U_6283))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6283),U_6284)) ),
    inference(clausify,[status(thm)],[f_1379_2]) ).

fof(f_1380_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_1380_2,plain,
    ! [U_6288,U_6287,U_6286] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6287),U_6288)),U_6286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6287),U_6286)),U_6288)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6286),U_6287)) ),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

cnf(f_1380_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6287),U_6288)),U_6286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6287),U_6286)),U_6288)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6286),U_6287)) ),
    inference(clausify,[status(thm)],[f_1380_2]) ).

fof(f_1381_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_1381_2,plain,
    ! [U_6291,U_6290,U_6289] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6290),U_6289)),U_6291) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6290),U_6291)),U_6289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6289),U_6290)) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

cnf(f_1381_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6290),U_6289)),U_6291) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6290),U_6291)),U_6289)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6289),U_6290)) ),
    inference(clausify,[status(thm)],[f_1381_2]) ).

fof(f_1382_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_1382_2,plain,
    ! [U_6294,U_6293,U_6292] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6294),U_6293)),U_6292) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6294),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6293),U_6292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6292),U_6293)) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

cnf(f_1382_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6294),U_6293)),U_6292) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6294),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6293),U_6292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6292),U_6293)) ),
    inference(clausify,[status(thm)],[f_1382_2]) ).

fof(f_1383_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_1383_2,plain,
    ! [U_6297,U_6296,U_6295] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6296),U_6295) = U_6297
          | U_6296 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6297),U_6295) )
        & ( U_6296 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6297),U_6295)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6296),U_6295) != U_6297 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6295),U_6296)) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

cnf(f_1383_3,plain,
    ( U_6296 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6297),U_6295)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6296),U_6295) != U_6297
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6295),U_6296)) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6296),U_6295) = U_6297
    | U_6296 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6297),U_6295)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6295),U_6296)) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

fof(f_1384_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_1384_2,plain,
    ! [U_6299,U_6298] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6299),U_6298)),U_6298) = U_6299
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6298),U_6299)) ),
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6299),U_6298)),U_6298) = U_6299
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6298),U_6299)) ),
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_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_1385_2,plain,
    ! [U_6302,U_6301,U_6300] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6301),U_6300)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6302),U_6300)),U_6301)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6302),U_6300)),U_6301))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6301),U_6300))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6300),U_6301)) ),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

cnf(f_1385_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6302),U_6300)),U_6301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6301),U_6300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6300),U_6301)) ),
    inference(clausify,[status(thm)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6301),U_6300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6302),U_6300)),U_6301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6300),U_6301)) ),
    inference(clausify,[status(thm)],[f_1385_2]) ).

fof(f_1386_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_1386_2,plain,
    ! [U_6305,U_6304,U_6303] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6304),U_6303)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6305),U_6304)),U_6303)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6303),U_6304)) ),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

cnf(f_1386_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6304),U_6303)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6305),U_6304)),U_6303)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6303),U_6304)) ),
    inference(clausify,[status(thm)],[f_1386_2]) ).

fof(f_1387_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_1387_2,plain,
    ! [U_6307,U_6306] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6307),U_6306)) = U_6307
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6306),U_6307)) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

cnf(f_1387_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6307),U_6306)) = U_6307
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6306),U_6307)) ),
    inference(clausify,[status(thm)],[f_1387_2]) ).

fof(f_1388_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_1388_2,plain,
    ! [U_6310,U_6309,U_6308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6309),U_6310)),U_6308)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6308),U_6309)) ),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

cnf(f_1388_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6309),U_6310)),U_6308)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6308),U_6309)) ),
    inference(clausify,[status(thm)],[f_1388_2]) ).

fof(f_1389_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_1389_2,plain,
    ! [U_6313,U_6312,U_6311] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6311),U_6312)),U_6313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6313),U_6312))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6313),U_6312)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6311),U_6312)),U_6313)) ) ),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

fof(f_1389_3,plain,
    ( ! [U_6319,U_6317,U_6315] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6315),U_6317)),U_6319))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6319),U_6317))) )
    & ! [U_6318,U_6316,U_6314] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6318),U_6316)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6314),U_6316)),U_6318)) ) ),
    inference(miniscope,[status(thm)],[f_1389_2]) ).

cnf(f_1389_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6318),U_6316)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6314),U_6316)),U_6318)) ),
    inference(clausify,[status(thm)],[f_1389_3]) ).

cnf(f_1389_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6315),U_6317)),U_6319))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6319),U_6317))) ),
    inference(clausify,[status(thm)],[f_1389_3]) ).

fof(f_1390_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_1390_2,plain,
    ! [U_6322,U_6321,U_6320] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6322),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6321),U_6320)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6322),U_6320)),U_6321)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6320),U_6321)) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

cnf(f_1390_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6322),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6321),U_6320)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6322),U_6320)),U_6321)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6320),U_6321)) ),
    inference(clausify,[status(thm)],[f_1390_2]) ).

fof(f_1391_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_1391_2,plain,
    ! [U_6323] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6323),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6323)
      | ~ class_Rings_Osemiring__1(U_6323) ),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

cnf(f_1391_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6323),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6323)
    | ~ class_Rings_Osemiring__1(U_6323) ),
    inference(clausify,[status(thm)],[f_1391_2]) ).

fof(f_1392_1,plain,
    ! [V_n_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).

fof(f_1392_2,plain,
    ! [U_6325,U_6324] :
      ( hBOOL(hAPP(hAPP(c_member(U_6324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6324),U_6325)),c_Int_Oring__1__class_OInts(U_6324)))
      | ~ class_Rings_Oring__1(U_6324) ),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

cnf(f_1392_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6324),U_6325)),c_Int_Oring__1__class_OInts(U_6324)))
    | ~ class_Rings_Oring__1(U_6324) ),
    inference(clausify,[status(thm)],[f_1392_2]) ).

fof(f_1393_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_1393_2,plain,
    ! [U_6326] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6326) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6326)),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

cnf(f_1393_3,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6326) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6326)),
    inference(clausify,[status(thm)],[f_1393_2]) ).

fof(f_1394_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).

fof(f_1394_2,plain,
    ! [U_6330,U_6329,U_6328,U_6327] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6328,tc_Nat_Onat),U_6329),U_6330)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6328,U_6327),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6327,U_6328),c_Nat_Osemiring__1__class_Oof__nat(U_6327)),U_6329)),U_6330)
      | ~ class_Rings_Osemiring__1(U_6327) ),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

cnf(f_1394_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6328,tc_Nat_Onat),U_6329),U_6330)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6328,U_6327),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6327,U_6328),c_Nat_Osemiring__1__class_Oof__nat(U_6327)),U_6329)),U_6330)
    | ~ class_Rings_Osemiring__1(U_6327) ),
    inference(clausify,[status(thm)],[f_1394_2]) ).

fof(f_1395_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_1395_2,plain,
    ! [U_6332,U_6331] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6331),hAPP(c_Nat_OSuc,U_6332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6331),c_Groups_Oone__class_Oone(U_6331)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6331),U_6332))
      | ~ class_Rings_Osemiring__1(U_6331) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

cnf(f_1395_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6331),hAPP(c_Nat_OSuc,U_6332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6331),c_Groups_Oone__class_Oone(U_6331)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6331),U_6332))
    | ~ class_Rings_Osemiring__1(U_6331) ),
    inference(clausify,[status(thm)],[f_1395_2]) ).

fof(f_1396_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).

fof(f_1396_2,plain,
    ! [U_6335,U_6334,U_6333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6333),U_6334)),hAPP(c_Finite__Set_Ocard(U_6333),hAPP(hAPP(c_Set_Oinsert(U_6333),U_6335),U_6334))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6333),U_6334)) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

cnf(f_1396_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6333),U_6334)),hAPP(c_Finite__Set_Ocard(U_6333),hAPP(hAPP(c_Set_Oinsert(U_6333),U_6335),U_6334))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6333),U_6334)) ),
    inference(clausify,[status(thm)],[f_1396_2]) ).

fof(f_1397_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_1397_2,plain,
    ! [U_6337,U_6336] :
      ( ( 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_6336),U_6337)))
        | ~ 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_6337))
        | ~ 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_6336)) )
      & ( ( 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_6337))
          & 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_6336)) )
        | ~ 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_6336),U_6337))) ) ),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ( ! [U_6341,U_6339] :
        ( 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_6339),U_6341)))
        | ~ 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_6341))
        | ~ 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_6339)) )
    & ! [U_6340,U_6338] :
        ( ( 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_6340))
          & 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_6338)) )
        | ~ 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_6338),U_6340))) ) ),
    inference(miniscope,[status(thm)],[f_1397_2]) ).

cnf(f_1397_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))),U_6338))
    | ~ 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_6338),U_6340))) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_5,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_6340))
    | ~ 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_6338),U_6340))) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_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_6339),U_6341)))
    | ~ 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_6341))
    | ~ 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_6339)) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

fof(f_1398_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_1398_2,plain,
    ! [U_6344,U_6343,U_6342] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6342),U_6343)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6342),U_6344)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6343),U_6344))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6342)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6343),U_6344))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6342))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6342),U_6343)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6342),U_6344))) ) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ( ! [U_6350,U_6348,U_6346] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6350)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6348),U_6350))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6346)) ) )
    & ! [U_6349,U_6347,U_6345] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6347),U_6349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6345))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6347)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6349))) ) ),
    inference(miniscope,[status(thm)],[f_1398_2]) ).

cnf(f_1398_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6347),U_6349))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6345))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6347)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6349))) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

cnf(f_1398_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6346))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6350))) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

cnf(f_1398_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6348),U_6350))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6346),U_6350))) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

fof(f_1399_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_1399_2,plain,
    ! [U_6353,U_6352,U_6351] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6351),U_6352)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6353),U_6352)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6351),U_6353))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6352)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6351),U_6353))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6352))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6351),U_6352)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6353),U_6352))) ) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ( ! [U_6359,U_6357,U_6355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6359),U_6357)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6355),U_6359))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6357)) ) )
    & ! [U_6358,U_6356,U_6354] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6354),U_6358))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6354),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6358),U_6356))) ) ),
    inference(miniscope,[status(thm)],[f_1399_2]) ).

cnf(f_1399_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6354),U_6358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6354),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6358),U_6356))) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

cnf(f_1399_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6357))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6359),U_6357))) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

cnf(f_1399_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6355),U_6359))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6359),U_6357))) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_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_1400_2,plain,
    ! [U_6362,U_6361,U_6360] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6362)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6361),U_6362)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6361),U_6362))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6362))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360)) ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

cnf(f_1400_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6361),U_6362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6362)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360)) ),
    inference(clausify,[status(thm)],[f_1400_2]) ).

cnf(f_1400_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_6360),U_6361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6360),U_6362)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6361),U_6362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360)) ),
    inference(clausify,[status(thm)],[f_1400_2]) ).

fof(f_1401_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__mono]) ).

fof(f_1401_2,plain,
    ! [U_6365,U_6364,U_6363] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6363),U_6365)),hAPP(c_Finite__Set_Ocard(U_6363),U_6364)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6363,tc_HOL_Obool)),U_6365),U_6364))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6363),U_6364)) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

cnf(f_1401_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6363),U_6365)),hAPP(c_Finite__Set_Ocard(U_6363),U_6364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6363,tc_HOL_Obool)),U_6365),U_6364))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6363),U_6364)) ),
    inference(clausify,[status(thm)],[f_1401_2]) ).

fof(f_1402_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).

fof(f_1402_2,plain,
    ! [U_6368,U_6367,U_6366] :
      ( U_6368 = U_6367
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6366),U_6367)),hAPP(c_Finite__Set_Ocard(U_6366),U_6368)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6366,tc_HOL_Obool)),U_6368),U_6367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6366),U_6367)) ),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

cnf(f_1402_3,plain,
    ( U_6368 = U_6367
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6366),U_6367)),hAPP(c_Finite__Set_Ocard(U_6366),U_6368)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6366,tc_HOL_Obool)),U_6368),U_6367))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6366),U_6367)) ),
    inference(clausify,[status(thm)],[f_1402_2]) ).

fof(f_1403_1,plain,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).

fof(f_1403_2,plain,
    ! [U_6372,U_6371,U_6370,U_6369] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6371),hAPP(c_Set_Oimage(U_6369,U_6371,U_6372),U_6370))),hAPP(c_Finite__Set_Ocard(U_6369),U_6370)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6369),U_6370)) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

cnf(f_1403_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6371),hAPP(c_Set_Oimage(U_6369,U_6371,U_6372),U_6370))),hAPP(c_Finite__Set_Ocard(U_6369),U_6370)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6369),U_6370)) ),
    inference(clausify,[status(thm)],[f_1403_2]) ).

fof(f_1404_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_1404_2,plain,
    ! [U_6375,U_6374,U_6373] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6375),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6374),U_6373))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6375),U_6373)),hAPP(c_Nat_OSuc,U_6374))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6373),U_6374)) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

cnf(f_1404_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6375),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6374),U_6373))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6375),U_6373)),hAPP(c_Nat_OSuc,U_6374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6373),U_6374)) ),
    inference(clausify,[status(thm)],[f_1404_2]) ).

fof(f_1405_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_1405_2,plain,
    ! [U_6378,U_6377,U_6376] :
      ( 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_6377),U_6376))),U_6378) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6376),U_6378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6376),U_6377)) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

cnf(f_1405_3,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_6377),U_6376))),U_6378) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6376),U_6378))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6376),U_6377)) ),
    inference(clausify,[status(thm)],[f_1405_2]) ).

fof(f_1406_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_1406_2,plain,
    ! [U_6383,U_6382,U_6381,U_6380,U_6379] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6379),U_6381)),U_6382) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6381)),U_6383)
          | U_6382 != 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_6380),U_6379)),U_6381)),U_6383) )
        & ( U_6382 = 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_6380),U_6379)),U_6381)),U_6383)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6379),U_6381)),U_6382) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6381)),U_6383) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6379),U_6380)) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

cnf(f_1406_3,plain,
    ( U_6382 = 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_6380),U_6379)),U_6381)),U_6383)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6379),U_6381)),U_6382) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6381)),U_6383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6379),U_6380)) ),
    inference(clausify,[status(thm)],[f_1406_2]) ).

cnf(f_1406_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6379),U_6381)),U_6382) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6381)),U_6383)
    | U_6382 != 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_6380),U_6379)),U_6381)),U_6383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6379),U_6380)) ),
    inference(clausify,[status(thm)],[f_1406_2]) ).

fof(f_1407_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_1407_2,plain,
    ! [U_6388,U_6387,U_6386,U_6385,U_6384] :
      ( 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_6384),U_6386)),U_6387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6386)),U_6388)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6387),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_6385),U_6384)),U_6386)),U_6388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6384),U_6385)) ),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

cnf(f_1407_3,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_6384),U_6386)),U_6387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6386)),U_6388)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6387),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_6385),U_6384)),U_6386)),U_6388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6384),U_6385)) ),
    inference(clausify,[status(thm)],[f_1407_2]) ).

fof(f_1408_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_1408_2,plain,
    ! [U_6393,U_6392,U_6391,U_6390,U_6389] :
      ( ( ( 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_6389),U_6391)),U_6392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6390),U_6391)),U_6393)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6392),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_6390),U_6389)),U_6391)),U_6393))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6392),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_6390),U_6389)),U_6391)),U_6393)))
          | ~ 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_6389),U_6391)),U_6392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6390),U_6391)),U_6393))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6389),U_6390)) ),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

cnf(f_1408_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6392),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_6390),U_6389)),U_6391)),U_6393)))
    | ~ 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_6389),U_6391)),U_6392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6390),U_6391)),U_6393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6389),U_6390)) ),
    inference(clausify,[status(thm)],[f_1408_2]) ).

cnf(f_1408_4,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_6389),U_6391)),U_6392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6390),U_6391)),U_6393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6392),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_6390),U_6389)),U_6391)),U_6393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6389),U_6390)) ),
    inference(clausify,[status(thm)],[f_1408_2]) ).

fof(f_1409_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_1409_2,plain,
    ! [U_6398,U_6397,U_6396,U_6395,U_6394] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6395),U_6396)),U_6397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6394),U_6396)),U_6398)
          | 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_6395),U_6394)),U_6396)),U_6397) != U_6398 )
        & ( 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_6395),U_6394)),U_6396)),U_6397) = U_6398
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6395),U_6396)),U_6397) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6394),U_6396)),U_6398) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6394),U_6395)) ),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

cnf(f_1409_3,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_6395),U_6394)),U_6396)),U_6397) = U_6398
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6395),U_6396)),U_6397) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6394),U_6396)),U_6398)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6394),U_6395)) ),
    inference(clausify,[status(thm)],[f_1409_2]) ).

cnf(f_1409_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6395),U_6396)),U_6397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6394),U_6396)),U_6398)
    | 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_6395),U_6394)),U_6396)),U_6397) != U_6398
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6394),U_6395)) ),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_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_1410_2,plain,
    ! [U_6403,U_6402,U_6401,U_6400,U_6399] :
      ( 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_6400),U_6401)),U_6402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6399),U_6401)),U_6403)) = 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_6400),U_6399)),U_6401)),U_6402)),U_6403)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),U_6400)) ),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

cnf(f_1410_3,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_6400),U_6401)),U_6402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6399),U_6401)),U_6403)) = 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_6400),U_6399)),U_6401)),U_6402)),U_6403)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),U_6400)) ),
    inference(clausify,[status(thm)],[f_1410_2]) ).

fof(f_1411_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_1411_2,plain,
    ! [U_6408,U_6407,U_6406,U_6405,U_6404] :
      ( ( ( 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_6405),U_6406)),U_6407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6404),U_6406)),U_6408)))
          | ~ 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_6405),U_6404)),U_6406)),U_6407)),U_6408)) )
        & ( 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_6405),U_6404)),U_6406)),U_6407)),U_6408))
          | ~ 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_6405),U_6406)),U_6407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6404),U_6406)),U_6408))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6404),U_6405)) ),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

cnf(f_1411_3,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_6405),U_6404)),U_6406)),U_6407)),U_6408))
    | ~ 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_6405),U_6406)),U_6407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6404),U_6406)),U_6408)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6404),U_6405)) ),
    inference(clausify,[status(thm)],[f_1411_2]) ).

cnf(f_1411_4,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_6405),U_6406)),U_6407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6404),U_6406)),U_6408)))
    | ~ 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_6405),U_6404)),U_6406)),U_6407)),U_6408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6404),U_6405)) ),
    inference(clausify,[status(thm)],[f_1411_2]) ).

fof(f_1412_1,plain,
    ! [V_A_2,V_y_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).

fof(f_1412_2,plain,
    ! [U_6412,U_6411,U_6410,U_6409] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,U_6409),hAPP(c_COMBK(U_6409,U_6410),U_6411)),U_6412) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6409),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6409),hAPP(c_Finite__Set_Ocard(U_6410),U_6412))),U_6411)
      | ~ class_Rings_Osemiring__1(U_6409) ),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

cnf(f_1412_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,U_6409),hAPP(c_COMBK(U_6409,U_6410),U_6411)),U_6412) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6409),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6409),hAPP(c_Finite__Set_Ocard(U_6410),U_6412))),U_6411)
    | ~ class_Rings_Osemiring__1(U_6409) ),
    inference(clausify,[status(thm)],[f_1412_2]) ).

fof(f_1413_1,plain,
    ! [V_n_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).

fof(f_1413_2,plain,
    ! [U_6414,U_6413] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6413),U_6414)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6414)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6414))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6413),U_6414))) ) )
      | ~ class_Rings_Olinordered__semidom(U_6413) ),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

cnf(f_1413_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6413),U_6414)))
    | ~ class_Rings_Olinordered__semidom(U_6413) ),
    inference(clausify,[status(thm)],[f_1413_2]) ).

cnf(f_1413_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6413),U_6414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6414))
    | ~ class_Rings_Olinordered__semidom(U_6413) ),
    inference(clausify,[status(thm)],[f_1413_2]) ).

fof(f_1414_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_1414_2,plain,
    ! [U_6419,U_6418,U_6417,U_6416,U_6415] :
      ( ( ( 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_6416),U_6417)),U_6418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6415),U_6417)),U_6419)))
          | ~ 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_6416),U_6415)),U_6417)),U_6418)),U_6419)) )
        & ( 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_6416),U_6415)),U_6417)),U_6418)),U_6419))
          | ~ 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_6416),U_6417)),U_6418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6415),U_6417)),U_6419))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6415),U_6416)) ),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

cnf(f_1414_3,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_6416),U_6415)),U_6417)),U_6418)),U_6419))
    | ~ 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_6416),U_6417)),U_6418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6415),U_6417)),U_6419)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6415),U_6416)) ),
    inference(clausify,[status(thm)],[f_1414_2]) ).

cnf(f_1414_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_6416),U_6417)),U_6418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6415),U_6417)),U_6419)))
    | ~ 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_6416),U_6415)),U_6417)),U_6418)),U_6419))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6415),U_6416)) ),
    inference(clausify,[status(thm)],[f_1414_2]) ).

fof(f_1415_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_1415_2,plain,
    ! [U_6424,U_6423,U_6422,U_6421,U_6420] :
      ( ( ( 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_6420),U_6422)),U_6423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6421),U_6422)),U_6424)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6423),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_6421),U_6420)),U_6422)),U_6424))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6423),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_6421),U_6420)),U_6422)),U_6424)))
          | ~ 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_6420),U_6422)),U_6423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6421),U_6422)),U_6424))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6420),U_6421)) ),
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

cnf(f_1415_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6423),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_6421),U_6420)),U_6422)),U_6424)))
    | ~ 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_6420),U_6422)),U_6423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6421),U_6422)),U_6424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6420),U_6421)) ),
    inference(clausify,[status(thm)],[f_1415_2]) ).

cnf(f_1415_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_6420),U_6422)),U_6423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6421),U_6422)),U_6424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6423),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_6421),U_6420)),U_6422)),U_6424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6420),U_6421)) ),
    inference(clausify,[status(thm)],[f_1415_2]) ).

fof(f_1416_1,plain,
    ! [V_A_2,V_B_2,T_a] :
      ( 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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).

fof(f_1416_2,plain,
    ! [U_6427,U_6426,U_6425] :
      ( 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_6425),U_6427)),hAPP(c_Finite__Set_Ocard(U_6425),U_6426))),hAPP(c_Finite__Set_Ocard(U_6425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6425,tc_HOL_Obool)),U_6427),U_6426))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6425),U_6426)) ),
    inference(variable_rename,[status(thm)],[f_1416_1]) ).

cnf(f_1416_3,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_6425),U_6427)),hAPP(c_Finite__Set_Ocard(U_6425),U_6426))),hAPP(c_Finite__Set_Ocard(U_6425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6425,tc_HOL_Obool)),U_6427),U_6426))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6425),U_6426)) ),
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).

fof(f_1417_2,plain,
    ! [U_6430,U_6429,U_6428] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6428,tc_HOL_Obool)),U_6429),hAPP(hAPP(c_Set_Oinsert(U_6428),U_6430),c_Orderings_Obot__class_Obot(tc_fun(U_6428,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_6428),U_6429)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6428),U_6429)) ),
    inference(variable_rename,[status(thm)],[f_1417_1]) ).

cnf(f_1417_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6428,tc_HOL_Obool)),U_6429),hAPP(hAPP(c_Set_Oinsert(U_6428),U_6430),c_Orderings_Obot__class_Obot(tc_fun(U_6428,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_6428),U_6429)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6428),U_6429)) ),
    inference(clausify,[status(thm)],[f_1417_2]) ).

fof(f_1418_1,plain,
    ! [V_n_2,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).

fof(f_1418_2,plain,
    ! [U_6432,U_6431] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6431),U_6432) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_6431,hAPP(hAPP(c_COMBC(U_6431,U_6431,U_6431),c_Groups_Oplus__class_Oplus(U_6431)),c_Groups_Oone__class_Oone(U_6431)),U_6432,c_Groups_Ozero__class_Ozero(U_6431))
      | ~ class_Rings_Osemiring__1(U_6431) ),
    inference(variable_rename,[status(thm)],[f_1418_1]) ).

cnf(f_1418_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6431),U_6432) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_6431,hAPP(hAPP(c_COMBC(U_6431,U_6431,U_6431),c_Groups_Oplus__class_Oplus(U_6431)),c_Groups_Oone__class_Oone(U_6431)),U_6432,c_Groups_Ozero__class_Ozero(U_6431))
    | ~ class_Rings_Osemiring__1(U_6431) ),
    inference(clausify,[status(thm)],[f_1418_2]) ).

fof(f_1419_1,plain,
    ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_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_a),V_A_2))),V_K_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) )
      | ~ class_Rings_Osemiring__1(T_b)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).

fof(f_1419_2,plain,
    ! [U_6438,U_6437,U_6436,U_6435,U_6434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6435,U_6434),U_6437),U_6436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6434),hAPP(c_Finite__Set_Ocard(U_6435),U_6436))),U_6438)))
      | ? [U_6433] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(U_6437,U_6433)),U_6438))
          & hBOOL(hAPP(hAPP(c_member(U_6435),U_6433),U_6436)) )
      | ~ class_Rings_Osemiring__1(U_6434)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_6434) ),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

fof(f_1419_3,plain,
    ! [U_6438,U_6437,U_6436,U_6435,U_6434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6435,U_6434),U_6437),U_6436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6434),hAPP(c_Finite__Set_Ocard(U_6435),U_6436))),U_6438)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(U_6437,sK123(U_6438,U_6437,U_6436,U_6435,U_6434))),U_6438))
        & hBOOL(hAPP(hAPP(c_member(U_6435),sK123(U_6438,U_6437,U_6436,U_6435,U_6434)),U_6436)) )
      | ~ class_Rings_Osemiring__1(U_6434)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_6434) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_6433,sK123(U_6438,U_6437,U_6436,U_6435,U_6434))],[f_1419_2]) ).

cnf(f_1419_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6435),sK123(U_6438,U_6437,U_6436,U_6435,U_6434)),U_6436))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6435,U_6434),U_6437),U_6436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6434),hAPP(c_Finite__Set_Ocard(U_6435),U_6436))),U_6438)))
    | ~ class_Rings_Osemiring__1(U_6434)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_6434) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

cnf(f_1419_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(U_6437,sK123(U_6438,U_6437,U_6436,U_6435,U_6434))),U_6438))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6434),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6435,U_6434),U_6437),U_6436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6434),hAPP(c_Finite__Set_Ocard(U_6435),U_6436))),U_6438)))
    | ~ class_Rings_Osemiring__1(U_6434)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_6434) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

fof(f_1420_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,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_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).

fof(f_1420_2,plain,
    ! [U_6444,U_6443,U_6442,U_6441,U_6440,U_6439] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6439),U_6440),c_SetInterval_Oord_OgreaterThanAtMost(U_6439,U_6441,U_6442,U_6443,U_6444)))
        | ~ hBOOL(hAPP(hAPP(U_6441,U_6440),U_6444))
        | ~ hBOOL(hAPP(hAPP(U_6442,U_6443),U_6440)) )
      & ( ( hBOOL(hAPP(hAPP(U_6441,U_6440),U_6444))
          & hBOOL(hAPP(hAPP(U_6442,U_6443),U_6440)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6439),U_6440),c_SetInterval_Oord_OgreaterThanAtMost(U_6439,U_6441,U_6442,U_6443,U_6444))) ) ),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

fof(f_1420_3,plain,
    ( ! [U_6456,U_6454,U_6452,U_6450,U_6448] :
        ( ! [U_6446] : hBOOL(hAPP(hAPP(c_member(U_6446),U_6448),c_SetInterval_Oord_OgreaterThanAtMost(U_6446,U_6450,U_6452,U_6454,U_6456)))
        | ~ hBOOL(hAPP(hAPP(U_6450,U_6448),U_6456))
        | ~ hBOOL(hAPP(hAPP(U_6452,U_6454),U_6448)) )
    & ! [U_6455,U_6453,U_6451,U_6449,U_6447] :
        ( ! [U_6445] : ~ hBOOL(hAPP(hAPP(c_member(U_6445),U_6447),c_SetInterval_Oord_OgreaterThanAtMost(U_6445,U_6449,U_6451,U_6453,U_6455)))
        | ( hBOOL(hAPP(hAPP(U_6449,U_6447),U_6455))
          & hBOOL(hAPP(hAPP(U_6451,U_6453),U_6447)) ) ) ),
    inference(miniscope,[status(thm)],[f_1420_2]) ).

cnf(f_1420_4,plain,
    ( hBOOL(hAPP(hAPP(U_6451,U_6453),U_6447))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6445),U_6447),c_SetInterval_Oord_OgreaterThanAtMost(U_6445,U_6449,U_6451,U_6453,U_6455))) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

cnf(f_1420_5,plain,
    ( hBOOL(hAPP(hAPP(U_6449,U_6447),U_6455))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6445),U_6447),c_SetInterval_Oord_OgreaterThanAtMost(U_6445,U_6449,U_6451,U_6453,U_6455))) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

cnf(f_1420_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6446),U_6448),c_SetInterval_Oord_OgreaterThanAtMost(U_6446,U_6450,U_6452,U_6454,U_6456)))
    | ~ hBOOL(hAPP(hAPP(U_6450,U_6448),U_6456))
    | ~ hBOOL(hAPP(hAPP(U_6452,U_6454),U_6448)) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

fof(f_1421_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,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_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).

fof(f_1421_2,plain,
    ! [U_6462,U_6461,U_6460,U_6459,U_6458,U_6457] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6457),U_6458),c_SetInterval_Oord_OatLeastLessThan(U_6457,U_6459,U_6460,U_6461,U_6462)))
        | ~ hBOOL(hAPP(hAPP(U_6460,U_6458),U_6462))
        | ~ hBOOL(hAPP(hAPP(U_6459,U_6461),U_6458)) )
      & ( ( hBOOL(hAPP(hAPP(U_6460,U_6458),U_6462))
          & hBOOL(hAPP(hAPP(U_6459,U_6461),U_6458)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6457),U_6458),c_SetInterval_Oord_OatLeastLessThan(U_6457,U_6459,U_6460,U_6461,U_6462))) ) ),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

fof(f_1421_3,plain,
    ( ! [U_6474,U_6472,U_6470,U_6468,U_6466] :
        ( ! [U_6464] : hBOOL(hAPP(hAPP(c_member(U_6464),U_6466),c_SetInterval_Oord_OatLeastLessThan(U_6464,U_6468,U_6470,U_6472,U_6474)))
        | ~ hBOOL(hAPP(hAPP(U_6470,U_6466),U_6474))
        | ~ hBOOL(hAPP(hAPP(U_6468,U_6472),U_6466)) )
    & ! [U_6473,U_6471,U_6469,U_6467,U_6465] :
        ( ! [U_6463] : ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6465),c_SetInterval_Oord_OatLeastLessThan(U_6463,U_6467,U_6469,U_6471,U_6473)))
        | ( hBOOL(hAPP(hAPP(U_6469,U_6465),U_6473))
          & hBOOL(hAPP(hAPP(U_6467,U_6471),U_6465)) ) ) ),
    inference(miniscope,[status(thm)],[f_1421_2]) ).

cnf(f_1421_4,plain,
    ( hBOOL(hAPP(hAPP(U_6467,U_6471),U_6465))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6465),c_SetInterval_Oord_OatLeastLessThan(U_6463,U_6467,U_6469,U_6471,U_6473))) ),
    inference(clausify,[status(thm)],[f_1421_3]) ).

cnf(f_1421_5,plain,
    ( hBOOL(hAPP(hAPP(U_6469,U_6465),U_6473))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6465),c_SetInterval_Oord_OatLeastLessThan(U_6463,U_6467,U_6469,U_6471,U_6473))) ),
    inference(clausify,[status(thm)],[f_1421_3]) ).

cnf(f_1421_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6464),U_6466),c_SetInterval_Oord_OatLeastLessThan(U_6464,U_6468,U_6470,U_6472,U_6474)))
    | ~ hBOOL(hAPP(hAPP(U_6470,U_6466),U_6474))
    | ~ hBOOL(hAPP(hAPP(U_6468,U_6472),U_6466)) ),
    inference(clausify,[status(thm)],[f_1421_3]) ).

fof(f_1422_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,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_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).

fof(f_1422_2,plain,
    ! [U_6479,U_6478,U_6477,U_6476,U_6475] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6475),U_6476),c_SetInterval_Oord_OgreaterThanLessThan(U_6475,U_6477,U_6478,U_6479)))
        | ~ hBOOL(hAPP(hAPP(U_6477,U_6476),U_6479))
        | ~ hBOOL(hAPP(hAPP(U_6477,U_6478),U_6476)) )
      & ( ( hBOOL(hAPP(hAPP(U_6477,U_6476),U_6479))
          & hBOOL(hAPP(hAPP(U_6477,U_6478),U_6476)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6475),U_6476),c_SetInterval_Oord_OgreaterThanLessThan(U_6475,U_6477,U_6478,U_6479))) ) ),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

fof(f_1422_3,plain,
    ( ! [U_6489,U_6487,U_6485,U_6483] :
        ( ! [U_6481] : hBOOL(hAPP(hAPP(c_member(U_6481),U_6483),c_SetInterval_Oord_OgreaterThanLessThan(U_6481,U_6485,U_6487,U_6489)))
        | ~ hBOOL(hAPP(hAPP(U_6485,U_6483),U_6489))
        | ~ hBOOL(hAPP(hAPP(U_6485,U_6487),U_6483)) )
    & ! [U_6488,U_6486,U_6484,U_6482] :
        ( ! [U_6480] : ~ hBOOL(hAPP(hAPP(c_member(U_6480),U_6482),c_SetInterval_Oord_OgreaterThanLessThan(U_6480,U_6484,U_6486,U_6488)))
        | ( hBOOL(hAPP(hAPP(U_6484,U_6482),U_6488))
          & hBOOL(hAPP(hAPP(U_6484,U_6486),U_6482)) ) ) ),
    inference(miniscope,[status(thm)],[f_1422_2]) ).

cnf(f_1422_4,plain,
    ( hBOOL(hAPP(hAPP(U_6484,U_6486),U_6482))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6480),U_6482),c_SetInterval_Oord_OgreaterThanLessThan(U_6480,U_6484,U_6486,U_6488))) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

cnf(f_1422_5,plain,
    ( hBOOL(hAPP(hAPP(U_6484,U_6482),U_6488))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6480),U_6482),c_SetInterval_Oord_OgreaterThanLessThan(U_6480,U_6484,U_6486,U_6488))) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

cnf(f_1422_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6481),U_6483),c_SetInterval_Oord_OgreaterThanLessThan(U_6481,U_6485,U_6487,U_6489)))
    | ~ hBOOL(hAPP(hAPP(U_6485,U_6483),U_6489))
    | ~ hBOOL(hAPP(hAPP(U_6485,U_6487),U_6483)) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

fof(f_1423_1,plain,
    ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,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_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).

fof(f_1423_2,plain,
    ! [U_6494,U_6493,U_6492,U_6491,U_6490] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6490),U_6491),c_SetInterval_Oord_OatLeastAtMost(U_6490,U_6492,U_6493,U_6494)))
        | ~ hBOOL(hAPP(hAPP(U_6492,U_6491),U_6494))
        | ~ hBOOL(hAPP(hAPP(U_6492,U_6493),U_6491)) )
      & ( ( hBOOL(hAPP(hAPP(U_6492,U_6491),U_6494))
          & hBOOL(hAPP(hAPP(U_6492,U_6493),U_6491)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6490),U_6491),c_SetInterval_Oord_OatLeastAtMost(U_6490,U_6492,U_6493,U_6494))) ) ),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

fof(f_1423_3,plain,
    ( ! [U_6504,U_6502,U_6500,U_6498] :
        ( ! [U_6496] : hBOOL(hAPP(hAPP(c_member(U_6496),U_6498),c_SetInterval_Oord_OatLeastAtMost(U_6496,U_6500,U_6502,U_6504)))
        | ~ hBOOL(hAPP(hAPP(U_6500,U_6498),U_6504))
        | ~ hBOOL(hAPP(hAPP(U_6500,U_6502),U_6498)) )
    & ! [U_6503,U_6501,U_6499,U_6497] :
        ( ! [U_6495] : ~ hBOOL(hAPP(hAPP(c_member(U_6495),U_6497),c_SetInterval_Oord_OatLeastAtMost(U_6495,U_6499,U_6501,U_6503)))
        | ( hBOOL(hAPP(hAPP(U_6499,U_6497),U_6503))
          & hBOOL(hAPP(hAPP(U_6499,U_6501),U_6497)) ) ) ),
    inference(miniscope,[status(thm)],[f_1423_2]) ).

cnf(f_1423_4,plain,
    ( hBOOL(hAPP(hAPP(U_6499,U_6501),U_6497))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6495),U_6497),c_SetInterval_Oord_OatLeastAtMost(U_6495,U_6499,U_6501,U_6503))) ),
    inference(clausify,[status(thm)],[f_1423_3]) ).

cnf(f_1423_5,plain,
    ( hBOOL(hAPP(hAPP(U_6499,U_6497),U_6503))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6495),U_6497),c_SetInterval_Oord_OatLeastAtMost(U_6495,U_6499,U_6501,U_6503))) ),
    inference(clausify,[status(thm)],[f_1423_3]) ).

cnf(f_1423_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6496),U_6498),c_SetInterval_Oord_OatLeastAtMost(U_6496,U_6500,U_6502,U_6504)))
    | ~ hBOOL(hAPP(hAPP(U_6500,U_6498),U_6504))
    | ~ hBOOL(hAPP(hAPP(U_6500,U_6502),U_6498)) ),
    inference(clausify,[status(thm)],[f_1423_3]) ).

fof(f_1424_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,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_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).

fof(f_1424_2,plain,
    ! [U_6508,U_6507,U_6506,U_6505] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6505),U_6506),c_SetInterval_Oord_OgreaterThan(U_6505,U_6507,U_6508)))
        | ~ hBOOL(hAPP(hAPP(U_6507,U_6508),U_6506)) )
      & ( hBOOL(hAPP(hAPP(U_6507,U_6508),U_6506))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6505),U_6506),c_SetInterval_Oord_OgreaterThan(U_6505,U_6507,U_6508))) ) ),
    inference(variable_rename,[status(thm)],[f_1424_1]) ).

fof(f_1424_3,plain,
    ( ! [U_6516,U_6514,U_6512] :
        ( ! [U_6510] : hBOOL(hAPP(hAPP(c_member(U_6510),U_6512),c_SetInterval_Oord_OgreaterThan(U_6510,U_6514,U_6516)))
        | ~ hBOOL(hAPP(hAPP(U_6514,U_6516),U_6512)) )
    & ! [U_6515,U_6513,U_6511] :
        ( ! [U_6509] : ~ hBOOL(hAPP(hAPP(c_member(U_6509),U_6511),c_SetInterval_Oord_OgreaterThan(U_6509,U_6513,U_6515)))
        | hBOOL(hAPP(hAPP(U_6513,U_6515),U_6511)) ) ),
    inference(miniscope,[status(thm)],[f_1424_2]) ).

cnf(f_1424_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6509),U_6511),c_SetInterval_Oord_OgreaterThan(U_6509,U_6513,U_6515)))
    | hBOOL(hAPP(hAPP(U_6513,U_6515),U_6511)) ),
    inference(clausify,[status(thm)],[f_1424_3]) ).

cnf(f_1424_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6510),U_6512),c_SetInterval_Oord_OgreaterThan(U_6510,U_6514,U_6516)))
    | ~ hBOOL(hAPP(hAPP(U_6514,U_6516),U_6512)) ),
    inference(clausify,[status(thm)],[f_1424_3]) ).

fof(f_1425_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_1425_2,plain,
    ! [U_6517] : 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_6517))),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

cnf(f_1425_3,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_6517))),
    inference(clausify,[status(thm)],[f_1425_2]) ).

fof(f_1426_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_1426_2,plain,
    ! [U_6520,U_6519,U_6518] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6520),U_6518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6520),U_6519)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6518),U_6519)) ),
    inference(variable_rename,[status(thm)],[f_1426_1]) ).

cnf(f_1426_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6520),U_6518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6520),U_6519)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6518),U_6519)) ),
    inference(clausify,[status(thm)],[f_1426_2]) ).

fof(f_1427_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_1427_2,plain,
    ! [U_6524,U_6523] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6523),U_6524))
        | ! [U_6522] : U_6524 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6523),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522)) )
      & ( ? [U_6521] : U_6524 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6523),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6523),U_6524)) ) ),
    inference(variable_rename,[status(thm)],[f_1427_1]) ).

fof(f_1427_3,plain,
    ( ! [U_6528,U_6526] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),U_6528))
        | ! [U_6522] : U_6528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6526),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522)) )
    & ! [U_6527,U_6525] :
        ( ? [U_6521] : U_6527 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6525),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6525),U_6527)) ) ),
    inference(miniscope,[status(thm)],[f_1427_2]) ).

fof(f_1427_4,plain,
    ( ! [U_6528,U_6526] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),U_6528))
        | ! [U_6522] : U_6528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6526),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522)) )
    & ! [U_6527,U_6525] :
        ( U_6527 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6525),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK124(U_6527,U_6525)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6525),U_6527)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_6521,sK124(U_6527,U_6525))],[f_1427_3]) ).

cnf(f_1427_5,plain,
    ( U_6527 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6525),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK124(U_6527,U_6525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6525),U_6527)) ),
    inference(clausify,[status(thm)],[f_1427_4]) ).

cnf(f_1427_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),U_6528))
    | U_6528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6526),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6522)) ),
    inference(clausify,[status(thm)],[f_1427_4]) ).

fof(f_1428_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_1428_2,plain,
    ! [U_6530,U_6529] :
      ( U_6529 = U_6530
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6530),U_6529))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6529),U_6530)) ),
    inference(variable_rename,[status(thm)],[f_1428_1]) ).

cnf(f_1428_3,plain,
    ( U_6529 = U_6530
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6530),U_6529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6529),U_6530)) ),
    inference(clausify,[status(thm)],[f_1428_2]) ).

fof(f_1429_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_1429_2,plain,
    ! [U_6533,U_6532,U_6531] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6531),U_6533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6532),U_6533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6531),U_6532)) ),
    inference(variable_rename,[status(thm)],[f_1429_1]) ).

cnf(f_1429_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6531),U_6533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6532),U_6533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6531),U_6532)) ),
    inference(clausify,[status(thm)],[f_1429_2]) ).

fof(f_1430_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_1430_2,plain,
    ! [U_6535,U_6534] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6534)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6535)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6534),U_6535)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6534),U_6535))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6534)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6535))) ) ),
    inference(variable_rename,[status(thm)],[f_1430_1]) ).

fof(f_1430_3,plain,
    ( ! [U_6539,U_6537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6537)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6539)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6537),U_6539)) )
    & ! [U_6538,U_6536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6536),U_6538))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6536)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538))) ) ),
    inference(miniscope,[status(thm)],[f_1430_2]) ).

cnf(f_1430_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6536),U_6538))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6536)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538))) ),
    inference(clausify,[status(thm)],[f_1430_3]) ).

cnf(f_1430_5,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_6537)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6539)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6537),U_6539)) ),
    inference(clausify,[status(thm)],[f_1430_3]) ).

fof(f_1431_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_1431_2,plain,
    ! [U_6541,U_6540] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6541),U_6540))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6540),U_6541)) ),
    inference(variable_rename,[status(thm)],[f_1431_1]) ).

cnf(f_1431_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6541),U_6540))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6540),U_6541)) ),
    inference(clausify,[status(thm)],[f_1431_2]) ).

fof(f_1432_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_1432_2,plain,
    ! [U_6542] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6542),U_6542)),
    inference(variable_rename,[status(thm)],[f_1432_1]) ).

cnf(f_1432_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6542),U_6542)),
    inference(clausify,[status(thm)],[f_1432_2]) ).

fof(f_1433_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_1433_2,plain,
    ! [U_6544,U_6543] :
      ( U_6543 = U_6544
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6544),U_6543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6543),U_6544)) ),
    inference(variable_rename,[status(thm)],[f_1433_1]) ).

cnf(f_1433_3,plain,
    ( U_6543 = U_6544
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6544),U_6543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6543),U_6544)) ),
    inference(clausify,[status(thm)],[f_1433_2]) ).

fof(f_1434_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_1434_2,plain,
    ! [U_6547,U_6546,U_6545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6545),U_6547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6546),U_6547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6545),U_6546)) ),
    inference(variable_rename,[status(thm)],[f_1434_1]) ).

cnf(f_1434_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6545),U_6547))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6546),U_6547))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6545),U_6546)) ),
    inference(clausify,[status(thm)],[f_1434_2]) ).

fof(f_1435_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_1435_2,plain,
    ! [U_6549,U_6548] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6548),U_6549))
      | U_6548 != U_6549 ),
    inference(variable_rename,[status(thm)],[f_1435_1]) ).

cnf(f_1435_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6548),U_6549))
    | U_6548 != U_6549 ),
    inference(clausify,[status(thm)],[f_1435_2]) ).

fof(f_1436_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_1436_2,plain,
    ! [U_6551,U_6550] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6551),U_6550))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6550),U_6551)) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

cnf(f_1436_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6551),U_6550))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6550),U_6551)) ),
    inference(clausify,[status(thm)],[f_1436_2]) ).

fof(f_1437_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_1437_2,plain,
    ! [U_6552] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6552),U_6552)),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

cnf(f_1437_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6552),U_6552)),
    inference(clausify,[status(thm)],[f_1437_2]) ).

fof(f_1438_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_1438_2,plain,
    ! [U_6554,U_6553] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6553),U_6554))
        | U_6553 = U_6554
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6553),U_6554)) )
      & ( ( U_6553 != U_6554
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6553),U_6554)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6553),U_6554)) ) ),
    inference(variable_rename,[status(thm)],[f_1438_1]) ).

fof(f_1438_3,plain,
    ( ! [U_6558,U_6556] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6556),U_6558))
        | U_6556 = U_6558
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6556),U_6558)) )
    & ! [U_6557,U_6555] :
        ( ( U_6555 != U_6557
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6555),U_6557)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6555),U_6557)) ) ),
    inference(miniscope,[status(thm)],[f_1438_2]) ).

cnf(f_1438_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6555),U_6557))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6555),U_6557)) ),
    inference(clausify,[status(thm)],[f_1438_3]) ).

cnf(f_1438_5,plain,
    ( U_6555 != U_6557
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6555),U_6557)) ),
    inference(clausify,[status(thm)],[f_1438_3]) ).

cnf(f_1438_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6556),U_6558))
    | U_6556 = U_6558
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6556),U_6558)) ),
    inference(clausify,[status(thm)],[f_1438_3]) ).

fof(f_1439_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_1439_2,plain,
    ! [U_6562,U_6561,U_6560,U_6559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6559),U_6561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6560),U_6562)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),U_6562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6559),U_6560)) ),
    inference(variable_rename,[status(thm)],[f_1439_1]) ).

cnf(f_1439_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6559),U_6561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6560),U_6562)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),U_6562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6559),U_6560)) ),
    inference(clausify,[status(thm)],[f_1439_2]) ).

fof(f_1440_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_1440_2,plain,
    ! [U_6564,U_6563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6563),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6563),U_6564)) ),
    inference(variable_rename,[status(thm)],[f_1440_1]) ).

cnf(f_1440_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6563),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6564))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6563),U_6564)) ),
    inference(clausify,[status(thm)],[f_1440_2]) ).

fof(f_1441_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_1441_2,plain,
    ! [U_6566,U_6565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6565),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6566)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6565),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6566)) ) ),
    inference(variable_rename,[status(thm)],[f_1441_1]) ).

fof(f_1441_3,plain,
    ( ! [U_6570,U_6568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6568),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6570))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6570)) )
    & ! [U_6569,U_6567] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6567),U_6569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6567),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6569)) ) ),
    inference(miniscope,[status(thm)],[f_1441_2]) ).

cnf(f_1441_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6567),U_6569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6567),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6569)) ),
    inference(clausify,[status(thm)],[f_1441_3]) ).

cnf(f_1441_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6568),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6570))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6570)) ),
    inference(clausify,[status(thm)],[f_1441_3]) ).

fof(f_1442_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_1442_2,plain,
    ! [U_6572,U_6571] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6572),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6571),U_6572)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6571),U_6572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6572),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1442_1]) ).

fof(f_1442_3,plain,
    ( ! [U_6576,U_6574] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6576),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6574),U_6576)) )
    & ! [U_6575,U_6573] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6573),U_6575))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6575),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1442_2]) ).

cnf(f_1442_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6573),U_6575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6575),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1442_3]) ).

cnf(f_1442_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6576),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6574),U_6576)) ),
    inference(clausify,[status(thm)],[f_1442_3]) ).

fof(f_1443_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_1443_2,plain,
    ! [U_6578,U_6577] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6578),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6577),U_6578)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6577),U_6578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6578),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

fof(f_1443_3,plain,
    ( ! [U_6582,U_6580] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6582),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6580),U_6582)) )
    & ! [U_6581,U_6579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6579),U_6581))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6581),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1443_2]) ).

cnf(f_1443_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6579),U_6581))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6581),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1443_3]) ).

cnf(f_1443_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6582),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6580),U_6582)) ),
    inference(clausify,[status(thm)],[f_1443_3]) ).

fof(f_1444_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_1444_2,plain,
    ! [U_6583] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6583)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6583)) ) ),
    inference(variable_rename,[status(thm)],[f_1444_1]) ).

fof(f_1444_3,plain,
    ( ! [U_6585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6585)) )
    & ! [U_6584] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6584))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6584)) ) ),
    inference(miniscope,[status(thm)],[f_1444_2]) ).

cnf(f_1444_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6584)) ),
    inference(clausify,[status(thm)],[f_1444_3]) ).

cnf(f_1444_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6585))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6585)) ),
    inference(clausify,[status(thm)],[f_1444_3]) ).

fof(f_1445_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_1445_2,plain,
    ! [U_6586] :
      ( 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_6586)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6586)) ),
    inference(variable_rename,[status(thm)],[f_1445_1]) ).

cnf(f_1445_3,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_6586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6586)) ),
    inference(clausify,[status(thm)],[f_1445_2]) ).

fof(f_1446_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_1446_2,plain,
    ! [U_6587] :
      ( ( 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_6587)),U_6587)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6587),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6587),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_6587)),U_6587)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

fof(f_1446_3,plain,
    ( ! [U_6589] :
        ( 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_6589)),U_6589)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6589),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6588),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_6588)),U_6588)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1446_2]) ).

cnf(f_1446_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6588),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_6588)),U_6588)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

cnf(f_1446_5,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_6589)),U_6589)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6589),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

fof(f_1447_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_1447_2,plain,
    ! [U_6592,U_6591,U_6590] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6592),U_6590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6592),U_6591)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6592))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6590),U_6591)) ),
    inference(variable_rename,[status(thm)],[f_1447_1]) ).

cnf(f_1447_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6592),U_6590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6592),U_6591)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6592))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6590),U_6591)) ),
    inference(clausify,[status(thm)],[f_1447_2]) ).

fof(f_1448_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_1448_2,plain,
    ! [U_6594,U_6593] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6593),U_6594) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_6594 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_6593 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_6594 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_6593 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6593),U_6594) != 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_6593)) ),
    inference(variable_rename,[status(thm)],[f_1448_1]) ).

cnf(f_1448_3,plain,
    ( U_6593 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6593),U_6594) != 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_6593)) ),
    inference(clausify,[status(thm)],[f_1448_2]) ).

cnf(f_1448_4,plain,
    ( U_6594 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6593),U_6594) != 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_6593)) ),
    inference(clausify,[status(thm)],[f_1448_2]) ).

cnf(f_1448_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6593),U_6594) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6594 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6593 != 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_6593)) ),
    inference(clausify,[status(thm)],[f_1448_2]) ).

fof(f_1449_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]) ).

cnf(f_1449_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(clausify,[status(thm)],[f_1449_1]) ).

fof(f_1450_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_1450_2,plain,
    ! [U_6595] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6595)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1450_1]) ).

cnf(f_1450_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6595)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1450_2]) ).

fof(f_1451_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_1451_2,plain,
    ! [U_6597,U_6596] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6596),U_6597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6596),U_6597)),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_6596),U_6597)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6596),U_6597)) ) ),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

fof(f_1451_3,plain,
    ( ! [U_6601,U_6599] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6599),U_6601))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6599),U_6601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6600,U_6598] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6598),U_6600)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6598),U_6600)) ) ),
    inference(miniscope,[status(thm)],[f_1451_2]) ).

cnf(f_1451_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6598),U_6600)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6598),U_6600)) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

cnf(f_1451_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6599),U_6601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6599),U_6601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

fof(f_1452_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_1452_2,plain,
    ! [U_6603,U_6602] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6603),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_6602 != U_6603
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6602),U_6603)) ) )
      & ( U_6602 = U_6603
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6602),U_6603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6603),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

fof(f_1452_3,plain,
    ( ! [U_6607,U_6605] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6607),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_6605 != U_6607
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6605),U_6607)) ) )
    & ! [U_6606,U_6604] :
        ( U_6604 = U_6606
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6604),U_6606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6606),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1452_2]) ).

cnf(f_1452_4,plain,
    ( U_6604 = U_6606
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6604),U_6606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6606),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

cnf(f_1452_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6605),U_6607))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6607),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

cnf(f_1452_6,plain,
    ( U_6605 != U_6607
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6607),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

fof(f_1453_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_1453_2,plain,
    ! [U_6610,U_6609,U_6608] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6608),U_6610)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6609),U_6610)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6608),U_6609)) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

cnf(f_1453_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6608),U_6610)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6609),U_6610)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6608),U_6609)) ),
    inference(clausify,[status(thm)],[f_1453_2]) ).

fof(f_1454_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_1454_2,plain,
    ! [U_6612,U_6611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6612),U_6611))
      | U_6611 = U_6612
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6611),U_6612)) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

cnf(f_1454_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6612),U_6611))
    | U_6611 = U_6612
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6611),U_6612)) ),
    inference(clausify,[status(thm)],[f_1454_2]) ).

fof(f_1455_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_1455_2,plain,
    ! [U_6614,U_6613] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6613) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6614)
        | U_6613 != U_6614 )
      & ( U_6613 = U_6614
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6613) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6614) ) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

fof(f_1455_3,plain,
    ( ! [U_6618,U_6616] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6616) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6618)
        | U_6616 != U_6618 )
    & ! [U_6617,U_6615] :
        ( U_6615 = U_6617
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6615) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6617) ) ),
    inference(miniscope,[status(thm)],[f_1455_2]) ).

cnf(f_1455_4,plain,
    ( U_6615 = U_6617
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6615) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6617) ),
    inference(clausify,[status(thm)],[f_1455_3]) ).

cnf(f_1455_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6616) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6618)
    | U_6616 != U_6618 ),
    inference(clausify,[status(thm)],[f_1455_3]) ).

fof(f_1456_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_1456_2,plain,
    ! [U_6619] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6619) = U_6619,
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

cnf(f_1456_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6619) = U_6619,
    inference(clausify,[status(thm)],[f_1456_2]) ).

fof(f_1457_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_1457_2,plain,
    ! [U_6620] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6620),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6620,
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

cnf(f_1457_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6620),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6620,
    inference(clausify,[status(thm)],[f_1457_2]) ).

fof(f_1458_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_1458_2,plain,
    ! [U_6623,U_6622,U_6621] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6621),U_6622)),U_6623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6621),U_6623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6622),U_6623)),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

cnf(f_1458_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6621),U_6622)),U_6623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6621),U_6623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6622),U_6623)),
    inference(clausify,[status(thm)],[f_1458_2]) ).

fof(f_1459_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_1459_2,plain,
    ! [U_6626,U_6625,U_6624] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6625),U_6626)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),U_6625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),U_6626)),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

cnf(f_1459_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6625),U_6626)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),U_6625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6624),U_6626)),
    inference(clausify,[status(thm)],[f_1459_2]) ).

fof(f_1460_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_1460_2,plain,
    ! [U_6629,U_6628,U_6627] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6627),U_6628)),U_6629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6628),U_6629)),
    inference(variable_rename,[status(thm)],[f_1460_1]) ).

cnf(f_1460_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6627),U_6628)),U_6629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6628),U_6629)),
    inference(clausify,[status(thm)],[f_1460_2]) ).

fof(f_1461_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_1461_2,plain,
    ! [U_6631,U_6630] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6630),U_6631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6631),U_6630),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

cnf(f_1461_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6630),U_6631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6631),U_6630),
    inference(clausify,[status(thm)],[f_1461_2]) ).

fof(f_1462_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_1462_2,plain,
    ! [U_6634,U_6633,U_6632] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6633),U_6634)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),U_6633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),U_6634)),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

cnf(f_1462_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6633),U_6634)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),U_6633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6632),U_6634)),
    inference(clausify,[status(thm)],[f_1462_2]) ).

fof(f_1463_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_1463_2,plain,
    ! [U_6637,U_6636,U_6635] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6635),U_6636)),U_6637) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6635),U_6637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6636),U_6637)),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

cnf(f_1463_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6635),U_6636)),U_6637) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6635),U_6637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6636),U_6637)),
    inference(clausify,[status(thm)],[f_1463_2]) ).

fof(f_1464_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_1464_2,plain,
    ! [U_6638] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6638),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6638,
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

cnf(f_1464_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6638),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6638,
    inference(clausify,[status(thm)],[f_1464_2]) ).

fof(f_1465_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_1465_2,plain,
    ! [U_6639] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6639) = U_6639,
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

cnf(f_1465_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6639) = U_6639,
    inference(clausify,[status(thm)],[f_1465_2]) ).

fof(f_1466_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_1466_2,plain,
    ! [U_6640] : 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_6640)),U_6640) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

cnf(f_1466_3,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_6640)),U_6640) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1466_2]) ).

fof(f_1467_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]) ).

cnf(f_1467_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1467_1]) ).

fof(f_1468_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_1468_2,plain,
    ! [U_6643,U_6642,U_6641] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6641),U_6642)),U_6643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6642),U_6643)),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

cnf(f_1468_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6641),U_6642)),U_6643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6642),U_6643)),
    inference(clausify,[status(thm)],[f_1468_2]) ).

fof(f_1469_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_1469_2,plain,
    ! [U_6646,U_6645,U_6644] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6644),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6645),U_6646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6644),U_6646)),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

cnf(f_1469_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6644),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6645),U_6646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6644),U_6646)),
    inference(clausify,[status(thm)],[f_1469_2]) ).

fof(f_1470_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_1470_2,plain,
    ! [U_6648,U_6647] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6647),U_6648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6648),U_6647),
    inference(variable_rename,[status(thm)],[f_1470_1]) ).

cnf(f_1470_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6647),U_6648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6648),U_6647),
    inference(clausify,[status(thm)],[f_1470_2]) ).

fof(f_1471_1,plain,
    ! [V_i_2,V_inc_2,T_a] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).

fof(f_1471_2,plain,
    ! [U_6651,U_6650,U_6649] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_6649,U_6650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6651) = U_6651
      | ~ class_Rings_Osemiring__1(U_6649) ),
    inference(variable_rename,[status(thm)],[f_1471_1]) ).

cnf(f_1471_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_6649,U_6650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6651) = U_6651
    | ~ class_Rings_Osemiring__1(U_6649) ),
    inference(clausify,[status(thm)],[f_1471_2]) ).

fof(f_1472_1,plain,
    ! [V_i_2,V_n_2,V_inc_2,T_a] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).

fof(f_1472_2,plain,
    ! [U_6655,U_6654,U_6653,U_6652] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_6652,U_6653,hAPP(c_Nat_OSuc,U_6654),U_6655) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_6652,U_6653,U_6654,hAPP(U_6653,U_6655))
      | ~ class_Rings_Osemiring__1(U_6652) ),
    inference(variable_rename,[status(thm)],[f_1472_1]) ).

cnf(f_1472_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_6652,U_6653,hAPP(c_Nat_OSuc,U_6654),U_6655) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_6652,U_6653,U_6654,hAPP(U_6653,U_6655))
    | ~ class_Rings_Osemiring__1(U_6652) ),
    inference(clausify,[status(thm)],[f_1472_2]) ).

fof(f_1473_1,plain,
    ! [V_y_2,V_x_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
          & ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).

fof(f_1473_2,plain,
    ! [U_6658,U_6657,U_6656] :
      ( ( hBOOL(hAPP(U_6656,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6657),U_6658))))
        | ( ~ hBOOL(hAPP(U_6656,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6657),U_6658)) )
        | ( ~ hBOOL(hAPP(U_6656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6657)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6658))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6658),U_6657)) ) )
      & ( ( ( hBOOL(hAPP(U_6656,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6657),U_6658)) )
          & ( hBOOL(hAPP(U_6656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6657)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6658))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6658),U_6657)) ) )
        | ~ hBOOL(hAPP(U_6656,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6657),U_6658)))) ) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

fof(f_1473_3,plain,
    ( ! [U_6664,U_6662,U_6660] :
        ( hBOOL(hAPP(U_6660,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6662),U_6664))))
        | ( ~ hBOOL(hAPP(U_6660,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6662),U_6664)) )
        | ( ~ hBOOL(hAPP(U_6660,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6662)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6664))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6664),U_6662)) ) )
    & ! [U_6663,U_6661,U_6659] :
        ( ( ( hBOOL(hAPP(U_6659,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6661),U_6663)) )
          & ( hBOOL(hAPP(U_6659,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6661)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6663))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6663),U_6661)) ) )
        | ~ hBOOL(hAPP(U_6659,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6661),U_6663)))) ) ),
    inference(miniscope,[status(thm)],[f_1473_2]) ).

cnf(f_1473_4,plain,
    ( hBOOL(hAPP(U_6659,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6661)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6663))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6663),U_6661))
    | ~ hBOOL(hAPP(U_6659,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6661),U_6663)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_5,plain,
    ( hBOOL(hAPP(U_6659,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6661),U_6663))
    | ~ hBOOL(hAPP(U_6659,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6661),U_6663)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6662),U_6664))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6664),U_6662))
    | hBOOL(hAPP(U_6660,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6662),U_6664)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_7,plain,
    ( ~ hBOOL(hAPP(U_6660,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6664),U_6662))
    | hBOOL(hAPP(U_6660,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6662),U_6664)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6662),U_6664))
    | ~ hBOOL(hAPP(U_6660,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6662)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6664))))
    | hBOOL(hAPP(U_6660,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6662),U_6664)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_9,plain,
    ( ~ hBOOL(hAPP(U_6660,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6660,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6662)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6664))))
    | hBOOL(hAPP(U_6660,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6662),U_6664)))) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

fof(f_1474_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_1474_2,plain,
    ! [U_6667,U_6666,U_6665] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6667),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_6666))
      | U_6665 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6665),U_6667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6665)) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

cnf(f_1474_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6667),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_6666))
    | U_6665 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6665),U_6667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6665)) ),
    inference(clausify,[status(thm)],[f_1474_2]) ).

fof(f_1475_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_1475_2,plain,
    ! [U_6670,U_6669,U_6668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6669),U_6668))
      | U_6668 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6668),U_6670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6668)) ),
    inference(variable_rename,[status(thm)],[f_1475_1]) ).

cnf(f_1475_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6669),U_6668))
    | U_6668 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6668),U_6670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6668)) ),
    inference(clausify,[status(thm)],[f_1475_2]) ).

fof(f_1476_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_1476_2,plain,
    ! [U_6676,U_6675,U_6674,U_6673,U_6672,U_6671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6675),U_6672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6674),U_6671))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6674))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6676))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6673),U_6671))
      | ~ 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_6674),U_6675)),U_6676)),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_6671),U_6672)),U_6673) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6674),U_6675)),U_6676) ),
    inference(variable_rename,[status(thm)],[f_1476_1]) ).

cnf(f_1476_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6675),U_6672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6674),U_6671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6674))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6673),U_6671))
    | ~ 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_6674),U_6675)),U_6676)),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_6671),U_6672)),U_6673) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6674),U_6675)),U_6676) ),
    inference(clausify,[status(thm)],[f_1476_2]) ).

fof(f_1477_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_1477_2,plain,
    ! [U_6681,U_6680,U_6679,U_6678,U_6677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6680),U_6678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6677),U_6679))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6677),U_6681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6681),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_6677),U_6678)),U_6679)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6677),U_6680)),U_6681))) ),
    inference(variable_rename,[status(thm)],[f_1477_1]) ).

cnf(f_1477_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6680),U_6678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6677),U_6679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6677),U_6681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6681),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_6677),U_6678)),U_6679)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6677),U_6680)),U_6681))) ),
    inference(clausify,[status(thm)],[f_1477_2]) ).

fof(f_1478_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_1478_2,plain,
    ! [U_6687,U_6686,U_6685,U_6684,U_6683,U_6682] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6683),U_6686))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6685),U_6682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6687),U_6685))
      | ~ 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_6685),U_6686)),U_6687)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6683)),U_6684) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6685),U_6686)),U_6687) ),
    inference(variable_rename,[status(thm)],[f_1478_1]) ).

cnf(f_1478_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6683),U_6686))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6685),U_6682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6687),U_6685))
    | ~ 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_6685),U_6686)),U_6687)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6683)),U_6684) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6685),U_6686)),U_6687) ),
    inference(clausify,[status(thm)],[f_1478_2]) ).

fof(f_1479_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_1479_2,plain,
    ! [U_6690,U_6689,U_6688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6690),U_6688))
      | ~ 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_6688),U_6689)),U_6690))) ),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

cnf(f_1479_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6690),U_6688))
    | ~ 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_6688),U_6689)),U_6690))) ),
    inference(clausify,[status(thm)],[f_1479_2]) ).

fof(f_1480_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_1480_2,plain,
    ! [U_6693,U_6692,U_6691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6692),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_6691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6693))
      | ~ 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_6691),U_6692)),U_6693)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1480_1]) ).

cnf(f_1480_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6692),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_6691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6693))
    | ~ 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_6691),U_6692)),U_6693)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1480_2]) ).

fof(f_1481_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_1481_2,plain,
    ! [U_6698,U_6697,U_6696,U_6695,U_6694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6695),U_6697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6698),U_6694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6696),U_6694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
      | ~ 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_6694),U_6695)),U_6696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6694),U_6697)),U_6698))) ),
    inference(variable_rename,[status(thm)],[f_1481_1]) ).

cnf(f_1481_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6695),U_6697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6698),U_6694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6696),U_6694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
    | ~ 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_6694),U_6695)),U_6696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6694),U_6697)),U_6698))) ),
    inference(clausify,[status(thm)],[f_1481_2]) ).

fof(f_1482_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]) ).

cnf(f_1482_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(clausify,[status(thm)],[f_1482_1]) ).

fof(f_1483_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_1483_2,plain,
    ! [U_6700,U_6699] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6699)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6700)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6699),U_6700)),
    inference(variable_rename,[status(thm)],[f_1483_1]) ).

cnf(f_1483_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6699)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6700)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6699),U_6700)),
    inference(clausify,[status(thm)],[f_1483_2]) ).

fof(f_1484_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_1484_2,plain,
    ! [U_6702,U_6701] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6701)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6702)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6701),U_6702)),
    inference(variable_rename,[status(thm)],[f_1484_1]) ).

cnf(f_1484_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6701)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6702)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6701),U_6702)),
    inference(clausify,[status(thm)],[f_1484_2]) ).

fof(f_1485_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_1485_2,plain,
    ! [U_6704,U_6703] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6703)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6704)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6703),U_6704)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6703),U_6704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6703)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6704))) ) ),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

fof(f_1485_3,plain,
    ( ! [U_6708,U_6706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6706)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6706),U_6708)) )
    & ! [U_6707,U_6705] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6705),U_6707))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6705)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6707))) ) ),
    inference(miniscope,[status(thm)],[f_1485_2]) ).

cnf(f_1485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6705),U_6707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6705)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6707))) ),
    inference(clausify,[status(thm)],[f_1485_3]) ).

cnf(f_1485_5,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_6706)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6708)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6706),U_6708)) ),
    inference(clausify,[status(thm)],[f_1485_3]) ).

fof(f_1486_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_1486_2,plain,
    ! [U_6710,U_6709] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6709)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6710)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6709),U_6710)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6709),U_6710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6709)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6710))) ) ),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

fof(f_1486_3,plain,
    ( ! [U_6714,U_6712] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6712)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6714)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6712),U_6714)) )
    & ! [U_6713,U_6711] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6711),U_6713))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6711)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6713))) ) ),
    inference(miniscope,[status(thm)],[f_1486_2]) ).

cnf(f_1486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6711),U_6713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6711)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6713))) ),
    inference(clausify,[status(thm)],[f_1486_3]) ).

cnf(f_1486_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_6712)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6714)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6712),U_6714)) ),
    inference(clausify,[status(thm)],[f_1486_3]) ).

fof(f_1487_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_1487_2,plain,
    ! [U_6716,U_6715] :
      ( 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_6715),U_6716)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6715)) ),
    inference(variable_rename,[status(thm)],[f_1487_1]) ).

cnf(f_1487_3,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_6715),U_6716)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6715)) ),
    inference(clausify,[status(thm)],[f_1487_2]) ).

fof(f_1488_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_1488_2,plain,
    ! [U_6718,U_6717] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6717),U_6718))
        | ~ 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_6717)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6718))) )
      & ( 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_6717)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6717),U_6718)) ) ),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

fof(f_1488_3,plain,
    ( ! [U_6722,U_6720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6720),U_6722))
        | ~ 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_6720)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6722))) )
    & ! [U_6721,U_6719] :
        ( 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_6719)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6721)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6719),U_6721)) ) ),
    inference(miniscope,[status(thm)],[f_1488_2]) ).

cnf(f_1488_4,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_6719)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6721)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6719),U_6721)) ),
    inference(clausify,[status(thm)],[f_1488_3]) ).

cnf(f_1488_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6720),U_6722))
    | ~ 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_6720)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6722))) ),
    inference(clausify,[status(thm)],[f_1488_3]) ).

fof(f_1489_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_1489_2,plain,
    ! [U_6724,U_6723] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6723),U_6724))
        | ~ 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_6723)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6724))) )
      & ( 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_6723)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6724)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6723),U_6724)) ) ),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

fof(f_1489_3,plain,
    ( ! [U_6728,U_6726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6726),U_6728))
        | ~ 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_6726)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6728))) )
    & ! [U_6727,U_6725] :
        ( 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_6725)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6727)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6725),U_6727)) ) ),
    inference(miniscope,[status(thm)],[f_1489_2]) ).

cnf(f_1489_4,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_6725)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6727)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6725),U_6727)) ),
    inference(clausify,[status(thm)],[f_1489_3]) ).

cnf(f_1489_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6726),U_6728))
    | ~ 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_6726)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6728))) ),
    inference(clausify,[status(thm)],[f_1489_3]) ).

fof(f_1490_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_1490_2,plain,
    ! [U_6730,U_6729] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6729),U_6730))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6729)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6730))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6729)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6730)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6729),U_6730)) ) ),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

fof(f_1490_3,plain,
    ( ! [U_6734,U_6732] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6732),U_6734))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6732)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6734))) )
    & ! [U_6733,U_6731] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6731)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6733)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6731),U_6733)) ) ),
    inference(miniscope,[status(thm)],[f_1490_2]) ).

cnf(f_1490_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6731)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6733)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6731),U_6733)) ),
    inference(clausify,[status(thm)],[f_1490_3]) ).

cnf(f_1490_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6732),U_6734))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6732)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6734))) ),
    inference(clausify,[status(thm)],[f_1490_3]) ).

fof(f_1491_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_1491_2,plain,
    ! [U_6736,U_6735] :
      ( ( U_6735 = U_6736
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6735) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6736) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6735) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6736)
        | U_6735 != U_6736 ) ),
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

fof(f_1491_3,plain,
    ( ! [U_6740,U_6738] :
        ( U_6738 = U_6740
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6738) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6740) )
    & ! [U_6739,U_6737] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6737) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6739)
        | U_6737 != U_6739 ) ),
    inference(miniscope,[status(thm)],[f_1491_2]) ).

cnf(f_1491_4,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6737) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6739)
    | U_6737 != U_6739 ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

cnf(f_1491_5,plain,
    ( U_6738 = U_6740
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6738) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6740) ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

fof(f_1492_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_1492_2,plain,
    ! [U_6742,U_6741] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6741) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6742)
        | U_6741 != U_6742 )
      & ( U_6741 = U_6742
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6741) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6742) ) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

fof(f_1492_3,plain,
    ( ! [U_6746,U_6744] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6744) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6746)
        | U_6744 != U_6746 )
    & ! [U_6745,U_6743] :
        ( U_6743 = U_6745
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6743) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6745) ) ),
    inference(miniscope,[status(thm)],[f_1492_2]) ).

cnf(f_1492_4,plain,
    ( U_6743 = U_6745
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6743) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6745) ),
    inference(clausify,[status(thm)],[f_1492_3]) ).

cnf(f_1492_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6744) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6746)
    | U_6744 != U_6746 ),
    inference(clausify,[status(thm)],[f_1492_3]) ).

fof(f_1493_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]) ).

cnf(f_1493_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(clausify,[status(thm)],[f_1493_1]) ).

fof(f_1494_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]) ).

cnf(f_1494_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(clausify,[status(thm)],[f_1494_1]) ).

fof(f_1495_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_1495_2,plain,
    ! [U_6747] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6747) = 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_6747)),
    inference(variable_rename,[status(thm)],[f_1495_1]) ).

cnf(f_1495_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6747) = 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_6747)),
    inference(clausify,[status(thm)],[f_1495_2]) ).

fof(f_1496_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_1496_2,plain,
    ! [U_6748] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6748))
        | ~ 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_6748))) )
      & ( 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_6748)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6748)) ) ),
    inference(variable_rename,[status(thm)],[f_1496_1]) ).

fof(f_1496_3,plain,
    ( ! [U_6750] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6750))
        | ~ 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_6750))) )
    & ! [U_6749] :
        ( 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_6749)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6749)) ) ),
    inference(miniscope,[status(thm)],[f_1496_2]) ).

cnf(f_1496_4,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_6749)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6749)) ),
    inference(clausify,[status(thm)],[f_1496_3]) ).

cnf(f_1496_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_6750))
    | ~ 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_6750))) ),
    inference(clausify,[status(thm)],[f_1496_3]) ).

fof(f_1497_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]) ).

cnf(f_1497_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(clausify,[status(thm)],[f_1497_1]) ).

fof(f_1498_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_1498_2,plain,
    ! [U_6752,U_6751] :
      ( 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_6751),U_6752)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6752))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6751)) ),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

cnf(f_1498_3,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_6751),U_6752)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6752))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6751)) ),
    inference(clausify,[status(thm)],[f_1498_2]) ).

fof(f_1499_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_1499_2,plain,
    ! [U_6753] : 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_6753))),
    inference(variable_rename,[status(thm)],[f_1499_1]) ).

cnf(f_1499_3,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_6753))),
    inference(clausify,[status(thm)],[f_1499_2]) ).

fof(f_1500_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_1500_2,plain,
    ! [U_6758] :
      ( ( ? [U_6757] :
            ( hBOOL(hAPP(U_6758,U_6757))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6757)) )
        | ! [U_6756] : ~ hBOOL(hAPP(U_6758,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) )
      & ( ? [U_6755] : hBOOL(hAPP(U_6758,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6755)))
        | ! [U_6754] :
            ( ~ hBOOL(hAPP(U_6758,U_6754))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6754)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1500_1]) ).

fof(f_1500_3,plain,
    ( ! [U_6760] :
        ( ? [U_6757] :
            ( hBOOL(hAPP(U_6760,U_6757))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6757)) )
        | ! [U_6756] : ~ hBOOL(hAPP(U_6760,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) )
    & ! [U_6759] :
        ( ? [U_6755] : hBOOL(hAPP(U_6759,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6755)))
        | ! [U_6754] :
            ( ~ hBOOL(hAPP(U_6759,U_6754))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6754)) ) ) ),
    inference(miniscope,[status(thm)],[f_1500_2]) ).

fof(f_1500_4,plain,
    ( ! [U_6760] :
        ( ? [U_6757] :
            ( hBOOL(hAPP(U_6760,U_6757))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6757)) )
        | ! [U_6756] : ~ hBOOL(hAPP(U_6760,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) )
    & ! [U_6759] :
        ( hBOOL(hAPP(U_6759,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK125(U_6759))))
        | ! [U_6754] :
            ( ~ hBOOL(hAPP(U_6759,U_6754))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6754)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_6755,sK125(U_6759))],[f_1500_3]) ).

fof(f_1500_5,plain,
    ( ! [U_6760] :
        ( ( hBOOL(hAPP(U_6760,sK126(U_6760)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_6760))) )
        | ! [U_6756] : ~ hBOOL(hAPP(U_6760,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) )
    & ! [U_6759] :
        ( hBOOL(hAPP(U_6759,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK125(U_6759))))
        | ! [U_6754] :
            ( ~ hBOOL(hAPP(U_6759,U_6754))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6754)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_6757,sK126(U_6760))],[f_1500_4]) ).

cnf(f_1500_6,plain,
    ( hBOOL(hAPP(U_6759,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK125(U_6759))))
    | ~ hBOOL(hAPP(U_6759,U_6754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6754)) ),
    inference(clausify,[status(thm)],[f_1500_5]) ).

cnf(f_1500_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_6760)))
    | ~ hBOOL(hAPP(U_6760,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) ),
    inference(clausify,[status(thm)],[f_1500_5]) ).

cnf(f_1500_8,plain,
    ( hBOOL(hAPP(U_6760,sK126(U_6760)))
    | ~ hBOOL(hAPP(U_6760,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6756))) ),
    inference(clausify,[status(thm)],[f_1500_5]) ).

fof(f_1501_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_1501_2,plain,
    ! [U_6765] :
      ( ( ! [U_6764] :
            ( hBOOL(hAPP(U_6765,U_6764))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) )
        | ? [U_6763] : ~ hBOOL(hAPP(U_6765,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6763))) )
      & ( ! [U_6762] : hBOOL(hAPP(U_6765,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762)))
        | ? [U_6761] :
            ( ~ hBOOL(hAPP(U_6765,U_6761))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6761)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1501_1]) ).

fof(f_1501_3,plain,
    ( ! [U_6767] :
        ( ! [U_6764] :
            ( hBOOL(hAPP(U_6767,U_6764))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) )
        | ? [U_6763] : ~ hBOOL(hAPP(U_6767,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6763))) )
    & ! [U_6766] :
        ( ! [U_6762] : hBOOL(hAPP(U_6766,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762)))
        | ? [U_6761] :
            ( ~ hBOOL(hAPP(U_6766,U_6761))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6761)) ) ) ),
    inference(miniscope,[status(thm)],[f_1501_2]) ).

fof(f_1501_4,plain,
    ( ! [U_6767] :
        ( ! [U_6764] :
            ( hBOOL(hAPP(U_6767,U_6764))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) )
        | ? [U_6763] : ~ hBOOL(hAPP(U_6767,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6763))) )
    & ! [U_6766] :
        ( ! [U_6762] : hBOOL(hAPP(U_6766,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762)))
        | ( ~ hBOOL(hAPP(U_6766,sK127(U_6766)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6766))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_6761,sK127(U_6766))],[f_1501_3]) ).

fof(f_1501_5,plain,
    ( ! [U_6767] :
        ( ! [U_6764] :
            ( hBOOL(hAPP(U_6767,U_6764))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) )
        | ~ hBOOL(hAPP(U_6767,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK128(U_6767)))) )
    & ! [U_6766] :
        ( ! [U_6762] : hBOOL(hAPP(U_6766,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762)))
        | ( ~ hBOOL(hAPP(U_6766,sK127(U_6766)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6766))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_6763,sK128(U_6767))],[f_1501_4]) ).

cnf(f_1501_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6766)))
    | hBOOL(hAPP(U_6766,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762))) ),
    inference(clausify,[status(thm)],[f_1501_5]) ).

cnf(f_1501_7,plain,
    ( ~ hBOOL(hAPP(U_6766,sK127(U_6766)))
    | hBOOL(hAPP(U_6766,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6762))) ),
    inference(clausify,[status(thm)],[f_1501_5]) ).

cnf(f_1501_8,plain,
    ( hBOOL(hAPP(U_6767,U_6764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764))
    | ~ hBOOL(hAPP(U_6767,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK128(U_6767)))) ),
    inference(clausify,[status(thm)],[f_1501_5]) ).

fof(f_1502_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]) ).

cnf(f_1502_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(clausify,[status(thm)],[f_1502_1]) ).

fof(f_1503_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,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_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).

fof(f_1503_2,plain,
    ! [U_6771,U_6770,U_6769,U_6768] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6768),U_6769),c_SetInterval_Oord_OatMost(U_6768,U_6770,U_6771)))
        | ~ hBOOL(hAPP(hAPP(U_6770,U_6769),U_6771)) )
      & ( hBOOL(hAPP(hAPP(U_6770,U_6769),U_6771))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6768),U_6769),c_SetInterval_Oord_OatMost(U_6768,U_6770,U_6771))) ) ),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

fof(f_1503_3,plain,
    ( ! [U_6779,U_6777,U_6775] :
        ( ! [U_6773] : hBOOL(hAPP(hAPP(c_member(U_6773),U_6775),c_SetInterval_Oord_OatMost(U_6773,U_6777,U_6779)))
        | ~ hBOOL(hAPP(hAPP(U_6777,U_6775),U_6779)) )
    & ! [U_6778,U_6776,U_6774] :
        ( ! [U_6772] : ~ hBOOL(hAPP(hAPP(c_member(U_6772),U_6774),c_SetInterval_Oord_OatMost(U_6772,U_6776,U_6778)))
        | hBOOL(hAPP(hAPP(U_6776,U_6774),U_6778)) ) ),
    inference(miniscope,[status(thm)],[f_1503_2]) ).

cnf(f_1503_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6772),U_6774),c_SetInterval_Oord_OatMost(U_6772,U_6776,U_6778)))
    | hBOOL(hAPP(hAPP(U_6776,U_6774),U_6778)) ),
    inference(clausify,[status(thm)],[f_1503_3]) ).

cnf(f_1503_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6773),U_6775),c_SetInterval_Oord_OatMost(U_6773,U_6777,U_6779)))
    | ~ hBOOL(hAPP(hAPP(U_6777,U_6775),U_6779)) ),
    inference(clausify,[status(thm)],[f_1503_3]) ).

fof(f_1504_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,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_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).

fof(f_1504_2,plain,
    ! [U_6783,U_6782,U_6781,U_6780] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6780),U_6781),c_SetInterval_Oord_OatLeast(U_6780,U_6782,U_6783)))
        | ~ hBOOL(hAPP(hAPP(U_6782,U_6783),U_6781)) )
      & ( hBOOL(hAPP(hAPP(U_6782,U_6783),U_6781))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6780),U_6781),c_SetInterval_Oord_OatLeast(U_6780,U_6782,U_6783))) ) ),
    inference(variable_rename,[status(thm)],[f_1504_1]) ).

fof(f_1504_3,plain,
    ( ! [U_6791,U_6789,U_6787] :
        ( ! [U_6785] : hBOOL(hAPP(hAPP(c_member(U_6785),U_6787),c_SetInterval_Oord_OatLeast(U_6785,U_6789,U_6791)))
        | ~ hBOOL(hAPP(hAPP(U_6789,U_6791),U_6787)) )
    & ! [U_6790,U_6788,U_6786] :
        ( ! [U_6784] : ~ hBOOL(hAPP(hAPP(c_member(U_6784),U_6786),c_SetInterval_Oord_OatLeast(U_6784,U_6788,U_6790)))
        | hBOOL(hAPP(hAPP(U_6788,U_6790),U_6786)) ) ),
    inference(miniscope,[status(thm)],[f_1504_2]) ).

cnf(f_1504_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6784),U_6786),c_SetInterval_Oord_OatLeast(U_6784,U_6788,U_6790)))
    | hBOOL(hAPP(hAPP(U_6788,U_6790),U_6786)) ),
    inference(clausify,[status(thm)],[f_1504_3]) ).

cnf(f_1504_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6785),U_6787),c_SetInterval_Oord_OatLeast(U_6785,U_6789,U_6791)))
    | ~ hBOOL(hAPP(hAPP(U_6789,U_6791),U_6787)) ),
    inference(clausify,[status(thm)],[f_1504_3]) ).

fof(f_1505_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,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_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).

fof(f_1505_2,plain,
    ! [U_6795,U_6794,U_6793,U_6792] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6792),U_6793),c_SetInterval_Oord_OlessThan(U_6792,U_6794,U_6795)))
        | ~ hBOOL(hAPP(hAPP(U_6794,U_6793),U_6795)) )
      & ( hBOOL(hAPP(hAPP(U_6794,U_6793),U_6795))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6792),U_6793),c_SetInterval_Oord_OlessThan(U_6792,U_6794,U_6795))) ) ),
    inference(variable_rename,[status(thm)],[f_1505_1]) ).

fof(f_1505_3,plain,
    ( ! [U_6803,U_6801,U_6799] :
        ( ! [U_6797] : hBOOL(hAPP(hAPP(c_member(U_6797),U_6799),c_SetInterval_Oord_OlessThan(U_6797,U_6801,U_6803)))
        | ~ hBOOL(hAPP(hAPP(U_6801,U_6799),U_6803)) )
    & ! [U_6802,U_6800,U_6798] :
        ( ! [U_6796] : ~ hBOOL(hAPP(hAPP(c_member(U_6796),U_6798),c_SetInterval_Oord_OlessThan(U_6796,U_6800,U_6802)))
        | hBOOL(hAPP(hAPP(U_6800,U_6798),U_6802)) ) ),
    inference(miniscope,[status(thm)],[f_1505_2]) ).

cnf(f_1505_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6796),U_6798),c_SetInterval_Oord_OlessThan(U_6796,U_6800,U_6802)))
    | hBOOL(hAPP(hAPP(U_6800,U_6798),U_6802)) ),
    inference(clausify,[status(thm)],[f_1505_3]) ).

cnf(f_1505_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6797),U_6799),c_SetInterval_Oord_OlessThan(U_6797,U_6801,U_6803)))
    | ~ hBOOL(hAPP(hAPP(U_6801,U_6799),U_6803)) ),
    inference(clausify,[status(thm)],[f_1505_3]) ).

fof(f_1506_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_1506_2,plain,
    ! [U_6805,U_6804] :
      ( ( c_Nat__Transfer_Otsub(U_6805,U_6804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6804),U_6805)) )
      & ( c_Nat__Transfer_Otsub(U_6805,U_6804) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6805),U_6804)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6804),U_6805)) ) ),
    inference(variable_rename,[status(thm)],[f_1506_1]) ).

fof(f_1506_3,plain,
    ( ! [U_6809,U_6807] :
        ( c_Nat__Transfer_Otsub(U_6809,U_6807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6807),U_6809)) )
    & ! [U_6808,U_6806] :
        ( c_Nat__Transfer_Otsub(U_6808,U_6806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6808),U_6806)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6806),U_6808)) ) ),
    inference(miniscope,[status(thm)],[f_1506_2]) ).

cnf(f_1506_4,plain,
    ( c_Nat__Transfer_Otsub(U_6808,U_6806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6808),U_6806)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6806),U_6808)) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_5,plain,
    ( c_Nat__Transfer_Otsub(U_6809,U_6807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6807),U_6809)) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

fof(f_1507_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_1507_2,plain,
    ! [U_6812,U_6811,U_6810] :
      ( ( ( ( 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_6810)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6812),U_6811)) = 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_6812),U_6811)) )
          & ( 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_6810)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6812),U_6811)) = 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_6812),U_6811)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6810),U_6811)) )
      & ( 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_6810)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6812),U_6811)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6812),U_6810)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6811),U_6810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6810),U_6811)) ) ),
    inference(variable_rename,[status(thm)],[f_1507_1]) ).

fof(f_1507_3,plain,
    ( ! [U_6818,U_6816,U_6814] :
        ( ( ( 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_6814)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6818),U_6816)) = 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_6818),U_6816)) )
          & ( 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_6814)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6818),U_6816)) = 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_6818),U_6816)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6814),U_6816)) )
    & ! [U_6817,U_6815,U_6813] :
        ( 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_6813)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6817),U_6815)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6817),U_6813)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6815),U_6813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6813),U_6815)) ) ),
    inference(miniscope,[status(thm)],[f_1507_2]) ).

cnf(f_1507_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_Ominus__class_Ominus(tc_Nat_Onat)),U_6813)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6817),U_6815)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6817),U_6813)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6815),U_6813))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6813),U_6815)) ),
    inference(clausify,[status(thm)],[f_1507_3]) ).

cnf(f_1507_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_6814)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6818),U_6816)) = 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_6818),U_6816))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6814),U_6816)) ),
    inference(clausify,[status(thm)],[f_1507_3]) ).

cnf(f_1507_6,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_6814)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6818),U_6816)) = 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_6818),U_6816))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6814),U_6816)) ),
    inference(clausify,[status(thm)],[f_1507_3]) ).

fof(f_1508_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).

fof(f_1508_2,plain,
    ! [U_6821,U_6820,U_6819] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_6819,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_6819,U_6820)),c_Predicate_OPowp(U_6819,U_6821)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6819,tc_HOL_Obool)),U_6820),U_6821)) ),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

cnf(f_1508_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_6819,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_6819,U_6820)),c_Predicate_OPowp(U_6819,U_6821)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6819,tc_HOL_Obool)),U_6820),U_6821)) ),
    inference(clausify,[status(thm)],[f_1508_2]) ).

fof(f_1509_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_1509_2,plain,
    ! [U_6823,U_6822] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6822),U_6823))),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

cnf(f_1509_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6822),U_6823))),
    inference(clausify,[status(thm)],[f_1509_2]) ).

fof(f_1510_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]) ).

cnf(f_1510_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(clausify,[status(thm)],[f_1510_1]) ).

fof(f_1511_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( V_b_2 = V_d_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).

fof(f_1511_2,plain,
    ! [U_6828,U_6827,U_6826,U_6825,U_6824] :
      ( U_6826 = U_6828
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6824),U_6827),U_6828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6824),U_6825),U_6826))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6824,U_6825),U_6826) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6824,U_6827),U_6828)
      | ~ class_Orderings_Olinorder(U_6824) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

cnf(f_1511_3,plain,
    ( U_6826 = U_6828
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6824),U_6827),U_6828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6824),U_6825),U_6826))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6824,U_6825),U_6826) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6824,U_6827),U_6828)
    | ~ class_Orderings_Olinorder(U_6824) ),
    inference(clausify,[status(thm)],[f_1511_2]) ).

fof(f_1512_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( V_a_2 = V_c_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).

fof(f_1512_2,plain,
    ! [U_6833,U_6832,U_6831,U_6830,U_6829] :
      ( U_6830 = U_6832
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6829),U_6832),U_6833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6829),U_6830),U_6831))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6829,U_6830),U_6831) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6829,U_6832),U_6833)
      | ~ class_Orderings_Olinorder(U_6829) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

cnf(f_1512_3,plain,
    ( U_6830 = U_6832
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6829),U_6832),U_6833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6829),U_6830),U_6831))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6829,U_6830),U_6831) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6829,U_6832),U_6833)
    | ~ class_Orderings_Olinorder(U_6829) ),
    inference(clausify,[status(thm)],[f_1512_2]) ).

fof(f_1513_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,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_a,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).

fof(f_1513_2,plain,
    ! [U_6838,U_6837,U_6836,U_6835,U_6834] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6835),U_6836) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6837),U_6838)
          | U_6836 != U_6838
          | U_6835 != U_6837 )
        & ( ( U_6836 = U_6838
            & U_6835 = U_6837 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6835),U_6836) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6837),U_6838) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6837),U_6838))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6835),U_6836))
      | ~ class_Orderings_Olinorder(U_6834) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

cnf(f_1513_3,plain,
    ( U_6835 = U_6837
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6835),U_6836) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6837),U_6838)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6837),U_6838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6835),U_6836))
    | ~ class_Orderings_Olinorder(U_6834) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

cnf(f_1513_4,plain,
    ( U_6836 = U_6838
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6835),U_6836) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6837),U_6838)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6837),U_6838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6835),U_6836))
    | ~ class_Orderings_Olinorder(U_6834) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

cnf(f_1513_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6835),U_6836) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6834,U_6837),U_6838)
    | U_6836 != U_6838
    | U_6835 != U_6837
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6837),U_6838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6834),U_6835),U_6836))
    | ~ class_Orderings_Olinorder(U_6834) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

fof(f_1514_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_1514_2,plain,
    ! [U_6841,U_6840,U_6839] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6839),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6840),U_6841)) = 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_6839),U_6840)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6840),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6840),U_6841)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6839),U_6840)) ),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

cnf(f_1514_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6839),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6840),U_6841)) = 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_6839),U_6840)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6840),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6840),U_6841)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6839),U_6840)) ),
    inference(clausify,[status(thm)],[f_1514_2]) ).

fof(f_1515_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_1515_2,plain,
    ! [U_6842] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6842),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_1515_1]) ).

cnf(f_1515_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6842),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_1515_2]) ).

fof(f_1516_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_1516_2,plain,
    ! [U_6843] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6843) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6843),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

cnf(f_1516_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6843) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6843),
    inference(clausify,[status(thm)],[f_1516_2]) ).

fof(f_1517_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_1517_2,plain,
    ! [U_6845,U_6844] :
      ( U_6844 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6845),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6844)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6844),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6845),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6844))))) ),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

cnf(f_1517_3,plain,
    ( U_6844 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6845),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6844)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6844),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6845),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6844))))) ),
    inference(clausify,[status(thm)],[f_1517_2]) ).

fof(f_1518_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_1518_2,plain,
    ! [U_6847,U_6846] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6846),U_6847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6847),U_6846),
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

cnf(f_1518_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6846),U_6847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6847),U_6846),
    inference(clausify,[status(thm)],[f_1518_2]) ).

fof(f_1519_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_1519_2,plain,
    ! [U_6849,U_6848] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6848),U_6849)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6848)),hAPP(c_Nat_OSuc,U_6849)),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

cnf(f_1519_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6848),U_6849)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6848)),hAPP(c_Nat_OSuc,U_6849)),
    inference(clausify,[status(thm)],[f_1519_2]) ).

fof(f_1520_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).

fof(f_1520_2,plain,
    ! [U_6852,U_6851,U_6850] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6850,U_6852),U_6851) = c_Orderings_Obot__class_Obot(tc_fun(U_6850,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6850),U_6851),U_6852))
      | ~ class_Orderings_Oorder(U_6850) ),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

cnf(f_1520_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6850,U_6852),U_6851) = c_Orderings_Obot__class_Obot(tc_fun(U_6850,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6850),U_6851),U_6852))
    | ~ class_Orderings_Oorder(U_6850) ),
    inference(clausify,[status(thm)],[f_1520_2]) ).

fof(f_1521_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(f_1521_2,plain,
    ! [U_6855,U_6854,U_6853] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_6853,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6853,U_6854),U_6855)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6853),U_6854),U_6855)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6853),U_6854),U_6855))
          | c_Orderings_Obot__class_Obot(tc_fun(U_6853,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6853,U_6854),U_6855) ) )
      | ~ class_Orderings_Oorder(U_6853) ),
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

cnf(f_1521_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6853),U_6854),U_6855))
    | c_Orderings_Obot__class_Obot(tc_fun(U_6853,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6853,U_6854),U_6855)
    | ~ class_Orderings_Oorder(U_6853) ),
    inference(clausify,[status(thm)],[f_1521_2]) ).

cnf(f_1521_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_6853,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6853,U_6854),U_6855)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6853),U_6854),U_6855))
    | ~ class_Orderings_Oorder(U_6853) ),
    inference(clausify,[status(thm)],[f_1521_2]) ).

fof(f_1522_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(f_1522_2,plain,
    ! [U_6858,U_6857,U_6856] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6856,U_6857),U_6858) = c_Orderings_Obot__class_Obot(tc_fun(U_6856,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6856),U_6857),U_6858)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6856),U_6857),U_6858))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6856,U_6857),U_6858) != c_Orderings_Obot__class_Obot(tc_fun(U_6856,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_6856) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

cnf(f_1522_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6856),U_6857),U_6858))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6856,U_6857),U_6858) != c_Orderings_Obot__class_Obot(tc_fun(U_6856,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_6856) ),
    inference(clausify,[status(thm)],[f_1522_2]) ).

cnf(f_1522_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6856,U_6857),U_6858) = c_Orderings_Obot__class_Obot(tc_fun(U_6856,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6856),U_6857),U_6858))
    | ~ class_Orderings_Oorder(U_6856) ),
    inference(clausify,[status(thm)],[f_1522_2]) ).

fof(f_1523_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).

fof(f_1523_2,plain,
    ! [U_6863,U_6862,U_6861,U_6860,U_6859] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6861),U_6863))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6862),U_6860)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6861),U_6860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6859,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6860),U_6861)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6862),U_6863)))
      | ~ class_Orderings_Olinorder(U_6859) ),
    inference(variable_rename,[status(thm)],[f_1523_1]) ).

cnf(f_1523_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6862),U_6860))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6861),U_6860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6859,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6860),U_6861)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6862),U_6863)))
    | ~ class_Orderings_Olinorder(U_6859) ),
    inference(clausify,[status(thm)],[f_1523_2]) ).

cnf(f_1523_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6861),U_6863))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),U_6861),U_6860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6859,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6860),U_6861)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6859,U_6862),U_6863)))
    | ~ class_Orderings_Olinorder(U_6859) ),
    inference(clausify,[status(thm)],[f_1523_2]) ).

fof(f_1524_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).

fof(f_1524_2,plain,
    ! [U_6867,U_6866,U_6865,U_6864] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6864),U_6865),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6866)),hAPP(c_Nat_OSuc,U_6867))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6864),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6864,tc_Nat_Onat),U_6865),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6866),U_6867))
      | ~ class_Groups_Ocomm__monoid__add(U_6864) ),
    inference(variable_rename,[status(thm)],[f_1524_1]) ).

cnf(f_1524_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6864),U_6865),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6866)),hAPP(c_Nat_OSuc,U_6867))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6864),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6864,tc_Nat_Onat),U_6865),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6866),U_6867))
    | ~ class_Groups_Ocomm__monoid__add(U_6864) ),
    inference(clausify,[status(thm)],[f_1524_2]) ).

fof(f_1525_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).

fof(f_1525_2,plain,
    ! [U_6871,U_6870,U_6869,U_6868] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6868,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6869),U_6870)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6870),U_6871)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6869),U_6871)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6868),U_6870),U_6871))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6868),U_6869),U_6870))
      | ~ class_Orderings_Olinorder(U_6868) ),
    inference(variable_rename,[status(thm)],[f_1525_1]) ).

cnf(f_1525_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6868,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6869),U_6870)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6870),U_6871)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6868,U_6869),U_6871)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6868),U_6870),U_6871))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6868),U_6869),U_6870))
    | ~ class_Orderings_Olinorder(U_6868) ),
    inference(clausify,[status(thm)],[f_1525_2]) ).

fof(f_1526_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).

fof(f_1526_2,plain,
    ! [U_6876,U_6875,U_6874,U_6873,U_6872] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6872),U_6873),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6874),U_6875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6876),U_6875))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6872),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6872,tc_Nat_Onat),U_6873),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6875))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6874),U_6876))
      | ~ class_Groups_Ocomm__monoid__add(U_6872) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

cnf(f_1526_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6872),U_6873),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6874),U_6875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6876),U_6875))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6872),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6872,tc_Nat_Onat),U_6873),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6875))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6874),U_6876))
    | ~ class_Groups_Ocomm__monoid__add(U_6872) ),
    inference(clausify,[status(thm)],[f_1526_2]) ).

fof(f_1527_1,plain,
    ! [V_m_2,V_n_2,V_i_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).

fof(f_1527_2,plain,
    ! [U_6880,U_6879,U_6878,U_6877] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6877,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6878),U_6880)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6878),U_6879)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6879),U_6880)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6877),U_6878),U_6879))
      | ~ class_Orderings_Olinorder(U_6877) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

cnf(f_1527_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6877,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6878),U_6880)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6878),U_6879)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6877,U_6879),U_6880)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6877),U_6878),U_6879))
    | ~ class_Orderings_Olinorder(U_6877) ),
    inference(clausify,[status(thm)],[f_1527_2]) ).

fof(f_1528_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).

fof(f_1528_2,plain,
    ! [U_6884,U_6883,U_6882,U_6881] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6881,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6881,U_6882),U_6883)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6881,U_6883),U_6884)) = c_Orderings_Obot__class_Obot(tc_fun(U_6881,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_6881) ),
    inference(variable_rename,[status(thm)],[f_1528_1]) ).

cnf(f_1528_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6881,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6881,U_6882),U_6883)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6881,U_6883),U_6884)) = c_Orderings_Obot__class_Obot(tc_fun(U_6881,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_6881) ),
    inference(clausify,[status(thm)],[f_1528_2]) ).

fof(f_1529_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_1529_2,plain,
    ! [U_6887,U_6886,U_6885] : 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_6885)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6886),U_6887)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6886),U_6885)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6887),U_6885)),
    inference(variable_rename,[status(thm)],[f_1529_1]) ).

cnf(f_1529_3,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_6885)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6886),U_6887)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6886),U_6885)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6887),U_6885)),
    inference(clausify,[status(thm)],[f_1529_2]) ).

fof(f_1530_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).

fof(f_1530_2,plain,
    ! [U_6892,U_6891,U_6890,U_6889,U_6888] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6888),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6889),U_6890))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6890),U_6891))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6889),U_6891))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6890),U_6891))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6889),U_6890))
      | ~ class_Groups_Ocomm__monoid__add(U_6888) ),
    inference(variable_rename,[status(thm)],[f_1530_1]) ).

cnf(f_1530_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6888),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6889),U_6890))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6890),U_6891))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6888),U_6892),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6889),U_6891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6890),U_6891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6889),U_6890))
    | ~ class_Groups_Ocomm__monoid__add(U_6888) ),
    inference(clausify,[status(thm)],[f_1530_2]) ).

fof(f_1531_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).

fof(f_1531_2,plain,
    ! [U_6897,U_6896,U_6895,U_6894,U_6893] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6894),U_6896))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6894),U_6895))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6895),U_6896))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6895),U_6896))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6894),U_6895))
      | ~ class_Groups_Oab__group__add(U_6893) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

cnf(f_1531_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6894),U_6896))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6894),U_6895))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6893),U_6897),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6895),U_6896))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6895),U_6896))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6894),U_6895))
    | ~ class_Groups_Oab__group__add(U_6893) ),
    inference(clausify,[status(thm)],[f_1531_2]) ).

fof(f_1532_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_1532_2,plain,
    ! [U_6898] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6898),hAPP(c_Nat_OSuc,U_6898)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6898),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1532_1]) ).

cnf(f_1532_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6898),hAPP(c_Nat_OSuc,U_6898)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6898),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1532_2]) ).

fof(f_1533_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_1533_2,plain,
    ! [U_6900,U_6899] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,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_6899,tc_HOL_Obool)),tc_fun(U_6899,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_6899,tc_HOL_Obool)),tc_fun(U_6899,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_6900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6900),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

cnf(f_1533_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,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_6899,tc_HOL_Obool)),tc_fun(U_6899,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_6899,tc_HOL_Obool)),tc_fun(U_6899,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_6900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6899,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6900),
    inference(clausify,[status(thm)],[f_1533_2]) ).

fof(f_1534_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).

fof(f_1534_2,plain,
    ! [U_6903,U_6902,U_6901] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6901,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6901),U_6902)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6901,U_6902),U_6903)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6901),U_6903)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6901),U_6902),U_6903))
      | ~ class_Orderings_Olinorder(U_6901) ),
    inference(variable_rename,[status(thm)],[f_1534_1]) ).

cnf(f_1534_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6901,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6901),U_6902)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6901,U_6902),U_6903)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6901),U_6903)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6901),U_6902),U_6903))
    | ~ class_Orderings_Olinorder(U_6901) ),
    inference(clausify,[status(thm)],[f_1534_2]) ).

fof(f_1535_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).

fof(f_1535_2,plain,
    ! [U_6906,U_6905,U_6904] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6904,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6904),U_6905)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6904,U_6905),U_6906)) = c_Orderings_Obot__class_Obot(tc_fun(U_6904,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_6904) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

cnf(f_1535_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6904,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6904),U_6905)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6904,U_6905),U_6906)) = c_Orderings_Obot__class_Obot(tc_fun(U_6904,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_6904) ),
    inference(clausify,[status(thm)],[f_1535_2]) ).

fof(f_1536_1,plain,
    ! [V_k_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).

fof(f_1536_2,plain,
    ! [U_6909,U_6908,U_6907] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6907),U_6908),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6909)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6907),U_6908),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6909))
      | hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_6907)
      | ~ class_Groups_Ocomm__monoid__add(U_6907) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

cnf(f_1536_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6907),U_6908),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6909)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6907),U_6908),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6909))
    | hAPP(U_6908,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_6907)
    | ~ class_Groups_Ocomm__monoid__add(U_6907) ),
    inference(clausify,[status(thm)],[f_1536_2]) ).

fof(f_1537_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).

fof(f_1537_2,plain,
    ! [U_6913,U_6912,U_6911,U_6910] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6910),U_6913),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6911),U_6912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6910),hAPP(U_6913,U_6911)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6910),U_6913),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6911)),U_6912)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6911),U_6912))
      | ~ class_Groups_Ocomm__monoid__add(U_6910) ),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

cnf(f_1537_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6910),U_6913),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6911),U_6912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6910),hAPP(U_6913,U_6911)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6910),U_6913),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6911)),U_6912)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6911),U_6912))
    | ~ class_Groups_Ocomm__monoid__add(U_6910) ),
    inference(clausify,[status(thm)],[f_1537_2]) ).

fof(f_1538_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_1538_2,plain,
    ! [U_6915,U_6914] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6914),hAPP(c_Nat_OSuc,U_6915)) = 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_6914),U_6915)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6914),hAPP(c_Nat_OSuc,U_6915)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6915),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6914),U_6915))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6914),U_6915)) ) ),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

fof(f_1538_3,plain,
    ( ! [U_6919,U_6917] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6917),hAPP(c_Nat_OSuc,U_6919)) = 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_6917),U_6919)) )
    & ! [U_6918,U_6916] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6916),hAPP(c_Nat_OSuc,U_6918)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6918),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6916),U_6918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6916),U_6918)) ) ),
    inference(miniscope,[status(thm)],[f_1538_2]) ).

cnf(f_1538_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6916),hAPP(c_Nat_OSuc,U_6918)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6918),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6916),U_6918))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6916),U_6918)) ),
    inference(clausify,[status(thm)],[f_1538_3]) ).

cnf(f_1538_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6917),hAPP(c_Nat_OSuc,U_6919)) = 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_6917),U_6919)) ),
    inference(clausify,[status(thm)],[f_1538_3]) ).

fof(f_1539_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(f_1539_2,plain,
    ! [U_6923,U_6922,U_6921,U_6920] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),hAPP(c_Nat_OSuc,U_6921))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6920),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),U_6921))),hAPP(U_6923,U_6921))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6921),U_6922)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),hAPP(c_Nat_OSuc,U_6921))) = c_Groups_Ozero__class_Ozero(U_6920)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6921),U_6922)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_6920) ),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

cnf(f_1539_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),hAPP(c_Nat_OSuc,U_6921))) = c_Groups_Ozero__class_Ozero(U_6920)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6921),U_6922))
    | ~ class_Groups_Ocomm__monoid__add(U_6920) ),
    inference(clausify,[status(thm)],[f_1539_2]) ).

cnf(f_1539_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),hAPP(c_Nat_OSuc,U_6921))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6920),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6920),U_6923),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6922),U_6921))),hAPP(U_6923,U_6921))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6921),U_6922))
    | ~ class_Groups_Ocomm__monoid__add(U_6920) ),
    inference(clausify,[status(thm)],[f_1539_2]) ).

fof(f_1540_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_1540_2,plain,
    ! [U_6925,U_6924] :
      ( 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_6924,U_6925)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6925))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6924)) ),
    inference(variable_rename,[status(thm)],[f_1540_1]) ).

cnf(f_1540_3,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_6924,U_6925)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6925))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6924)) ),
    inference(clausify,[status(thm)],[f_1540_2]) ).

fof(f_1541_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_1541_2,plain,
    ! [U_6927,U_6926] :
      ( c_Nat__Transfer_Otsub(U_6927,U_6926) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6927),U_6926)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6926),U_6927)) ),
    inference(variable_rename,[status(thm)],[f_1541_1]) ).

cnf(f_1541_3,plain,
    ( c_Nat__Transfer_Otsub(U_6927,U_6926) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6927),U_6926)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6926),U_6927)) ),
    inference(clausify,[status(thm)],[f_1541_2]) ).

fof(f_1542_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_1542_2,plain,
    ! [U_6929,U_6928] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6928),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6929)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6928),U_6929)),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

cnf(f_1542_3,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6928),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6929)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6928),U_6929)),
    inference(clausify,[status(thm)],[f_1542_2]) ).

fof(f_1543_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).

fof(f_1543_2,plain,
    ! [U_6935,U_6934] :
      ( ( ! [U_6933] :
            ( hBOOL(hAPP(U_6935,U_6933))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6934)) )
        | ? [U_6932] :
            ( ~ hBOOL(hAPP(U_6935,U_6932))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6932),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6934))) ) )
      & ( ! [U_6931] :
            ( hBOOL(hAPP(U_6935,U_6931))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6934))) )
        | ? [U_6930] :
            ( ~ hBOOL(hAPP(U_6935,U_6930))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6930),U_6934)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1543_1]) ).

fof(f_1543_3,plain,
    ( ! [U_6939,U_6937] :
        ( ! [U_6933] :
            ( hBOOL(hAPP(U_6939,U_6933))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6937)) )
        | ? [U_6932] :
            ( ~ hBOOL(hAPP(U_6939,U_6932))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6932),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6937))) ) )
    & ! [U_6938,U_6936] :
        ( ! [U_6931] :
            ( hBOOL(hAPP(U_6938,U_6931))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6936))) )
        | ? [U_6930] :
            ( ~ hBOOL(hAPP(U_6938,U_6930))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6930),U_6936)) ) ) ),
    inference(miniscope,[status(thm)],[f_1543_2]) ).

fof(f_1543_4,plain,
    ( ! [U_6939,U_6937] :
        ( ! [U_6933] :
            ( hBOOL(hAPP(U_6939,U_6933))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6937)) )
        | ? [U_6932] :
            ( ~ hBOOL(hAPP(U_6939,U_6932))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6932),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6937))) ) )
    & ! [U_6938,U_6936] :
        ( ! [U_6931] :
            ( hBOOL(hAPP(U_6938,U_6931))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6936))) )
        | ( ~ hBOOL(hAPP(U_6938,sK129(U_6938,U_6936)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_6938,U_6936)),U_6936)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_6930,sK129(U_6938,U_6936))],[f_1543_3]) ).

fof(f_1543_5,plain,
    ( ! [U_6939,U_6937] :
        ( ! [U_6933] :
            ( hBOOL(hAPP(U_6939,U_6933))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6937)) )
        | ( ~ hBOOL(hAPP(U_6939,sK130(U_6939,U_6937)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK130(U_6939,U_6937)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6937))) ) )
    & ! [U_6938,U_6936] :
        ( ! [U_6931] :
            ( hBOOL(hAPP(U_6938,U_6931))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6936))) )
        | ( ~ hBOOL(hAPP(U_6938,sK129(U_6938,U_6936)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_6938,U_6936)),U_6936)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_6932,sK130(U_6939,U_6937))],[f_1543_4]) ).

cnf(f_1543_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK129(U_6938,U_6936)),U_6936))
    | hBOOL(hAPP(U_6938,U_6931))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6936))) ),
    inference(clausify,[status(thm)],[f_1543_5]) ).

cnf(f_1543_7,plain,
    ( ~ hBOOL(hAPP(U_6938,sK129(U_6938,U_6936)))
    | hBOOL(hAPP(U_6938,U_6931))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6936))) ),
    inference(clausify,[status(thm)],[f_1543_5]) ).

cnf(f_1543_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK130(U_6939,U_6937)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6937)))
    | hBOOL(hAPP(U_6939,U_6933))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6937)) ),
    inference(clausify,[status(thm)],[f_1543_5]) ).

cnf(f_1543_9,plain,
    ( ~ hBOOL(hAPP(U_6939,sK130(U_6939,U_6937)))
    | hBOOL(hAPP(U_6939,U_6933))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6933),U_6937)) ),
    inference(clausify,[status(thm)],[f_1543_5]) ).

fof(f_1544_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).

fof(f_1544_2,plain,
    ! [U_6945,U_6944] :
      ( ( ? [U_6943] :
            ( hBOOL(hAPP(U_6945,U_6943))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6943),U_6944)) )
        | ! [U_6942] :
            ( ~ hBOOL(hAPP(U_6945,U_6942))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6944))) ) )
      & ( ? [U_6941] :
            ( hBOOL(hAPP(U_6945,U_6941))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6941),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6944))) )
        | ! [U_6940] :
            ( ~ hBOOL(hAPP(U_6945,U_6940))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6944)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1544_1]) ).

fof(f_1544_3,plain,
    ( ! [U_6949,U_6947] :
        ( ? [U_6943] :
            ( hBOOL(hAPP(U_6949,U_6943))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6943),U_6947)) )
        | ! [U_6942] :
            ( ~ hBOOL(hAPP(U_6949,U_6942))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6947))) ) )
    & ! [U_6948,U_6946] :
        ( ? [U_6941] :
            ( hBOOL(hAPP(U_6948,U_6941))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6941),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6946))) )
        | ! [U_6940] :
            ( ~ hBOOL(hAPP(U_6948,U_6940))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6946)) ) ) ),
    inference(miniscope,[status(thm)],[f_1544_2]) ).

fof(f_1544_4,plain,
    ( ! [U_6949,U_6947] :
        ( ? [U_6943] :
            ( hBOOL(hAPP(U_6949,U_6943))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6943),U_6947)) )
        | ! [U_6942] :
            ( ~ hBOOL(hAPP(U_6949,U_6942))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6947))) ) )
    & ! [U_6948,U_6946] :
        ( ( hBOOL(hAPP(U_6948,sK131(U_6948,U_6946)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK131(U_6948,U_6946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6946))) )
        | ! [U_6940] :
            ( ~ hBOOL(hAPP(U_6948,U_6940))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6946)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_6941,sK131(U_6948,U_6946))],[f_1544_3]) ).

fof(f_1544_5,plain,
    ( ! [U_6949,U_6947] :
        ( ( hBOOL(hAPP(U_6949,sK132(U_6949,U_6947)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK132(U_6949,U_6947)),U_6947)) )
        | ! [U_6942] :
            ( ~ hBOOL(hAPP(U_6949,U_6942))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6947))) ) )
    & ! [U_6948,U_6946] :
        ( ( hBOOL(hAPP(U_6948,sK131(U_6948,U_6946)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK131(U_6948,U_6946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6946))) )
        | ! [U_6940] :
            ( ~ hBOOL(hAPP(U_6948,U_6940))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6946)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6943,sK132(U_6949,U_6947))],[f_1544_4]) ).

cnf(f_1544_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK131(U_6948,U_6946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6946)))
    | ~ hBOOL(hAPP(U_6948,U_6940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6946)) ),
    inference(clausify,[status(thm)],[f_1544_5]) ).

cnf(f_1544_7,plain,
    ( hBOOL(hAPP(U_6948,sK131(U_6948,U_6946)))
    | ~ hBOOL(hAPP(U_6948,U_6940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6940),U_6946)) ),
    inference(clausify,[status(thm)],[f_1544_5]) ).

cnf(f_1544_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK132(U_6949,U_6947)),U_6947))
    | ~ hBOOL(hAPP(U_6949,U_6942))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6947))) ),
    inference(clausify,[status(thm)],[f_1544_5]) ).

cnf(f_1544_9,plain,
    ( hBOOL(hAPP(U_6949,sK132(U_6949,U_6947)))
    | ~ hBOOL(hAPP(U_6949,U_6942))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6942),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6947))) ),
    inference(clausify,[status(thm)],[f_1544_5]) ).

fof(f_1545_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_1545_2,plain,
    ! [U_6954,U_6953,U_6952,U_6951] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6954)))
      | ? [U_6950] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6950)),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,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_6950),U_6953))),U_6954))) ),
    inference(variable_rename,[status(thm)],[f_1545_1]) ).

fof(f_1545_3,plain,
    ! [U_6954,U_6953,U_6952,U_6951] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6954)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK133(U_6954,U_6953,U_6952,U_6951))),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,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),sK133(U_6954,U_6953,U_6952,U_6951)),U_6953))),U_6954))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6950,sK133(U_6954,U_6953,U_6952,U_6951))],[f_1545_2]) ).

cnf(f_1545_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6954)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK133(U_6954,U_6953,U_6952,U_6951))),U_6952)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6951,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),sK133(U_6954,U_6953,U_6952,U_6951)),U_6953))),U_6954))) ),
    inference(clausify,[status(thm)],[f_1545_3]) ).

fof(f_1546_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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_a,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_1546_2,plain,
    ! [U_6959,U_6958,U_6957,U_6956] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6957) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6959)
      | ? [U_6955] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6955)),U_6957) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,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_6955),U_6958))),U_6959) ),
    inference(variable_rename,[status(thm)],[f_1546_1]) ).

fof(f_1546_3,plain,
    ! [U_6959,U_6958,U_6957,U_6956] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6957) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6959)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK134(U_6959,U_6958,U_6957,U_6956))),U_6957) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,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),sK134(U_6959,U_6958,U_6957,U_6956)),U_6958))),U_6959) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6955,sK134(U_6959,U_6958,U_6957,U_6956))],[f_1546_2]) ).

cnf(f_1546_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6957) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6959)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK134(U_6959,U_6958,U_6957,U_6956))),U_6957) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6956,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),sK134(U_6959,U_6958,U_6957,U_6956)),U_6958))),U_6959) ),
    inference(clausify,[status(thm)],[f_1546_3]) ).

fof(f_1547_1,plain,
    ! [V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_1547_2,plain,
    ! [U_6963,U_6962,U_6961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6962)),U_6963))
      | ? [U_6960] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6960)),U_6962)),U_6963)) ),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

fof(f_1547_3,plain,
    ! [U_6963,U_6962,U_6961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6962)),U_6963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK135(U_6963,U_6962,U_6961))),U_6962)),U_6963)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6960,sK135(U_6963,U_6962,U_6961))],[f_1547_2]) ).

cnf(f_1547_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_6962)),U_6963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_6961,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK135(U_6963,U_6962,U_6961))),U_6962)),U_6963)) ),
    inference(clausify,[status(thm)],[f_1547_3]) ).

fof(f_1548_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).

fof(f_1548_2,plain,
    ! [U_6966,U_6965,U_6964] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6964,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_6964),U_6965),c_Orderings_Obot__class_Obot(tc_fun(U_6964,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6964,U_6965,U_6966)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6964,U_6965),U_6966)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6964),U_6965),U_6966))
      | ~ class_Orderings_Olinorder(U_6964) ),
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

cnf(f_1548_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6964,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_6964),U_6965),c_Orderings_Obot__class_Obot(tc_fun(U_6964,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6964,U_6965,U_6966)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6964,U_6965),U_6966)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6964),U_6965),U_6966))
    | ~ class_Orderings_Olinorder(U_6964) ),
    inference(clausify,[status(thm)],[f_1548_2]) ).

fof(f_1549_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_1549_2,plain,
    ! [U_6968,U_6967] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6967,U_6968))),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

cnf(f_1549_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6967,U_6968))),
    inference(clausify,[status(thm)],[f_1549_2]) ).

fof(f_1550_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_1550_2,plain,
    ! [U_6970,U_6969] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6969),U_6970))),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

cnf(f_1550_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6969),U_6970))),
    inference(clausify,[status(thm)],[f_1550_2]) ).

fof(f_1551_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_1551_2,plain,
    ! [U_6972,U_6971] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6971,U_6972))),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

cnf(f_1551_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6971,U_6972))),
    inference(clausify,[status(thm)],[f_1551_2]) ).

fof(f_1552_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_1552_2,plain,
    ! [U_6974,U_6973] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6973),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6974) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6973,U_6974),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

cnf(f_1552_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6973),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6974) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6973,U_6974),
    inference(clausify,[status(thm)],[f_1552_2]) ).

fof(f_1553_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_1553_2,plain,
    ! [U_6975] : 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_6975))),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

cnf(f_1553_3,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_6975))),
    inference(clausify,[status(thm)],[f_1553_2]) ).

fof(f_1554_1,plain,
    ! [V_k_2,V_l_2,T_a] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).

fof(f_1554_2,plain,
    ! [U_6978,U_6977,U_6976] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_6976,U_6978,U_6977) = c_Orderings_Obot__class_Obot(tc_fun(U_6976,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6976),U_6977),U_6978))
      | ~ class_Orderings_Oorder(U_6976) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

cnf(f_1554_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_6976,U_6978,U_6977) = c_Orderings_Obot__class_Obot(tc_fun(U_6976,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6976),U_6977),U_6978))
    | ~ class_Orderings_Oorder(U_6976) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

fof(f_1555_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_1555_2,plain,
    ! [U_6980,U_6979] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6979)),U_6980) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6979,U_6980),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

cnf(f_1555_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6979)),U_6980) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6979,U_6980),
    inference(clausify,[status(thm)],[f_1555_2]) ).

fof(f_1556_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_1556_2,plain,
    ! [U_6982,U_6981] : 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_6981)),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_6982),U_6981))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6981),U_6982),
    inference(variable_rename,[status(thm)],[f_1556_1]) ).

cnf(f_1556_3,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_6981)),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_6982),U_6981))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6981),U_6982),
    inference(clausify,[status(thm)],[f_1556_2]) ).

fof(f_1557_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).

fof(f_1557_2,plain,
    ! [U_6986,U_6985,U_6984,U_6983] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6983,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6983,U_6984,U_6985)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6983,U_6985),U_6986)) = c_Orderings_Obot__class_Obot(tc_fun(U_6983,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_6983) ),
    inference(variable_rename,[status(thm)],[f_1557_1]) ).

cnf(f_1557_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6983,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6983,U_6984,U_6985)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6983,U_6985),U_6986)) = c_Orderings_Obot__class_Obot(tc_fun(U_6983,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_6983) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

fof(f_1558_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_1558_2,plain,
    ! [U_6988,U_6987] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6987,U_6988)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6988),hAPP(c_Nat_OSuc,U_6987)),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

cnf(f_1558_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_6987,U_6988)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6988),hAPP(c_Nat_OSuc,U_6987)),
    inference(clausify,[status(thm)],[f_1558_2]) ).

fof(f_1559_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).

fof(f_1559_2,plain,
    ! [U_6992,U_6991,U_6990,U_6989] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6989,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6989,U_6990,U_6991)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6989,U_6991),U_6992)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_6989,U_6990,U_6992)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6989),U_6991),U_6992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6989),U_6990),U_6991))
      | ~ class_Orderings_Olinorder(U_6989) ),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

cnf(f_1559_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6989,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6989,U_6990,U_6991)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6989,U_6991),U_6992)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_6989,U_6990,U_6992)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6989),U_6991),U_6992))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6989),U_6990),U_6991))
    | ~ class_Orderings_Olinorder(U_6989) ),
    inference(clausify,[status(thm)],[f_1559_2]) ).

fof(f_1560_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).

fof(f_1560_2,plain,
    ! [U_6995,U_6994,U_6993] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6993,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6993,U_6994,U_6995)),hAPP(hAPP(c_Set_Oinsert(U_6993),U_6995),c_Orderings_Obot__class_Obot(tc_fun(U_6993,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6993,U_6994,U_6995)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),U_6994),U_6995))
      | ~ class_Orderings_Olinorder(U_6993) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

cnf(f_1560_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6993,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6993,U_6994,U_6995)),hAPP(hAPP(c_Set_Oinsert(U_6993),U_6995),c_Orderings_Obot__class_Obot(tc_fun(U_6993,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6993,U_6994,U_6995)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),U_6994),U_6995))
    | ~ class_Orderings_Olinorder(U_6993) ),
    inference(clausify,[status(thm)],[f_1560_2]) ).

fof(f_1561_1,plain,
    ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
      ( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) != c_Groups_Ozero__class_Ozero(T_b)
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).

fof(f_1561_2,plain,
    ! [U_7001,U_7000,U_6999,U_6998,U_6997] :
      ( hAPP(U_7000,U_7001) = c_Groups_Ozero__class_Ozero(U_6997)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6998),U_7001),U_6999))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6998,U_6997),U_7000),U_6999) != c_Groups_Ozero__class_Ozero(U_6997)
      | ? [U_6996] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),c_Groups_Ozero__class_Ozero(U_6997)),hAPP(U_7000,U_6996)))
          & hBOOL(hAPP(hAPP(c_member(U_6998),U_6996),U_6999)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6998),U_6999))
      | ~ class_Groups_Oordered__ab__group__add(U_6997) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

fof(f_1561_3,plain,
    ! [U_7001,U_7000,U_6999,U_6998,U_6997] :
      ( hAPP(U_7000,U_7001) = c_Groups_Ozero__class_Ozero(U_6997)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6998),U_7001),U_6999))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6998,U_6997),U_7000),U_6999) != c_Groups_Ozero__class_Ozero(U_6997)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),c_Groups_Ozero__class_Ozero(U_6997)),hAPP(U_7000,sK136(U_7001,U_7000,U_6999,U_6998,U_6997))))
        & hBOOL(hAPP(hAPP(c_member(U_6998),sK136(U_7001,U_7000,U_6999,U_6998,U_6997)),U_6999)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6998),U_6999))
      | ~ class_Groups_Oordered__ab__group__add(U_6997) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6996,sK136(U_7001,U_7000,U_6999,U_6998,U_6997))],[f_1561_2]) ).

cnf(f_1561_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6998),sK136(U_7001,U_7000,U_6999,U_6998,U_6997)),U_6999))
    | hAPP(U_7000,U_7001) = c_Groups_Ozero__class_Ozero(U_6997)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6998),U_7001),U_6999))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6998,U_6997),U_7000),U_6999) != c_Groups_Ozero__class_Ozero(U_6997)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6998),U_6999))
    | ~ class_Groups_Oordered__ab__group__add(U_6997) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

cnf(f_1561_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),c_Groups_Ozero__class_Ozero(U_6997)),hAPP(U_7000,sK136(U_7001,U_7000,U_6999,U_6998,U_6997))))
    | hAPP(U_7000,U_7001) = c_Groups_Ozero__class_Ozero(U_6997)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6998),U_7001),U_6999))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6998,U_6997),U_7000),U_6999) != c_Groups_Ozero__class_Ozero(U_6997)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6998),U_6999))
    | ~ class_Groups_Oordered__ab__group__add(U_6997) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

fof(f_1562_1,plain,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) != V_B_2
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).

fof(f_1562_2,plain,
    ! [U_7008,U_7007,U_7006,U_7005,U_7004,U_7003] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),hAPP(U_7006,U_7008)),U_7007))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7004),U_7008),U_7005))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7004,U_7003),U_7006),U_7005) != U_7007
      | ? [U_7002] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),c_Groups_Ozero__class_Ozero(U_7003)),hAPP(U_7006,U_7002)))
          & hBOOL(hAPP(hAPP(c_member(U_7004),U_7002),U_7005)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7004),U_7005))
      | ~ class_Groups_Oordered__ab__group__add(U_7003) ),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

fof(f_1562_3,plain,
    ! [U_7008,U_7007,U_7006,U_7005,U_7004,U_7003] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),hAPP(U_7006,U_7008)),U_7007))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7004),U_7008),U_7005))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7004,U_7003),U_7006),U_7005) != U_7007
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),c_Groups_Ozero__class_Ozero(U_7003)),hAPP(U_7006,sK137(U_7008,U_7007,U_7006,U_7005,U_7004,U_7003))))
        & hBOOL(hAPP(hAPP(c_member(U_7004),sK137(U_7008,U_7007,U_7006,U_7005,U_7004,U_7003)),U_7005)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7004),U_7005))
      | ~ class_Groups_Oordered__ab__group__add(U_7003) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_7002,sK137(U_7008,U_7007,U_7006,U_7005,U_7004,U_7003))],[f_1562_2]) ).

cnf(f_1562_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7004),sK137(U_7008,U_7007,U_7006,U_7005,U_7004,U_7003)),U_7005))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),hAPP(U_7006,U_7008)),U_7007))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7004),U_7008),U_7005))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7004,U_7003),U_7006),U_7005) != U_7007
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7004),U_7005))
    | ~ class_Groups_Oordered__ab__group__add(U_7003) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

cnf(f_1562_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),c_Groups_Ozero__class_Ozero(U_7003)),hAPP(U_7006,sK137(U_7008,U_7007,U_7006,U_7005,U_7004,U_7003))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7003),hAPP(U_7006,U_7008)),U_7007))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7004),U_7008),U_7005))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7004,U_7003),U_7006),U_7005) != U_7007
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7004),U_7005))
    | ~ class_Groups_Oordered__ab__group__add(U_7003) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

fof(f_1563_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]) ).

cnf(f_1563_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(clausify,[status(thm)],[f_1563_1]) ).

fof(f_1564_1,plain,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))
      | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) ),
    inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).

fof(f_1564_2,plain,
    ! [U_7012,U_7011,U_7010] :
      ( 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_7011),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7010),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))) = 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_7011)),U_7010)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))
      | ? [U_7009] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7010,U_7009)),hAPP(U_7011,U_7009))) ),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

fof(f_1564_3,plain,
    ! [U_7012,U_7011,U_7010] :
      ( 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_7011),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7010),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))) = 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_7011)),U_7010)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7010,sK138(U_7012,U_7011,U_7010))),hAPP(U_7011,sK138(U_7012,U_7011,U_7010)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_7009,sK138(U_7012,U_7011,U_7010))],[f_1564_2]) ).

cnf(f_1564_4,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_7011),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7010),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))) = 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_7011)),U_7010)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7012))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_7010,sK138(U_7012,U_7011,U_7010))),hAPP(U_7011,sK138(U_7012,U_7011,U_7010)))) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

fof(f_1565_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a)
          | 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_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(f_1565_2,plain,
    ! [U_7016,U_7015,U_7014,U_7013] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7013),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_7013,U_7013),hAPP(hAPP(c_COMBB(U_7013,tc_fun(U_7013,U_7013),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_7013)),U_7016)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7013,tc_Nat_Onat),U_7016),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_7014,U_7015)) = c_Groups_Ozero__class_Ozero(U_7013)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7013),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_7013,U_7013),hAPP(hAPP(c_COMBB(U_7013,tc_fun(U_7013,U_7013),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_7013)),U_7016)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7013,tc_Nat_Onat),U_7016),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_7014,U_7015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7013),hAPP(U_7016,U_7014)),hAPP(U_7016,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7015),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015)) ) )
      | ~ class_Groups_Oab__group__add(U_7013) ),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

cnf(f_1565_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7013),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_7013,U_7013),hAPP(hAPP(c_COMBB(U_7013,tc_fun(U_7013,U_7013),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_7013)),U_7016)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7013,tc_Nat_Onat),U_7016),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_7014,U_7015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7013),hAPP(U_7016,U_7014)),hAPP(U_7016,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7015),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015))
    | ~ class_Groups_Oab__group__add(U_7013) ),
    inference(clausify,[status(thm)],[f_1565_2]) ).

cnf(f_1565_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7013),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_7013,U_7013),hAPP(hAPP(c_COMBB(U_7013,tc_fun(U_7013,U_7013),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_7013)),U_7016)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7013,tc_Nat_Onat),U_7016),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_7014,U_7015)) = c_Groups_Ozero__class_Ozero(U_7013)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015))
    | ~ class_Groups_Oab__group__add(U_7013) ),
    inference(clausify,[status(thm)],[f_1565_2]) ).

fof(f_1566_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_1566_2,plain,
    ! [U_7018,U_7017] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7017,U_7018))),
    inference(variable_rename,[status(thm)],[f_1566_1]) ).

cnf(f_1566_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7017,U_7018))),
    inference(clausify,[status(thm)],[f_1566_2]) ).

fof(f_1567_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_1567_2,plain,
    ! [U_7020,U_7019] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7019,U_7020))),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

cnf(f_1567_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7019,U_7020))),
    inference(clausify,[status(thm)],[f_1567_2]) ).

fof(f_1568_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_1568_2,plain,
    ! [U_7022,U_7021] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7021,U_7022))),
    inference(variable_rename,[status(thm)],[f_1568_1]) ).

cnf(f_1568_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7021,U_7022))),
    inference(clausify,[status(thm)],[f_1568_2]) ).

fof(f_1569_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).

fof(f_1569_2,plain,
    ! [U_7025,U_7024,U_7023] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7024) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7025)
          | U_7024 != U_7025 )
        & ( U_7024 = U_7025
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7024) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7025) ) )
      | ~ class_Orderings_Olinorder(U_7023) ),
    inference(variable_rename,[status(thm)],[f_1569_1]) ).

cnf(f_1569_3,plain,
    ( U_7024 = U_7025
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7024) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7025)
    | ~ class_Orderings_Olinorder(U_7023) ),
    inference(clausify,[status(thm)],[f_1569_2]) ).

cnf(f_1569_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7024) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7023),U_7025)
    | U_7024 != U_7025
    | ~ class_Orderings_Olinorder(U_7023) ),
    inference(clausify,[status(thm)],[f_1569_2]) ).

fof(f_1570_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_1570_2,plain,
    ! [U_7027,U_7026] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7026),U_7027) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7026,U_7027),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

cnf(f_1570_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7026),U_7027) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7026,U_7027),
    inference(clausify,[status(thm)],[f_1570_2]) ).

fof(f_1571_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).

fof(f_1571_2,plain,
    ! [U_7031,U_7030,U_7029,U_7028] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7028,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7028,U_7029,U_7030)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7028,U_7030,U_7031)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7028,U_7029,U_7031)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),U_7030),U_7031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),U_7029),U_7030))
      | ~ class_Orderings_Olinorder(U_7028) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

cnf(f_1571_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7028,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7028,U_7029,U_7030)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7028,U_7030,U_7031)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7028,U_7029,U_7031)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),U_7030),U_7031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),U_7029),U_7030))
    | ~ class_Orderings_Olinorder(U_7028) ),
    inference(clausify,[status(thm)],[f_1571_2]) ).

fof(f_1572_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).

fof(f_1572_2,plain,
    ! [U_7035,U_7034,U_7033,U_7032] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7032,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7032,U_7033,U_7034)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7032,U_7034,U_7035)) = c_Orderings_Obot__class_Obot(tc_fun(U_7032,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7032) ),
    inference(variable_rename,[status(thm)],[f_1572_1]) ).

cnf(f_1572_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7032,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7032,U_7033,U_7034)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7032,U_7034,U_7035)) = c_Orderings_Obot__class_Obot(tc_fun(U_7032,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7032) ),
    inference(clausify,[status(thm)],[f_1572_2]) ).

fof(f_1573_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).

fof(f_1573_2,plain,
    ! [U_7038,U_7037,U_7036] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7036,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7036,U_7037,U_7038)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7036),U_7038)) = c_Orderings_Obot__class_Obot(tc_fun(U_7036,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7036) ),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

cnf(f_1573_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7036,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7036,U_7037,U_7038)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7036),U_7038)) = c_Orderings_Obot__class_Obot(tc_fun(U_7036,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7036) ),
    inference(clausify,[status(thm)],[f_1573_2]) ).

fof(f_1574_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).

fof(f_1574_2,plain,
    ! [U_7041,U_7040,U_7039] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7039,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7039,U_7040,U_7041)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7039),U_7041)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7039),U_7040)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7039),U_7040),U_7041))
      | ~ class_Orderings_Olinorder(U_7039) ),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

cnf(f_1574_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7039,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7039,U_7040,U_7041)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7039),U_7041)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7039),U_7040)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7039),U_7040),U_7041))
    | ~ class_Orderings_Olinorder(U_7039) ),
    inference(clausify,[status(thm)],[f_1574_2]) ).

fof(f_1575_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).

fof(f_1575_2,plain,
    ! [U_7044,U_7043,U_7042] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7042,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7042,U_7043,U_7044)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7042),U_7044)) = c_Orderings_Obot__class_Obot(tc_fun(U_7042,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7042) ),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

cnf(f_1575_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7042,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7042,U_7043,U_7044)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7042),U_7044)) = c_Orderings_Obot__class_Obot(tc_fun(U_7042,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7042) ),
    inference(clausify,[status(thm)],[f_1575_2]) ).

fof(f_1576_1,plain,
    ! [V_P_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).

fof(f_1576_2,plain,
    ! [U_7048,U_7047,U_7046,U_7045] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7045),U_7048),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7046,U_7047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7045),hAPP(U_7048,U_7046)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7045),U_7048),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7046,U_7047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7046),U_7047))
      | ~ class_Groups_Ocomm__monoid__add(U_7045) ),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

cnf(f_1576_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7045),U_7048),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7046,U_7047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7045),hAPP(U_7048,U_7046)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7045),U_7048),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7046,U_7047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7046),U_7047))
    | ~ class_Groups_Ocomm__monoid__add(U_7045) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

fof(f_1577_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).

fof(f_1577_2,plain,
    ! [U_7054,U_7053] :
      ( ( ! [U_7052] :
            ( hBOOL(hAPP(U_7054,U_7052))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7053)) )
        | ? [U_7051] :
            ( ~ hBOOL(hAPP(U_7054,U_7051))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7051),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7053))) ) )
      & ( ! [U_7050] :
            ( hBOOL(hAPP(U_7054,U_7050))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7053))) )
        | ? [U_7049] :
            ( ~ hBOOL(hAPP(U_7054,U_7049))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7049),U_7053)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

fof(f_1577_3,plain,
    ( ! [U_7058,U_7056] :
        ( ! [U_7052] :
            ( hBOOL(hAPP(U_7058,U_7052))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7056)) )
        | ? [U_7051] :
            ( ~ hBOOL(hAPP(U_7058,U_7051))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7051),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7056))) ) )
    & ! [U_7057,U_7055] :
        ( ! [U_7050] :
            ( hBOOL(hAPP(U_7057,U_7050))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7055))) )
        | ? [U_7049] :
            ( ~ hBOOL(hAPP(U_7057,U_7049))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7049),U_7055)) ) ) ),
    inference(miniscope,[status(thm)],[f_1577_2]) ).

fof(f_1577_4,plain,
    ( ! [U_7058,U_7056] :
        ( ! [U_7052] :
            ( hBOOL(hAPP(U_7058,U_7052))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7056)) )
        | ? [U_7051] :
            ( ~ hBOOL(hAPP(U_7058,U_7051))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7051),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7056))) ) )
    & ! [U_7057,U_7055] :
        ( ! [U_7050] :
            ( hBOOL(hAPP(U_7057,U_7050))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7055))) )
        | ( ~ hBOOL(hAPP(U_7057,sK139(U_7057,U_7055)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK139(U_7057,U_7055)),U_7055)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_7049,sK139(U_7057,U_7055))],[f_1577_3]) ).

fof(f_1577_5,plain,
    ( ! [U_7058,U_7056] :
        ( ! [U_7052] :
            ( hBOOL(hAPP(U_7058,U_7052))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7056)) )
        | ( ~ hBOOL(hAPP(U_7058,sK140(U_7058,U_7056)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK140(U_7058,U_7056)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7056))) ) )
    & ! [U_7057,U_7055] :
        ( ! [U_7050] :
            ( hBOOL(hAPP(U_7057,U_7050))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7055))) )
        | ( ~ hBOOL(hAPP(U_7057,sK139(U_7057,U_7055)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK139(U_7057,U_7055)),U_7055)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_7051,sK140(U_7058,U_7056))],[f_1577_4]) ).

cnf(f_1577_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK139(U_7057,U_7055)),U_7055))
    | hBOOL(hAPP(U_7057,U_7050))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7055))) ),
    inference(clausify,[status(thm)],[f_1577_5]) ).

cnf(f_1577_7,plain,
    ( ~ hBOOL(hAPP(U_7057,sK139(U_7057,U_7055)))
    | hBOOL(hAPP(U_7057,U_7050))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7055))) ),
    inference(clausify,[status(thm)],[f_1577_5]) ).

cnf(f_1577_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK140(U_7058,U_7056)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7056)))
    | hBOOL(hAPP(U_7058,U_7052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7056)) ),
    inference(clausify,[status(thm)],[f_1577_5]) ).

cnf(f_1577_9,plain,
    ( ~ hBOOL(hAPP(U_7058,sK140(U_7058,U_7056)))
    | hBOOL(hAPP(U_7058,U_7052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7052),U_7056)) ),
    inference(clausify,[status(thm)],[f_1577_5]) ).

fof(f_1578_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).

fof(f_1578_2,plain,
    ! [U_7064,U_7063] :
      ( ( ? [U_7062] :
            ( hBOOL(hAPP(U_7064,U_7062))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7063)) )
        | ! [U_7061] :
            ( ~ hBOOL(hAPP(U_7064,U_7061))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7063))) ) )
      & ( ? [U_7060] :
            ( hBOOL(hAPP(U_7064,U_7060))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7060),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7063))) )
        | ! [U_7059] :
            ( ~ hBOOL(hAPP(U_7064,U_7059))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7063)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1578_1]) ).

fof(f_1578_3,plain,
    ( ! [U_7068,U_7066] :
        ( ? [U_7062] :
            ( hBOOL(hAPP(U_7068,U_7062))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7066)) )
        | ! [U_7061] :
            ( ~ hBOOL(hAPP(U_7068,U_7061))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7066))) ) )
    & ! [U_7067,U_7065] :
        ( ? [U_7060] :
            ( hBOOL(hAPP(U_7067,U_7060))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7060),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7065))) )
        | ! [U_7059] :
            ( ~ hBOOL(hAPP(U_7067,U_7059))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7065)) ) ) ),
    inference(miniscope,[status(thm)],[f_1578_2]) ).

fof(f_1578_4,plain,
    ( ! [U_7068,U_7066] :
        ( ? [U_7062] :
            ( hBOOL(hAPP(U_7068,U_7062))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7062),U_7066)) )
        | ! [U_7061] :
            ( ~ hBOOL(hAPP(U_7068,U_7061))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7066))) ) )
    & ! [U_7067,U_7065] :
        ( ( hBOOL(hAPP(U_7067,sK141(U_7067,U_7065)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK141(U_7067,U_7065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7065))) )
        | ! [U_7059] :
            ( ~ hBOOL(hAPP(U_7067,U_7059))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7065)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_7060,sK141(U_7067,U_7065))],[f_1578_3]) ).

fof(f_1578_5,plain,
    ( ! [U_7068,U_7066] :
        ( ( hBOOL(hAPP(U_7068,sK142(U_7068,U_7066)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK142(U_7068,U_7066)),U_7066)) )
        | ! [U_7061] :
            ( ~ hBOOL(hAPP(U_7068,U_7061))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7066))) ) )
    & ! [U_7067,U_7065] :
        ( ( hBOOL(hAPP(U_7067,sK141(U_7067,U_7065)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK141(U_7067,U_7065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7065))) )
        | ! [U_7059] :
            ( ~ hBOOL(hAPP(U_7067,U_7059))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7065)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_7062,sK142(U_7068,U_7066))],[f_1578_4]) ).

cnf(f_1578_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK141(U_7067,U_7065)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7065)))
    | ~ hBOOL(hAPP(U_7067,U_7059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7065)) ),
    inference(clausify,[status(thm)],[f_1578_5]) ).

cnf(f_1578_7,plain,
    ( hBOOL(hAPP(U_7067,sK141(U_7067,U_7065)))
    | ~ hBOOL(hAPP(U_7067,U_7059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7059),U_7065)) ),
    inference(clausify,[status(thm)],[f_1578_5]) ).

cnf(f_1578_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK142(U_7068,U_7066)),U_7066))
    | ~ hBOOL(hAPP(U_7068,U_7061))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7066))) ),
    inference(clausify,[status(thm)],[f_1578_5]) ).

cnf(f_1578_9,plain,
    ( hBOOL(hAPP(U_7068,sK142(U_7068,U_7066)))
    | ~ hBOOL(hAPP(U_7068,U_7061))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7061),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7066))) ),
    inference(clausify,[status(thm)],[f_1578_5]) ).

fof(f_1579_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_1579_2,plain,
    ! [U_7070,U_7069] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7069),hAPP(c_Nat_OSuc,U_7070)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7069,U_7070),
    inference(variable_rename,[status(thm)],[f_1579_1]) ).

cnf(f_1579_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7069),hAPP(c_Nat_OSuc,U_7070)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7069,U_7070),
    inference(clausify,[status(thm)],[f_1579_2]) ).

fof(f_1580_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).

fof(f_1580_2,plain,
    ! [U_7073,U_7072,U_7071] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7071,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7071),U_7072),c_Orderings_Obot__class_Obot(tc_fun(U_7071,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7071,U_7072,U_7073)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7071,U_7072,U_7073)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7071),U_7072),U_7073))
      | ~ class_Orderings_Olinorder(U_7071) ),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

cnf(f_1580_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7071,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7071),U_7072),c_Orderings_Obot__class_Obot(tc_fun(U_7071,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7071,U_7072,U_7073)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7071,U_7072,U_7073)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7071),U_7072),U_7073))
    | ~ class_Orderings_Olinorder(U_7071) ),
    inference(clausify,[status(thm)],[f_1580_2]) ).

fof(f_1581_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(f_1581_2,plain,
    ! [U_7076,U_7075,U_7074] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_7074,U_7075,U_7076) = c_Orderings_Obot__class_Obot(tc_fun(U_7074,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_7074,U_7075,U_7076) != c_Orderings_Obot__class_Obot(tc_fun(U_7074,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_7074) ),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

cnf(f_1581_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_7074,U_7075,U_7076) != c_Orderings_Obot__class_Obot(tc_fun(U_7074,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7074) ),
    inference(clausify,[status(thm)],[f_1581_2]) ).

cnf(f_1581_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_7074,U_7075,U_7076) = c_Orderings_Obot__class_Obot(tc_fun(U_7074,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076))
    | ~ class_Orderings_Oorder(U_7074) ),
    inference(clausify,[status(thm)],[f_1581_2]) ).

fof(f_1582_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(f_1582_2,plain,
    ! [U_7079,U_7078,U_7077] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7077,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7077,U_7078,U_7079)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079))
          | c_Orderings_Obot__class_Obot(tc_fun(U_7077,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_7077,U_7078,U_7079) ) )
      | ~ class_Orderings_Oorder(U_7077) ),
    inference(variable_rename,[status(thm)],[f_1582_1]) ).

cnf(f_1582_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079))
    | c_Orderings_Obot__class_Obot(tc_fun(U_7077,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_7077,U_7078,U_7079)
    | ~ class_Orderings_Oorder(U_7077) ),
    inference(clausify,[status(thm)],[f_1582_2]) ).

cnf(f_1582_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_7077,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7077,U_7078,U_7079)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079))
    | ~ class_Orderings_Oorder(U_7077) ),
    inference(clausify,[status(thm)],[f_1582_2]) ).

fof(f_1583_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).

fof(f_1583_2,plain,
    ! [U_7082,U_7081,U_7080] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_7080,U_7082,U_7081) = c_Orderings_Obot__class_Obot(tc_fun(U_7080,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7080),U_7081),U_7082))
      | ~ class_Orderings_Oorder(U_7080) ),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

cnf(f_1583_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_7080,U_7082,U_7081) = c_Orderings_Obot__class_Obot(tc_fun(U_7080,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7080),U_7081),U_7082))
    | ~ class_Orderings_Oorder(U_7080) ),
    inference(clausify,[status(thm)],[f_1583_2]) ).

fof(f_1584_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(f_1584_2,plain,
    ! [U_7087,U_7086,U_7085,U_7084,U_7083] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7085),U_7087))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7086),U_7084)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7084),U_7085)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7085),U_7087))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7086),U_7084)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7084),U_7085))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087))) ) )
      | ~ class_Orderings_Oorder(U_7083) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

cnf(f_1584_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7086),U_7084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7084),U_7085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087)))
    | ~ class_Orderings_Oorder(U_7083) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

cnf(f_1584_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7085),U_7087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7084),U_7085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087)))
    | ~ class_Orderings_Oorder(U_7083) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

cnf(f_1584_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7084),U_7085))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087)))
    | ~ class_Orderings_Oorder(U_7083) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

cnf(f_1584_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7085),U_7087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7083),U_7086),U_7084))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7083,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7084,U_7085)),c_SetInterval_Oord__class_OatLeastAtMost(U_7083,U_7086,U_7087)))
    | ~ class_Orderings_Oorder(U_7083) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

fof(f_1585_1,plain,
    ! [V_a_2,T_a] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).

fof(f_1585_2,plain,
    ! [U_7089,U_7088] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_7088,U_7089,U_7089) = hAPP(hAPP(c_Set_Oinsert(U_7088),U_7089),c_Orderings_Obot__class_Obot(tc_fun(U_7088,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_7088) ),
    inference(variable_rename,[status(thm)],[f_1585_1]) ).

cnf(f_1585_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_7088,U_7089,U_7089) = hAPP(hAPP(c_Set_Oinsert(U_7088),U_7089),c_Orderings_Obot__class_Obot(tc_fun(U_7088,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_7088) ),
    inference(clausify,[status(thm)],[f_1585_2]) ).

fof(f_1586_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,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_a,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).

fof(f_1586_2,plain,
    ! [U_7093,U_7092,U_7091,U_7090] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_7090,U_7091,U_7092) = hAPP(hAPP(c_Set_Oinsert(U_7090),U_7093),c_Orderings_Obot__class_Obot(tc_fun(U_7090,tc_HOL_Obool)))
          | U_7092 != U_7093
          | U_7091 != U_7092 )
        & ( ( U_7092 = U_7093
            & U_7091 = U_7092 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_7090,U_7091,U_7092) != hAPP(hAPP(c_Set_Oinsert(U_7090),U_7093),c_Orderings_Obot__class_Obot(tc_fun(U_7090,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_7090) ),
    inference(variable_rename,[status(thm)],[f_1586_1]) ).

cnf(f_1586_3,plain,
    ( U_7091 = U_7092
    | c_SetInterval_Oord__class_OatLeastAtMost(U_7090,U_7091,U_7092) != hAPP(hAPP(c_Set_Oinsert(U_7090),U_7093),c_Orderings_Obot__class_Obot(tc_fun(U_7090,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_7090) ),
    inference(clausify,[status(thm)],[f_1586_2]) ).

cnf(f_1586_4,plain,
    ( U_7092 = U_7093
    | c_SetInterval_Oord__class_OatLeastAtMost(U_7090,U_7091,U_7092) != hAPP(hAPP(c_Set_Oinsert(U_7090),U_7093),c_Orderings_Obot__class_Obot(tc_fun(U_7090,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_7090) ),
    inference(clausify,[status(thm)],[f_1586_2]) ).

cnf(f_1586_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_7090,U_7091,U_7092) = hAPP(hAPP(c_Set_Oinsert(U_7090),U_7093),c_Orderings_Obot__class_Obot(tc_fun(U_7090,tc_HOL_Obool)))
    | U_7092 != U_7093
    | U_7091 != U_7092
    | ~ class_Orderings_Oorder(U_7090) ),
    inference(clausify,[status(thm)],[f_1586_2]) ).

fof(f_1587_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
      | V_a_2 != V_b_2
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).

fof(f_1587_2,plain,
    ! [U_7096,U_7095,U_7094] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_7094,U_7095,U_7096) = hAPP(hAPP(c_Set_Oinsert(U_7094),U_7095),c_Orderings_Obot__class_Obot(tc_fun(U_7094,tc_HOL_Obool)))
      | U_7095 != U_7096
      | ~ class_Orderings_Oorder(U_7094) ),
    inference(variable_rename,[status(thm)],[f_1587_1]) ).

cnf(f_1587_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_7094,U_7095,U_7096) = hAPP(hAPP(c_Set_Oinsert(U_7094),U_7095),c_Orderings_Obot__class_Obot(tc_fun(U_7094,tc_HOL_Obool)))
    | U_7095 != U_7096
    | ~ class_Orderings_Oorder(U_7094) ),
    inference(clausify,[status(thm)],[f_1587_2]) ).

fof(f_1588_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).

fof(f_1588_2,plain,
    ! [U_7100,U_7099,U_7098,U_7097] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7097,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7097,U_7098,U_7099)),c_SetInterval_Oord__class_OatLeastAtMost(U_7097,U_7099,U_7100)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7097,U_7098,U_7100)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7097),U_7099),U_7100))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),U_7098),U_7099))
      | ~ class_Orderings_Olinorder(U_7097) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

cnf(f_1588_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7097,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7097,U_7098,U_7099)),c_SetInterval_Oord__class_OatLeastAtMost(U_7097,U_7099,U_7100)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7097,U_7098,U_7100)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7097),U_7099),U_7100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),U_7098),U_7099))
    | ~ class_Orderings_Olinorder(U_7097) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

fof(f_1589_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_1589_2,plain,
    ! [U_7102,U_7101] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7101,U_7102)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7101),hAPP(c_Nat_OSuc,U_7102)),
    inference(variable_rename,[status(thm)],[f_1589_1]) ).

cnf(f_1589_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7101,U_7102)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7101),hAPP(c_Nat_OSuc,U_7102)),
    inference(clausify,[status(thm)],[f_1589_2]) ).

fof(f_1590_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).

fof(f_1590_2,plain,
    ! [U_7106,U_7105,U_7104,U_7103] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7103),U_7104),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7105),hAPP(c_Nat_OSuc,U_7106))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7103),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7103,tc_Nat_Onat),U_7104),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7105,U_7106))
      | ~ class_Groups_Ocomm__monoid__add(U_7103) ),
    inference(variable_rename,[status(thm)],[f_1590_1]) ).

cnf(f_1590_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7103),U_7104),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7105),hAPP(c_Nat_OSuc,U_7106))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7103),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7103,tc_Nat_Onat),U_7104),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7105,U_7106))
    | ~ class_Groups_Ocomm__monoid__add(U_7103) ),
    inference(clausify,[status(thm)],[f_1590_2]) ).

fof(f_1591_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).

fof(f_1591_2,plain,
    ! [U_7111,U_7110,U_7109,U_7108,U_7107] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7107),U_7108),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7109),U_7110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7111),U_7110))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7107),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7107,tc_Nat_Onat),U_7108),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7110))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7109,U_7111))
      | ~ class_Groups_Ocomm__monoid__add(U_7107) ),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

cnf(f_1591_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7107),U_7108),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7109),U_7110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7111),U_7110))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7107),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7107,tc_Nat_Onat),U_7108),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7110))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7109,U_7111))
    | ~ class_Groups_Ocomm__monoid__add(U_7107) ),
    inference(clausify,[status(thm)],[f_1591_2]) ).

fof(f_1592_1,plain,
    ! [V_k_2,V_l_2,T_a] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).

fof(f_1592_2,plain,
    ! [U_7114,U_7113,U_7112] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7112,U_7114,U_7113) = c_Orderings_Obot__class_Obot(tc_fun(U_7112,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7112),U_7113),U_7114))
      | ~ class_Orderings_Oorder(U_7112) ),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

cnf(f_1592_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7112,U_7114,U_7113) = c_Orderings_Obot__class_Obot(tc_fun(U_7112,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7112),U_7113),U_7114))
    | ~ class_Orderings_Oorder(U_7112) ),
    inference(clausify,[status(thm)],[f_1592_2]) ).

fof(f_1593_1,plain,
    ! [V_l_2,V_k_2,T_a] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(f_1593_2,plain,
    ! [U_7117,U_7116,U_7115] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7115,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7115,U_7116,U_7117)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7115),U_7116),U_7117)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7115),U_7116),U_7117))
          | c_Orderings_Obot__class_Obot(tc_fun(U_7115,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_7115,U_7116,U_7117) ) )
      | ~ class_Orderings_Oorder(U_7115) ),
    inference(variable_rename,[status(thm)],[f_1593_1]) ).

cnf(f_1593_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7115),U_7116),U_7117))
    | c_Orderings_Obot__class_Obot(tc_fun(U_7115,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_7115,U_7116,U_7117)
    | ~ class_Orderings_Oorder(U_7115) ),
    inference(clausify,[status(thm)],[f_1593_2]) ).

cnf(f_1593_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_7115,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7115,U_7116,U_7117)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7115),U_7116),U_7117))
    | ~ class_Orderings_Oorder(U_7115) ),
    inference(clausify,[status(thm)],[f_1593_2]) ).

fof(f_1594_1,plain,
    ! [V_l_2,V_k_2,T_a] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(f_1594_2,plain,
    ! [U_7120,U_7119,U_7118] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7118,U_7119,U_7120) = c_Orderings_Obot__class_Obot(tc_fun(U_7118,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7118),U_7119),U_7120)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7118),U_7119),U_7120))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_7118,U_7119,U_7120) != c_Orderings_Obot__class_Obot(tc_fun(U_7118,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_7118) ),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

cnf(f_1594_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7118),U_7119),U_7120))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_7118,U_7119,U_7120) != c_Orderings_Obot__class_Obot(tc_fun(U_7118,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7118) ),
    inference(clausify,[status(thm)],[f_1594_2]) ).

cnf(f_1594_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7118,U_7119,U_7120) = c_Orderings_Obot__class_Obot(tc_fun(U_7118,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7118),U_7119),U_7120))
    | ~ class_Orderings_Oorder(U_7118) ),
    inference(clausify,[status(thm)],[f_1594_2]) ).

fof(f_1595_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).

fof(f_1595_2,plain,
    ! [U_7124,U_7123,U_7122,U_7121] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7121,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7122,U_7123)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7123,U_7124)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7122,U_7124)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7121),U_7123),U_7124))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7121),U_7122),U_7123))
      | ~ class_Orderings_Olinorder(U_7121) ),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

cnf(f_1595_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7121,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7122,U_7123)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7123,U_7124)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7121,U_7122,U_7124)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7121),U_7123),U_7124))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7121),U_7122),U_7123))
    | ~ class_Orderings_Olinorder(U_7121) ),
    inference(clausify,[status(thm)],[f_1595_2]) ).

fof(f_1596_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).

fof(f_1596_2,plain,
    ! [U_7128,U_7127,U_7126,U_7125] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7125,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7125,U_7126,U_7127)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7125,U_7127,U_7128)) = c_Orderings_Obot__class_Obot(tc_fun(U_7125,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7125) ),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

cnf(f_1596_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7125,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7125,U_7126,U_7127)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7125,U_7127,U_7128)) = c_Orderings_Obot__class_Obot(tc_fun(U_7125,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7125) ),
    inference(clausify,[status(thm)],[f_1596_2]) ).

fof(f_1597_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_1597_2,plain,
    ! [U_7131,U_7130,U_7129] : 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_7129)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7130,U_7131)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7130),U_7129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7131),U_7129)),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

cnf(f_1597_3,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_7129)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7130,U_7131)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7130),U_7129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7131),U_7129)),
    inference(clausify,[status(thm)],[f_1597_2]) ).

fof(f_1598_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_1598_2,plain,
    ! [U_7133,U_7132] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7132,U_7133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7133),U_7132),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

cnf(f_1598_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7132,U_7133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7133),U_7132),
    inference(clausify,[status(thm)],[f_1598_2]) ).

fof(f_1599_1,plain,
    ! [V_k_2,V_i_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).

fof(f_1599_2,plain,
    ! [U_7136,U_7135,U_7134] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7134),U_7135),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7134),U_7136)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7134),U_7136),U_7135)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7134),U_7136),U_7135))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7134),U_7135),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7134),U_7136))) ) )
      | ~ class_Orderings_Oord(U_7134) ),
    inference(variable_rename,[status(thm)],[f_1599_1]) ).

cnf(f_1599_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7134),U_7136),U_7135))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7134),U_7135),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7134),U_7136)))
    | ~ class_Orderings_Oord(U_7134) ),
    inference(clausify,[status(thm)],[f_1599_2]) ).

cnf(f_1599_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7134),U_7135),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7134),U_7136)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7134),U_7136),U_7135))
    | ~ class_Orderings_Oord(U_7134) ),
    inference(clausify,[status(thm)],[f_1599_2]) ).

fof(f_1600_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).

fof(f_1600_2,plain,
    ! [U_7139,U_7138,U_7137] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7137,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7138)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7139)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7137),U_7139),U_7138)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7137),U_7139),U_7138))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7137,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7138)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7139))) ) )
      | ~ class_Orderings_Olinorder(U_7137) ),
    inference(variable_rename,[status(thm)],[f_1600_1]) ).

cnf(f_1600_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7137),U_7139),U_7138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7137,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7138)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7139)))
    | ~ class_Orderings_Olinorder(U_7137) ),
    inference(clausify,[status(thm)],[f_1600_2]) ).

cnf(f_1600_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7137,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7138)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7137),U_7139)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7137),U_7139),U_7138))
    | ~ class_Orderings_Olinorder(U_7137) ),
    inference(clausify,[status(thm)],[f_1600_2]) ).

fof(f_1601_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_1601_2,plain,
    ! [U_7141,U_7140] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7140,U_7141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7141)),U_7140),
    inference(variable_rename,[status(thm)],[f_1601_1]) ).

cnf(f_1601_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7140,U_7141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7141)),U_7140),
    inference(clausify,[status(thm)],[f_1601_2]) ).

fof(f_1602_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_1602_2,plain,
    ! [U_7143,U_7142] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7142,hAPP(c_Nat_OSuc,U_7143)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7143)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7142,U_7143))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7142),hAPP(c_Nat_OSuc,U_7143))) ),
    inference(variable_rename,[status(thm)],[f_1602_1]) ).

cnf(f_1602_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7142,hAPP(c_Nat_OSuc,U_7143)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7143)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7142,U_7143))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7142),hAPP(c_Nat_OSuc,U_7143))) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

fof(f_1603_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_1603_2,plain,
    ! [U_7145,U_7144] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7144),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7145)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7144),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7145))
      | hAPP(U_7144,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1603_1]) ).

cnf(f_1603_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7144),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7145)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_7144),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7145))
    | hAPP(U_7144,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1603_2]) ).

fof(f_1604_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).

fof(f_1604_2,plain,
    ! [U_7149,U_7148,U_7147,U_7146] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7146,U_7147),U_7148)),c_SetInterval_Oord__class_OatLeastAtMost(U_7146,U_7148,U_7149)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7146,U_7147,U_7149)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7146),U_7148),U_7149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7146),U_7147),U_7148))
      | ~ class_Orderings_Olinorder(U_7146) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

cnf(f_1604_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7146,U_7147),U_7148)),c_SetInterval_Oord__class_OatLeastAtMost(U_7146,U_7148,U_7149)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7146,U_7147,U_7149)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7146),U_7148),U_7149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7146),U_7147),U_7148))
    | ~ class_Orderings_Olinorder(U_7146) ),
    inference(clausify,[status(thm)],[f_1604_2]) ).

fof(f_1605_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).

fof(f_1605_2,plain,
    ! [U_7153,U_7152,U_7151,U_7150] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7150,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7150,U_7151),U_7152)),c_SetInterval_Oord__class_OatLeastAtMost(U_7150,U_7152,U_7153)) = c_Orderings_Obot__class_Obot(tc_fun(U_7150,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7150) ),
    inference(variable_rename,[status(thm)],[f_1605_1]) ).

cnf(f_1605_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7150,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7150,U_7151),U_7152)),c_SetInterval_Oord__class_OatLeastAtMost(U_7150,U_7152,U_7153)) = c_Orderings_Obot__class_Obot(tc_fun(U_7150,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7150) ),
    inference(clausify,[status(thm)],[f_1605_2]) ).

fof(f_1606_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(f_1606_2,plain,
    ! [U_7158,U_7157,U_7156,U_7155,U_7154] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7156),U_7158))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7157),U_7155)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7156),U_7158))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7155)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7156),U_7158))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7157),U_7155)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7156),U_7158))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7155)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158))) ) )
      | ~ class_Orderings_Oorder(U_7154) ),
    inference(variable_rename,[status(thm)],[f_1606_1]) ).

cnf(f_1606_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7156),U_7158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7156),U_7158))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7157),U_7155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7155),U_7156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7157),U_7155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7156),U_7158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7154),U_7156),U_7158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7156),U_7158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),U_7157),U_7158))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7154,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7155,U_7156)),c_SetInterval_Oord__class_OatLeastAtMost(U_7154,U_7157,U_7158)))
    | ~ class_Orderings_Oorder(U_7154) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

fof(f_1607_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).

fof(f_1607_2,plain,
    ! [U_7161,U_7160,U_7159] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7159),U_7160)),c_SetInterval_Oord__class_OatLeastAtMost(U_7159,U_7160,U_7161)) = c_Orderings_Obot__class_Obot(tc_fun(U_7159,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7159) ),
    inference(variable_rename,[status(thm)],[f_1607_1]) ).

cnf(f_1607_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7159),U_7160)),c_SetInterval_Oord__class_OatLeastAtMost(U_7159,U_7160,U_7161)) = c_Orderings_Obot__class_Obot(tc_fun(U_7159,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7159) ),
    inference(clausify,[status(thm)],[f_1607_2]) ).

fof(f_1608_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).

fof(f_1608_2,plain,
    ! [U_7165,U_7164,U_7163,U_7162] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7162,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7162,U_7163,U_7164)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7162,U_7164,U_7165)) = c_Orderings_Obot__class_Obot(tc_fun(U_7162,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7162) ),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

cnf(f_1608_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7162,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7162,U_7163,U_7164)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7162,U_7164,U_7165)) = c_Orderings_Obot__class_Obot(tc_fun(U_7162,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7162) ),
    inference(clausify,[status(thm)],[f_1608_2]) ).

fof(f_1609_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).

fof(f_1609_2,plain,
    ! [U_7169,U_7168,U_7167,U_7166] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7166,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7166,U_7167,U_7168)),c_SetInterval_Oord__class_OatLeastAtMost(U_7166,U_7168,U_7169)) = c_Orderings_Obot__class_Obot(tc_fun(U_7166,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7166) ),
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

cnf(f_1609_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7166,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7166,U_7167,U_7168)),c_SetInterval_Oord__class_OatLeastAtMost(U_7166,U_7168,U_7169)) = c_Orderings_Obot__class_Obot(tc_fun(U_7166,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7166) ),
    inference(clausify,[status(thm)],[f_1609_2]) ).

fof(f_1610_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]) ).

cnf(f_1610_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(clausify,[status(thm)],[f_1610_1]) ).

fof(f_1611_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).

fof(f_1611_2,plain,
    ! [U_7173,U_7172,U_7171,U_7170] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7170),U_7173),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7171,U_7172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7170),hAPP(U_7173,U_7171)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7170),U_7173),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7171),U_7172)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7171),U_7172))
      | ~ class_Groups_Ocomm__monoid__add(U_7170) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

cnf(f_1611_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7170),U_7173),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7171,U_7172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7170),hAPP(U_7173,U_7171)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7170),U_7173),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7171),U_7172)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7171),U_7172))
    | ~ class_Groups_Ocomm__monoid__add(U_7170) ),
    inference(clausify,[status(thm)],[f_1611_2]) ).

fof(f_1612_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).

fof(f_1612_2,plain,
    ! [U_7177,U_7176,U_7175,U_7174] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7174,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7174,U_7175,U_7176)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7174,U_7176,U_7177)) = c_Orderings_Obot__class_Obot(tc_fun(U_7174,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7174) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

cnf(f_1612_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7174,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7174,U_7175,U_7176)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7174,U_7176,U_7177)) = c_Orderings_Obot__class_Obot(tc_fun(U_7174,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7174) ),
    inference(clausify,[status(thm)],[f_1612_2]) ).

fof(f_1613_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_1613_2,plain,
    ! [U_7178] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7178)) = 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_7178)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7178)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

cnf(f_1613_3,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7178)) = 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_7178)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7178)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1613_2]) ).

fof(f_1614_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a)
          | ~ 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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(f_1614_2,plain,
    ! [U_7182,U_7181,U_7180,U_7179] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,hAPP(c_Nat_OSuc,U_7180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7179),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,U_7180))),hAPP(U_7182,hAPP(c_Nat_OSuc,U_7180)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7180)),U_7181)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,hAPP(c_Nat_OSuc,U_7180))) = c_Groups_Ozero__class_Ozero(U_7179)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7180)),U_7181)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_7179) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

cnf(f_1614_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,hAPP(c_Nat_OSuc,U_7180))) = c_Groups_Ozero__class_Ozero(U_7179)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7180)),U_7181))
    | ~ class_Groups_Ocomm__monoid__add(U_7179) ),
    inference(clausify,[status(thm)],[f_1614_2]) ).

cnf(f_1614_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,hAPP(c_Nat_OSuc,U_7180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7179),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7179),U_7182),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7181,U_7180))),hAPP(U_7182,hAPP(c_Nat_OSuc,U_7180)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7180)),U_7181))
    | ~ class_Groups_Ocomm__monoid__add(U_7179) ),
    inference(clausify,[status(thm)],[f_1614_2]) ).

fof(f_1615_1,plain,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).

fof(f_1615_2,plain,
    ! [U_7187,U_7186,U_7185,U_7184,U_7183] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7184,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),U_7187))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7183),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7184,U_7185))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),U_7187))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_7183) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

cnf(f_1615_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7184,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),U_7187))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7183),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7184,U_7185))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7183),U_7186),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),U_7187))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7185),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_7183) ),
    inference(clausify,[status(thm)],[f_1615_2]) ).

fof(f_1616_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).

fof(f_1616_2,plain,
    ! [U_7191,U_7190,U_7189,U_7188] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7188,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7188,U_7189,U_7190)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7188,U_7190,U_7191)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7188,U_7189,U_7191)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7188),U_7190),U_7191))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7188),U_7189),U_7190))
      | ~ class_Orderings_Olinorder(U_7188) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

cnf(f_1616_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7188,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7188,U_7189,U_7190)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7188,U_7190,U_7191)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7188,U_7189,U_7191)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7188),U_7190),U_7191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7188),U_7189),U_7190))
    | ~ class_Orderings_Olinorder(U_7188) ),
    inference(clausify,[status(thm)],[f_1616_2]) ).

fof(f_1617_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).

fof(f_1617_2,plain,
    ! [U_7194,U_7193,U_7192] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7192,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7192,U_7193),U_7194)),hAPP(hAPP(c_Set_Oinsert(U_7192),U_7194),c_Orderings_Obot__class_Obot(tc_fun(U_7192,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_7192,U_7193,U_7194)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7192),U_7193),U_7194))
      | ~ class_Orderings_Olinorder(U_7192) ),
    inference(variable_rename,[status(thm)],[f_1617_1]) ).

cnf(f_1617_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7192,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7192,U_7193),U_7194)),hAPP(hAPP(c_Set_Oinsert(U_7192),U_7194),c_Orderings_Obot__class_Obot(tc_fun(U_7192,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_7192,U_7193,U_7194)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7192),U_7193),U_7194))
    | ~ class_Orderings_Olinorder(U_7192) ),
    inference(clausify,[status(thm)],[f_1617_2]) ).

fof(f_1618_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).

fof(f_1618_2,plain,
    ! [U_7198,U_7197,U_7196,U_7195] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7195,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7195,U_7196,U_7197)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7195,U_7197,U_7198)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7195,U_7196),U_7198)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7195),U_7197),U_7198))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7195),U_7196),U_7197))
      | ~ class_Orderings_Olinorder(U_7195) ),
    inference(variable_rename,[status(thm)],[f_1618_1]) ).

cnf(f_1618_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7195,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7195,U_7196,U_7197)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7195,U_7197,U_7198)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7195,U_7196),U_7198)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7195),U_7197),U_7198))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7195),U_7196),U_7197))
    | ~ class_Orderings_Olinorder(U_7195) ),
    inference(clausify,[status(thm)],[f_1618_2]) ).

fof(f_1619_1,plain,
    ! [V_n_2,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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).

fof(f_1619_2,plain,
    ! [U_7200,U_7199] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7199),c_Groups_Oone__class_Oone(U_7199)),c_Groups_Oone__class_Oone(U_7199))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7199),c_Nat_Osemiring__1__class_Oof__nat(U_7199)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7200))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7199),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7199),U_7200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7199),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7199),U_7200)),c_Groups_Oone__class_Oone(U_7199)))
      | ~ class_Rings_Ocomm__semiring__1(U_7199) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

cnf(f_1619_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7199),c_Groups_Oone__class_Oone(U_7199)),c_Groups_Oone__class_Oone(U_7199))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7199),c_Nat_Osemiring__1__class_Oof__nat(U_7199)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7200))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7199),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7199),U_7200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7199),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7199),U_7200)),c_Groups_Oone__class_Oone(U_7199)))
    | ~ class_Rings_Ocomm__semiring__1(U_7199) ),
    inference(clausify,[status(thm)],[f_1619_2]) ).

fof(f_1620_1,plain,
    ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_1620_2,plain,
    ! [U_7203,U_7202,U_7201] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7201,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7202)),U_7203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7201,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7201,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7202)),U_7203)),hAPP(U_7203,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

cnf(f_1620_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7201,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7202)),U_7203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7201,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7201,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7202)),U_7203)),hAPP(U_7203,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1620_2]) ).

fof(f_1621_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_1621_2,plain,
    ! [U_7204] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7204) = 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_7204)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7204)) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

cnf(f_1621_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7204) = 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_7204)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7204)) ),
    inference(clausify,[status(thm)],[f_1621_2]) ).

fof(f_1622_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).

fof(f_1622_2,plain,
    ! [U_7207,U_7206,U_7205] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7205,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7205,U_7206,U_7207)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7205),U_7207)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7205),U_7206)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7205),U_7206),U_7207))
      | ~ class_Orderings_Olinorder(U_7205) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

cnf(f_1622_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7205,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7205,U_7206,U_7207)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7205),U_7207)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7205),U_7206)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7205),U_7206),U_7207))
    | ~ class_Orderings_Olinorder(U_7205) ),
    inference(clausify,[status(thm)],[f_1622_2]) ).

fof(f_1623_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).

fof(f_1623_2,plain,
    ! [U_7212,U_7211,U_7210] :
      ( ! [U_7209] :
          ( hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7212),U_7210))))
          | ~ hBOOL(hAPP(U_7211,U_7209)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7212))
      | ? [U_7208] :
          ( ~ hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7208),U_7210)))
          & hBOOL(hAPP(U_7211,U_7208)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

fof(f_1623_3,plain,
    ! [U_7212,U_7211,U_7210] :
      ( ! [U_7209] :
          ( hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7212),U_7210))))
          | ~ hBOOL(hAPP(U_7211,U_7209)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7212))
      | ( ~ hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK143(U_7212,U_7211,U_7210)),U_7210)))
        & hBOOL(hAPP(U_7211,sK143(U_7212,U_7211,U_7210))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_7208,sK143(U_7212,U_7211,U_7210))],[f_1623_2]) ).

cnf(f_1623_4,plain,
    ( hBOOL(hAPP(U_7211,sK143(U_7212,U_7211,U_7210)))
    | hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7212),U_7210))))
    | ~ hBOOL(hAPP(U_7211,U_7209))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7212))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_5,plain,
    ( ~ hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK143(U_7212,U_7211,U_7210)),U_7210)))
    | hBOOL(hAPP(U_7211,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7212),U_7210))))
    | ~ hBOOL(hAPP(U_7211,U_7209))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7212))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7210)) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

fof(f_1624_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).

fof(f_1624_2,plain,
    ! [U_7217,U_7216,U_7215] :
      ( hAPP(U_7216,hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),U_7217)) = hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),hAPP(c_Set_Oimage(U_7215,U_7215,U_7216),U_7217))
      | U_7217 = c_Orderings_Obot__class_Obot(tc_fun(U_7215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7215),U_7217))
      | ? [U_7214,U_7213] : hAPP(U_7216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),U_7214),U_7213)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),hAPP(U_7216,U_7214)),hAPP(U_7216,U_7213))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_7215) ),
    inference(variable_rename,[status(thm)],[f_1624_1]) ).

fof(f_1624_3,plain,
    ! [U_7217,U_7216,U_7215] :
      ( hAPP(U_7216,hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),U_7217)) = hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),hAPP(c_Set_Oimage(U_7215,U_7215,U_7216),U_7217))
      | U_7217 = c_Orderings_Obot__class_Obot(tc_fun(U_7215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7215),U_7217))
      | ? [U_7213] : hAPP(U_7216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),sK144(U_7217,U_7216,U_7215)),U_7213)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),hAPP(U_7216,sK144(U_7217,U_7216,U_7215))),hAPP(U_7216,U_7213))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_7215) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_7214,sK144(U_7217,U_7216,U_7215))],[f_1624_2]) ).

fof(f_1624_4,plain,
    ! [U_7217,U_7216,U_7215] :
      ( hAPP(U_7216,hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),U_7217)) = hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),hAPP(c_Set_Oimage(U_7215,U_7215,U_7216),U_7217))
      | U_7217 = c_Orderings_Obot__class_Obot(tc_fun(U_7215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7215),U_7217))
      | hAPP(U_7216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),sK144(U_7217,U_7216,U_7215)),sK145(U_7217,U_7216,U_7215))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),hAPP(U_7216,sK144(U_7217,U_7216,U_7215))),hAPP(U_7216,sK145(U_7217,U_7216,U_7215)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_7215) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_7213,sK145(U_7217,U_7216,U_7215))],[f_1624_3]) ).

cnf(f_1624_5,plain,
    ( hAPP(U_7216,hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),U_7217)) = hAPP(c_Finite__Set_Ofold1(U_7215,c_Groups_Otimes__class_Otimes(U_7215)),hAPP(c_Set_Oimage(U_7215,U_7215,U_7216),U_7217))
    | U_7217 = c_Orderings_Obot__class_Obot(tc_fun(U_7215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7215),U_7217))
    | hAPP(U_7216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),sK144(U_7217,U_7216,U_7215)),sK145(U_7217,U_7216,U_7215))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7215),hAPP(U_7216,sK144(U_7217,U_7216,U_7215))),hAPP(U_7216,sK145(U_7217,U_7216,U_7215)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_7215) ),
    inference(clausify,[status(thm)],[f_1624_4]) ).

fof(f_1625_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).

fof(f_1625_2,plain,
    ! [U_7222,U_7221,U_7220] :
      ( ! [U_7219] :
          ( hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7222),U_7220))))
          | ~ hBOOL(hAPP(U_7221,U_7219)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7222))
      | ? [U_7218] :
          ( ~ hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7218),U_7220)))
          & hBOOL(hAPP(U_7221,U_7218)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7220)) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

fof(f_1625_3,plain,
    ! [U_7222,U_7221,U_7220] :
      ( ! [U_7219] :
          ( hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7222),U_7220))))
          | ~ hBOOL(hAPP(U_7221,U_7219)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7222))
      | ( ~ hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK146(U_7222,U_7221,U_7220)),U_7220)))
        & hBOOL(hAPP(U_7221,sK146(U_7222,U_7221,U_7220))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7220)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_7218,sK146(U_7222,U_7221,U_7220))],[f_1625_2]) ).

cnf(f_1625_4,plain,
    ( hBOOL(hAPP(U_7221,sK146(U_7222,U_7221,U_7220)))
    | hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7222),U_7220))))
    | ~ hBOOL(hAPP(U_7221,U_7219))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7222))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7220)) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

cnf(f_1625_5,plain,
    ( ~ hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK146(U_7222,U_7221,U_7220)),U_7220)))
    | hBOOL(hAPP(U_7221,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7222),U_7220))))
    | ~ hBOOL(hAPP(U_7221,U_7219))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7222))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7220)) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

fof(f_1626_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_1626_2,plain,
    ! [U_7224,U_7223] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7223,U_7224))),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

cnf(f_1626_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7223,U_7224))),
    inference(clausify,[status(thm)],[f_1626_2]) ).

fof(f_1627_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_1627_2,plain,
    ! [U_7225] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7225))),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

cnf(f_1627_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7225))),
    inference(clausify,[status(thm)],[f_1627_2]) ).

fof(f_1628_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_1628_2,plain,
    ! [U_7226] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7226) = 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_7226))),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

cnf(f_1628_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7226) = 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_7226))),
    inference(clausify,[status(thm)],[f_1628_2]) ).

fof(f_1629_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).

fof(f_1629_2,plain,
    ! [U_7229,U_7228,U_7227] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7228) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7229)
          | U_7228 != U_7229 )
        & ( U_7228 = U_7229
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7228) != hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7229) ) )
      | ~ class_Orderings_Olinorder(U_7227) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

cnf(f_1629_3,plain,
    ( U_7228 = U_7229
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7228) != hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7229)
    | ~ class_Orderings_Olinorder(U_7227) ),
    inference(clausify,[status(thm)],[f_1629_2]) ).

cnf(f_1629_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7228) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7227),U_7229)
    | U_7228 != U_7229
    | ~ class_Orderings_Olinorder(U_7227) ),
    inference(clausify,[status(thm)],[f_1629_2]) ).

fof(f_1630_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).

fof(f_1630_2,plain,
    ! [U_7232,U_7231,U_7230] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7231) = hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7232)
          | U_7231 != U_7232 )
        & ( U_7231 = U_7232
          | hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7231) != hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7232) ) )
      | ~ class_Orderings_Olinorder(U_7230) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

cnf(f_1630_3,plain,
    ( U_7231 = U_7232
    | hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7231) != hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7232)
    | ~ class_Orderings_Olinorder(U_7230) ),
    inference(clausify,[status(thm)],[f_1630_2]) ).

cnf(f_1630_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7231) = hAPP(c_SetInterval_Oord__class_OatMost(U_7230),U_7232)
    | U_7231 != U_7232
    | ~ class_Orderings_Olinorder(U_7230) ),
    inference(clausify,[status(thm)],[f_1630_2]) ).

fof(f_1631_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_1631_2,plain,
    ! [U_7234,U_7233] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7233,U_7234) = 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_7233),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7234))),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

cnf(f_1631_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7233,U_7234) = 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_7233),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7234))),
    inference(clausify,[status(thm)],[f_1631_2]) ).

fof(f_1632_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_1632_2,plain,
    ! [U_7235] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7235)) = U_7235,
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

cnf(f_1632_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7235)) = U_7235,
    inference(clausify,[status(thm)],[f_1632_2]) ).

fof(f_1633_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]) ).

cnf(f_1633_2,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_1633_1]) ).

fof(f_1634_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]) ).

cnf(f_1634_2,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_1634_1]) ).

fof(f_1635_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).

fof(f_1635_2,plain,
    ! [U_7240] :
      ( ( ? [U_7239] : hBOOL(hAPP(U_7240,U_7239))
        | ! [U_7238] :
            ( ~ hBOOL(hAPP(U_7240,hAPP(c_Int_Onat,U_7238)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7238)) ) )
      & ( ? [U_7237] :
            ( hBOOL(hAPP(U_7240,hAPP(c_Int_Onat,U_7237)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7237)) )
        | ! [U_7236] : ~ hBOOL(hAPP(U_7240,U_7236)) ) ),
    inference(variable_rename,[status(thm)],[f_1635_1]) ).

fof(f_1635_3,plain,
    ( ! [U_7242] :
        ( ? [U_7239] : hBOOL(hAPP(U_7242,U_7239))
        | ! [U_7238] :
            ( ~ hBOOL(hAPP(U_7242,hAPP(c_Int_Onat,U_7238)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7238)) ) )
    & ! [U_7241] :
        ( ? [U_7237] :
            ( hBOOL(hAPP(U_7241,hAPP(c_Int_Onat,U_7237)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7237)) )
        | ! [U_7236] : ~ hBOOL(hAPP(U_7241,U_7236)) ) ),
    inference(miniscope,[status(thm)],[f_1635_2]) ).

fof(f_1635_4,plain,
    ( ! [U_7242] :
        ( ? [U_7239] : hBOOL(hAPP(U_7242,U_7239))
        | ! [U_7238] :
            ( ~ hBOOL(hAPP(U_7242,hAPP(c_Int_Onat,U_7238)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7238)) ) )
    & ! [U_7241] :
        ( ( hBOOL(hAPP(U_7241,hAPP(c_Int_Onat,sK147(U_7241))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK147(U_7241))) )
        | ! [U_7236] : ~ hBOOL(hAPP(U_7241,U_7236)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_7237,sK147(U_7241))],[f_1635_3]) ).

fof(f_1635_5,plain,
    ( ! [U_7242] :
        ( hBOOL(hAPP(U_7242,sK148(U_7242)))
        | ! [U_7238] :
            ( ~ hBOOL(hAPP(U_7242,hAPP(c_Int_Onat,U_7238)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7238)) ) )
    & ! [U_7241] :
        ( ( hBOOL(hAPP(U_7241,hAPP(c_Int_Onat,sK147(U_7241))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK147(U_7241))) )
        | ! [U_7236] : ~ hBOOL(hAPP(U_7241,U_7236)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_7239,sK148(U_7242))],[f_1635_4]) ).

cnf(f_1635_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK147(U_7241)))
    | ~ hBOOL(hAPP(U_7241,U_7236)) ),
    inference(clausify,[status(thm)],[f_1635_5]) ).

cnf(f_1635_7,plain,
    ( hBOOL(hAPP(U_7241,hAPP(c_Int_Onat,sK147(U_7241))))
    | ~ hBOOL(hAPP(U_7241,U_7236)) ),
    inference(clausify,[status(thm)],[f_1635_5]) ).

cnf(f_1635_8,plain,
    ( hBOOL(hAPP(U_7242,sK148(U_7242)))
    | ~ hBOOL(hAPP(U_7242,hAPP(c_Int_Onat,U_7238)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7238)) ),
    inference(clausify,[status(thm)],[f_1635_5]) ).

fof(f_1636_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat]) ).

fof(f_1636_2,plain,
    ! [U_7247] :
      ( ( ! [U_7246] : hBOOL(hAPP(U_7247,U_7246))
        | ? [U_7245] :
            ( ~ hBOOL(hAPP(U_7247,hAPP(c_Int_Onat,U_7245)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7245)) ) )
      & ( ! [U_7244] :
            ( hBOOL(hAPP(U_7247,hAPP(c_Int_Onat,U_7244)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7244)) )
        | ? [U_7243] : ~ hBOOL(hAPP(U_7247,U_7243)) ) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

fof(f_1636_3,plain,
    ( ! [U_7249] :
        ( ! [U_7246] : hBOOL(hAPP(U_7249,U_7246))
        | ? [U_7245] :
            ( ~ hBOOL(hAPP(U_7249,hAPP(c_Int_Onat,U_7245)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7245)) ) )
    & ! [U_7248] :
        ( ! [U_7244] :
            ( hBOOL(hAPP(U_7248,hAPP(c_Int_Onat,U_7244)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7244)) )
        | ? [U_7243] : ~ hBOOL(hAPP(U_7248,U_7243)) ) ),
    inference(miniscope,[status(thm)],[f_1636_2]) ).

fof(f_1636_4,plain,
    ( ! [U_7249] :
        ( ! [U_7246] : hBOOL(hAPP(U_7249,U_7246))
        | ? [U_7245] :
            ( ~ hBOOL(hAPP(U_7249,hAPP(c_Int_Onat,U_7245)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7245)) ) )
    & ! [U_7248] :
        ( ! [U_7244] :
            ( hBOOL(hAPP(U_7248,hAPP(c_Int_Onat,U_7244)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7244)) )
        | ~ hBOOL(hAPP(U_7248,sK149(U_7248))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_7243,sK149(U_7248))],[f_1636_3]) ).

fof(f_1636_5,plain,
    ( ! [U_7249] :
        ( ! [U_7246] : hBOOL(hAPP(U_7249,U_7246))
        | ( ~ hBOOL(hAPP(U_7249,hAPP(c_Int_Onat,sK150(U_7249))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK150(U_7249))) ) )
    & ! [U_7248] :
        ( ! [U_7244] :
            ( hBOOL(hAPP(U_7248,hAPP(c_Int_Onat,U_7244)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7244)) )
        | ~ hBOOL(hAPP(U_7248,sK149(U_7248))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_7245,sK150(U_7249))],[f_1636_4]) ).

cnf(f_1636_6,plain,
    ( hBOOL(hAPP(U_7248,hAPP(c_Int_Onat,U_7244)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7244))
    | ~ hBOOL(hAPP(U_7248,sK149(U_7248))) ),
    inference(clausify,[status(thm)],[f_1636_5]) ).

cnf(f_1636_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK150(U_7249)))
    | hBOOL(hAPP(U_7249,U_7246)) ),
    inference(clausify,[status(thm)],[f_1636_5]) ).

cnf(f_1636_8,plain,
    ( ~ hBOOL(hAPP(U_7249,hAPP(c_Int_Onat,sK150(U_7249))))
    | hBOOL(hAPP(U_7249,U_7246)) ),
    inference(clausify,[status(thm)],[f_1636_5]) ).

fof(f_1637_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_1637_2,plain,
    ! [U_7251,U_7250] :
      ( ( ( hAPP(c_Int_Onat,U_7250) = hAPP(c_Int_Onat,U_7251)
          | U_7250 != U_7251 )
        & ( U_7250 = U_7251
          | hAPP(c_Int_Onat,U_7250) != hAPP(c_Int_Onat,U_7251) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7250)) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

cnf(f_1637_3,plain,
    ( U_7250 = U_7251
    | hAPP(c_Int_Onat,U_7250) != hAPP(c_Int_Onat,U_7251)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7250)) ),
    inference(clausify,[status(thm)],[f_1637_2]) ).

cnf(f_1637_4,plain,
    ( hAPP(c_Int_Onat,U_7250) = hAPP(c_Int_Onat,U_7251)
    | U_7250 != U_7251
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7250)) ),
    inference(clausify,[status(thm)],[f_1637_2]) ).

fof(f_1638_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_1638_2,plain,
    ! [U_7253,U_7252] :
      ( ( ( hAPP(c_Int_Onat,U_7252) = hAPP(c_Int_Onat,U_7253)
          | U_7252 != U_7253 )
        & ( U_7252 = U_7253
          | hAPP(c_Int_Onat,U_7252) != hAPP(c_Int_Onat,U_7253) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7253))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252)) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

cnf(f_1638_3,plain,
    ( U_7252 = U_7253
    | hAPP(c_Int_Onat,U_7252) != hAPP(c_Int_Onat,U_7253)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7253))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252)) ),
    inference(clausify,[status(thm)],[f_1638_2]) ).

cnf(f_1638_4,plain,
    ( hAPP(c_Int_Onat,U_7252) = hAPP(c_Int_Onat,U_7253)
    | U_7252 != U_7253
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7253))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252)) ),
    inference(clausify,[status(thm)],[f_1638_2]) ).

fof(f_1639_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_1639_2,plain,
    ! [U_7255,U_7254] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7254),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7255) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7254,U_7255),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

cnf(f_1639_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7254),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7255) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7254,U_7255),
    inference(clausify,[status(thm)],[f_1639_2]) ).

fof(f_1640_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_1640_2,plain,
    ! [U_7257,U_7256] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7256,U_7257)) = 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_7257),U_7256)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

cnf(f_1640_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7256,U_7257)) = 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_7257),U_7256)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1640_2]) ).

fof(f_1641_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]) ).

cnf(f_1641_2,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_1641_1]) ).

fof(f_1642_1,plain,
    ! [V_n_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).

fof(f_1642_2,plain,
    ! [U_7259,U_7258] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7258),U_7259)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7258),U_7259)) = hAPP(hAPP(c_Set_Oinsert(U_7258),U_7259),c_Orderings_Obot__class_Obot(tc_fun(U_7258,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_7258) ),
    inference(variable_rename,[status(thm)],[f_1642_1]) ).

cnf(f_1642_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7258),U_7259)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7258),U_7259)) = hAPP(hAPP(c_Set_Oinsert(U_7258),U_7259),c_Orderings_Obot__class_Obot(tc_fun(U_7258,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_7258) ),
    inference(clausify,[status(thm)],[f_1642_2]) ).

fof(f_1643_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_1643_2,plain,
    ! [U_7260] : 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_7260)) = U_7260,
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

cnf(f_1643_3,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_7260)) = U_7260,
    inference(clausify,[status(thm)],[f_1643_2]) ).

fof(f_1644_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_1644_2,plain,
    ! [U_7262,U_7261] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7261),U_7262) = 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_7261)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7262))),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

cnf(f_1644_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7261),U_7262) = 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_7261)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7262))),
    inference(clausify,[status(thm)],[f_1644_2]) ).

fof(f_1645_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_1645_2,plain,
    ! [U_7264,U_7263] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7263,U_7264)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7264),U_7263)),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

cnf(f_1645_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7263,U_7264)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7264),U_7263)),
    inference(clausify,[status(thm)],[f_1645_2]) ).

fof(f_1646_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_1646_2,plain,
    ! [U_7265] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7265) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7265),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

cnf(f_1646_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7265) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7265),
    inference(clausify,[status(thm)],[f_1646_2]) ).

fof(f_1647_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]) ).

cnf(f_1647_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(clausify,[status(thm)],[f_1647_1]) ).

fof(f_1648_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_1648_2,plain,
    ! [U_7266] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7266)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7266),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

cnf(f_1648_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7266)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7266),
    inference(clausify,[status(thm)],[f_1648_2]) ).

fof(f_1649_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_1649_2,plain,
    ! [U_7267] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7267)) = hAPP(c_Nat_OSuc,U_7267),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

cnf(f_1649_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7267)) = hAPP(c_Nat_OSuc,U_7267),
    inference(clausify,[status(thm)],[f_1649_2]) ).

fof(f_1650_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_1650_2,plain,
    ! [U_7268] :
      ( ( hAPP(c_Int_Onat,U_7268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7268),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7268),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_7268) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

fof(f_1650_3,plain,
    ( ! [U_7270] :
        ( hAPP(c_Int_Onat,U_7270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7270),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_7269) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1650_2]) ).

cnf(f_1650_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7269),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_7269) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_5,plain,
    ( hAPP(c_Int_Onat,U_7270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7270),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

fof(f_1651_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_1651_2,plain,
    ! [U_7271] :
      ( hAPP(c_Int_Onat,U_7271) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7271),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1651_1]) ).

cnf(f_1651_3,plain,
    ( hAPP(c_Int_Onat,U_7271) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7271),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1651_2]) ).

fof(f_1652_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_1652_2,plain,
    ! [U_7273,U_7272] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7272)),hAPP(c_Int_Onat,U_7273)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7272),U_7273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7273)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7272),U_7273))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7273)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7272)),hAPP(c_Int_Onat,U_7273))) ) ),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

fof(f_1652_3,plain,
    ( ! [U_7277,U_7275] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7275)),hAPP(c_Int_Onat,U_7277)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7275),U_7277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) )
    & ! [U_7276,U_7274] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7274),U_7276))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7276)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7274)),hAPP(c_Int_Onat,U_7276))) ) ),
    inference(miniscope,[status(thm)],[f_1652_2]) ).

cnf(f_1652_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7276))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7274)),hAPP(c_Int_Onat,U_7276))) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7274),U_7276))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7274)),hAPP(c_Int_Onat,U_7276))) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7275)),hAPP(c_Int_Onat,U_7277)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7275),U_7277))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

fof(f_1653_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_1653_2,plain,
    ! [U_7279,U_7278] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7279)),hAPP(c_Int_Onat,U_7278)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7279),U_7278)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7279),U_7278))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7279)),hAPP(c_Int_Onat,U_7278))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ),
    inference(variable_rename,[status(thm)],[f_1653_1]) ).

cnf(f_1653_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7279),U_7278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7279)),hAPP(c_Int_Onat,U_7278)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ),
    inference(clausify,[status(thm)],[f_1653_2]) ).

cnf(f_1653_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7279)),hAPP(c_Int_Onat,U_7278)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7279),U_7278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ),
    inference(clausify,[status(thm)],[f_1653_2]) ).

fof(f_1654_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_1654_2,plain,
    ! [U_7280] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7280)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7280)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7280)),
    inference(variable_rename,[status(thm)],[f_1654_1]) ).

cnf(f_1654_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7280)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7280)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7280)),
    inference(clausify,[status(thm)],[f_1654_2]) ).

fof(f_1655_1,plain,
    ! [V_k_2,V_i_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).

fof(f_1655_2,plain,
    ! [U_7283,U_7282,U_7281] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7281),U_7282),hAPP(c_SetInterval_Oord__class_OatLeast(U_7281),U_7283)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7281),U_7283),U_7282)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7281),U_7283),U_7282))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7281),U_7282),hAPP(c_SetInterval_Oord__class_OatLeast(U_7281),U_7283))) ) )
      | ~ class_Orderings_Oord(U_7281) ),
    inference(variable_rename,[status(thm)],[f_1655_1]) ).

cnf(f_1655_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7281),U_7283),U_7282))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7281),U_7282),hAPP(c_SetInterval_Oord__class_OatLeast(U_7281),U_7283)))
    | ~ class_Orderings_Oord(U_7281) ),
    inference(clausify,[status(thm)],[f_1655_2]) ).

cnf(f_1655_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7281),U_7282),hAPP(c_SetInterval_Oord__class_OatLeast(U_7281),U_7283)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7281),U_7283),U_7282))
    | ~ class_Orderings_Oord(U_7281) ),
    inference(clausify,[status(thm)],[f_1655_2]) ).

fof(f_1656_1,plain,
    ! [V_k_2,V_i_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).

fof(f_1656_2,plain,
    ! [U_7286,U_7285,U_7284] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7284),U_7285),hAPP(c_SetInterval_Oord__class_OatMost(U_7284),U_7286)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7284),U_7285),U_7286)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7284),U_7285),U_7286))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7284),U_7285),hAPP(c_SetInterval_Oord__class_OatMost(U_7284),U_7286))) ) )
      | ~ class_Orderings_Oord(U_7284) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

cnf(f_1656_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7284),U_7285),U_7286))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7284),U_7285),hAPP(c_SetInterval_Oord__class_OatMost(U_7284),U_7286)))
    | ~ class_Orderings_Oord(U_7284) ),
    inference(clausify,[status(thm)],[f_1656_2]) ).

cnf(f_1656_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7284),U_7285),hAPP(c_SetInterval_Oord__class_OatMost(U_7284),U_7286)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7284),U_7285),U_7286))
    | ~ class_Orderings_Oord(U_7284) ),
    inference(clausify,[status(thm)],[f_1656_2]) ).

fof(f_1657_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_1657_2,plain,
    ! [U_7288,U_7287] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7287)),hAPP(c_Int_Onat,U_7288)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7287),U_7288)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7287),U_7288))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7287)),hAPP(c_Int_Onat,U_7288))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7287)) ),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

cnf(f_1657_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7287),U_7288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7287)),hAPP(c_Int_Onat,U_7288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7287)) ),
    inference(clausify,[status(thm)],[f_1657_2]) ).

cnf(f_1657_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7287)),hAPP(c_Int_Onat,U_7288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7287),U_7288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7287)) ),
    inference(clausify,[status(thm)],[f_1657_2]) ).

fof(f_1658_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]) ).

cnf(f_1658_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(clausify,[status(thm)],[f_1658_1]) ).

fof(f_1659_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_1659_2,plain,
    ! [U_7289] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7289)) = U_7289
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7289)) ),
    inference(variable_rename,[status(thm)],[f_1659_1]) ).

cnf(f_1659_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7289)) = U_7289
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7289)) ),
    inference(clausify,[status(thm)],[f_1659_2]) ).

fof(f_1660_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_1660_2,plain,
    ! [U_7291,U_7290] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7290) = U_7291
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7291))
        | U_7290 != hAPP(c_Int_Onat,U_7291) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7291))
          & U_7290 = hAPP(c_Int_Onat,U_7291) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7290) != U_7291 ) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

fof(f_1660_3,plain,
    ( ! [U_7295,U_7293] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7293) = U_7295
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7295))
        | U_7293 != hAPP(c_Int_Onat,U_7295) )
    & ! [U_7294,U_7292] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7294))
          & U_7292 = hAPP(c_Int_Onat,U_7294) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7292) != U_7294 ) ),
    inference(miniscope,[status(thm)],[f_1660_2]) ).

cnf(f_1660_4,plain,
    ( U_7292 = hAPP(c_Int_Onat,U_7294)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7292) != U_7294 ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

cnf(f_1660_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7294))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7292) != U_7294 ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

cnf(f_1660_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7293) = U_7295
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7295))
    | U_7293 != hAPP(c_Int_Onat,U_7295) ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

fof(f_1661_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_1661_2,plain,
    ! [U_7296] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7296)) = 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_7296)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7296)) = U_7296
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7296)) ) ),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

fof(f_1661_3,plain,
    ( ! [U_7298] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7298)) = 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_7298)) )
    & ! [U_7297] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7297)) = U_7297
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7297)) ) ),
    inference(miniscope,[status(thm)],[f_1661_2]) ).

cnf(f_1661_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7297)) = U_7297
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7297)) ),
    inference(clausify,[status(thm)],[f_1661_3]) ).

cnf(f_1661_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7298)) = 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_7298)) ),
    inference(clausify,[status(thm)],[f_1661_3]) ).

fof(f_1662_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_1662_2,plain,
    ! [U_7300,U_7299] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7299),hAPP(c_Int_Onat,U_7300)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7299)),U_7300)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7299)),U_7300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7299),hAPP(c_Int_Onat,U_7300))) ) ),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

fof(f_1662_3,plain,
    ( ! [U_7304,U_7302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7302),hAPP(c_Int_Onat,U_7304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7302)),U_7304)) )
    & ! [U_7303,U_7301] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7301)),U_7303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7301),hAPP(c_Int_Onat,U_7303))) ) ),
    inference(miniscope,[status(thm)],[f_1662_2]) ).

cnf(f_1662_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_7301)),U_7303))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7301),hAPP(c_Int_Onat,U_7303))) ),
    inference(clausify,[status(thm)],[f_1662_3]) ).

cnf(f_1662_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7302),hAPP(c_Int_Onat,U_7304)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7302)),U_7304)) ),
    inference(clausify,[status(thm)],[f_1662_3]) ).

fof(f_1663_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).

fof(f_1663_2,plain,
    ! [U_7307,U_7306,U_7305] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7305,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7306)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7307)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7305),U_7306),U_7307)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7305),U_7306),U_7307))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7305,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7306)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7307))) ) )
      | ~ class_Orderings_Oorder(U_7305) ),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

cnf(f_1663_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7305),U_7306),U_7307))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7305,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7306)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7307)))
    | ~ class_Orderings_Oorder(U_7305) ),
    inference(clausify,[status(thm)],[f_1663_2]) ).

cnf(f_1663_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7305,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7306)),hAPP(c_SetInterval_Oord__class_OatMost(U_7305),U_7307)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7305),U_7306),U_7307))
    | ~ class_Orderings_Oorder(U_7305) ),
    inference(clausify,[status(thm)],[f_1663_2]) ).

fof(f_1664_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).

fof(f_1664_2,plain,
    ! [U_7310,U_7309,U_7308] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7309)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7310)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7308),U_7310),U_7309)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7308),U_7310),U_7309))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7309)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7310))) ) )
      | ~ class_Orderings_Oorder(U_7308) ),
    inference(variable_rename,[status(thm)],[f_1664_1]) ).

cnf(f_1664_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7308),U_7310),U_7309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7309)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7310)))
    | ~ class_Orderings_Oorder(U_7308) ),
    inference(clausify,[status(thm)],[f_1664_2]) ).

cnf(f_1664_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7308,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7309)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7308),U_7310)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7308),U_7310),U_7309))
    | ~ class_Orderings_Oorder(U_7308) ),
    inference(clausify,[status(thm)],[f_1664_2]) ).

fof(f_1665_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]) ).

cnf(f_1665_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(clausify,[status(thm)],[f_1665_1]) ).

fof(f_1666_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_1666_2,plain,
    ! [U_7312,U_7311] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7312),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7311,U_7312),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

cnf(f_1666_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7312),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7311,U_7312),
    inference(clausify,[status(thm)],[f_1666_2]) ).

fof(f_1667_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_1667_2,plain,
    ! [U_7313] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7313)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_7313),
    inference(variable_rename,[status(thm)],[f_1667_1]) ).

cnf(f_1667_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7313)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_7313),
    inference(clausify,[status(thm)],[f_1667_2]) ).

fof(f_1668_1,plain,
    ! [V_A_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).

fof(f_1668_2,plain,
    ! [U_7316,U_7315,U_7314] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7314),U_7315),U_7316) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7314),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7314,tc_Int_Oint),U_7315),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7316))
      | ~ class_Groups_Ocomm__monoid__mult(U_7314)
      | ~ class_Groups_Ocomm__monoid__add(U_7314) ),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

cnf(f_1668_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7314),U_7315),U_7316) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7314),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7314,tc_Int_Oint),U_7315),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7316))
    | ~ class_Groups_Ocomm__monoid__mult(U_7314)
    | ~ class_Groups_Ocomm__monoid__add(U_7314) ),
    inference(clausify,[status(thm)],[f_1668_2]) ).

fof(f_1669_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_1669_2,plain,
    ! [U_7317] : 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_7317)) = hAPP(c_Int_Onat,U_7317),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

cnf(f_1669_3,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_7317)) = hAPP(c_Int_Onat,U_7317),
    inference(clausify,[status(thm)],[f_1669_2]) ).

fof(f_1670_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_1670_2,plain,
    ! [U_7319,U_7318] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7318),U_7319)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7319),U_7318)),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

cnf(f_1670_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7318),U_7319)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7319),U_7318)),
    inference(clausify,[status(thm)],[f_1670_2]) ).

fof(f_1671_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_1671_2,plain,
    ! [U_7320] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7320)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7320)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7320))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7320))) ) ),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

fof(f_1671_3,plain,
    ( ! [U_7322] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7322)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) )
    & ! [U_7321] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7321))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7321))) ) ),
    inference(miniscope,[status(thm)],[f_1671_2]) ).

cnf(f_1671_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7321))) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

cnf(f_1671_5,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_7322)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

fof(f_1672_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_1672_2,plain,
    ! [U_7324,U_7323] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7324)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7324)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7324))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7324))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323)) ),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

cnf(f_1672_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323)) ),
    inference(clausify,[status(thm)],[f_1672_2]) ).

cnf(f_1672_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7323)) ),
    inference(clausify,[status(thm)],[f_1672_2]) ).

fof(f_1673_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_1673_2,plain,
    ! [U_7326,U_7325] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7325)),hAPP(c_Int_Onat,U_7326)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7325),U_7326)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7325),U_7326))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7325)),hAPP(c_Int_Onat,U_7326))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325)) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

cnf(f_1673_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7325),U_7326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7325)),hAPP(c_Int_Onat,U_7326)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325)) ),
    inference(clausify,[status(thm)],[f_1673_2]) ).

cnf(f_1673_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7325)),hAPP(c_Int_Onat,U_7326)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7325),U_7326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325)) ),
    inference(clausify,[status(thm)],[f_1673_2]) ).

fof(f_1674_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_1674_2,plain,
    ! [U_7328,U_7327] :
      ( ( U_7327 = hAPP(c_Int_Onat,U_7328)
        | ( U_7327 != 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_7328)) )
        | ( U_7328 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7327)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7328)) ) )
      & ( ( ( U_7327 = 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_7328)) )
          & ( U_7328 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7327)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7328)) ) )
        | U_7327 != hAPP(c_Int_Onat,U_7328) ) ),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

fof(f_1674_3,plain,
    ( ! [U_7332,U_7330] :
        ( U_7330 = hAPP(c_Int_Onat,U_7332)
        | ( U_7330 != 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_7332)) )
        | ( U_7332 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7330)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7332)) ) )
    & ! [U_7331,U_7329] :
        ( ( ( U_7329 = 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_7331)) )
          & ( U_7331 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7329)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7331)) ) )
        | U_7329 != hAPP(c_Int_Onat,U_7331) ) ),
    inference(miniscope,[status(thm)],[f_1674_2]) ).

cnf(f_1674_4,plain,
    ( U_7331 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7329)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7331))
    | U_7329 != hAPP(c_Int_Onat,U_7331) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_5,plain,
    ( U_7329 = 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_7331))
    | U_7329 != hAPP(c_Int_Onat,U_7331) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7332))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7332))
    | U_7330 = hAPP(c_Int_Onat,U_7332) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_7,plain,
    ( U_7330 != 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_7332))
    | U_7330 = hAPP(c_Int_Onat,U_7332) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7332))
    | U_7332 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7330)
    | U_7330 = hAPP(c_Int_Onat,U_7332) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_9,plain,
    ( U_7330 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7332 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7330)
    | U_7330 = hAPP(c_Int_Onat,U_7332) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

fof(f_1675_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_1675_2,plain,
    ! [U_7334,U_7333] :
      ( ( hAPP(c_Int_Onat,U_7333) = U_7334
        | ( U_7334 != 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_7333)) )
        | ( U_7333 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7334)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7333)) ) )
      & ( ( ( U_7334 = 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_7333)) )
          & ( U_7333 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7334)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7333)) ) )
        | hAPP(c_Int_Onat,U_7333) != U_7334 ) ),
    inference(variable_rename,[status(thm)],[f_1675_1]) ).

fof(f_1675_3,plain,
    ( ! [U_7338,U_7336] :
        ( hAPP(c_Int_Onat,U_7336) = U_7338
        | ( U_7338 != 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_7336)) )
        | ( U_7336 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7338)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7336)) ) )
    & ! [U_7337,U_7335] :
        ( ( ( U_7337 = 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_7335)) )
          & ( U_7335 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7337)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335)) ) )
        | hAPP(c_Int_Onat,U_7335) != U_7337 ) ),
    inference(miniscope,[status(thm)],[f_1675_2]) ).

cnf(f_1675_4,plain,
    ( U_7335 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7337)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7335))
    | hAPP(c_Int_Onat,U_7335) != U_7337 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

cnf(f_1675_5,plain,
    ( U_7337 = 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_7335))
    | hAPP(c_Int_Onat,U_7335) != U_7337 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

cnf(f_1675_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7336))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7336))
    | hAPP(c_Int_Onat,U_7336) = U_7338 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

cnf(f_1675_7,plain,
    ( U_7338 != 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_7336))
    | hAPP(c_Int_Onat,U_7336) = U_7338 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

cnf(f_1675_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7336))
    | U_7336 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7338)
    | hAPP(c_Int_Onat,U_7336) = U_7338 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

cnf(f_1675_9,plain,
    ( U_7338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7336 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7338)
    | hAPP(c_Int_Onat,U_7336) = U_7338 ),
    inference(clausify,[status(thm)],[f_1675_3]) ).

fof(f_1676_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_1676_2,plain,
    ! [U_7340,U_7339] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7340))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339)) ) ),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

cnf(f_1676_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339)) ),
    inference(clausify,[status(thm)],[f_1676_2]) ).

cnf(f_1676_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7339)) ),
    inference(clausify,[status(thm)],[f_1676_2]) ).

cnf(f_1676_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7340)) ),
    inference(clausify,[status(thm)],[f_1676_2]) ).

cnf(f_1676_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7339)),hAPP(c_Int_Onat,U_7340)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7339),U_7340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7340)) ),
    inference(clausify,[status(thm)],[f_1676_2]) ).

fof(f_1677_1,plain,
    ! [V_i_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,B_n))
            & V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [B_n] :
              ( hBOOL(hAPP(V_P_2,B_n))
              | V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__nat]) ).

fof(f_1677_2,plain,
    ! [U_7344,U_7343] :
      ( ( hBOOL(hAPP(U_7343,hAPP(c_Int_Onat,U_7344)))
        | ( ~ hBOOL(hAPP(U_7343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_7342] :
            ( ~ hBOOL(hAPP(U_7343,U_7342))
            & U_7344 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7342) ) )
      & ( ( ( hBOOL(hAPP(U_7343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7341] :
              ( hBOOL(hAPP(U_7343,U_7341))
              | U_7344 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7341) ) )
        | ~ hBOOL(hAPP(U_7343,hAPP(c_Int_Onat,U_7344))) ) ),
    inference(variable_rename,[status(thm)],[f_1677_1]) ).

fof(f_1677_3,plain,
    ( ! [U_7348,U_7346] :
        ( hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348)))
        | ( ~ hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7348),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_7342] :
            ( ~ hBOOL(hAPP(U_7346,U_7342))
            & U_7348 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7342) ) )
    & ! [U_7347,U_7345] :
        ( ( ( hBOOL(hAPP(U_7345,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7347),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7341] :
              ( hBOOL(hAPP(U_7345,U_7341))
              | U_7347 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7341) ) )
        | ~ hBOOL(hAPP(U_7345,hAPP(c_Int_Onat,U_7347))) ) ),
    inference(miniscope,[status(thm)],[f_1677_2]) ).

fof(f_1677_4,plain,
    ( ! [U_7348,U_7346] :
        ( hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348)))
        | ( ~ hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7348),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7346,sK151(U_7348,U_7346)))
          & U_7348 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK151(U_7348,U_7346)) ) )
    & ! [U_7347,U_7345] :
        ( ( ( hBOOL(hAPP(U_7345,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7347),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7341] :
              ( hBOOL(hAPP(U_7345,U_7341))
              | U_7347 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7341) ) )
        | ~ hBOOL(hAPP(U_7345,hAPP(c_Int_Onat,U_7347))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_7342,sK151(U_7348,U_7346))],[f_1677_3]) ).

cnf(f_1677_5,plain,
    ( hBOOL(hAPP(U_7345,U_7341))
    | U_7347 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7341)
    | ~ hBOOL(hAPP(U_7345,hAPP(c_Int_Onat,U_7347))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

cnf(f_1677_6,plain,
    ( hBOOL(hAPP(U_7345,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7347),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7345,hAPP(c_Int_Onat,U_7347))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

cnf(f_1677_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7348 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK151(U_7348,U_7346))
    | hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

cnf(f_1677_8,plain,
    ( ~ hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_7348 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK151(U_7348,U_7346))
    | hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

cnf(f_1677_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7346,sK151(U_7348,U_7346)))
    | hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

cnf(f_1677_10,plain,
    ( ~ hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_7346,sK151(U_7348,U_7346)))
    | hBOOL(hAPP(U_7346,hAPP(c_Int_Onat,U_7348))) ),
    inference(clausify,[status(thm)],[f_1677_4]) ).

fof(f_1678_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_1678_2,plain,
    ! [U_7350,U_7349] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7349)),hAPP(c_Int_Onat,U_7350)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7349),U_7350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7349)) ),
    inference(variable_rename,[status(thm)],[f_1678_1]) ).

cnf(f_1678_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7349)),hAPP(c_Int_Onat,U_7350)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7349),U_7350))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7350))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7349)) ),
    inference(clausify,[status(thm)],[f_1678_2]) ).

fof(f_1679_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_1679_2,plain,
    ! [U_7352,U_7351] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7351),U_7352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7351)),hAPP(c_Int_Onat,U_7352))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

cnf(f_1679_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7351),U_7352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7351)),hAPP(c_Int_Onat,U_7352))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7351)) ),
    inference(clausify,[status(thm)],[f_1679_2]) ).

fof(f_1680_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_1680_2,plain,
    ! [U_7354,U_7353] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7353)),hAPP(c_Int_Onat,U_7354)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7353),U_7354))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7354))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7353)) ),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

cnf(f_1680_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7353)),hAPP(c_Int_Onat,U_7354)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7353),U_7354))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7354))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7353)) ),
    inference(clausify,[status(thm)],[f_1680_2]) ).

fof(f_1681_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_1681_2,plain,
    ! [U_7356,U_7355] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7355),U_7356)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

cnf(f_1681_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7355),U_7356)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
    inference(clausify,[status(thm)],[f_1681_2]) ).

fof(f_1682_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_1682_2,plain,
    ! [U_7358,U_7357] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7357),U_7358) = 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_7357)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7358))),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

cnf(f_1682_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7357),U_7358) = 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_7357)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7358))),
    inference(clausify,[status(thm)],[f_1682_2]) ).

fof(f_1683_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_1683_2,plain,
    ! [U_7360,U_7359] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7360),U_7359)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7360)),hAPP(c_Int_Onat,U_7359))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7359)) ),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

cnf(f_1683_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7360),U_7359)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7360)),hAPP(c_Int_Onat,U_7359))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7359)) ),
    inference(clausify,[status(thm)],[f_1683_2]) ).

fof(f_1684_1,plain,
    ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),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_1684_2,plain,
    ! [U_7363,U_7362,U_7361] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7361,tc_Nat_Onat),U_7362),U_7363) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7361,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7361),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7362)),U_7363)),
    inference(variable_rename,[status(thm)],[f_1684_1]) ).

cnf(f_1684_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7361,tc_Nat_Onat),U_7362),U_7363) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7361,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7361),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7362)),U_7363)),
    inference(clausify,[status(thm)],[f_1684_2]) ).

fof(f_1685_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]) ).

cnf(f_1685_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(clausify,[status(thm)],[f_1685_1]) ).

fof(f_1686_1,plain,
    ! [V_n_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).

fof(f_1686_2,plain,
    ! [U_7366,U_7365,U_7364] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7364),U_7365),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7366))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7364),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7364),U_7365),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7366))),hAPP(U_7365,hAPP(c_Nat_OSuc,U_7366)))
      | ~ class_Groups_Ocomm__monoid__add(U_7364) ),
    inference(variable_rename,[status(thm)],[f_1686_1]) ).

cnf(f_1686_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7364),U_7365),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7366))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7364),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7364),U_7365),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7366))),hAPP(U_7365,hAPP(c_Nat_OSuc,U_7366)))
    | ~ class_Groups_Ocomm__monoid__add(U_7364) ),
    inference(clausify,[status(thm)],[f_1686_2]) ).

fof(f_1687_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]) ).

cnf(f_1687_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(clausify,[status(thm)],[f_1687_1]) ).

fof(f_1688_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_1688_2,plain,
    ! [U_7368,U_7367] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7367)),hAPP(c_Int_Onat,U_7368)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7367,U_7368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7367)) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

cnf(f_1688_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7367)),hAPP(c_Int_Onat,U_7368)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7367,U_7368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7367)) ),
    inference(clausify,[status(thm)],[f_1688_2]) ).

fof(f_1689_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).

fof(f_1689_2,plain,
    ! [U_7371,U_7370,U_7369] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7369,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7369,U_7370),U_7371)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7369),U_7371)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7369),U_7370)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7369),U_7370),U_7371))
      | ~ class_Orderings_Olinorder(U_7369) ),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

cnf(f_1689_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7369,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7369,U_7370),U_7371)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7369),U_7371)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7369),U_7370)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7369),U_7370),U_7371))
    | ~ class_Orderings_Olinorder(U_7369) ),
    inference(clausify,[status(thm)],[f_1689_2]) ).

fof(f_1690_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_1690_2,plain,
    ! [U_7373,U_7372] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7373,U_7372) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_7373),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7373),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7372),U_7373)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7373,U_7372) = 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_7372),U_7373)) ) ),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

fof(f_1690_3,plain,
    ( ! [U_7377,U_7375] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7377,U_7375) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_7377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7377),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7375))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7375),U_7377)) )
    & ! [U_7376,U_7374] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7376,U_7374) = 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_7374),U_7376)) ) ),
    inference(miniscope,[status(thm)],[f_1690_2]) ).

cnf(f_1690_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7376,U_7374) = 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_7374),U_7376)) ),
    inference(clausify,[status(thm)],[f_1690_3]) ).

cnf(f_1690_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7377,U_7375) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_7377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7377),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7375))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7375),U_7377)) ),
    inference(clausify,[status(thm)],[f_1690_3]) ).

fof(f_1691_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).

fof(f_1691_2,plain,
    ! [U_7380,U_7379,U_7378] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7378,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7378,U_7379),U_7380)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7378),U_7380)) = c_Orderings_Obot__class_Obot(tc_fun(U_7378,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7378) ),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

cnf(f_1691_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7378,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7378,U_7379),U_7380)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7378),U_7380)) = c_Orderings_Obot__class_Obot(tc_fun(U_7378,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7378) ),
    inference(clausify,[status(thm)],[f_1691_2]) ).

fof(f_1692_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]) ).

cnf(f_1692_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(clausify,[status(thm)],[f_1692_1]) ).

fof(f_1693_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).

fof(f_1693_2,plain,
    ! [U_7383,U_7382,U_7381] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7381,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7381),U_7382)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7381,U_7382,U_7383)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7381),U_7383)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7381),U_7382),U_7383))
      | ~ class_Orderings_Olinorder(U_7381) ),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

cnf(f_1693_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7381,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7381),U_7382)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7381,U_7382,U_7383)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7381),U_7383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7381),U_7382),U_7383))
    | ~ class_Orderings_Olinorder(U_7381) ),
    inference(clausify,[status(thm)],[f_1693_2]) ).

fof(f_1694_1,plain,
    ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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_1694_2,plain,
    ! [U_7387,U_7386,U_7385,U_7384] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7385)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool),tc_Nat_Onat),U_7386),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7387))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7387,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7385),U_7387))),U_7386),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

cnf(f_1694_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7385)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool),tc_Nat_Onat),U_7386),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7387))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7384,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7387,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7385),U_7387))),U_7386),
    inference(clausify,[status(thm)],[f_1694_2]) ).

fof(f_1695_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).

fof(f_1695_2,plain,
    ! [U_7390,U_7389,U_7388] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7388,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7388),U_7389)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7388,U_7389,U_7390)) = c_Orderings_Obot__class_Obot(tc_fun(U_7388,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7388) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

cnf(f_1695_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7388,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7388),U_7389)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7388,U_7389,U_7390)) = c_Orderings_Obot__class_Obot(tc_fun(U_7388,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7388) ),
    inference(clausify,[status(thm)],[f_1695_2]) ).

fof(f_1696_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).

fof(f_1696_2,plain,
    ! [U_7393,U_7392,U_7391] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7391,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7391,U_7392,U_7393)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7391),U_7393)) = c_Orderings_Obot__class_Obot(tc_fun(U_7391,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7391) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

cnf(f_1696_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7391,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7391,U_7392,U_7393)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7391),U_7393)) = c_Orderings_Obot__class_Obot(tc_fun(U_7391,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7391) ),
    inference(clausify,[status(thm)],[f_1696_2]) ).

fof(f_1697_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).

fof(f_1697_2,plain,
    ! [U_7396,U_7395,U_7394] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7394,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7394),U_7395)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7394,U_7395,U_7396)) = c_Orderings_Obot__class_Obot(tc_fun(U_7394,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_7394) ),
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

cnf(f_1697_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7394,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7394),U_7395)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7394,U_7395,U_7396)) = c_Orderings_Obot__class_Obot(tc_fun(U_7394,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_7394) ),
    inference(clausify,[status(thm)],[f_1697_2]) ).

fof(f_1698_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_1698_2,plain,
    ! [U_7397] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7397)) = 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_7397)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7397),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_1698_1]) ).

cnf(f_1698_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7397)) = 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_7397)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7397),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1698_2]) ).

fof(f_1699_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_1699_2,plain,
    ! [U_7398] :
      ( ( 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_7398)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7398)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7398))
        | ~ 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_7398))) ) ),
    inference(variable_rename,[status(thm)],[f_1699_1]) ).

fof(f_1699_3,plain,
    ( ! [U_7400] :
        ( 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_7400)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7400)) )
    & ! [U_7399] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7399))
        | ~ 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_7399))) ) ),
    inference(miniscope,[status(thm)],[f_1699_2]) ).

cnf(f_1699_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7399))
    | ~ 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_7399))) ),
    inference(clausify,[status(thm)],[f_1699_3]) ).

cnf(f_1699_5,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_7400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7400)) ),
    inference(clausify,[status(thm)],[f_1699_3]) ).

fof(f_1700_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_1700_2,plain,
    ! [U_7402,U_7401] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7401)),U_7402))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7401),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7401),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7401)),U_7402)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7401)) ),
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

cnf(f_1700_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7401),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7401)),U_7402))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7401)) ),
    inference(clausify,[status(thm)],[f_1700_2]) ).

cnf(f_1700_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7401)),U_7402))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7401),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7401)) ),
    inference(clausify,[status(thm)],[f_1700_2]) ).

fof(f_1701_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_1701_2,plain,
    ! [U_7403] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7403)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7403)) ),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

cnf(f_1701_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7403)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7403)) ),
    inference(clausify,[status(thm)],[f_1701_2]) ).

fof(f_1702_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_1702_2,plain,
    ! [U_7405,U_7404] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7404,U_7405)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

cnf(f_1702_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7404,U_7405)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_1702_2]) ).

fof(f_1703_1,plain,
    ! [V_u_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).

fof(f_1703_2,plain,
    ! [U_7407,U_7406] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7406,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7406),U_7407)),hAPP(hAPP(c_Set_Oinsert(U_7406),U_7407),c_Orderings_Obot__class_Obot(tc_fun(U_7406,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_7406),U_7407)
      | ~ class_Orderings_Olinorder(U_7406) ),
    inference(variable_rename,[status(thm)],[f_1703_1]) ).

cnf(f_1703_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7406,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7406),U_7407)),hAPP(hAPP(c_Set_Oinsert(U_7406),U_7407),c_Orderings_Obot__class_Obot(tc_fun(U_7406,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_7406),U_7407)
    | ~ class_Orderings_Olinorder(U_7406) ),
    inference(clausify,[status(thm)],[f_1703_2]) ).

fof(f_1704_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).

fof(f_1704_2,plain,
    ! [U_7410,U_7409,U_7408] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7408,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7408),U_7409)),c_SetInterval_Oord__class_OatLeastAtMost(U_7408,U_7409,U_7410)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7408),U_7410)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7408),U_7409),U_7410))
      | ~ class_Orderings_Olinorder(U_7408) ),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

cnf(f_1704_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7408,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7408),U_7409)),c_SetInterval_Oord__class_OatLeastAtMost(U_7408,U_7409,U_7410)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7408),U_7410)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7408),U_7409),U_7410))
    | ~ class_Orderings_Olinorder(U_7408) ),
    inference(clausify,[status(thm)],[f_1704_2]) ).

fof(f_1705_1,plain,
    ! [V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).

fof(f_1705_2,plain,
    ! [U_7412,U_7411] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7411,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7411),U_7412),c_Orderings_Obot__class_Obot(tc_fun(U_7411,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7411),U_7412)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7411),U_7412)
      | ~ class_Orderings_Olinorder(U_7411) ),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

cnf(f_1705_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7411,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7411),U_7412),c_Orderings_Obot__class_Obot(tc_fun(U_7411,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7411),U_7412)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7411),U_7412)
    | ~ class_Orderings_Olinorder(U_7411) ),
    inference(clausify,[status(thm)],[f_1705_2]) ).

fof(f_1706_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).

fof(f_1706_2,plain,
    ! [U_7415,U_7414,U_7413] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7413,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7413,U_7414,U_7415)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7413),U_7415)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7413),U_7414)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7413),U_7414),U_7415))
      | ~ class_Orderings_Olinorder(U_7413) ),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

cnf(f_1706_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7413,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7413,U_7414,U_7415)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7413),U_7415)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7413),U_7414)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7413),U_7414),U_7415))
    | ~ class_Orderings_Olinorder(U_7413) ),
    inference(clausify,[status(thm)],[f_1706_2]) ).

fof(f_1707_1,plain,
    ! [V_u_2,V_l_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).

fof(f_1707_2,plain,
    ! [U_7418,U_7417,U_7416] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7416,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7416),U_7417)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7416,U_7417,U_7418)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7416),U_7418)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),U_7417),U_7418))
      | ~ class_Orderings_Olinorder(U_7416) ),
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

cnf(f_1707_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7416,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7416),U_7417)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7416,U_7417,U_7418)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7416),U_7418)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7416),U_7417),U_7418))
    | ~ class_Orderings_Olinorder(U_7416) ),
    inference(clausify,[status(thm)],[f_1707_2]) ).

fof(f_1708_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_1708_2,plain,
    ! [U_7420,U_7419] : c_Int_Onat__aux(U_7419,U_7420) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7419)),U_7420),
    inference(variable_rename,[status(thm)],[f_1708_1]) ).

cnf(f_1708_3,plain,
    c_Int_Onat__aux(U_7419,U_7420) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7419)),U_7420),
    inference(clausify,[status(thm)],[f_1708_2]) ).

fof(f_1709_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]) ).

cnf(f_1709_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(clausify,[status(thm)],[f_1709_1]) ).

fof(f_1710_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_1710_2,plain,
    ! [U_7426,U_7425,U_7424] :
      ( ! [U_7423] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
          | ? [U_7422] :
              ( ? [U_7421] :
                  ( U_7423 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7421),U_7422)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7421),U_7426)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7422),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7424))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ! [U_7426,U_7425,U_7424] :
      ( ! [U_7423] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
          | ( ? [U_7421] :
                ( U_7423 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7421),sK152(U_7426,U_7425,U_7424,U_7423))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7421),U_7426)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK152(U_7426,U_7425,U_7424,U_7423)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7424))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_7422,sK152(U_7426,U_7425,U_7424,U_7423))],[f_1710_2]) ).

fof(f_1710_4,plain,
    ! [U_7426,U_7425,U_7424] :
      ( ! [U_7423] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
          | ( U_7423 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK153(U_7426,U_7425,U_7424,U_7423)),sK152(U_7426,U_7425,U_7424,U_7423))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK153(U_7426,U_7425,U_7424,U_7423)),U_7426))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK152(U_7426,U_7425,U_7424,U_7423)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7424))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_7421,sK153(U_7426,U_7425,U_7424,U_7423))],[f_1710_3]) ).

cnf(f_1710_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK152(U_7426,U_7425,U_7424,U_7423)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7424)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(clausify,[status(thm)],[f_1710_4]) ).

cnf(f_1710_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK153(U_7426,U_7425,U_7424,U_7423)),U_7426))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(clausify,[status(thm)],[f_1710_4]) ).

cnf(f_1710_7,plain,
    ( U_7423 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK153(U_7426,U_7425,U_7424,U_7423)),sK152(U_7426,U_7425,U_7424,U_7423))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7423),U_7424)),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
    inference(clausify,[status(thm)],[f_1710_4]) ).

fof(f_1711_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_1711_2,plain,
    ! [U_7432,U_7431,U_7430] :
      ( ! [U_7429] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
          | ? [U_7428] :
              ( ? [U_7427] :
                  ( U_7429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7427),U_7428)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7427),U_7432)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7428),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7430))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

fof(f_1711_3,plain,
    ! [U_7432,U_7431,U_7430] :
      ( ! [U_7429] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
          | ( ? [U_7427] :
                ( U_7429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7427),sK154(U_7432,U_7431,U_7430,U_7429))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7427),U_7432)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_7432,U_7431,U_7430,U_7429)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7430))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_7428,sK154(U_7432,U_7431,U_7430,U_7429))],[f_1711_2]) ).

fof(f_1711_4,plain,
    ! [U_7432,U_7431,U_7430] :
      ( ! [U_7429] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
          | ( U_7429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK155(U_7432,U_7431,U_7430,U_7429)),sK154(U_7432,U_7431,U_7430,U_7429))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK155(U_7432,U_7431,U_7430,U_7429)),U_7432))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_7432,U_7431,U_7430,U_7429)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7430))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_7427,sK155(U_7432,U_7431,U_7430,U_7429))],[f_1711_3]) ).

cnf(f_1711_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_7432,U_7431,U_7430,U_7429)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7430)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(clausify,[status(thm)],[f_1711_4]) ).

cnf(f_1711_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK155(U_7432,U_7431,U_7430,U_7429)),U_7432))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(clausify,[status(thm)],[f_1711_4]) ).

cnf(f_1711_7,plain,
    ( U_7429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK155(U_7432,U_7431,U_7430,U_7429)),sK154(U_7432,U_7431,U_7430,U_7429))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7429),U_7430)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),U_7429))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7431),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7430)) ),
    inference(clausify,[status(thm)],[f_1711_4]) ).

fof(f_1712_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_1712_2,plain,
    ! [U_7438,U_7437,U_7436] :
      ( ! [U_7435] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
          | U_7435 = U_7437
          | ? [U_7434] :
              ( ? [U_7433] :
                  ( U_7435 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7433),U_7434)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7433),U_7438)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7434),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7436))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

fof(f_1712_3,plain,
    ! [U_7438,U_7437,U_7436] :
      ( ! [U_7435] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
          | U_7435 = U_7437
          | ( ? [U_7433] :
                ( U_7435 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7433),sK156(U_7438,U_7437,U_7436,U_7435))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7433),U_7438)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_7438,U_7437,U_7436,U_7435)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7436))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_7434,sK156(U_7438,U_7437,U_7436,U_7435))],[f_1712_2]) ).

fof(f_1712_4,plain,
    ! [U_7438,U_7437,U_7436] :
      ( ! [U_7435] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
          | U_7435 = U_7437
          | ( U_7435 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_7438,U_7437,U_7436,U_7435)),sK156(U_7438,U_7437,U_7436,U_7435))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_7438,U_7437,U_7436,U_7435)),U_7438))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_7438,U_7437,U_7436,U_7435)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7436))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_7433,sK157(U_7438,U_7437,U_7436,U_7435))],[f_1712_3]) ).

cnf(f_1712_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_7438,U_7437,U_7436,U_7435)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7436)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
    | U_7435 = U_7437
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(clausify,[status(thm)],[f_1712_4]) ).

cnf(f_1712_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_7438,U_7437,U_7436,U_7435)),U_7438))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
    | U_7435 = U_7437
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(clausify,[status(thm)],[f_1712_4]) ).

cnf(f_1712_7,plain,
    ( U_7435 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_7438,U_7437,U_7436,U_7435)),sK156(U_7438,U_7437,U_7436,U_7435))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7435),U_7436) != U_7437
    | U_7435 = U_7437
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7437),U_7438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7436)) ),
    inference(clausify,[status(thm)],[f_1712_4]) ).

fof(f_1713_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_1713_2,plain,
    ! [U_7444,U_7443,U_7442] :
      ( ! [U_7441] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
          | U_7441 = U_7443
          | ? [U_7440] :
              ( ? [U_7439] :
                  ( U_7441 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7439),U_7440)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7439),U_7444)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7440),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7442))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(variable_rename,[status(thm)],[f_1713_1]) ).

fof(f_1713_3,plain,
    ! [U_7444,U_7443,U_7442] :
      ( ! [U_7441] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
          | U_7441 = U_7443
          | ( ? [U_7439] :
                ( U_7441 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7439),sK158(U_7444,U_7443,U_7442,U_7441))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7439),U_7444)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_7444,U_7443,U_7442,U_7441)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7442))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_7440,sK158(U_7444,U_7443,U_7442,U_7441))],[f_1713_2]) ).

fof(f_1713_4,plain,
    ! [U_7444,U_7443,U_7442] :
      ( ! [U_7441] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
          | U_7441 = U_7443
          | ( U_7441 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK159(U_7444,U_7443,U_7442,U_7441)),sK158(U_7444,U_7443,U_7442,U_7441))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_7444,U_7443,U_7442,U_7441)),U_7444))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_7444,U_7443,U_7442,U_7441)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7442))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_7439,sK159(U_7444,U_7443,U_7442,U_7441))],[f_1713_3]) ).

cnf(f_1713_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_7444,U_7443,U_7442,U_7441)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7442)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
    | U_7441 = U_7443
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(clausify,[status(thm)],[f_1713_4]) ).

cnf(f_1713_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_7444,U_7443,U_7442,U_7441)),U_7444))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
    | U_7441 = U_7443
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(clausify,[status(thm)],[f_1713_4]) ).

cnf(f_1713_7,plain,
    ( U_7441 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK159(U_7444,U_7443,U_7442,U_7441)),sK158(U_7444,U_7443,U_7442,U_7441))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7441),U_7442) != U_7443
    | U_7441 = U_7443
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7443),U_7444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7442)) ),
    inference(clausify,[status(thm)],[f_1713_4]) ).

fof(f_1714_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_1714_2,plain,
    ! [U_7446,U_7445] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7445),U_7446) = 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_7445)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7446)))
      | ~ c_Nat__Transfer_Onat__set(U_7446)
      | ~ c_Nat__Transfer_Onat__set(U_7445) ),
    inference(variable_rename,[status(thm)],[f_1714_1]) ).

cnf(f_1714_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7445),U_7446) = 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_7445)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7446)))
    | ~ c_Nat__Transfer_Onat__set(U_7446)
    | ~ c_Nat__Transfer_Onat__set(U_7445) ),
    inference(clausify,[status(thm)],[f_1714_2]) ).

fof(f_1715_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_1715_2,plain,
    ! [U_7448,U_7447] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7447),U_7448) = 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_7447)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7448)))
      | ~ c_Nat__Transfer_Onat__set(U_7448)
      | ~ c_Nat__Transfer_Onat__set(U_7447) ),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

cnf(f_1715_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7447),U_7448) = 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_7447)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7448)))
    | ~ c_Nat__Transfer_Onat__set(U_7448)
    | ~ c_Nat__Transfer_Onat__set(U_7447) ),
    inference(clausify,[status(thm)],[f_1715_2]) ).

fof(f_1716_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_1716_2,plain,
    ! [U_7453,U_7452,U_7451] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
      | ? [U_7450] :
          ( ? [U_7449] :
              ( U_7452 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7449),U_7450)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7449),U_7453)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7450),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7451))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

fof(f_1716_3,plain,
    ! [U_7453,U_7452,U_7451] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
      | ( ? [U_7449] :
            ( U_7452 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7449),sK160(U_7453,U_7452,U_7451))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7449),U_7453)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7453,U_7452,U_7451)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7451))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_7450,sK160(U_7453,U_7452,U_7451))],[f_1716_2]) ).

fof(f_1716_4,plain,
    ! [U_7453,U_7452,U_7451] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
      | ( U_7452 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK161(U_7453,U_7452,U_7451)),sK160(U_7453,U_7452,U_7451))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_7453,U_7452,U_7451)),U_7453))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7453,U_7452,U_7451)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7451))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_7449,sK161(U_7453,U_7452,U_7451))],[f_1716_3]) ).

cnf(f_1716_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7453,U_7452,U_7451)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7451)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

cnf(f_1716_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_7453,U_7452,U_7451)),U_7453))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

cnf(f_1716_7,plain,
    ( U_7452 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK161(U_7453,U_7452,U_7451)),sK160(U_7453,U_7452,U_7451))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),U_7451) = U_7452
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7452),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7451)) ),
    inference(clausify,[status(thm)],[f_1716_4]) ).

fof(f_1717_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_1717_2,plain,
    ! [U_7458,U_7457,U_7456] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
      | ? [U_7455] :
          ( ? [U_7454] :
              ( U_7457 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7454),U_7455)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7454),U_7458)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7455),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7456))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

fof(f_1717_3,plain,
    ! [U_7458,U_7457,U_7456] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
      | ( ? [U_7454] :
            ( U_7457 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7454),sK162(U_7458,U_7457,U_7456))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7454),U_7458)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_7458,U_7457,U_7456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7456))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_7455,sK162(U_7458,U_7457,U_7456))],[f_1717_2]) ).

fof(f_1717_4,plain,
    ! [U_7458,U_7457,U_7456] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
      | ( U_7457 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK163(U_7458,U_7457,U_7456)),sK162(U_7458,U_7457,U_7456))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_7458,U_7457,U_7456)),U_7458))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_7458,U_7457,U_7456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7456))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_7454,sK163(U_7458,U_7457,U_7456))],[f_1717_3]) ).

cnf(f_1717_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_7458,U_7457,U_7456)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7456)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

cnf(f_1717_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_7458,U_7457,U_7456)),U_7458))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

cnf(f_1717_7,plain,
    ( U_7457 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK163(U_7458,U_7457,U_7456)),sK162(U_7458,U_7457,U_7456))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),U_7456) = U_7457
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7457),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7456)) ),
    inference(clausify,[status(thm)],[f_1717_4]) ).

fof(f_1718_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_1718_2,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ! [U_7461] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
          | ? [U_7460] :
              ( ? [U_7459] :
                  ( U_7461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7459),U_7460)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7459),U_7464)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7460),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7462))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

fof(f_1718_3,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ! [U_7461] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
          | ( ? [U_7459] :
                ( U_7461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7459),sK164(U_7464,U_7463,U_7462,U_7461))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7459),U_7464)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_7464,U_7463,U_7462,U_7461)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7462))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_7460,sK164(U_7464,U_7463,U_7462,U_7461))],[f_1718_2]) ).

fof(f_1718_4,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ! [U_7461] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
          | ( U_7461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK165(U_7464,U_7463,U_7462,U_7461)),sK164(U_7464,U_7463,U_7462,U_7461))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_7464,U_7463,U_7462,U_7461)),U_7464))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_7464,U_7463,U_7462,U_7461)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7462))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_7459,sK165(U_7464,U_7463,U_7462,U_7461))],[f_1718_3]) ).

cnf(f_1718_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_7464,U_7463,U_7462,U_7461)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7462)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(clausify,[status(thm)],[f_1718_4]) ).

cnf(f_1718_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_7464,U_7463,U_7462,U_7461)),U_7464))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(clausify,[status(thm)],[f_1718_4]) ).

cnf(f_1718_7,plain,
    ( U_7461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK165(U_7464,U_7463,U_7462,U_7461)),sK164(U_7464,U_7463,U_7462,U_7461))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7461),U_7462)),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7461),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7463),U_7464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7462)) ),
    inference(clausify,[status(thm)],[f_1718_4]) ).

fof(f_1719_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]) ).

cnf(f_1719_2,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1719_1]) ).

fof(f_1720_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_1720_2,plain,
    ! [U_7466,U_7465] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7465),U_7466))
      | ~ c_Nat__Transfer_Onat__set(U_7466)
      | ~ c_Nat__Transfer_Onat__set(U_7465) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

cnf(f_1720_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7465),U_7466))
    | ~ c_Nat__Transfer_Onat__set(U_7466)
    | ~ c_Nat__Transfer_Onat__set(U_7465) ),
    inference(clausify,[status(thm)],[f_1720_2]) ).

fof(f_1721_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_1721_2,plain,
    ! [U_7468,U_7467] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7467),U_7468))
      | ~ c_Nat__Transfer_Onat__set(U_7468)
      | ~ c_Nat__Transfer_Onat__set(U_7467) ),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

cnf(f_1721_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7467),U_7468))
    | ~ c_Nat__Transfer_Onat__set(U_7468)
    | ~ c_Nat__Transfer_Onat__set(U_7467) ),
    inference(clausify,[status(thm)],[f_1721_2]) ).

fof(f_1722_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_1722_2,plain,
    ! [U_7471] :
      ( ( c_Nat__Transfer_Onat__set(U_7471)
        | ? [U_7470] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7470))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7470),U_7471)) ) )
      & ( ! [U_7469] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7469))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7469),U_7471)) )
        | ~ c_Nat__Transfer_Onat__set(U_7471) ) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

fof(f_1722_3,plain,
    ( ! [U_7473] :
        ( c_Nat__Transfer_Onat__set(U_7473)
        | ? [U_7470] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7470))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7470),U_7473)) ) )
    & ! [U_7472] :
        ( ! [U_7469] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7469))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7469),U_7472)) )
        | ~ c_Nat__Transfer_Onat__set(U_7472) ) ),
    inference(miniscope,[status(thm)],[f_1722_2]) ).

fof(f_1722_4,plain,
    ( ! [U_7473] :
        ( c_Nat__Transfer_Onat__set(U_7473)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK166(U_7473)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_7473)),U_7473)) ) )
    & ! [U_7472] :
        ( ! [U_7469] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7469))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7469),U_7472)) )
        | ~ c_Nat__Transfer_Onat__set(U_7472) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_7470,sK166(U_7473))],[f_1722_3]) ).

cnf(f_1722_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7469))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7469),U_7472))
    | ~ c_Nat__Transfer_Onat__set(U_7472) ),
    inference(clausify,[status(thm)],[f_1722_4]) ).

cnf(f_1722_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_7473)),U_7473))
    | c_Nat__Transfer_Onat__set(U_7473) ),
    inference(clausify,[status(thm)],[f_1722_4]) ).

cnf(f_1722_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK166(U_7473)))
    | c_Nat__Transfer_Onat__set(U_7473) ),
    inference(clausify,[status(thm)],[f_1722_4]) ).

fof(f_1723_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_1723_2,plain,
    ! [U_7474] : 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_7474)),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

cnf(f_1723_3,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_7474)),
    inference(clausify,[status(thm)],[f_1723_2]) ).

fof(f_1724_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_1724_2,plain,
    ! [U_7476,U_7475] :
      ( ( ( U_7475 = U_7476
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7475) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7476) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7475) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7476)
          | U_7475 != U_7476 ) )
      | ~ c_Nat__Transfer_Onat__set(U_7476)
      | ~ c_Nat__Transfer_Onat__set(U_7475) ),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

cnf(f_1724_3,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7475) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7476)
    | U_7475 != U_7476
    | ~ c_Nat__Transfer_Onat__set(U_7476)
    | ~ c_Nat__Transfer_Onat__set(U_7475) ),
    inference(clausify,[status(thm)],[f_1724_2]) ).

cnf(f_1724_4,plain,
    ( U_7475 = U_7476
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7475) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7476)
    | ~ c_Nat__Transfer_Onat__set(U_7476)
    | ~ c_Nat__Transfer_Onat__set(U_7475) ),
    inference(clausify,[status(thm)],[f_1724_2]) ).

fof(f_1725_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_1725_2,plain,
    ! [U_7478,U_7477] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7477,U_7478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7477)) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

cnf(f_1725_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7477,U_7478))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7477)) ),
    inference(clausify,[status(thm)],[f_1725_2]) ).

fof(f_1726_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_1726_2,plain,
    ! [U_7480,U_7479] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7480))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7480),U_7479))
      | ~ c_Nat__Transfer_Onat__set(U_7479) ),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

cnf(f_1726_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7480))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7480),U_7479))
    | ~ c_Nat__Transfer_Onat__set(U_7479) ),
    inference(clausify,[status(thm)],[f_1726_2]) ).

fof(f_1727_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_1727_2,plain,
    ! [U_7481] :
      ( 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_7481)) = U_7481
      | ~ c_Nat__Transfer_Onat__set(U_7481) ),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

cnf(f_1727_3,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_7481)) = U_7481
    | ~ c_Nat__Transfer_Onat__set(U_7481) ),
    inference(clausify,[status(thm)],[f_1727_2]) ).

fof(f_1728_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_1728_2,plain,
    ! [U_7482] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7482))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7482))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7482)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7482)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_7482) ),
    inference(variable_rename,[status(thm)],[f_1728_1]) ).

cnf(f_1728_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7482)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7482))
    | ~ c_Nat__Transfer_Onat__set(U_7482) ),
    inference(clausify,[status(thm)],[f_1728_2]) ).

cnf(f_1728_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7482)))
    | ~ c_Nat__Transfer_Onat__set(U_7482) ),
    inference(clausify,[status(thm)],[f_1728_2]) ).

fof(f_1729_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_1729_2,plain,
    ! [U_7483] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7483) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7483))
      | ~ c_Nat__Transfer_Onat__set(U_7483) ),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

cnf(f_1729_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7483) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7483))
    | ~ c_Nat__Transfer_Onat__set(U_7483) ),
    inference(clausify,[status(thm)],[f_1729_2]) ).

fof(f_1730_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_1730_2,plain,
    ! [U_7485,U_7484] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7484),U_7485))
          | ~ 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_7484)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7485))) )
        & ( 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_7484)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7485)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7484),U_7485)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_7485)
      | ~ c_Nat__Transfer_Onat__set(U_7484) ),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

cnf(f_1730_3,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_7484)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7484),U_7485))
    | ~ c_Nat__Transfer_Onat__set(U_7485)
    | ~ c_Nat__Transfer_Onat__set(U_7484) ),
    inference(clausify,[status(thm)],[f_1730_2]) ).

cnf(f_1730_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7484),U_7485))
    | ~ 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_7484)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7485)))
    | ~ c_Nat__Transfer_Onat__set(U_7485)
    | ~ c_Nat__Transfer_Onat__set(U_7484) ),
    inference(clausify,[status(thm)],[f_1730_2]) ).

fof(f_1731_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_1731_2,plain,
    ! [U_7487,U_7486] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7486),U_7487))
          | ~ 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_7486)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7487))) )
        & ( 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_7486)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7487)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7486),U_7487)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_7487)
      | ~ c_Nat__Transfer_Onat__set(U_7486) ),
    inference(variable_rename,[status(thm)],[f_1731_1]) ).

cnf(f_1731_3,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_7486)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7487)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7486),U_7487))
    | ~ c_Nat__Transfer_Onat__set(U_7487)
    | ~ c_Nat__Transfer_Onat__set(U_7486) ),
    inference(clausify,[status(thm)],[f_1731_2]) ).

cnf(f_1731_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7486),U_7487))
    | ~ 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_7486)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7487)))
    | ~ c_Nat__Transfer_Onat__set(U_7487)
    | ~ c_Nat__Transfer_Onat__set(U_7486) ),
    inference(clausify,[status(thm)],[f_1731_2]) ).

fof(f_1732_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).

fof(f_1732_2,plain,
    ! [U_7490,U_7489,U_7488] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7488),U_7490),U_7489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7488),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7488,tc_Nat_Onat),U_7490),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7489))
      | ~ c_Nat__Transfer_Onat__set(U_7489)
      | ~ class_Groups_Ocomm__monoid__mult(U_7488)
      | ~ class_Groups_Ocomm__monoid__add(U_7488) ),
    inference(variable_rename,[status(thm)],[f_1732_1]) ).

cnf(f_1732_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7488),U_7490),U_7489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7488),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7488,tc_Nat_Onat),U_7490),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7489))
    | ~ c_Nat__Transfer_Onat__set(U_7489)
    | ~ class_Groups_Ocomm__monoid__mult(U_7488)
    | ~ class_Groups_Ocomm__monoid__add(U_7488) ),
    inference(clausify,[status(thm)],[f_1732_2]) ).

fof(f_1733_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_1733_2,plain,
    ! [U_7496,U_7495,U_7494] :
      ( ! [U_7493] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
          | ? [U_7492] :
              ( ? [U_7491] :
                  ( U_7493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7491),U_7492)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7491),U_7496)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7492),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7494))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(variable_rename,[status(thm)],[f_1733_1]) ).

fof(f_1733_3,plain,
    ! [U_7496,U_7495,U_7494] :
      ( ! [U_7493] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
          | ( ? [U_7491] :
                ( U_7493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7491),sK167(U_7496,U_7495,U_7494,U_7493))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7491),U_7496)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_7496,U_7495,U_7494,U_7493)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7494))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_7492,sK167(U_7496,U_7495,U_7494,U_7493))],[f_1733_2]) ).

fof(f_1733_4,plain,
    ! [U_7496,U_7495,U_7494] :
      ( ! [U_7493] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
          | ( U_7493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK168(U_7496,U_7495,U_7494,U_7493)),sK167(U_7496,U_7495,U_7494,U_7493))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_7496,U_7495,U_7494,U_7493)),U_7496))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_7496,U_7495,U_7494,U_7493)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7494))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_7491,sK168(U_7496,U_7495,U_7494,U_7493))],[f_1733_3]) ).

cnf(f_1733_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_7496,U_7495,U_7494,U_7493)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7494)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(clausify,[status(thm)],[f_1733_4]) ).

cnf(f_1733_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_7496,U_7495,U_7494,U_7493)),U_7496))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(clausify,[status(thm)],[f_1733_4]) ).

cnf(f_1733_7,plain,
    ( U_7493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK168(U_7496,U_7495,U_7494,U_7493)),sK167(U_7496,U_7495,U_7494,U_7493))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7493),U_7494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7495),U_7493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7495),U_7496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) ),
    inference(clausify,[status(thm)],[f_1733_4]) ).

fof(f_1734_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_1734_2,plain,
    ! [U_7502,U_7501,U_7500] :
      ( ! [U_7499] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
          | ? [U_7498] :
              ( ? [U_7497] :
                  ( U_7499 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7497),U_7498)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7497),U_7501)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7498),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7500))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

fof(f_1734_3,plain,
    ! [U_7502,U_7501,U_7500] :
      ( ! [U_7499] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
          | ( ? [U_7497] :
                ( U_7499 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7497),sK169(U_7502,U_7501,U_7500,U_7499))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7497),U_7501)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_7502,U_7501,U_7500,U_7499)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7500))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_7498,sK169(U_7502,U_7501,U_7500,U_7499))],[f_1734_2]) ).

fof(f_1734_4,plain,
    ! [U_7502,U_7501,U_7500] :
      ( ! [U_7499] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
          | ( U_7499 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK170(U_7502,U_7501,U_7500,U_7499)),sK169(U_7502,U_7501,U_7500,U_7499))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_7502,U_7501,U_7500,U_7499)),U_7501))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_7502,U_7501,U_7500,U_7499)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7500))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_7497,sK170(U_7502,U_7501,U_7500,U_7499))],[f_1734_3]) ).

cnf(f_1734_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_7502,U_7501,U_7500,U_7499)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7500)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(clausify,[status(thm)],[f_1734_4]) ).

cnf(f_1734_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_7502,U_7501,U_7500,U_7499)),U_7501))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(clausify,[status(thm)],[f_1734_4]) ).

cnf(f_1734_7,plain,
    ( U_7499 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK170(U_7502,U_7501,U_7500,U_7499)),sK169(U_7502,U_7501,U_7500,U_7499))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7499),U_7500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7502),U_7499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7500)) ),
    inference(clausify,[status(thm)],[f_1734_4]) ).

fof(f_1735_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_1735_2,plain,
    ! [U_7508,U_7507,U_7506] :
      ( ! [U_7505] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
          | ? [U_7504] :
              ( ? [U_7503] :
                  ( U_7505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7503),U_7504)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7503),U_7507)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7504),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7506))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

fof(f_1735_3,plain,
    ! [U_7508,U_7507,U_7506] :
      ( ! [U_7505] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
          | ( ? [U_7503] :
                ( U_7505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7503),sK171(U_7508,U_7507,U_7506,U_7505))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7503),U_7507)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_7508,U_7507,U_7506,U_7505)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7506))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_7504,sK171(U_7508,U_7507,U_7506,U_7505))],[f_1735_2]) ).

fof(f_1735_4,plain,
    ! [U_7508,U_7507,U_7506] :
      ( ! [U_7505] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
          | ( U_7505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK172(U_7508,U_7507,U_7506,U_7505)),sK171(U_7508,U_7507,U_7506,U_7505))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_7508,U_7507,U_7506,U_7505)),U_7507))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_7508,U_7507,U_7506,U_7505)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7506))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_7503,sK172(U_7508,U_7507,U_7506,U_7505))],[f_1735_3]) ).

cnf(f_1735_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_7508,U_7507,U_7506,U_7505)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7506)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(clausify,[status(thm)],[f_1735_4]) ).

cnf(f_1735_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_7508,U_7507,U_7506,U_7505)),U_7507))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(clausify,[status(thm)],[f_1735_4]) ).

cnf(f_1735_7,plain,
    ( U_7505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK172(U_7508,U_7507,U_7506,U_7505)),sK171(U_7508,U_7507,U_7506,U_7505))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7505),U_7506)),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7505),U_7508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7506)) ),
    inference(clausify,[status(thm)],[f_1735_4]) ).

fof(f_1736_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_1736_2,plain,
    ! [U_7510,U_7509] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7509),U_7510))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7509)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7510))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7509)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7510)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7509),U_7510)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_7510)
      | ~ c_Nat__Transfer_Ois__nat(U_7509) ),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

cnf(f_1736_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7509)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7510)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7509),U_7510))
    | ~ c_Nat__Transfer_Onat__set(U_7510)
    | ~ c_Nat__Transfer_Ois__nat(U_7509) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7509),U_7510))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7509)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7510)))
    | ~ c_Nat__Transfer_Onat__set(U_7510)
    | ~ c_Nat__Transfer_Ois__nat(U_7509) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

fof(f_1737_1,plain,
    ! [V_P_2,V_d_2] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) )
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ? [B_x,B_k] :
          ( ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
          | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2))))
            & hBOOL(hAPP(V_P_2,B_x)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex]) ).

fof(f_1737_2,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ? [U_7512,U_7511] :
          ( ( ~ hBOOL(hAPP(U_7518,U_7512))
            & hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7511),U_7517)))) )
          | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7511),U_7517))))
            & hBOOL(hAPP(U_7518,U_7512)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

fof(f_1737_3,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ? [U_7522] :
          ( ? [U_7520] : hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7520),U_7517))))
          & ~ hBOOL(hAPP(U_7518,U_7522)) )
      | ? [U_7521] :
          ( ? [U_7519] : ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7519),U_7517))))
          & hBOOL(hAPP(U_7518,U_7521)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(miniscope,[status(thm)],[f_1737_2]) ).

fof(f_1737_4,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ? [U_7522] :
          ( ? [U_7520] : hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7520),U_7517))))
          & ~ hBOOL(hAPP(U_7518,U_7522)) )
      | ( ? [U_7519] : ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7519),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_7521,sK173(U_7518,U_7517))],[f_1737_3]) ).

fof(f_1737_5,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ? [U_7522] :
          ( ? [U_7520] : hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7520),U_7517))))
          & ~ hBOOL(hAPP(U_7518,U_7522)) )
      | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_7519,sK174(U_7518,U_7517))],[f_1737_4]) ).

fof(f_1737_6,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ( ? [U_7520] : hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7520),U_7517))))
        & ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517))) )
      | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_7522,sK175(U_7518,U_7517))],[f_1737_5]) ).

fof(f_1737_7,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ? [U_7514] :
              ( hBOOL(hAPP(U_7518,U_7514))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
        & ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517))) )
      | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_7520,sK176(U_7518,U_7517))],[f_1737_6]) ).

fof(f_1737_8,plain,
    ! [U_7518,U_7517] :
      ( ( ( ? [U_7516] : hBOOL(hAPP(U_7518,U_7516))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ( hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
        & ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517))) )
      | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_7514,sK177(U_7518,U_7517))],[f_1737_7]) ).

fof(f_1737_9,plain,
    ! [U_7518,U_7517] :
      ( ( ( hBOOL(hAPP(U_7518,sK178(U_7518,U_7517)))
          | ! [U_7515] :
              ( ~ hBOOL(hAPP(U_7518,U_7515))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) ) )
        & ( ( hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517))) )
          | ! [U_7513] : ~ hBOOL(hAPP(U_7518,U_7513)) ) )
      | ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
        & ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517))) )
      | ( ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
        & hBOOL(hAPP(U_7518,sK173(U_7518,U_7517))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_7516,sK178(U_7518,U_7517))],[f_1737_8]) ).

cnf(f_1737_10,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_11,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_12,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_13,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_14,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_15,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_7518,U_7517)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_16,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_17,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK177(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_18,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK178(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7515))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_19,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK173(U_7518,U_7517)))
    | hBOOL(hAPP(U_7518,sK178(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7515))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_20,plain,
    ( ~ hBOOL(hAPP(U_7518,sK175(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK178(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7515))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

cnf(f_1737_21,plain,
    ( hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK175(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK176(U_7518,U_7517)),U_7517))))
    | ~ hBOOL(hAPP(U_7518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_7518,U_7517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK174(U_7518,U_7517)),U_7517))))
    | hBOOL(hAPP(U_7518,sK178(U_7518,U_7517)))
    | ~ hBOOL(hAPP(U_7518,U_7515))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7515),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7517)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7517)) ),
    inference(clausify,[status(thm)],[f_1737_9]) ).

fof(f_1738_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]) ).

cnf(f_1738_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1738_1]) ).

fof(f_1739_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_1739_2,plain,
    ! [U_7524,U_7523] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7523),U_7524))
      | ~ c_Nat__Transfer_Ois__nat(U_7524)
      | ~ c_Nat__Transfer_Ois__nat(U_7523) ),
    inference(variable_rename,[status(thm)],[f_1739_1]) ).

cnf(f_1739_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7523),U_7524))
    | ~ c_Nat__Transfer_Ois__nat(U_7524)
    | ~ c_Nat__Transfer_Ois__nat(U_7523) ),
    inference(clausify,[status(thm)],[f_1739_2]) ).

fof(f_1740_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_1740_2,plain,
    ! [U_7525] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7525)),
    inference(variable_rename,[status(thm)],[f_1740_1]) ).

cnf(f_1740_3,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7525)),
    inference(clausify,[status(thm)],[f_1740_2]) ).

fof(f_1741_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]) ).

cnf(f_1741_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1741_1]) ).

fof(f_1742_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_1742_2,plain,
    ! [U_7527,U_7526] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7526),U_7527))
      | ~ c_Nat__Transfer_Ois__nat(U_7527)
      | ~ c_Nat__Transfer_Ois__nat(U_7526) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

cnf(f_1742_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7526),U_7527))
    | ~ c_Nat__Transfer_Ois__nat(U_7527)
    | ~ c_Nat__Transfer_Ois__nat(U_7526) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

fof(f_1743_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_1743_2,plain,
    ! [U_7529,U_7528] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7528,U_7529))
      | ~ c_Nat__Transfer_Ois__nat(U_7529)
      | ~ c_Nat__Transfer_Ois__nat(U_7528) ),
    inference(variable_rename,[status(thm)],[f_1743_1]) ).

cnf(f_1743_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7528,U_7529))
    | ~ c_Nat__Transfer_Ois__nat(U_7529)
    | ~ c_Nat__Transfer_Ois__nat(U_7528) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

fof(f_1744_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_1744_2,plain,
    ! [U_7530] :
      ( ( c_Nat__Transfer_Ois__nat(U_7530)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7530)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7530))
        | ~ c_Nat__Transfer_Ois__nat(U_7530) ) ),
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

fof(f_1744_3,plain,
    ( ! [U_7532] :
        ( c_Nat__Transfer_Ois__nat(U_7532)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532)) )
    & ! [U_7531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7531))
        | ~ c_Nat__Transfer_Ois__nat(U_7531) ) ),
    inference(miniscope,[status(thm)],[f_1744_2]) ).

cnf(f_1744_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7531))
    | ~ c_Nat__Transfer_Ois__nat(U_7531) ),
    inference(clausify,[status(thm)],[f_1744_3]) ).

cnf(f_1744_5,plain,
    ( c_Nat__Transfer_Ois__nat(U_7532)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532)) ),
    inference(clausify,[status(thm)],[f_1744_3]) ).

fof(f_1745_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_1745_2,plain,
    ! [U_7534,U_7533] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7533,U_7534))
      | ~ c_Nat__Transfer_Ois__nat(U_7533) ),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

cnf(f_1745_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7533,U_7534))
    | ~ c_Nat__Transfer_Ois__nat(U_7533) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

fof(f_1746_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_1746_2,plain,
    ! [U_7536,U_7535] :
      ( c_Nat__Transfer_Ois__nat(U_7536)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7536),U_7535))
      | ~ c_Nat__Transfer_Onat__set(U_7535) ),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

cnf(f_1746_3,plain,
    ( c_Nat__Transfer_Ois__nat(U_7536)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7536),U_7535))
    | ~ c_Nat__Transfer_Onat__set(U_7535) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

fof(f_1747_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_1747_2,plain,
    ! [U_7538,U_7537] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7537,U_7538) = 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_7537),hAPP(c_Int_Onat,U_7538)))
      | ~ c_Nat__Transfer_Ois__nat(U_7538)
      | ~ c_Nat__Transfer_Ois__nat(U_7537) ),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

cnf(f_1747_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7537,U_7538) = 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_7537),hAPP(c_Int_Onat,U_7538)))
    | ~ c_Nat__Transfer_Ois__nat(U_7538)
    | ~ c_Nat__Transfer_Ois__nat(U_7537) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

fof(f_1748_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),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_a),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).

fof(f_1748_2,plain,
    ! [U_7542,U_7541,U_7540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Int_Oint),U_7542),U_7541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_7540),c_Int_Onat),U_7542)),U_7541))
      | ? [U_7539] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_7542,U_7539))
          & hBOOL(hAPP(hAPP(c_member(U_7540),U_7539),U_7541)) ) ),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

fof(f_1748_3,plain,
    ! [U_7542,U_7541,U_7540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Int_Oint),U_7542),U_7541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_7540),c_Int_Onat),U_7542)),U_7541))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_7542,sK179(U_7542,U_7541,U_7540)))
        & hBOOL(hAPP(hAPP(c_member(U_7540),sK179(U_7542,U_7541,U_7540)),U_7541)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_7539,sK179(U_7542,U_7541,U_7540))],[f_1748_2]) ).

cnf(f_1748_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7540),sK179(U_7542,U_7541,U_7540)),U_7541))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Int_Oint),U_7542),U_7541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_7540),c_Int_Onat),U_7542)),U_7541)) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

cnf(f_1748_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_7542,sK179(U_7542,U_7541,U_7540)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Int_Oint),U_7542),U_7541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7540,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_7540),c_Int_Onat),U_7542)),U_7541)) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

fof(f_1749_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_1749_2,plain,
    ! [U_7548,U_7547,U_7546] :
      ( ! [U_7545] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
          | ? [U_7544] :
              ( ? [U_7543] :
                  ( U_7545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7543),U_7544)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7543),U_7547)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7544),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7546))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

fof(f_1749_3,plain,
    ! [U_7548,U_7547,U_7546] :
      ( ! [U_7545] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
          | ( ? [U_7543] :
                ( U_7545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7543),sK180(U_7548,U_7547,U_7546,U_7545))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7543),U_7547)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_7548,U_7547,U_7546,U_7545)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7546))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_7544,sK180(U_7548,U_7547,U_7546,U_7545))],[f_1749_2]) ).

fof(f_1749_4,plain,
    ! [U_7548,U_7547,U_7546] :
      ( ! [U_7545] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
          | ( U_7545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_7548,U_7547,U_7546,U_7545)),sK180(U_7548,U_7547,U_7546,U_7545))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_7548,U_7547,U_7546,U_7545)),U_7547))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_7548,U_7547,U_7546,U_7545)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7546))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_7543,sK181(U_7548,U_7547,U_7546,U_7545))],[f_1749_3]) ).

cnf(f_1749_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_7548,U_7547,U_7546,U_7545)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7546)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(clausify,[status(thm)],[f_1749_4]) ).

cnf(f_1749_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_7548,U_7547,U_7546,U_7545)),U_7547))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(clausify,[status(thm)],[f_1749_4]) ).

cnf(f_1749_7,plain,
    ( U_7545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_7548,U_7547,U_7546,U_7545)),sK180(U_7548,U_7547,U_7546,U_7545))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7545),U_7546)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),U_7545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7546)) ),
    inference(clausify,[status(thm)],[f_1749_4]) ).

fof(f_1750_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_1750_2,plain,
    ! [U_7554,U_7553,U_7552] :
      ( ! [U_7551] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
          | ? [U_7550] :
              ( ? [U_7549] :
                  ( U_7551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7549),U_7550)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7549),U_7553)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7550),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7552))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

fof(f_1750_3,plain,
    ! [U_7554,U_7553,U_7552] :
      ( ! [U_7551] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
          | ( ? [U_7549] :
                ( U_7551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7549),sK182(U_7554,U_7553,U_7552,U_7551))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7549),U_7553)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_7554,U_7553,U_7552,U_7551)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7552))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_7550,sK182(U_7554,U_7553,U_7552,U_7551))],[f_1750_2]) ).

fof(f_1750_4,plain,
    ! [U_7554,U_7553,U_7552] :
      ( ! [U_7551] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
          | ( U_7551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK183(U_7554,U_7553,U_7552,U_7551)),sK182(U_7554,U_7553,U_7552,U_7551))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_7554,U_7553,U_7552,U_7551)),U_7553))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_7554,U_7553,U_7552,U_7551)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7552))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_7549,sK183(U_7554,U_7553,U_7552,U_7551))],[f_1750_3]) ).

cnf(f_1750_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_7554,U_7553,U_7552,U_7551)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7552)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(clausify,[status(thm)],[f_1750_4]) ).

cnf(f_1750_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_7554,U_7553,U_7552,U_7551)),U_7553))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(clausify,[status(thm)],[f_1750_4]) ).

cnf(f_1750_7,plain,
    ( U_7551 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK183(U_7554,U_7553,U_7552,U_7551)),sK182(U_7554,U_7553,U_7552,U_7551))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7551),U_7552)),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7551),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7552)) ),
    inference(clausify,[status(thm)],[f_1750_4]) ).

fof(f_1751_1,plain,
    ! [V_n_2,V_P_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) )
      | ~ hBOOL(hAPP(V_P_2,V_n_2))
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_1751_2,plain,
    ! [U_7558,U_7557] :
      ( ? [U_7556] :
          ( hBOOL(hAPP(U_7557,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7556),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_7555] :
              ( ~ hBOOL(hAPP(U_7557,U_7555))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7555),U_7556)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7556),U_7558)) )
      | ~ hBOOL(hAPP(U_7557,U_7558))
      | hBOOL(hAPP(U_7557,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

fof(f_1751_3,plain,
    ! [U_7558,U_7557] :
      ( ( hBOOL(hAPP(U_7557,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK184(U_7558,U_7557)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_7555] :
            ( ~ hBOOL(hAPP(U_7557,U_7555))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7555),sK184(U_7558,U_7557))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK184(U_7558,U_7557)),U_7558)) )
      | ~ hBOOL(hAPP(U_7557,U_7558))
      | hBOOL(hAPP(U_7557,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_7556,sK184(U_7558,U_7557))],[f_1751_2]) ).

cnf(f_1751_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK184(U_7558,U_7557)),U_7558))
    | ~ hBOOL(hAPP(U_7557,U_7558))
    | hBOOL(hAPP(U_7557,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_5,plain,
    ( ~ hBOOL(hAPP(U_7557,U_7555))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7555),sK184(U_7558,U_7557)))
    | ~ hBOOL(hAPP(U_7557,U_7558))
    | hBOOL(hAPP(U_7557,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_6,plain,
    ( hBOOL(hAPP(U_7557,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK184(U_7558,U_7557)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(U_7557,U_7558))
    | hBOOL(hAPP(U_7557,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

fof(f_1752_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_1752_2,plain,
    ! [U_7560] :
      ( ? [U_7559] :
          ( U_7560 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7559)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7559)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7560)) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

fof(f_1752_3,plain,
    ! [U_7560] :
      ( ( U_7560 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK185(U_7560))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK185(U_7560))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7560)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_7559,sK185(U_7560))],[f_1752_2]) ).

cnf(f_1752_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK185(U_7560)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7560)) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_5,plain,
    ( U_7560 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK185(U_7560))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7560)) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

fof(f_1753_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).

fof(f_1753_2,plain,
    ! [U_7566,U_7565,U_7564,U_7563,U_7562] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7564) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7565)
      | ? [U_7561] :
          ( hAPP(U_7566,U_7561) != c_Groups_Ozero__class_Ozero(U_7562)
          & hBOOL(hAPP(hAPP(c_member(U_7563),U_7561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7563,tc_HOL_Obool)),U_7564),U_7565))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7563,tc_HOL_Obool)),U_7565),U_7564))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7563),U_7564))
      | ~ class_Groups_Ocomm__monoid__add(U_7562) ),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

fof(f_1753_3,plain,
    ! [U_7566,U_7565,U_7564,U_7563,U_7562] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7564) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7565)
      | ( hAPP(U_7566,sK186(U_7566,U_7565,U_7564,U_7563,U_7562)) != c_Groups_Ozero__class_Ozero(U_7562)
        & hBOOL(hAPP(hAPP(c_member(U_7563),sK186(U_7566,U_7565,U_7564,U_7563,U_7562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7563,tc_HOL_Obool)),U_7564),U_7565))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7563,tc_HOL_Obool)),U_7565),U_7564))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7563),U_7564))
      | ~ class_Groups_Ocomm__monoid__add(U_7562) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_7561,sK186(U_7566,U_7565,U_7564,U_7563,U_7562))],[f_1753_2]) ).

cnf(f_1753_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7563),sK186(U_7566,U_7565,U_7564,U_7563,U_7562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7563,tc_HOL_Obool)),U_7564),U_7565)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7564) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7565)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7563,tc_HOL_Obool)),U_7565),U_7564))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7563),U_7564))
    | ~ class_Groups_Ocomm__monoid__add(U_7562) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

cnf(f_1753_5,plain,
    ( hAPP(U_7566,sK186(U_7566,U_7565,U_7564,U_7563,U_7562)) != c_Groups_Ozero__class_Ozero(U_7562)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7564) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7563,U_7562),U_7566),U_7565)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7563,tc_HOL_Obool)),U_7565),U_7564))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7563),U_7564))
    | ~ class_Groups_Ocomm__monoid__add(U_7562) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

fof(f_1754_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).

fof(f_1754_2,plain,
    ! [U_7572,U_7571,U_7570,U_7569,U_7568] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7570)
      | ? [U_7567] :
          ( hAPP(U_7572,U_7567) != c_Groups_Ozero__class_Ozero(U_7568)
          & hBOOL(hAPP(hAPP(c_member(U_7569),U_7567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7569,tc_HOL_Obool)),U_7570),U_7571))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7569,tc_HOL_Obool)),U_7571),U_7570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7569),U_7570))
      | ~ class_Groups_Ocomm__monoid__add(U_7568) ),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ! [U_7572,U_7571,U_7570,U_7569,U_7568] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7570)
      | ( hAPP(U_7572,sK187(U_7572,U_7571,U_7570,U_7569,U_7568)) != c_Groups_Ozero__class_Ozero(U_7568)
        & hBOOL(hAPP(hAPP(c_member(U_7569),sK187(U_7572,U_7571,U_7570,U_7569,U_7568)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7569,tc_HOL_Obool)),U_7570),U_7571))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7569,tc_HOL_Obool)),U_7571),U_7570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7569),U_7570))
      | ~ class_Groups_Ocomm__monoid__add(U_7568) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_7567,sK187(U_7572,U_7571,U_7570,U_7569,U_7568))],[f_1754_2]) ).

cnf(f_1754_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7569),sK187(U_7572,U_7571,U_7570,U_7569,U_7568)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7569,tc_HOL_Obool)),U_7570),U_7571)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7570)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7569,tc_HOL_Obool)),U_7571),U_7570))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7569),U_7570))
    | ~ class_Groups_Ocomm__monoid__add(U_7568) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

cnf(f_1754_5,plain,
    ( hAPP(U_7572,sK187(U_7572,U_7571,U_7570,U_7569,U_7568)) != c_Groups_Ozero__class_Ozero(U_7568)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7569,U_7568),U_7572),U_7570)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7569,tc_HOL_Obool)),U_7571),U_7570))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7569),U_7570))
    | ~ class_Groups_Ocomm__monoid__add(U_7568) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

fof(f_1755_1,plain,
    ! [V_P_2,V_A_2,V_F_2,T_a] :
      ( hBOOL(hAPP(V_P_2,V_F_2))
      | ? [B_a,B_F] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F)))
          & hBOOL(hAPP(V_P_2,B_F))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) )
      | ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).

fof(f_1755_2,plain,
    ! [U_7578,U_7577,U_7576,U_7575] :
      ( hBOOL(hAPP(U_7578,U_7576))
      | ? [U_7574,U_7573] :
          ( ~ hBOOL(hAPP(U_7578,hAPP(hAPP(c_Set_Oinsert(U_7575),U_7574),U_7573)))
          & hBOOL(hAPP(U_7578,U_7573))
          & ~ hBOOL(hAPP(hAPP(c_member(U_7575),U_7574),U_7573))
          & hBOOL(hAPP(hAPP(c_member(U_7575),U_7574),U_7577))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7573)) )
      | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

fof(f_1755_3,plain,
    ! [U_7578,U_7577,U_7576,U_7575] :
      ( hBOOL(hAPP(U_7578,U_7576))
      | ? [U_7573] :
          ( ~ hBOOL(hAPP(U_7578,hAPP(hAPP(c_Set_Oinsert(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),U_7573)))
          & hBOOL(hAPP(U_7578,U_7573))
          & ~ hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),U_7573))
          & hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),U_7577))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7573)) )
      | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_7574,sK188(U_7578,U_7577,U_7576,U_7575))],[f_1755_2]) ).

fof(f_1755_4,plain,
    ! [U_7578,U_7577,U_7576,U_7575] :
      ( hBOOL(hAPP(U_7578,U_7576))
      | ( ~ hBOOL(hAPP(U_7578,hAPP(hAPP(c_Set_Oinsert(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),sK189(U_7578,U_7577,U_7576,U_7575))))
        & hBOOL(hAPP(U_7578,sK189(U_7578,U_7577,U_7576,U_7575)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),sK189(U_7578,U_7577,U_7576,U_7575)))
        & hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),U_7577))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),sK189(U_7578,U_7577,U_7576,U_7575))) )
      | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_7573,sK189(U_7578,U_7577,U_7576,U_7575))],[f_1755_3]) ).

cnf(f_1755_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),sK189(U_7578,U_7577,U_7576,U_7575)))
    | hBOOL(hAPP(U_7578,U_7576))
    | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(clausify,[status(thm)],[f_1755_4]) ).

cnf(f_1755_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),U_7577))
    | hBOOL(hAPP(U_7578,U_7576))
    | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(clausify,[status(thm)],[f_1755_4]) ).

cnf(f_1755_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),sK189(U_7578,U_7577,U_7576,U_7575)))
    | hBOOL(hAPP(U_7578,U_7576))
    | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(clausify,[status(thm)],[f_1755_4]) ).

cnf(f_1755_8,plain,
    ( hBOOL(hAPP(U_7578,sK189(U_7578,U_7577,U_7576,U_7575)))
    | hBOOL(hAPP(U_7578,U_7576))
    | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(clausify,[status(thm)],[f_1755_4]) ).

cnf(f_1755_9,plain,
    ( ~ hBOOL(hAPP(U_7578,hAPP(hAPP(c_Set_Oinsert(U_7575),sK188(U_7578,U_7577,U_7576,U_7575)),sK189(U_7578,U_7577,U_7576,U_7575))))
    | hBOOL(hAPP(U_7578,U_7576))
    | ~ hBOOL(hAPP(U_7578,c_Orderings_Obot__class_Obot(tc_fun(U_7575,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7575,tc_HOL_Obool)),U_7576),U_7577))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7575),U_7576)) ),
    inference(clausify,[status(thm)],[f_1755_4]) ).

fof(f_1756_1,plain,
    ! [V_a_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton]) ).

fof(f_1756_2,plain,
    ! [U_7582,U_7581,U_7580,U_7579] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7579,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_7579,U_7580,U_7581),hAPP(hAPP(c_Set_Oinsert(U_7580),U_7582),c_Orderings_Obot__class_Obot(tc_fun(U_7580,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_7579),c_HOL_OThe(U_7579,hAPP(hAPP(c_COMBC(U_7579,U_7580,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_7580,tc_fun(U_7580,tc_HOL_Obool),U_7579),c_fequal),U_7581)),U_7582))),c_Orderings_Obot__class_Obot(tc_fun(U_7579,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_7579,U_7580,U_7581,c_Orderings_Otop__class_Otop(tc_fun(U_7579,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

cnf(f_1756_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7579,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_7579,U_7580,U_7581),hAPP(hAPP(c_Set_Oinsert(U_7580),U_7582),c_Orderings_Obot__class_Obot(tc_fun(U_7580,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_7579),c_HOL_OThe(U_7579,hAPP(hAPP(c_COMBC(U_7579,U_7580,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_7580,tc_fun(U_7580,tc_HOL_Obool),U_7579),c_fequal),U_7581)),U_7582))),c_Orderings_Obot__class_Obot(tc_fun(U_7579,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_7579,U_7580,U_7581,c_Orderings_Otop__class_Otop(tc_fun(U_7579,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1756_2]) ).

fof(f_1757_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_1757_2,plain,
    ! [U_7585,U_7584,U_7583] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7584),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_7584),U_7585))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7583))),U_7585))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7583)) ),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

cnf(f_1757_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7584),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_7584),U_7585))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7583))),U_7585))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7583)) ),
    inference(clausify,[status(thm)],[f_1757_2]) ).

fof(f_1758_1,plain,
    ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__on__empty]) ).

fof(f_1758_2,plain,
    ! [U_7588,U_7587,U_7586] : c_Fun_Oinj__on(U_7586,U_7587,U_7588,c_Orderings_Obot__class_Obot(tc_fun(U_7586,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

cnf(f_1758_3,plain,
    c_Fun_Oinj__on(U_7586,U_7587,U_7588,c_Orderings_Obot__class_Obot(tc_fun(U_7586,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1758_2]) ).

fof(f_1759_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).

fof(f_1759_2,plain,
    ! [U_7592,U_7591,U_7590,U_7589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7589),hAPP(c_Groups_Oabs__class_Oabs(U_7589),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),U_7591),U_7592))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),hAPP(hAPP(c_COMBB(U_7589,U_7589,U_7590),c_Groups_Oabs__class_Oabs(U_7589)),U_7591)),U_7592)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7589) ),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

cnf(f_1759_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7589),hAPP(c_Groups_Oabs__class_Oabs(U_7589),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),U_7591),U_7592))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),hAPP(hAPP(c_COMBB(U_7589,U_7589,U_7590),c_Groups_Oabs__class_Oabs(U_7589)),U_7591)),U_7592)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7589) ),
    inference(clausify,[status(thm)],[f_1759_2]) ).

fof(f_1760_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).

fof(f_1760_2,plain,
    ! [U_7596,U_7595,U_7594,U_7593] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7593),c_Groups_Ozero__class_Ozero(U_7593)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),hAPP(hAPP(c_COMBB(U_7593,U_7593,U_7594),c_Groups_Oabs__class_Oabs(U_7593)),U_7595)),U_7596)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7593) ),
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

cnf(f_1760_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7593),c_Groups_Ozero__class_Ozero(U_7593)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),hAPP(hAPP(c_COMBB(U_7593,U_7593,U_7594),c_Groups_Oabs__class_Oabs(U_7593)),U_7595)),U_7596)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7593) ),
    inference(clausify,[status(thm)],[f_1760_2]) ).

fof(f_1761_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_1761_2,plain,
    ! [U_7598,U_7597] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7597),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)
      | ~ class_Rings_Olinordered__idom(U_7597) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

cnf(f_1761_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7597),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)
    | ~ class_Rings_Olinordered__idom(U_7597) ),
    inference(clausify,[status(thm)],[f_1761_2]) ).

fof(f_1762_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_1762_2,plain,
    ! [U_7601,U_7600,U_7599] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7599),U_7600),U_7601))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7599),hAPP(c_Groups_Oabs__class_Oabs(U_7599),U_7600)),U_7601))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7599) ),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

cnf(f_1762_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7599),U_7600),U_7601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7599),hAPP(c_Groups_Oabs__class_Oabs(U_7599),U_7600)),U_7601))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7599) ),
    inference(clausify,[status(thm)],[f_1762_2]) ).

fof(f_1763_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_1763_2,plain,
    ! [U_7603,U_7602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7602),U_7603),hAPP(c_Groups_Oabs__class_Oabs(U_7602),U_7603)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7602) ),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

cnf(f_1763_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7602),U_7603),hAPP(c_Groups_Oabs__class_Oabs(U_7602),U_7603)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7602) ),
    inference(clausify,[status(thm)],[f_1763_2]) ).

fof(f_1764_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).

fof(f_1764_2,plain,
    ! [U_7605,U_7604] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7604),U_7605) = c_Groups_Ozero__class_Ozero(U_7604)
          | U_7605 != c_Groups_Ozero__class_Ozero(U_7604) )
        & ( U_7605 = c_Groups_Ozero__class_Ozero(U_7604)
          | hAPP(c_Groups_Oabs__class_Oabs(U_7604),U_7605) != c_Groups_Ozero__class_Ozero(U_7604) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7604) ),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

cnf(f_1764_3,plain,
    ( U_7605 = c_Groups_Ozero__class_Ozero(U_7604)
    | hAPP(c_Groups_Oabs__class_Oabs(U_7604),U_7605) != c_Groups_Ozero__class_Ozero(U_7604)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7604) ),
    inference(clausify,[status(thm)],[f_1764_2]) ).

cnf(f_1764_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7604),U_7605) = c_Groups_Ozero__class_Ozero(U_7604)
    | U_7605 != c_Groups_Ozero__class_Ozero(U_7604)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7604) ),
    inference(clausify,[status(thm)],[f_1764_2]) ).

fof(f_1765_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_1765_2,plain,
    ! [U_7606] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7606),c_Groups_Ozero__class_Ozero(U_7606)) = c_Groups_Ozero__class_Ozero(U_7606)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7606) ),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

cnf(f_1765_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7606),c_Groups_Ozero__class_Ozero(U_7606)) = c_Groups_Ozero__class_Ozero(U_7606)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7606) ),
    inference(clausify,[status(thm)],[f_1765_2]) ).

fof(f_1766_1,plain,
    ! [T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__fun]) ).

fof(f_1766_2,plain,
    ! [U_7610,U_7609,U_7608,U_7607] :
      ( c_Fun_Oinj__on(U_7607,tc_fun(U_7610,U_7608),hAPP(hAPP(c_COMBB(U_7608,tc_fun(U_7610,U_7608),U_7607),c_COMBK(U_7608,U_7610)),U_7609),c_Orderings_Otop__class_Otop(tc_fun(U_7607,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_7607,U_7608,U_7609,c_Orderings_Otop__class_Otop(tc_fun(U_7607,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1766_1]) ).

cnf(f_1766_3,plain,
    ( c_Fun_Oinj__on(U_7607,tc_fun(U_7610,U_7608),hAPP(hAPP(c_COMBB(U_7608,tc_fun(U_7610,U_7608),U_7607),c_COMBK(U_7608,U_7610)),U_7609),c_Orderings_Otop__class_Otop(tc_fun(U_7607,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_7607,U_7608,U_7609,c_Orderings_Otop__class_Otop(tc_fun(U_7607,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1766_2]) ).

fof(f_1767_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | V_x_2 = V_y_2
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__contraD]) ).

fof(f_1767_2,plain,
    ! [U_7616,U_7615,U_7614,U_7613,U_7612,U_7611] :
      ( hAPP(U_7613,U_7615) != hAPP(U_7613,U_7616)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7611),U_7616),U_7614))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7611),U_7615),U_7614))
      | U_7615 = U_7616
      | ~ c_Fun_Oinj__on(U_7611,U_7612,U_7613,U_7614) ),
    inference(variable_rename,[status(thm)],[f_1767_1]) ).

cnf(f_1767_3,plain,
    ( hAPP(U_7613,U_7615) != hAPP(U_7613,U_7616)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7611),U_7616),U_7614))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7611),U_7615),U_7614))
    | U_7615 = U_7616
    | ~ c_Fun_Oinj__on(U_7611,U_7612,U_7613,U_7614) ),
    inference(clausify,[status(thm)],[f_1767_2]) ).

fof(f_1768_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( ( 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_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff]) ).

fof(f_1768_2,plain,
    ! [U_7622,U_7621,U_7620,U_7619,U_7618,U_7617] :
      ( ( ( hAPP(U_7619,U_7621) = hAPP(U_7619,U_7622)
          | U_7621 != U_7622 )
        & ( U_7621 = U_7622
          | hAPP(U_7619,U_7621) != hAPP(U_7619,U_7622) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7622),U_7620))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7621),U_7620))
      | ~ c_Fun_Oinj__on(U_7617,U_7618,U_7619,U_7620) ),
    inference(variable_rename,[status(thm)],[f_1768_1]) ).

cnf(f_1768_3,plain,
    ( U_7621 = U_7622
    | hAPP(U_7619,U_7621) != hAPP(U_7619,U_7622)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7622),U_7620))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7621),U_7620))
    | ~ c_Fun_Oinj__on(U_7617,U_7618,U_7619,U_7620) ),
    inference(clausify,[status(thm)],[f_1768_2]) ).

cnf(f_1768_4,plain,
    ( hAPP(U_7619,U_7621) = hAPP(U_7619,U_7622)
    | U_7621 != U_7622
    | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7622),U_7620))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7617),U_7621),U_7620))
    | ~ c_Fun_Oinj__on(U_7617,U_7618,U_7619,U_7620) ),
    inference(clausify,[status(thm)],[f_1768_2]) ).

fof(f_1769_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),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_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__onD]) ).

fof(f_1769_2,plain,
    ! [U_7628,U_7627,U_7626,U_7625,U_7624,U_7623] :
      ( U_7627 = U_7628
      | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7628),U_7626))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7627),U_7626))
      | hAPP(U_7625,U_7627) != hAPP(U_7625,U_7628)
      | ~ c_Fun_Oinj__on(U_7623,U_7624,U_7625,U_7626) ),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

cnf(f_1769_3,plain,
    ( U_7627 = U_7628
    | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7628),U_7626))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7623),U_7627),U_7626))
    | hAPP(U_7625,U_7627) != hAPP(U_7625,U_7628)
    | ~ c_Fun_Oinj__on(U_7623,U_7624,U_7625,U_7626) ),
    inference(clausify,[status(thm)],[f_1769_2]) ).

fof(f_1770_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_1770_2,plain,
    ! [U_7630,U_7629] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7629),hAPP(c_Groups_Oabs__class_Oabs(U_7629),U_7630)) = hAPP(c_Groups_Oabs__class_Oabs(U_7629),U_7630)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7629) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

cnf(f_1770_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7629),hAPP(c_Groups_Oabs__class_Oabs(U_7629),U_7630)) = hAPP(c_Groups_Oabs__class_Oabs(U_7629),U_7630)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7629) ),
    inference(clausify,[status(thm)],[f_1770_2]) ).

fof(f_1771_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( ( c_Fun_Oinj__on(T_a,T_b,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_a),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_a),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_a),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).

fof(f_1771_2,plain,
    ! [U_7638,U_7637,U_7636,U_7635] :
      ( ( c_Fun_Oinj__on(U_7635,U_7636,U_7637,U_7638)
        | ? [U_7634] :
            ( ? [U_7633] :
                ( U_7634 != U_7633
                & hAPP(U_7637,U_7634) = hAPP(U_7637,U_7633)
                & hBOOL(hAPP(hAPP(c_member(U_7635),U_7633),U_7638)) )
            & hBOOL(hAPP(hAPP(c_member(U_7635),U_7634),U_7638)) ) )
      & ( ! [U_7632] :
            ( ! [U_7631] :
                ( U_7632 = U_7631
                | hAPP(U_7637,U_7632) != hAPP(U_7637,U_7631)
                | ~ hBOOL(hAPP(hAPP(c_member(U_7635),U_7631),U_7638)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7635),U_7632),U_7638)) )
        | ~ c_Fun_Oinj__on(U_7635,U_7636,U_7637,U_7638) ) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

fof(f_1771_3,plain,
    ( ! [U_7646,U_7644,U_7642,U_7640] :
        ( c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646)
        | ? [U_7634] :
            ( ? [U_7633] :
                ( U_7634 != U_7633
                & hAPP(U_7644,U_7634) = hAPP(U_7644,U_7633)
                & hBOOL(hAPP(hAPP(c_member(U_7640),U_7633),U_7646)) )
            & hBOOL(hAPP(hAPP(c_member(U_7640),U_7634),U_7646)) ) )
    & ! [U_7645,U_7643,U_7641,U_7639] :
        ( ! [U_7632] :
            ( ! [U_7631] :
                ( U_7632 = U_7631
                | hAPP(U_7643,U_7632) != hAPP(U_7643,U_7631)
                | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7631),U_7645)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7632),U_7645)) )
        | ~ c_Fun_Oinj__on(U_7639,U_7641,U_7643,U_7645) ) ),
    inference(miniscope,[status(thm)],[f_1771_2]) ).

fof(f_1771_4,plain,
    ( ! [U_7646,U_7644,U_7642,U_7640] :
        ( c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646)
        | ( ? [U_7633] :
              ( sK190(U_7646,U_7644,U_7642,U_7640) != U_7633
              & hAPP(U_7644,sK190(U_7646,U_7644,U_7642,U_7640)) = hAPP(U_7644,U_7633)
              & hBOOL(hAPP(hAPP(c_member(U_7640),U_7633),U_7646)) )
          & hBOOL(hAPP(hAPP(c_member(U_7640),sK190(U_7646,U_7644,U_7642,U_7640)),U_7646)) ) )
    & ! [U_7645,U_7643,U_7641,U_7639] :
        ( ! [U_7632] :
            ( ! [U_7631] :
                ( U_7632 = U_7631
                | hAPP(U_7643,U_7632) != hAPP(U_7643,U_7631)
                | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7631),U_7645)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7632),U_7645)) )
        | ~ c_Fun_Oinj__on(U_7639,U_7641,U_7643,U_7645) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_7634,sK190(U_7646,U_7644,U_7642,U_7640))],[f_1771_3]) ).

fof(f_1771_5,plain,
    ( ! [U_7646,U_7644,U_7642,U_7640] :
        ( c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646)
        | ( sK190(U_7646,U_7644,U_7642,U_7640) != sK191(U_7646,U_7644,U_7642,U_7640)
          & hAPP(U_7644,sK190(U_7646,U_7644,U_7642,U_7640)) = hAPP(U_7644,sK191(U_7646,U_7644,U_7642,U_7640))
          & hBOOL(hAPP(hAPP(c_member(U_7640),sK191(U_7646,U_7644,U_7642,U_7640)),U_7646))
          & hBOOL(hAPP(hAPP(c_member(U_7640),sK190(U_7646,U_7644,U_7642,U_7640)),U_7646)) ) )
    & ! [U_7645,U_7643,U_7641,U_7639] :
        ( ! [U_7632] :
            ( ! [U_7631] :
                ( U_7632 = U_7631
                | hAPP(U_7643,U_7632) != hAPP(U_7643,U_7631)
                | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7631),U_7645)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7632),U_7645)) )
        | ~ c_Fun_Oinj__on(U_7639,U_7641,U_7643,U_7645) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_7633,sK191(U_7646,U_7644,U_7642,U_7640))],[f_1771_4]) ).

cnf(f_1771_6,plain,
    ( U_7632 = U_7631
    | hAPP(U_7643,U_7632) != hAPP(U_7643,U_7631)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7631),U_7645))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7639),U_7632),U_7645))
    | ~ c_Fun_Oinj__on(U_7639,U_7641,U_7643,U_7645) ),
    inference(clausify,[status(thm)],[f_1771_5]) ).

cnf(f_1771_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7640),sK190(U_7646,U_7644,U_7642,U_7640)),U_7646))
    | c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646) ),
    inference(clausify,[status(thm)],[f_1771_5]) ).

cnf(f_1771_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7640),sK191(U_7646,U_7644,U_7642,U_7640)),U_7646))
    | c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646) ),
    inference(clausify,[status(thm)],[f_1771_5]) ).

cnf(f_1771_9,plain,
    ( hAPP(U_7644,sK190(U_7646,U_7644,U_7642,U_7640)) = hAPP(U_7644,sK191(U_7646,U_7644,U_7642,U_7640))
    | c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646) ),
    inference(clausify,[status(thm)],[f_1771_5]) ).

cnf(f_1771_10,plain,
    ( sK190(U_7646,U_7644,U_7642,U_7640) != sK191(U_7646,U_7644,U_7642,U_7640)
    | c_Fun_Oinj__on(U_7640,U_7642,U_7644,U_7646) ),
    inference(clausify,[status(thm)],[f_1771_5]) ).

fof(f_1772_1,plain,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id2]) ).

fof(f_1772_2,plain,
    ! [U_7648,U_7647] : c_Fun_Oinj__on(U_7647,U_7647,c_COMBI(U_7647),U_7648),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

cnf(f_1772_3,plain,
    c_Fun_Oinj__on(U_7647,U_7647,c_COMBI(U_7647),U_7648),
    inference(clausify,[status(thm)],[f_1772_2]) ).

fof(f_1773_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__diff]) ).

fof(f_1773_2,plain,
    ! [U_7653,U_7652,U_7651,U_7650,U_7649] :
      ( c_Fun_Oinj__on(U_7649,U_7650,U_7651,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7649,tc_HOL_Obool)),U_7652),U_7653))
      | ~ c_Fun_Oinj__on(U_7649,U_7650,U_7651,U_7652) ),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

cnf(f_1773_3,plain,
    ( c_Fun_Oinj__on(U_7649,U_7650,U_7651,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7649,tc_HOL_Obool)),U_7652),U_7653))
    | ~ c_Fun_Oinj__on(U_7649,U_7650,U_7651,U_7652) ),
    inference(clausify,[status(thm)],[f_1773_2]) ).

fof(f_1774_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_1774_2,plain,
    ! [U_7654] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7654),c_Groups_Oone__class_Oone(U_7654)) = c_Groups_Oone__class_Oone(U_7654)
      | ~ class_Rings_Olinordered__idom(U_7654) ),
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

cnf(f_1774_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7654),c_Groups_Oone__class_Oone(U_7654)) = c_Groups_Oone__class_Oone(U_7654)
    | ~ class_Rings_Olinordered__idom(U_7654) ),
    inference(clausify,[status(thm)],[f_1774_2]) ).

fof(f_1775_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_1775_2,plain,
    ! [U_7657,U_7656,U_7655] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7655),U_7656),U_7657)) = hAPP(c_Groups_Oabs__class_Oabs(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7655),U_7657),U_7656))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7655) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

cnf(f_1775_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7655),U_7656),U_7657)) = hAPP(c_Groups_Oabs__class_Oabs(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7655),U_7657),U_7656))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7655) ),
    inference(clausify,[status(thm)],[f_1775_2]) ).

fof(f_1776_1,plain,
    ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2]) ).

fof(f_1776_2,plain,
    ! [U_7663,U_7662,U_7661,U_7660,U_7659,U_7658] :
      ( c_Fun_Oinj__on(U_7658,U_7660,U_7662,U_7663)
      | ~ c_Fun_Oinj__on(U_7658,U_7659,hAPP(c_Fun_Ocomp(U_7660,U_7659,U_7658,U_7661),U_7662),U_7663) ),
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

cnf(f_1776_3,plain,
    ( c_Fun_Oinj__on(U_7658,U_7660,U_7662,U_7663)
    | ~ c_Fun_Oinj__on(U_7658,U_7659,hAPP(c_Fun_Ocomp(U_7660,U_7659,U_7658,U_7661),U_7662),U_7663) ),
    inference(clausify,[status(thm)],[f_1776_2]) ).

fof(f_1777_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Int]) ).

fof(f_1777_2,plain,
    ! [U_7668,U_7667,U_7666,U_7665,U_7664] :
      ( c_Fun_Oinj__on(U_7664,U_7665,U_7666,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7664,tc_HOL_Obool)),U_7667),U_7668))
      | ~ c_Fun_Oinj__on(U_7664,U_7665,U_7666,U_7668)
      | ~ c_Fun_Oinj__on(U_7664,U_7665,U_7666,U_7667) ),
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

cnf(f_1777_3,plain,
    ( c_Fun_Oinj__on(U_7664,U_7665,U_7666,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7664,tc_HOL_Obool)),U_7667),U_7668))
    | ~ c_Fun_Oinj__on(U_7664,U_7665,U_7666,U_7668)
    | ~ c_Fun_Oinj__on(U_7664,U_7665,U_7666,U_7667) ),
    inference(clausify,[status(thm)],[f_1777_2]) ).

fof(f_1778_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_1778_2,plain,
    ! [U_7670,U_7669] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7669),hAPP(c_Groups_Oabs__class_Oabs(U_7669),U_7670)),hAPP(c_Groups_Oabs__class_Oabs(U_7669),U_7670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7669),U_7670),U_7670)
      | ~ class_Rings_Olinordered__idom(U_7669) ),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

cnf(f_1778_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7669),hAPP(c_Groups_Oabs__class_Oabs(U_7669),U_7670)),hAPP(c_Groups_Oabs__class_Oabs(U_7669),U_7670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7669),U_7670),U_7670)
    | ~ class_Rings_Olinordered__idom(U_7669) ),
    inference(clausify,[status(thm)],[f_1778_2]) ).

fof(f_1779_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_1779_2,plain,
    ! [U_7673,U_7672,U_7671] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7671),U_7672),U_7673)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7671),hAPP(c_Groups_Oabs__class_Oabs(U_7671),U_7672)),hAPP(c_Groups_Oabs__class_Oabs(U_7671),U_7673))
      | ~ class_Rings_Olinordered__idom(U_7671) ),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

cnf(f_1779_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7671),U_7672),U_7673)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7671),hAPP(c_Groups_Oabs__class_Oabs(U_7671),U_7672)),hAPP(c_Groups_Oabs__class_Oabs(U_7671),U_7673))
    | ~ class_Rings_Olinordered__idom(U_7671) ),
    inference(clausify,[status(thm)],[f_1779_2]) ).

fof(f_1780_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_1780_2,plain,
    ! [U_7676,U_7675,U_7674] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7675)),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7676))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7675)),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7676))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7674) ),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

cnf(f_1780_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7675)),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7676))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7675)),hAPP(c_Groups_Oabs__class_Oabs(U_7674),U_7676))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7674) ),
    inference(clausify,[status(thm)],[f_1780_2]) ).

fof(f_1781_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( ( ( 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_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__eq]) ).

fof(f_1781_2,plain,
    ! [U_7681,U_7680,U_7679,U_7678,U_7677] :
      ( ( ( hAPP(U_7679,U_7680) = hAPP(U_7679,U_7681)
          | U_7680 != U_7681 )
        & ( U_7680 = U_7681
          | hAPP(U_7679,U_7680) != hAPP(U_7679,U_7681) ) )
      | ~ c_Fun_Oinj__on(U_7677,U_7678,U_7679,c_Orderings_Otop__class_Otop(tc_fun(U_7677,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

fof(f_1781_3,plain,
    ! [U_7681,U_7680,U_7679] :
      ( ! [U_7678,U_7677] : ~ c_Fun_Oinj__on(U_7677,U_7678,U_7679,c_Orderings_Otop__class_Otop(tc_fun(U_7677,tc_HOL_Obool)))
      | ( ( hAPP(U_7679,U_7680) = hAPP(U_7679,U_7681)
          | U_7680 != U_7681 )
        & ( U_7680 = U_7681
          | hAPP(U_7679,U_7680) != hAPP(U_7679,U_7681) ) ) ),
    inference(miniscope,[status(thm)],[f_1781_2]) ).

cnf(f_1781_4,plain,
    ( U_7680 = U_7681
    | hAPP(U_7679,U_7680) != hAPP(U_7679,U_7681)
    | ~ c_Fun_Oinj__on(U_7677,U_7678,U_7679,c_Orderings_Otop__class_Otop(tc_fun(U_7677,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1781_3]) ).

cnf(f_1781_5,plain,
    ( hAPP(U_7679,U_7680) = hAPP(U_7679,U_7681)
    | U_7680 != U_7681
    | ~ c_Fun_Oinj__on(U_7677,U_7678,U_7679,c_Orderings_Otop__class_Otop(tc_fun(U_7677,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1781_3]) ).

fof(f_1782_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
      ( 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_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_injD]) ).

fof(f_1782_2,plain,
    ! [U_7686,U_7685,U_7684,U_7683,U_7682] :
      ( U_7685 = U_7686
      | hAPP(U_7684,U_7685) != hAPP(U_7684,U_7686)
      | ~ c_Fun_Oinj__on(U_7682,U_7683,U_7684,c_Orderings_Otop__class_Otop(tc_fun(U_7682,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

fof(f_1782_3,plain,
    ! [U_7686,U_7685,U_7684] :
      ( ! [U_7683,U_7682] : ~ c_Fun_Oinj__on(U_7682,U_7683,U_7684,c_Orderings_Otop__class_Otop(tc_fun(U_7682,tc_HOL_Obool)))
      | U_7685 = U_7686
      | hAPP(U_7684,U_7685) != hAPP(U_7684,U_7686) ),
    inference(miniscope,[status(thm)],[f_1782_2]) ).

cnf(f_1782_4,plain,
    ( ~ c_Fun_Oinj__on(U_7682,U_7683,U_7684,c_Orderings_Otop__class_Otop(tc_fun(U_7682,tc_HOL_Obool)))
    | U_7685 = U_7686
    | hAPP(U_7684,U_7685) != hAPP(U_7684,U_7686) ),
    inference(clausify,[status(thm)],[f_1782_3]) ).

fof(f_1783_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__inj__on]) ).

fof(f_1783_2,plain,
    ! [U_7691,U_7690,U_7689,U_7688,U_7687] :
      ( c_Fun_Oinj__on(U_7687,U_7688,U_7689,U_7691)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7687,tc_HOL_Obool)),U_7691),U_7690))
      | ~ c_Fun_Oinj__on(U_7687,U_7688,U_7689,U_7690) ),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

cnf(f_1783_3,plain,
    ( c_Fun_Oinj__on(U_7687,U_7688,U_7689,U_7691)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7687,tc_HOL_Obool)),U_7691),U_7690))
    | ~ c_Fun_Oinj__on(U_7687,U_7688,U_7689,U_7690) ),
    inference(clausify,[status(thm)],[f_1783_2]) ).

fof(f_1784_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_1784_2,plain,
    ! [U_7692] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_7692),
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

cnf(f_1784_3,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_7692),
    inference(clausify,[status(thm)],[f_1784_2]) ).

fof(f_1785_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_1785_2,plain,
    ! [U_7693] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7693)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7693),
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

cnf(f_1785_3,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7693)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7693),
    inference(clausify,[status(thm)],[f_1785_2]) ).

fof(f_1786_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_1786_2,plain,
    ! [U_7695,U_7694] : 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_7694),U_7695),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

cnf(f_1786_3,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_7694),U_7695),
    inference(clausify,[status(thm)],[f_1786_2]) ).

fof(f_1787_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).

fof(f_1787_2,plain,
    ! [U_7699,U_7698,U_7697,U_7696] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7696),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7697,U_7696),hAPP(hAPP(c_COMBB(U_7696,U_7696,U_7697),c_Groups_Oabs__class_Oabs(U_7696)),U_7698)),U_7699)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7697,U_7696),hAPP(hAPP(c_COMBB(U_7696,U_7696,U_7697),c_Groups_Oabs__class_Oabs(U_7696)),U_7698)),U_7699)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7696) ),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

cnf(f_1787_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7696),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7697,U_7696),hAPP(hAPP(c_COMBB(U_7696,U_7696,U_7697),c_Groups_Oabs__class_Oabs(U_7696)),U_7698)),U_7699)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7697,U_7696),hAPP(hAPP(c_COMBB(U_7696,U_7696,U_7697),c_Groups_Oabs__class_Oabs(U_7696)),U_7698)),U_7699)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7696) ),
    inference(clausify,[status(thm)],[f_1787_2]) ).

fof(f_1788_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_1788_2,plain,
    ! [U_7701,U_7700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7700),c_Groups_Ozero__class_Ozero(U_7700)),hAPP(c_Groups_Oabs__class_Oabs(U_7700),U_7701)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7700) ),
    inference(variable_rename,[status(thm)],[f_1788_1]) ).

cnf(f_1788_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7700),c_Groups_Ozero__class_Ozero(U_7700)),hAPP(c_Groups_Oabs__class_Oabs(U_7700),U_7701)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7700) ),
    inference(clausify,[status(thm)],[f_1788_2]) ).

fof(f_1789_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).

fof(f_1789_2,plain,
    ! [U_7703,U_7702] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7702),hAPP(c_Groups_Oabs__class_Oabs(U_7702),U_7703)),c_Groups_Ozero__class_Ozero(U_7702)))
          | U_7703 != c_Groups_Ozero__class_Ozero(U_7702) )
        & ( U_7703 = c_Groups_Ozero__class_Ozero(U_7702)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7702),hAPP(c_Groups_Oabs__class_Oabs(U_7702),U_7703)),c_Groups_Ozero__class_Ozero(U_7702))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7702) ),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

cnf(f_1789_3,plain,
    ( U_7703 = c_Groups_Ozero__class_Ozero(U_7702)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7702),hAPP(c_Groups_Oabs__class_Oabs(U_7702),U_7703)),c_Groups_Ozero__class_Ozero(U_7702)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7702) ),
    inference(clausify,[status(thm)],[f_1789_2]) ).

cnf(f_1789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7702),hAPP(c_Groups_Oabs__class_Oabs(U_7702),U_7703)),c_Groups_Ozero__class_Ozero(U_7702)))
    | U_7703 != c_Groups_Ozero__class_Ozero(U_7702)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7702) ),
    inference(clausify,[status(thm)],[f_1789_2]) ).

fof(f_1790_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_1790_2,plain,
    ! [U_7705,U_7704] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7704),U_7705) = U_7705
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7704),c_Groups_Ozero__class_Ozero(U_7704)),U_7705))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7704) ),
    inference(variable_rename,[status(thm)],[f_1790_1]) ).

cnf(f_1790_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7704),U_7705) = U_7705
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7704),c_Groups_Ozero__class_Ozero(U_7704)),U_7705))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7704) ),
    inference(clausify,[status(thm)],[f_1790_2]) ).

fof(f_1791_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_1791_2,plain,
    ! [U_7707,U_7706] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7706),hAPP(c_Groups_Oabs__class_Oabs(U_7706),U_7707)),c_Groups_Ozero__class_Ozero(U_7706)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7706) ),
    inference(variable_rename,[status(thm)],[f_1791_1]) ).

cnf(f_1791_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7706),hAPP(c_Groups_Oabs__class_Oabs(U_7706),U_7707)),c_Groups_Ozero__class_Ozero(U_7706)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7706) ),
    inference(clausify,[status(thm)],[f_1791_2]) ).

fof(f_1792_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 != 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(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).

fof(f_1792_2,plain,
    ! [U_7709,U_7708] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7708),c_Groups_Ozero__class_Ozero(U_7708)),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709)))
          | U_7709 = c_Groups_Ozero__class_Ozero(U_7708) )
        & ( U_7709 != c_Groups_Ozero__class_Ozero(U_7708)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7708),c_Groups_Ozero__class_Ozero(U_7708)),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7708) ),
    inference(variable_rename,[status(thm)],[f_1792_1]) ).

cnf(f_1792_3,plain,
    ( U_7709 != c_Groups_Ozero__class_Ozero(U_7708)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7708),c_Groups_Ozero__class_Ozero(U_7708)),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7708) ),
    inference(clausify,[status(thm)],[f_1792_2]) ).

cnf(f_1792_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7708),c_Groups_Ozero__class_Ozero(U_7708)),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709)))
    | U_7709 = c_Groups_Ozero__class_Ozero(U_7708)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7708) ),
    inference(clausify,[status(thm)],[f_1792_2]) ).

fof(f_1793_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_1793_2,plain,
    ! [U_7711,U_7710] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7710),U_7711) = U_7711
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7710),c_Groups_Ozero__class_Ozero(U_7710)),U_7711))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7710) ),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

cnf(f_1793_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7710),U_7711) = U_7711
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7710),c_Groups_Ozero__class_Ozero(U_7710)),U_7711))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7710) ),
    inference(clausify,[status(thm)],[f_1793_2]) ).

fof(f_1794_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_1794_2,plain,
    ! [U_7714,U_7713,U_7712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7712),hAPP(c_Groups_Oabs__class_Oabs(U_7712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7712),U_7713),U_7714))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7712),hAPP(c_Groups_Oabs__class_Oabs(U_7712),U_7713)),hAPP(c_Groups_Oabs__class_Oabs(U_7712),U_7714))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7712) ),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

cnf(f_1794_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7712),hAPP(c_Groups_Oabs__class_Oabs(U_7712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7712),U_7713),U_7714))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7712),hAPP(c_Groups_Oabs__class_Oabs(U_7712),U_7713)),hAPP(c_Groups_Oabs__class_Oabs(U_7712),U_7714))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7712) ),
    inference(clausify,[status(thm)],[f_1794_2]) ).

fof(f_1795_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageD]) ).

fof(f_1795_2,plain,
    ! [U_7718,U_7717,U_7716,U_7715] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7716),U_7718))
      | ~ c_Fun_Oinj__on(U_7716,U_7715,U_7717,U_7718)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7715),hAPP(c_Set_Oimage(U_7716,U_7715,U_7717),U_7718))) ),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

cnf(f_1795_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7716),U_7718))
    | ~ c_Fun_Oinj__on(U_7716,U_7715,U_7717,U_7718)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7715),hAPP(c_Set_Oimage(U_7716,U_7715,U_7717),U_7718))) ),
    inference(clausify,[status(thm)],[f_1795_2]) ).

fof(f_1796_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_1796_2,plain,
    ! [U_7723,U_7722,U_7721,U_7720,U_7719] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7720)),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7722))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7719),U_7721),U_7723)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7722)),U_7723))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7720)),U_7721))
      | ~ class_Rings_Olinordered__idom(U_7719) ),
    inference(variable_rename,[status(thm)],[f_1796_1]) ).

cnf(f_1796_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7720)),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7722))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7719),U_7721),U_7723)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7722)),U_7723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7719),hAPP(c_Groups_Oabs__class_Oabs(U_7719),U_7720)),U_7721))
    | ~ class_Rings_Olinordered__idom(U_7719) ),
    inference(clausify,[status(thm)],[f_1796_2]) ).

fof(f_1797_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_1797_2,plain,
    ! [U_7726,U_7725,U_7724] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7724),hAPP(c_Groups_Oabs__class_Oabs(U_7724),U_7725)),hAPP(c_Groups_Oabs__class_Oabs(U_7724),U_7726))),hAPP(c_Groups_Oabs__class_Oabs(U_7724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7724),U_7726),U_7725))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7724) ),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

cnf(f_1797_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7724),hAPP(c_Groups_Oabs__class_Oabs(U_7724),U_7725)),hAPP(c_Groups_Oabs__class_Oabs(U_7724),U_7726))),hAPP(c_Groups_Oabs__class_Oabs(U_7724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7724),U_7726),U_7725))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7724) ),
    inference(clausify,[status(thm)],[f_1797_2]) ).

fof(f_1798_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_1798_2,plain,
    ! [U_7729,U_7728,U_7727] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7727),hAPP(c_Groups_Oabs__class_Oabs(U_7727),U_7728)),hAPP(c_Groups_Oabs__class_Oabs(U_7727),U_7729))),hAPP(c_Groups_Oabs__class_Oabs(U_7727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7727),U_7728),U_7729))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7727) ),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

cnf(f_1798_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7727),hAPP(c_Groups_Oabs__class_Oabs(U_7727),U_7728)),hAPP(c_Groups_Oabs__class_Oabs(U_7727),U_7729))),hAPP(c_Groups_Oabs__class_Oabs(U_7727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7727),U_7728),U_7729))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7727) ),
    inference(clausify,[status(thm)],[f_1798_2]) ).

fof(f_1799_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_1799_2,plain,
    ! [U_7732,U_7731,U_7730] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),hAPP(c_Groups_Oabs__class_Oabs(U_7730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7730),hAPP(c_Groups_Oabs__class_Oabs(U_7730),U_7731)),hAPP(c_Groups_Oabs__class_Oabs(U_7730),U_7732)))),hAPP(c_Groups_Oabs__class_Oabs(U_7730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7730),U_7731),U_7732))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7730) ),
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

cnf(f_1799_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),hAPP(c_Groups_Oabs__class_Oabs(U_7730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7730),hAPP(c_Groups_Oabs__class_Oabs(U_7730),U_7731)),hAPP(c_Groups_Oabs__class_Oabs(U_7730),U_7732)))),hAPP(c_Groups_Oabs__class_Oabs(U_7730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7730),U_7731),U_7732))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7730) ),
    inference(clausify,[status(thm)],[f_1799_2]) ).

fof(f_1800_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff]) ).

fof(f_1800_2,plain,
    ! [U_7737,U_7736,U_7735,U_7734,U_7733] :
      ( ( ( hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7736) = hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7737)
          | U_7736 != U_7737 )
        & ( U_7736 = U_7737
          | hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7736) != hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7737) ) )
      | ~ c_Fun_Oinj__on(U_7733,U_7734,U_7735,c_Orderings_Otop__class_Otop(tc_fun(U_7733,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1800_1]) ).

cnf(f_1800_3,plain,
    ( U_7736 = U_7737
    | hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7736) != hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7737)
    | ~ c_Fun_Oinj__on(U_7733,U_7734,U_7735,c_Orderings_Otop__class_Otop(tc_fun(U_7733,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1800_2]) ).

cnf(f_1800_4,plain,
    ( hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7736) = hAPP(c_Set_Oimage(U_7733,U_7734,U_7735),U_7737)
    | U_7736 != U_7737
    | ~ c_Fun_Oinj__on(U_7733,U_7734,U_7735,c_Orderings_Otop__class_Otop(tc_fun(U_7733,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1800_2]) ).

fof(f_1801_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff]) ).

fof(f_1801_2,plain,
    ! [U_7742,U_7741,U_7740,U_7739,U_7738] :
      ( ( ( hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7741) = hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7742)
          | U_7741 != U_7742 )
        & ( U_7741 = U_7742
          | hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7741) != hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7742) ) )
      | ~ c_Fun_Oinj__on(U_7738,U_7739,U_7740,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7738,tc_HOL_Obool)),U_7741),U_7742)) ),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

cnf(f_1801_3,plain,
    ( U_7741 = U_7742
    | hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7741) != hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7742)
    | ~ c_Fun_Oinj__on(U_7738,U_7739,U_7740,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7738,tc_HOL_Obool)),U_7741),U_7742)) ),
    inference(clausify,[status(thm)],[f_1801_2]) ).

cnf(f_1801_4,plain,
    ( hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7741) = hAPP(c_Set_Oimage(U_7738,U_7739,U_7740),U_7742)
    | U_7741 != U_7742
    | ~ c_Fun_Oinj__on(U_7738,U_7739,U_7740,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7738,tc_HOL_Obool)),U_7741),U_7742)) ),
    inference(clausify,[status(thm)],[f_1801_2]) ).

fof(f_1802_1,plain,
    ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( ( ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
          | ~ c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) )
        & ( c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2)
          | ~ c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff]) ).

fof(f_1802_2,plain,
    ! [U_7748,U_7747,U_7746,U_7745,U_7744,U_7743] :
      ( ( ( c_Fun_Oinj__on(U_7744,U_7747,U_7748,hAPP(c_Set_Oimage(U_7743,U_7744,U_7745),U_7746))
          | ~ c_Fun_Oinj__on(U_7743,U_7747,hAPP(c_Fun_Ocomp(U_7744,U_7747,U_7743,U_7748),U_7745),U_7746) )
        & ( c_Fun_Oinj__on(U_7743,U_7747,hAPP(c_Fun_Ocomp(U_7744,U_7747,U_7743,U_7748),U_7745),U_7746)
          | ~ c_Fun_Oinj__on(U_7744,U_7747,U_7748,hAPP(c_Set_Oimage(U_7743,U_7744,U_7745),U_7746)) ) )
      | ~ c_Fun_Oinj__on(U_7743,U_7744,U_7745,U_7746) ),
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

cnf(f_1802_3,plain,
    ( c_Fun_Oinj__on(U_7743,U_7747,hAPP(c_Fun_Ocomp(U_7744,U_7747,U_7743,U_7748),U_7745),U_7746)
    | ~ c_Fun_Oinj__on(U_7744,U_7747,U_7748,hAPP(c_Set_Oimage(U_7743,U_7744,U_7745),U_7746))
    | ~ c_Fun_Oinj__on(U_7743,U_7744,U_7745,U_7746) ),
    inference(clausify,[status(thm)],[f_1802_2]) ).

cnf(f_1802_4,plain,
    ( c_Fun_Oinj__on(U_7744,U_7747,U_7748,hAPP(c_Set_Oimage(U_7743,U_7744,U_7745),U_7746))
    | ~ c_Fun_Oinj__on(U_7743,U_7747,hAPP(c_Fun_Ocomp(U_7744,U_7747,U_7743,U_7748),U_7745),U_7746)
    | ~ c_Fun_Oinj__on(U_7743,U_7744,U_7745,U_7746) ),
    inference(clausify,[status(thm)],[f_1802_2]) ).

fof(f_1803_1,plain,
    ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on]) ).

fof(f_1803_2,plain,
    ! [U_7754,U_7753,U_7752,U_7751,U_7750,U_7749] :
      ( c_Fun_Oinj__on(U_7749,U_7753,hAPP(c_Fun_Ocomp(U_7750,U_7753,U_7749,U_7754),U_7751),U_7752)
      | ~ c_Fun_Oinj__on(U_7750,U_7753,U_7754,hAPP(c_Set_Oimage(U_7749,U_7750,U_7751),U_7752))
      | ~ c_Fun_Oinj__on(U_7749,U_7750,U_7751,U_7752) ),
    inference(variable_rename,[status(thm)],[f_1803_1]) ).

cnf(f_1803_3,plain,
    ( c_Fun_Oinj__on(U_7749,U_7753,hAPP(c_Fun_Ocomp(U_7750,U_7753,U_7749,U_7754),U_7751),U_7752)
    | ~ c_Fun_Oinj__on(U_7750,U_7753,U_7754,hAPP(c_Set_Oimage(U_7749,U_7750,U_7751),U_7752))
    | ~ c_Fun_Oinj__on(U_7749,U_7750,U_7751,U_7752) ),
    inference(clausify,[status(thm)],[f_1803_2]) ).

fof(f_1804_1,plain,
    ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
      ( c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI]) ).

fof(f_1804_2,plain,
    ! [U_7760,U_7759,U_7758,U_7757,U_7756,U_7755] :
      ( c_Fun_Oinj__on(U_7757,U_7756,U_7758,hAPP(c_Set_Oimage(U_7755,U_7757,U_7759),U_7760))
      | ~ c_Fun_Oinj__on(U_7755,U_7756,hAPP(c_Fun_Ocomp(U_7757,U_7756,U_7755,U_7758),U_7759),U_7760) ),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

cnf(f_1804_3,plain,
    ( c_Fun_Oinj__on(U_7757,U_7756,U_7758,hAPP(c_Set_Oimage(U_7755,U_7757,U_7759),U_7760))
    | ~ c_Fun_Oinj__on(U_7755,U_7756,hAPP(c_Fun_Ocomp(U_7757,U_7756,U_7755,U_7758),U_7759),U_7760) ),
    inference(clausify,[status(thm)],[f_1804_2]) ).

fof(f_1805_1,plain,
    ! [V_g_2,T_c,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__comp]) ).

fof(f_1805_2,plain,
    ! [U_7765,U_7764,U_7763,U_7762,U_7761] :
      ( c_Fun_Oinj__on(U_7764,U_7762,hAPP(c_Fun_Ocomp(U_7761,U_7762,U_7764,U_7763),U_7765),c_Orderings_Otop__class_Otop(tc_fun(U_7764,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_7764,U_7761,U_7765,c_Orderings_Otop__class_Otop(tc_fun(U_7764,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_7761,U_7762,U_7763,c_Orderings_Otop__class_Otop(tc_fun(U_7761,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

cnf(f_1805_3,plain,
    ( c_Fun_Oinj__on(U_7764,U_7762,hAPP(c_Fun_Ocomp(U_7761,U_7762,U_7764,U_7763),U_7765),c_Orderings_Otop__class_Otop(tc_fun(U_7764,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_7764,U_7761,U_7765,c_Orderings_Otop__class_Otop(tc_fun(U_7764,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_7761,U_7762,U_7763,c_Orderings_Otop__class_Otop(tc_fun(U_7761,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1805_2]) ).

fof(f_1806_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__image]) ).

fof(f_1806_2,plain,
    ! [U_7769,U_7768,U_7767,U_7766] :
      ( hAPP(c_Finite__Set_Ocard(U_7767),hAPP(c_Set_Oimage(U_7766,U_7767,U_7768),U_7769)) = hAPP(c_Finite__Set_Ocard(U_7766),U_7769)
      | ~ c_Fun_Oinj__on(U_7766,U_7767,U_7768,U_7769) ),
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

cnf(f_1806_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7767),hAPP(c_Set_Oimage(U_7766,U_7767,U_7768),U_7769)) = hAPP(c_Finite__Set_Ocard(U_7766),U_7769)
    | ~ c_Fun_Oinj__on(U_7766,U_7767,U_7768,U_7769) ),
    inference(clausify,[status(thm)],[f_1806_2]) ).

fof(f_1807_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset]) ).

fof(f_1807_2,plain,
    ! [U_7774,U_7773,U_7772,U_7771,U_7770] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7771,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7770,U_7771,U_7772),U_7774)),hAPP(c_Set_Oimage(U_7770,U_7771,U_7772),U_7773)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7770,tc_HOL_Obool)),U_7774),U_7773))
      | ~ c_Fun_Oinj__on(U_7770,U_7771,U_7772,U_7773) ),
    inference(variable_rename,[status(thm)],[f_1807_1]) ).

cnf(f_1807_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7771,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7770,U_7771,U_7772),U_7774)),hAPP(c_Set_Oimage(U_7770,U_7771,U_7772),U_7773)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7770,tc_HOL_Obool)),U_7774),U_7773))
    | ~ c_Fun_Oinj__on(U_7770,U_7771,U_7772,U_7773) ),
    inference(clausify,[status(thm)],[f_1807_2]) ).

fof(f_1808_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_1808_2,plain,
    ! [U_7776,U_7775] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7775) = 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_7775),U_7776)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1808_1]) ).

cnf(f_1808_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7775) = 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_7775),U_7776)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1808_2]) ).

fof(f_1809_1,plain,
    ! [T_a] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inj__of__nat]) ).

fof(f_1809_2,plain,
    ! [U_7777] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_7777,c_Nat_Osemiring__1__class_Oof__nat(U_7777),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_7777) ),
    inference(variable_rename,[status(thm)],[f_1809_1]) ).

cnf(f_1809_3,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_7777,c_Nat_Osemiring__1__class_Oof__nat(U_7777),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_7777) ),
    inference(clausify,[status(thm)],[f_1809_2]) ).

fof(f_1810_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]) ).

cnf(f_1810_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(clausify,[status(thm)],[f_1810_1]) ).

fof(f_1811_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff]) ).

fof(f_1811_2,plain,
    ! [U_7782,U_7781,U_7780,U_7779,U_7778] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7779),hAPP(U_7780,U_7781)),hAPP(c_Set_Oimage(U_7778,U_7779,U_7780),U_7782)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7778),U_7781),U_7782)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_7778),U_7781),U_7782))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7779),hAPP(U_7780,U_7781)),hAPP(c_Set_Oimage(U_7778,U_7779,U_7780),U_7782))) ) )
      | ~ c_Fun_Oinj__on(U_7778,U_7779,U_7780,c_Orderings_Otop__class_Otop(tc_fun(U_7778,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

cnf(f_1811_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7778),U_7781),U_7782))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7779),hAPP(U_7780,U_7781)),hAPP(c_Set_Oimage(U_7778,U_7779,U_7780),U_7782)))
    | ~ c_Fun_Oinj__on(U_7778,U_7779,U_7780,c_Orderings_Otop__class_Otop(tc_fun(U_7778,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1811_2]) ).

cnf(f_1811_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7779),hAPP(U_7780,U_7781)),hAPP(c_Set_Oimage(U_7778,U_7779,U_7780),U_7782)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7778),U_7781),U_7782))
    | ~ c_Fun_Oinj__on(U_7778,U_7779,U_7780,c_Orderings_Otop__class_Otop(tc_fun(U_7778,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1811_2]) ).

fof(f_1812_1,plain,
    ! [V_b_2,V_f_2,T_b,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,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_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_range__ex1__eq]) ).

fof(f_1812_2,plain,
    ! [U_7790,U_7789,U_7788,U_7787] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
          | ! [U_7786] :
              ( ? [U_7785] :
                  ( U_7785 != U_7786
                  & U_7790 = hAPP(U_7789,U_7785) )
              | U_7790 != hAPP(U_7789,U_7786) ) )
        & ( ? [U_7784] :
              ( ! [U_7783] :
                  ( U_7783 = U_7784
                  | U_7790 != hAPP(U_7789,U_7783) )
              & U_7790 = hAPP(U_7789,U_7784) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

fof(f_1812_3,plain,
    ! [U_7790,U_7789,U_7788,U_7787] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
          | ! [U_7786] :
              ( ? [U_7785] :
                  ( U_7785 != U_7786
                  & U_7790 = hAPP(U_7789,U_7785) )
              | U_7790 != hAPP(U_7789,U_7786) ) )
        & ( ( ! [U_7783] :
                ( U_7783 = sK192(U_7790,U_7789,U_7788,U_7787)
                | U_7790 != hAPP(U_7789,U_7783) )
            & U_7790 = hAPP(U_7789,sK192(U_7790,U_7789,U_7788,U_7787)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_7784,sK192(U_7790,U_7789,U_7788,U_7787))],[f_1812_2]) ).

fof(f_1812_4,plain,
    ! [U_7790,U_7789,U_7788,U_7787] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
          | ! [U_7786] :
              ( ( sK193(U_7790,U_7789,U_7788,U_7787,U_7786) != U_7786
                & U_7790 = hAPP(U_7789,sK193(U_7790,U_7789,U_7788,U_7787,U_7786)) )
              | U_7790 != hAPP(U_7789,U_7786) ) )
        & ( ( ! [U_7783] :
                ( U_7783 = sK192(U_7790,U_7789,U_7788,U_7787)
                | U_7790 != hAPP(U_7789,U_7783) )
            & U_7790 = hAPP(U_7789,sK192(U_7790,U_7789,U_7788,U_7787)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_7785,sK193(U_7790,U_7789,U_7788,U_7787,U_7786))],[f_1812_3]) ).

cnf(f_1812_5,plain,
    ( U_7790 = hAPP(U_7789,sK192(U_7790,U_7789,U_7788,U_7787))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_6,plain,
    ( U_7783 = sK192(U_7790,U_7789,U_7788,U_7787)
    | U_7790 != hAPP(U_7789,U_7783)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_7,plain,
    ( U_7790 = hAPP(U_7789,sK193(U_7790,U_7789,U_7788,U_7787,U_7786))
    | U_7790 != hAPP(U_7789,U_7786)
    | hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_8,plain,
    ( sK193(U_7790,U_7789,U_7788,U_7787,U_7786) != U_7786
    | U_7790 != hAPP(U_7789,U_7786)
    | hBOOL(hAPP(hAPP(c_member(U_7788),U_7790),hAPP(c_Set_Oimage(U_7787,U_7788,U_7789),c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_7787,U_7788,U_7789,c_Orderings_Otop__class_Otop(tc_fun(U_7787,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

fof(f_1813_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_1813_2,plain,
    ! [U_7793,U_7792,U_7791] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7791),hAPP(c_Groups_Oabs__class_Oabs(U_7791),U_7793)),U_7792) = hAPP(c_Groups_Oabs__class_Oabs(U_7791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7791),U_7793),U_7792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7791),c_Groups_Ozero__class_Ozero(U_7791)),U_7792))
      | ~ class_Rings_Olinordered__idom(U_7791) ),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

cnf(f_1813_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7791),hAPP(c_Groups_Oabs__class_Oabs(U_7791),U_7793)),U_7792) = hAPP(c_Groups_Oabs__class_Oabs(U_7791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7791),U_7793),U_7792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7791),c_Groups_Ozero__class_Ozero(U_7791)),U_7792))
    | ~ class_Rings_Olinordered__idom(U_7791) ),
    inference(clausify,[status(thm)],[f_1813_2]) ).

fof(f_1814_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_1814_2,plain,
    ! [U_7796,U_7795,U_7794] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),U_7795),U_7796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7795)),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7796))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7796),c_Groups_Ozero__class_Ozero(U_7794)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7796)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7795),c_Groups_Ozero__class_Ozero(U_7794)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795)) )
      | ~ class_Rings_Oordered__ring__abs(U_7794) ),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

cnf(f_1814_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),U_7795),U_7796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7795)),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7796))
    | ~ class_Rings_Oordered__ring__abs(U_7794) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

cnf(f_1814_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7796),c_Groups_Ozero__class_Ozero(U_7794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),U_7795),U_7796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7795)),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7796))
    | ~ class_Rings_Oordered__ring__abs(U_7794) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

cnf(f_1814_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7795),c_Groups_Ozero__class_Ozero(U_7794)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),U_7795),U_7796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7795)),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7796))
    | ~ class_Rings_Oordered__ring__abs(U_7794) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

cnf(f_1814_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7796),c_Groups_Ozero__class_Ozero(U_7794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7794),U_7795),c_Groups_Ozero__class_Ozero(U_7794)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),U_7795),U_7796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7794),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7795)),hAPP(c_Groups_Oabs__class_Oabs(U_7794),U_7796))
    | ~ class_Rings_Oordered__ring__abs(U_7794) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

fof(f_1815_1,plain,
    ! [V_A_H_2,T_b,T_a,V_A_2] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2))
              & c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) )
          | ! [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) != V_A_2 )
        & ( ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2))
              | ~ c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) ) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj]) ).

fof(f_1815_2,plain,
    ! [U_7804,U_7803,U_7802,U_7801] :
      ( ( ( ? [U_7800] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7800),U_7801)),U_7804))
              & c_Fun_Oinj__on(U_7802,U_7803,U_7800,U_7801) )
          | ! [U_7799] : hAPP(c_Set_Oimage(U_7803,U_7802,U_7799),U_7804) != U_7801 )
        & ( ? [U_7798] : hAPP(c_Set_Oimage(U_7803,U_7802,U_7798),U_7804) = U_7801
          | ! [U_7797] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7797),U_7801)),U_7804))
              | ~ c_Fun_Oinj__on(U_7802,U_7803,U_7797,U_7801) ) ) )
      | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

fof(f_1815_3,plain,
    ! [U_7804,U_7803,U_7802,U_7801] :
      ( ( ( ? [U_7800] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7800),U_7801)),U_7804))
              & c_Fun_Oinj__on(U_7802,U_7803,U_7800,U_7801) )
          | ! [U_7799] : hAPP(c_Set_Oimage(U_7803,U_7802,U_7799),U_7804) != U_7801 )
        & ( hAPP(c_Set_Oimage(U_7803,U_7802,sK194(U_7804,U_7803,U_7802,U_7801)),U_7804) = U_7801
          | ! [U_7797] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7797),U_7801)),U_7804))
              | ~ c_Fun_Oinj__on(U_7802,U_7803,U_7797,U_7801) ) ) )
      | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_7798,sK194(U_7804,U_7803,U_7802,U_7801))],[f_1815_2]) ).

fof(f_1815_4,plain,
    ! [U_7804,U_7803,U_7802,U_7801] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,sK195(U_7804,U_7803,U_7802,U_7801)),U_7801)),U_7804))
            & c_Fun_Oinj__on(U_7802,U_7803,sK195(U_7804,U_7803,U_7802,U_7801),U_7801) )
          | ! [U_7799] : hAPP(c_Set_Oimage(U_7803,U_7802,U_7799),U_7804) != U_7801 )
        & ( hAPP(c_Set_Oimage(U_7803,U_7802,sK194(U_7804,U_7803,U_7802,U_7801)),U_7804) = U_7801
          | ! [U_7797] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7797),U_7801)),U_7804))
              | ~ c_Fun_Oinj__on(U_7802,U_7803,U_7797,U_7801) ) ) )
      | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_7800,sK195(U_7804,U_7803,U_7802,U_7801))],[f_1815_3]) ).

cnf(f_1815_5,plain,
    ( hAPP(c_Set_Oimage(U_7803,U_7802,sK194(U_7804,U_7803,U_7802,U_7801)),U_7804) = U_7801
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,U_7797),U_7801)),U_7804))
    | ~ c_Fun_Oinj__on(U_7802,U_7803,U_7797,U_7801)
    | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1815_4]) ).

cnf(f_1815_6,plain,
    ( c_Fun_Oinj__on(U_7802,U_7803,sK195(U_7804,U_7803,U_7802,U_7801),U_7801)
    | hAPP(c_Set_Oimage(U_7803,U_7802,U_7799),U_7804) != U_7801
    | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1815_4]) ).

cnf(f_1815_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7803,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7802,U_7803,sK195(U_7804,U_7803,U_7802,U_7801)),U_7801)),U_7804))
    | hAPP(c_Set_Oimage(U_7803,U_7802,U_7799),U_7804) != U_7801
    | U_7801 = c_Orderings_Obot__class_Obot(tc_fun(U_7802,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1815_4]) ).

fof(f_1816_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj__inj]) ).

fof(f_1816_2,plain,
    ! [U_7807,U_7806,U_7805] :
      ( c_Fun_Oinj__on(U_7805,U_7805,U_7807,U_7806)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7805,tc_HOL_Obool)),U_7806),hAPP(c_Set_Oimage(U_7805,U_7805,U_7807),U_7806)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7806)) ),
    inference(variable_rename,[status(thm)],[f_1816_1]) ).

cnf(f_1816_3,plain,
    ( c_Fun_Oinj__on(U_7805,U_7805,U_7807,U_7806)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7805,tc_HOL_Obool)),U_7806),hAPP(c_Set_Oimage(U_7805,U_7805,U_7807),U_7806)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7806)) ),
    inference(clausify,[status(thm)],[f_1816_2]) ).

fof(f_1817_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2
      | ~ c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_endo__inj__surj]) ).

fof(f_1817_2,plain,
    ! [U_7810,U_7809,U_7808] :
      ( hAPP(c_Set_Oimage(U_7808,U_7808,U_7810),U_7809) = U_7809
      | ~ c_Fun_Oinj__on(U_7808,U_7808,U_7810,U_7809)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7808,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7808,U_7808,U_7810),U_7809)),U_7809))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7808),U_7809)) ),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

cnf(f_1817_3,plain,
    ( hAPP(c_Set_Oimage(U_7808,U_7808,U_7810),U_7809) = U_7809
    | ~ c_Fun_Oinj__on(U_7808,U_7808,U_7810,U_7809)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7808,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7808,U_7808,U_7810),U_7809)),U_7809))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7808),U_7809)) ),
    inference(clausify,[status(thm)],[f_1817_2]) ).

fof(f_1818_1,plain,
    ! [V_f_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj]) ).

fof(f_1818_2,plain,
    ! [U_7812,U_7811] :
      ( hAPP(c_Set_Oimage(U_7811,U_7811,U_7812),c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_7811,U_7811,U_7812,c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7811),c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

cnf(f_1818_3,plain,
    ( hAPP(c_Set_Oimage(U_7811,U_7811,U_7812),c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_7811,U_7811,U_7812,c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7811),c_Orderings_Otop__class_Otop(tc_fun(U_7811,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1818_2]) ).

fof(f_1819_1,plain,
    ! [V_f_2,T_a] :
      ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj]) ).

fof(f_1819_2,plain,
    ! [U_7814,U_7813] :
      ( c_Fun_Oinj__on(U_7813,U_7813,U_7814,c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_7813,U_7813,U_7814),c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7813),c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_1819_1]) ).

cnf(f_1819_3,plain,
    ( c_Fun_Oinj__on(U_7813,U_7813,U_7814,c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_7813,U_7813,U_7814),c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7813),c_Orderings_Otop__class_Otop(tc_fun(U_7813,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1819_2]) ).

fof(f_1820_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_1820_2,plain,
    ! [U_7819,U_7818,U_7817,U_7816,U_7815] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7815),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),U_7816),U_7817)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),U_7818),U_7819)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),U_7816),U_7818))),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),U_7817),U_7819)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7815) ),
    inference(variable_rename,[status(thm)],[f_1820_1]) ).

cnf(f_1820_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7815),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),U_7816),U_7817)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),U_7818),U_7819)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7815),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),U_7816),U_7818))),hAPP(c_Groups_Oabs__class_Oabs(U_7815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7815),U_7817),U_7819)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7815) ),
    inference(clausify,[status(thm)],[f_1820_2]) ).

fof(f_1821_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_1821_2,plain,
    ! [U_7822,U_7821,U_7820] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7820),hAPP(c_Groups_Oabs__class_Oabs(U_7820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7820),U_7821),U_7822))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7820),hAPP(c_Groups_Oabs__class_Oabs(U_7820),U_7821)),hAPP(c_Groups_Oabs__class_Oabs(U_7820),U_7822))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7820) ),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

cnf(f_1821_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7820),hAPP(c_Groups_Oabs__class_Oabs(U_7820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7820),U_7821),U_7822))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7820),hAPP(c_Groups_Oabs__class_Oabs(U_7820),U_7821)),hAPP(c_Groups_Oabs__class_Oabs(U_7820),U_7822))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7820) ),
    inference(clausify,[status(thm)],[f_1821_2]) ).

fof(f_1822_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,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_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff]) ).

fof(f_1822_2,plain,
    ! [U_7827,U_7826,U_7825,U_7824,U_7823] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7826)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7827)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7823,tc_HOL_Obool)),U_7826),U_7827)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7823,tc_HOL_Obool)),U_7826),U_7827))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7826)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7827))) ) )
      | ~ c_Fun_Oinj__on(U_7823,U_7824,U_7825,c_Orderings_Otop__class_Otop(tc_fun(U_7823,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

cnf(f_1822_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7823,tc_HOL_Obool)),U_7826),U_7827))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7826)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7827)))
    | ~ c_Fun_Oinj__on(U_7823,U_7824,U_7825,c_Orderings_Otop__class_Otop(tc_fun(U_7823,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1822_2]) ).

cnf(f_1822_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7826)),hAPP(c_Set_Oimage(U_7823,U_7824,U_7825),U_7827)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7823,tc_HOL_Obool)),U_7826),U_7827))
    | ~ c_Fun_Oinj__on(U_7823,U_7824,U_7825,c_Orderings_Otop__class_Otop(tc_fun(U_7823,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1822_2]) ).

fof(f_1823_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int]) ).

fof(f_1823_2,plain,
    ! [U_7833,U_7832,U_7831,U_7830,U_7829,U_7828] :
      ( hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7828,tc_HOL_Obool)),U_7832),U_7833)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7829,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),U_7832)),hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),U_7833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7828,tc_HOL_Obool)),U_7833),U_7831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7828,tc_HOL_Obool)),U_7832),U_7831))
      | ~ c_Fun_Oinj__on(U_7828,U_7829,U_7830,U_7831) ),
    inference(variable_rename,[status(thm)],[f_1823_1]) ).

cnf(f_1823_3,plain,
    ( hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7828,tc_HOL_Obool)),U_7832),U_7833)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7829,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),U_7832)),hAPP(c_Set_Oimage(U_7828,U_7829,U_7830),U_7833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7828,tc_HOL_Obool)),U_7833),U_7831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7828,tc_HOL_Obool)),U_7832),U_7831))
    | ~ c_Fun_Oinj__on(U_7828,U_7829,U_7830,U_7831) ),
    inference(clausify,[status(thm)],[f_1823_2]) ).

fof(f_1824_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__Int]) ).

fof(f_1824_2,plain,
    ! [U_7838,U_7837,U_7836,U_7835,U_7834] :
      ( hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7834,tc_HOL_Obool)),U_7837),U_7838)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7835,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),U_7837)),hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),U_7838))
      | ~ c_Fun_Oinj__on(U_7834,U_7835,U_7836,c_Orderings_Otop__class_Otop(tc_fun(U_7834,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

cnf(f_1824_3,plain,
    ( hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7834,tc_HOL_Obool)),U_7837),U_7838)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7835,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),U_7837)),hAPP(c_Set_Oimage(U_7834,U_7835,U_7836),U_7838))
    | ~ c_Fun_Oinj__on(U_7834,U_7835,U_7836,c_Orderings_Otop__class_Otop(tc_fun(U_7834,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1824_2]) ).

fof(f_1825_1,plain,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( ( ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
          | hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_a),V_A_2) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
          | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card]) ).

fof(f_1825_2,plain,
    ! [U_7842,U_7841,U_7840,U_7839] :
      ( ( ( c_Fun_Oinj__on(U_7839,U_7841,U_7842,U_7840)
          | hAPP(c_Finite__Set_Ocard(U_7841),hAPP(c_Set_Oimage(U_7839,U_7841,U_7842),U_7840)) != hAPP(c_Finite__Set_Ocard(U_7839),U_7840) )
        & ( hAPP(c_Finite__Set_Ocard(U_7841),hAPP(c_Set_Oimage(U_7839,U_7841,U_7842),U_7840)) = hAPP(c_Finite__Set_Ocard(U_7839),U_7840)
          | ~ c_Fun_Oinj__on(U_7839,U_7841,U_7842,U_7840) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7839),U_7840)) ),
    inference(variable_rename,[status(thm)],[f_1825_1]) ).

cnf(f_1825_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7841),hAPP(c_Set_Oimage(U_7839,U_7841,U_7842),U_7840)) = hAPP(c_Finite__Set_Ocard(U_7839),U_7840)
    | ~ c_Fun_Oinj__on(U_7839,U_7841,U_7842,U_7840)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7839),U_7840)) ),
    inference(clausify,[status(thm)],[f_1825_2]) ).

cnf(f_1825_4,plain,
    ( c_Fun_Oinj__on(U_7839,U_7841,U_7842,U_7840)
    | hAPP(c_Finite__Set_Ocard(U_7841),hAPP(c_Set_Oimage(U_7839,U_7841,U_7842),U_7840)) != hAPP(c_Finite__Set_Ocard(U_7839),U_7840)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7839),U_7840)) ),
    inference(clausify,[status(thm)],[f_1825_2]) ).

fof(f_1826_1,plain,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      | hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on]) ).

fof(f_1826_2,plain,
    ! [U_7846,U_7845,U_7844,U_7843] :
      ( c_Fun_Oinj__on(U_7843,U_7845,U_7846,U_7844)
      | hAPP(c_Finite__Set_Ocard(U_7845),hAPP(c_Set_Oimage(U_7843,U_7845,U_7846),U_7844)) != hAPP(c_Finite__Set_Ocard(U_7843),U_7844)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7843),U_7844)) ),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

cnf(f_1826_3,plain,
    ( c_Fun_Oinj__on(U_7843,U_7845,U_7846,U_7844)
    | hAPP(c_Finite__Set_Ocard(U_7845),hAPP(c_Set_Oimage(U_7843,U_7845,U_7846),U_7844)) != hAPP(c_Finite__Set_Ocard(U_7843),U_7844)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7843),U_7844)) ),
    inference(clausify,[status(thm)],[f_1826_2]) ).

fof(f_1827_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff]) ).

fof(f_1827_2,plain,
    ! [U_7852,U_7851,U_7850,U_7849,U_7848,U_7847] :
      ( hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7847,tc_HOL_Obool)),U_7851),U_7852)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7848,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),U_7851)),hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),U_7852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7847,tc_HOL_Obool)),U_7852),U_7850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7847,tc_HOL_Obool)),U_7851),U_7850))
      | ~ c_Fun_Oinj__on(U_7847,U_7848,U_7849,U_7850) ),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

cnf(f_1827_3,plain,
    ( hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7847,tc_HOL_Obool)),U_7851),U_7852)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7848,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),U_7851)),hAPP(c_Set_Oimage(U_7847,U_7848,U_7849),U_7852))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7847,tc_HOL_Obool)),U_7852),U_7850))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7847,tc_HOL_Obool)),U_7851),U_7850))
    | ~ c_Fun_Oinj__on(U_7847,U_7848,U_7849,U_7850) ),
    inference(clausify,[status(thm)],[f_1827_2]) ).

fof(f_1828_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__set__diff]) ).

fof(f_1828_2,plain,
    ! [U_7857,U_7856,U_7855,U_7854,U_7853] :
      ( hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7853,tc_HOL_Obool)),U_7856),U_7857)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7854,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),U_7856)),hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),U_7857))
      | ~ c_Fun_Oinj__on(U_7853,U_7854,U_7855,c_Orderings_Otop__class_Otop(tc_fun(U_7853,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

cnf(f_1828_3,plain,
    ( hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7853,tc_HOL_Obool)),U_7856),U_7857)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7854,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),U_7856)),hAPP(c_Set_Oimage(U_7853,U_7854,U_7855),U_7857))
    | ~ c_Fun_Oinj__on(U_7853,U_7854,U_7855,c_Orderings_Otop__class_Otop(tc_fun(U_7853,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1828_2]) ).

fof(f_1829_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex]) ).

fof(f_1829_2,plain,
    ! [U_7863,U_7862,U_7861,U_7860,U_7859,U_7858] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7860,U_7858),U_7863),hAPP(c_Set_Oimage(U_7859,U_7860,U_7861),U_7862)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7859,U_7858),hAPP(c_Fun_Ocomp(U_7860,U_7858,U_7859,U_7863),U_7861)),U_7862)
      | ~ c_Fun_Oinj__on(U_7859,U_7860,U_7861,U_7862)
      | ~ class_Groups_Ocomm__monoid__add(U_7858) ),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

cnf(f_1829_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7860,U_7858),U_7863),hAPP(c_Set_Oimage(U_7859,U_7860,U_7861),U_7862)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7859,U_7858),hAPP(c_Fun_Ocomp(U_7860,U_7858,U_7859,U_7863),U_7861)),U_7862)
    | ~ c_Fun_Oinj__on(U_7859,U_7860,U_7861,U_7862)
    | ~ class_Groups_Ocomm__monoid__add(U_7858) ),
    inference(clausify,[status(thm)],[f_1829_2]) ).

fof(f_1830_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole]) ).

fof(f_1830_2,plain,
    ! [U_7867,U_7866,U_7865,U_7864] :
      ( ~ c_Fun_Oinj__on(U_7865,U_7864,U_7866,U_7867)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7864),hAPP(c_Set_Oimage(U_7865,U_7864,U_7866),U_7867))),hAPP(c_Finite__Set_Ocard(U_7865),U_7867))) ),
    inference(variable_rename,[status(thm)],[f_1830_1]) ).

cnf(f_1830_3,plain,
    ( ~ c_Fun_Oinj__on(U_7865,U_7864,U_7866,U_7867)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7864),hAPP(c_Set_Oimage(U_7865,U_7864,U_7866),U_7867))),hAPP(c_Finite__Set_Ocard(U_7865),U_7867))) ),
    inference(clausify,[status(thm)],[f_1830_2]) ).

fof(f_1831_1,plain,
    ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(f_1831_2,plain,
    ! [U_7873,U_7872,U_7871,U_7870,U_7869,U_7868] :
      ( c_Fun_Oinj__on(U_7868,U_7869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_7868,U_7869),U_7870),U_7873),U_7872),U_7871)
      | hBOOL(hAPP(hAPP(c_member(U_7869),U_7872),hAPP(c_Set_Oimage(U_7868,U_7869,U_7870),U_7871)))
      | ~ c_Fun_Oinj__on(U_7868,U_7869,U_7870,U_7871) ),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

cnf(f_1831_3,plain,
    ( c_Fun_Oinj__on(U_7868,U_7869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_7868,U_7869),U_7870),U_7873),U_7872),U_7871)
    | hBOOL(hAPP(hAPP(c_member(U_7869),U_7872),hAPP(c_Set_Oimage(U_7868,U_7869,U_7870),U_7871)))
    | ~ c_Fun_Oinj__on(U_7868,U_7869,U_7870,U_7871) ),
    inference(clausify,[status(thm)],[f_1831_2]) ).

fof(f_1832_1,plain,
    ! [V_h_2,T_b,V_F_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2)))
      | ~ c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageI]) ).

fof(f_1832_2,plain,
    ! [U_7877,U_7876,U_7875,U_7874] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7876),hAPP(c_Set_Ovimage(U_7876,U_7874,U_7877),U_7875)))
      | ~ c_Fun_Oinj__on(U_7876,U_7874,U_7877,c_Orderings_Otop__class_Otop(tc_fun(U_7876,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7874),U_7875)) ),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

cnf(f_1832_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7876),hAPP(c_Set_Ovimage(U_7876,U_7874,U_7877),U_7875)))
    | ~ c_Fun_Oinj__on(U_7876,U_7874,U_7877,c_Orderings_Otop__class_Otop(tc_fun(U_7876,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7874),U_7875)) ),
    inference(clausify,[status(thm)],[f_1832_2]) ).

fof(f_1833_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq]) ).

fof(f_1833_2,plain,
    ! [U_7881,U_7880,U_7879,U_7878] :
      ( hAPP(c_Set_Ovimage(U_7878,U_7879,U_7880),hAPP(c_Set_Oimage(U_7878,U_7879,U_7880),U_7881)) = U_7881
      | ~ c_Fun_Oinj__on(U_7878,U_7879,U_7880,c_Orderings_Otop__class_Otop(tc_fun(U_7878,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

cnf(f_1833_3,plain,
    ( hAPP(c_Set_Ovimage(U_7878,U_7879,U_7880),hAPP(c_Set_Oimage(U_7878,U_7879,U_7880),U_7881)) = U_7881
    | ~ c_Fun_Oinj__on(U_7878,U_7879,U_7880,c_Orderings_Otop__class_Otop(tc_fun(U_7878,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1833_2]) ).

fof(f_1834_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_1834_2,plain,
    ! [U_7882] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7882)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_7882 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_7882 = 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_7882)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

fof(f_1834_3,plain,
    ( ! [U_7884] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7884)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_7884 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7883] :
        ( U_7883 = 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_7883)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1834_2]) ).

cnf(f_1834_4,plain,
    ( U_7883 = 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_7883)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1834_3]) ).

cnf(f_1834_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7884)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_7884 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1834_3]) ).

fof(f_1835_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_1835_2,plain,
    ! [U_7886,U_7885] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7885),U_7886))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7885))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7886))),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

cnf(f_1835_3,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_7885),U_7886))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7885))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7886))),
    inference(clausify,[status(thm)],[f_1835_2]) ).

fof(f_1836_1,plain,
    ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__singleton]) ).

fof(f_1836_2,plain,
    ! [U_7887] : c_Fun_Oinj__on(U_7887,tc_fun(U_7887,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7887,tc_fun(U_7887,tc_HOL_Obool),tc_fun(U_7887,tc_HOL_Obool)),c_Set_Oinsert(U_7887)),c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_7887,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

cnf(f_1836_3,plain,
    c_Fun_Oinj__on(U_7887,tc_fun(U_7887,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7887,tc_fun(U_7887,tc_HOL_Obool),tc_fun(U_7887,tc_HOL_Obool)),c_Set_Oinsert(U_7887)),c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_7887,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1836_2]) ).

fof(f_1837_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex]) ).

fof(f_1837_2,plain,
    ! [U_7892,U_7891,U_7890,U_7889,U_7888] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7889,U_7888),U_7892),hAPP(c_Set_Oimage(U_7889,U_7889,U_7891),U_7890)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7889,U_7888),hAPP(c_Fun_Ocomp(U_7889,U_7888,U_7889,U_7892),U_7891)),U_7890)
      | ~ c_Fun_Oinj__on(U_7889,U_7889,U_7891,U_7890)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7889),U_7890))
      | ~ class_Groups_Ocomm__monoid__add(U_7888) ),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

cnf(f_1837_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7889,U_7888),U_7892),hAPP(c_Set_Oimage(U_7889,U_7889,U_7891),U_7890)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7889,U_7888),hAPP(c_Fun_Ocomp(U_7889,U_7888,U_7889,U_7892),U_7891)),U_7890)
    | ~ c_Fun_Oinj__on(U_7889,U_7889,U_7891,U_7890)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7889),U_7890))
    | ~ class_Groups_Ocomm__monoid__add(U_7888) ),
    inference(clausify,[status(thm)],[f_1837_2]) ).

fof(f_1838_1,plain,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),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_a),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_a,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_a,T_b,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__bij__eq]) ).

fof(f_1838_2,plain,
    ! [U_7898,U_7897,U_7896,U_7895,U_7894,U_7893] :
      ( hAPP(c_Finite__Set_Ocard(U_7893),U_7896) = hAPP(c_Finite__Set_Ocard(U_7894),U_7897)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7894),U_7897))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7893),U_7896))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7893,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7894,U_7893,U_7898),U_7897)),U_7896))
      | ~ c_Fun_Oinj__on(U_7894,U_7893,U_7898,U_7897)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7894,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7893,U_7894,U_7895),U_7896)),U_7897))
      | ~ c_Fun_Oinj__on(U_7893,U_7894,U_7895,U_7896) ),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

cnf(f_1838_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7893),U_7896) = hAPP(c_Finite__Set_Ocard(U_7894),U_7897)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7894),U_7897))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7893),U_7896))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7893,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7894,U_7893,U_7898),U_7897)),U_7896))
    | ~ c_Fun_Oinj__on(U_7894,U_7893,U_7898,U_7897)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7894,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7893,U_7894,U_7895),U_7896)),U_7897))
    | ~ c_Fun_Oinj__on(U_7893,U_7894,U_7895,U_7896) ),
    inference(clausify,[status(thm)],[f_1838_2]) ).

fof(f_1839_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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_a,T_b,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetI]) ).

fof(f_1839_2,plain,
    ! [U_7903,U_7902,U_7901,U_7900,U_7899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7899,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_7899,U_7900,U_7901),U_7902)),U_7903))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7900,tc_HOL_Obool)),U_7902),hAPP(c_Set_Oimage(U_7899,U_7900,U_7901),U_7903)))
      | ~ c_Fun_Oinj__on(U_7899,U_7900,U_7901,c_Orderings_Otop__class_Otop(tc_fun(U_7899,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

cnf(f_1839_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7899,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_7899,U_7900,U_7901),U_7902)),U_7903))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7900,tc_HOL_Obool)),U_7902),hAPP(c_Set_Oimage(U_7899,U_7900,U_7901),U_7903)))
    | ~ c_Fun_Oinj__on(U_7899,U_7900,U_7901,c_Orderings_Otop__class_Otop(tc_fun(U_7899,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1839_2]) ).

fof(f_1840_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
      ( ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__insert]) ).

fof(f_1840_2,plain,
    ! [U_7908,U_7907,U_7906,U_7905,U_7904] :
      ( ( c_Fun_Oinj__on(U_7904,U_7905,U_7906,hAPP(hAPP(c_Set_Oinsert(U_7904),U_7907),U_7908))
        | hBOOL(hAPP(hAPP(c_member(U_7905),hAPP(U_7906,U_7907)),hAPP(c_Set_Oimage(U_7904,U_7905,U_7906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7904,tc_HOL_Obool)),U_7908),hAPP(hAPP(c_Set_Oinsert(U_7904),U_7907),c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_7904,U_7905,U_7906,U_7908) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7905),hAPP(U_7906,U_7907)),hAPP(c_Set_Oimage(U_7904,U_7905,U_7906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7904,tc_HOL_Obool)),U_7908),hAPP(hAPP(c_Set_Oinsert(U_7904),U_7907),c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_7904,U_7905,U_7906,U_7908) )
        | ~ c_Fun_Oinj__on(U_7904,U_7905,U_7906,hAPP(hAPP(c_Set_Oinsert(U_7904),U_7907),U_7908)) ) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

fof(f_1840_3,plain,
    ( ! [U_7918,U_7916,U_7914,U_7912,U_7910] :
        ( c_Fun_Oinj__on(U_7910,U_7912,U_7914,hAPP(hAPP(c_Set_Oinsert(U_7910),U_7916),U_7918))
        | hBOOL(hAPP(hAPP(c_member(U_7912),hAPP(U_7914,U_7916)),hAPP(c_Set_Oimage(U_7910,U_7912,U_7914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7910,tc_HOL_Obool)),U_7918),hAPP(hAPP(c_Set_Oinsert(U_7910),U_7916),c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_7910,U_7912,U_7914,U_7918) )
    & ! [U_7917,U_7915,U_7913,U_7911,U_7909] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7911),hAPP(U_7913,U_7915)),hAPP(c_Set_Oimage(U_7909,U_7911,U_7913),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7909,tc_HOL_Obool)),U_7917),hAPP(hAPP(c_Set_Oinsert(U_7909),U_7915),c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_7909,U_7911,U_7913,U_7917) )
        | ~ c_Fun_Oinj__on(U_7909,U_7911,U_7913,hAPP(hAPP(c_Set_Oinsert(U_7909),U_7915),U_7917)) ) ),
    inference(miniscope,[status(thm)],[f_1840_2]) ).

cnf(f_1840_4,plain,
    ( c_Fun_Oinj__on(U_7909,U_7911,U_7913,U_7917)
    | ~ c_Fun_Oinj__on(U_7909,U_7911,U_7913,hAPP(hAPP(c_Set_Oinsert(U_7909),U_7915),U_7917)) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

cnf(f_1840_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7911),hAPP(U_7913,U_7915)),hAPP(c_Set_Oimage(U_7909,U_7911,U_7913),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7909,tc_HOL_Obool)),U_7917),hAPP(hAPP(c_Set_Oinsert(U_7909),U_7915),c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_7909,U_7911,U_7913,hAPP(hAPP(c_Set_Oinsert(U_7909),U_7915),U_7917)) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

cnf(f_1840_6,plain,
    ( c_Fun_Oinj__on(U_7910,U_7912,U_7914,hAPP(hAPP(c_Set_Oinsert(U_7910),U_7916),U_7918))
    | hBOOL(hAPP(hAPP(c_member(U_7912),hAPP(U_7914,U_7916)),hAPP(c_Set_Oimage(U_7910,U_7912,U_7914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7910,tc_HOL_Obool)),U_7918),hAPP(hAPP(c_Set_Oinsert(U_7910),U_7916),c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_7910,U_7912,U_7914,U_7918) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

fof(f_1841_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
          & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un]) ).

fof(f_1841_2,plain,
    ! [U_7923,U_7922,U_7921,U_7920,U_7919] :
      ( ( c_Fun_Oinj__on(U_7919,U_7920,U_7921,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7919,tc_HOL_Obool)),U_7922),U_7923))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7920,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7919,U_7920,U_7921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7922),U_7923))),hAPP(c_Set_Oimage(U_7919,U_7920,U_7921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7923),U_7922))) != c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_7919,U_7920,U_7921,U_7923)
        | ~ c_Fun_Oinj__on(U_7919,U_7920,U_7921,U_7922) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7920,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7919,U_7920,U_7921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7922),U_7923))),hAPP(c_Set_Oimage(U_7919,U_7920,U_7921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7919,tc_HOL_Obool)),U_7923),U_7922))) = c_Orderings_Obot__class_Obot(tc_fun(U_7920,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_7919,U_7920,U_7921,U_7923)
          & c_Fun_Oinj__on(U_7919,U_7920,U_7921,U_7922) )
        | ~ c_Fun_Oinj__on(U_7919,U_7920,U_7921,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7919,tc_HOL_Obool)),U_7922),U_7923)) ) ),
    inference(variable_rename,[status(thm)],[f_1841_1]) ).

fof(f_1841_3,plain,
    ( ! [U_7933,U_7931,U_7929,U_7927,U_7925] :
        ( c_Fun_Oinj__on(U_7925,U_7927,U_7929,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7925,tc_HOL_Obool)),U_7931),U_7933))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7927,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7925,U_7927,U_7929),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7925,tc_HOL_Obool)),U_7931),U_7933))),hAPP(c_Set_Oimage(U_7925,U_7927,U_7929),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7925,tc_HOL_Obool)),U_7933),U_7931))) != c_Orderings_Obot__class_Obot(tc_fun(U_7927,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_7925,U_7927,U_7929,U_7933)
        | ~ c_Fun_Oinj__on(U_7925,U_7927,U_7929,U_7931) )
    & ! [U_7932,U_7930,U_7928,U_7926,U_7924] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7926,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7924,U_7926,U_7928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932))),hAPP(c_Set_Oimage(U_7924,U_7926,U_7928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7924,tc_HOL_Obool)),U_7932),U_7930))) = c_Orderings_Obot__class_Obot(tc_fun(U_7926,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_7924,U_7926,U_7928,U_7932)
          & c_Fun_Oinj__on(U_7924,U_7926,U_7928,U_7930) )
        | ~ c_Fun_Oinj__on(U_7924,U_7926,U_7928,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932)) ) ),
    inference(miniscope,[status(thm)],[f_1841_2]) ).

cnf(f_1841_4,plain,
    ( c_Fun_Oinj__on(U_7924,U_7926,U_7928,U_7930)
    | ~ c_Fun_Oinj__on(U_7924,U_7926,U_7928,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932)) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

cnf(f_1841_5,plain,
    ( c_Fun_Oinj__on(U_7924,U_7926,U_7928,U_7932)
    | ~ c_Fun_Oinj__on(U_7924,U_7926,U_7928,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932)) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

cnf(f_1841_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7926,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7924,U_7926,U_7928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932))),hAPP(c_Set_Oimage(U_7924,U_7926,U_7928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7924,tc_HOL_Obool)),U_7932),U_7930))) = c_Orderings_Obot__class_Obot(tc_fun(U_7926,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_7924,U_7926,U_7928,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7924,tc_HOL_Obool)),U_7930),U_7932)) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

cnf(f_1841_7,plain,
    ( c_Fun_Oinj__on(U_7925,U_7927,U_7929,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7925,tc_HOL_Obool)),U_7931),U_7933))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7927,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7925,U_7927,U_7929),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7925,tc_HOL_Obool)),U_7931),U_7933))),hAPP(c_Set_Oimage(U_7925,U_7927,U_7929),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7925,tc_HOL_Obool)),U_7933),U_7931))) != c_Orderings_Obot__class_Obot(tc_fun(U_7927,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_7925,U_7927,U_7929,U_7933)
    | ~ c_Fun_Oinj__on(U_7925,U_7927,U_7929,U_7931) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

fof(f_1842_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__inj__on__le]) ).

fof(f_1842_2,plain,
    ! [U_7938,U_7937,U_7936,U_7935,U_7934] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7934),U_7937)),hAPP(c_Finite__Set_Ocard(U_7935),U_7938)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7935),U_7938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7935,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7934,U_7935,U_7936),U_7937)),U_7938))
      | ~ c_Fun_Oinj__on(U_7934,U_7935,U_7936,U_7937) ),
    inference(variable_rename,[status(thm)],[f_1842_1]) ).

cnf(f_1842_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7934),U_7937)),hAPP(c_Finite__Set_Ocard(U_7935),U_7938)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7935),U_7938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7935,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7934,U_7935,U_7936),U_7937)),U_7938))
    | ~ c_Fun_Oinj__on(U_7934,U_7935,U_7936,U_7937) ),
    inference(clausify,[status(thm)],[f_1842_2]) ).

fof(f_1843_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2))
              | ~ c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le]) ).

fof(f_1843_2,plain,
    ! [U_7944,U_7943,U_7942,U_7941] :
      ( ( ( ? [U_7940] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,U_7940),U_7942)),U_7944))
              & c_Fun_Oinj__on(U_7941,U_7943,U_7940,U_7942) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944)))
          | ! [U_7939] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,U_7939),U_7942)),U_7944))
              | ~ c_Fun_Oinj__on(U_7941,U_7943,U_7939,U_7942) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7943),U_7944))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7941),U_7942)) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

fof(f_1843_3,plain,
    ! [U_7944,U_7943,U_7942,U_7941] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,sK196(U_7944,U_7943,U_7942,U_7941)),U_7942)),U_7944))
            & c_Fun_Oinj__on(U_7941,U_7943,sK196(U_7944,U_7943,U_7942,U_7941),U_7942) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944)))
          | ! [U_7939] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,U_7939),U_7942)),U_7944))
              | ~ c_Fun_Oinj__on(U_7941,U_7943,U_7939,U_7942) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7943),U_7944))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7941),U_7942)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_7940,sK196(U_7944,U_7943,U_7942,U_7941))],[f_1843_2]) ).

cnf(f_1843_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,U_7939),U_7942)),U_7944))
    | ~ c_Fun_Oinj__on(U_7941,U_7943,U_7939,U_7942)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7943),U_7944))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7941),U_7942)) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

cnf(f_1843_5,plain,
    ( c_Fun_Oinj__on(U_7941,U_7943,sK196(U_7944,U_7943,U_7942,U_7941),U_7942)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7943),U_7944))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7941),U_7942)) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

cnf(f_1843_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7943,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7941,U_7943,sK196(U_7944,U_7943,U_7942,U_7941)),U_7942)),U_7944))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7941),U_7942)),hAPP(c_Finite__Set_Ocard(U_7943),U_7944)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7943),U_7944))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7941),U_7942)) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

fof(f_1844_1,plain,
    ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,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(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__reindex]) ).

fof(f_1844_2,plain,
    ! [U_7951,U_7950,U_7949,U_7948,U_7947,U_7946,U_7945] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7945,U_7948,c_Groups_Otimes__class_Otimes(U_7945)),U_7950),U_7951),hAPP(c_Set_Oimage(U_7946,U_7948,U_7949),U_7947)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7945,U_7946,c_Groups_Otimes__class_Otimes(U_7945)),hAPP(c_Fun_Ocomp(U_7948,U_7945,U_7946,U_7950),U_7949)),U_7951),U_7947)
      | ~ c_Fun_Oinj__on(U_7946,U_7948,U_7949,U_7947)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7946),U_7947))
      | ~ class_Groups_Oab__semigroup__mult(U_7945) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

cnf(f_1844_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7945,U_7948,c_Groups_Otimes__class_Otimes(U_7945)),U_7950),U_7951),hAPP(c_Set_Oimage(U_7946,U_7948,U_7949),U_7947)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7945,U_7946,c_Groups_Otimes__class_Otimes(U_7945)),hAPP(c_Fun_Ocomp(U_7948,U_7945,U_7946,U_7950),U_7949)),U_7951),U_7947)
    | ~ c_Fun_Oinj__on(U_7946,U_7948,U_7949,U_7947)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7946),U_7947))
    | ~ class_Groups_Oab__semigroup__mult(U_7945) ),
    inference(clausify,[status(thm)],[f_1844_2]) ).

fof(f_1845_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_1845_2,plain,
    ! [U_7954,U_7953,U_7952] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7953),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7954),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_7954),U_7953))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7952))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7952)) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

cnf(f_1845_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7953),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7954),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_7954),U_7953))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7952))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7952)) ),
    inference(clausify,[status(thm)],[f_1845_2]) ).

fof(f_1846_1,plain,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,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))
      | ~ c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex]) ).

fof(f_1846_2,plain,
    ! [U_7962,U_7961,U_7960,U_7959,U_7958,U_7957,U_7956,U_7955] :
      ( hAPP(hAPP(U_7959,U_7962),hAPP(c_Set_Oimage(U_7956,U_7956,U_7961),U_7960)) = hAPP(hAPP(U_7959,hAPP(c_Fun_Ocomp(U_7956,U_7955,U_7956,U_7962),U_7961)),U_7960)
      | ~ c_Fun_Oinj__on(U_7956,U_7956,U_7961,U_7960)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7956),U_7960))
      | ~ c_Finite__Set_Ofolding__image(U_7955,U_7956,U_7957,U_7958,U_7959) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

cnf(f_1846_3,plain,
    ( hAPP(hAPP(U_7959,U_7962),hAPP(c_Set_Oimage(U_7956,U_7956,U_7961),U_7960)) = hAPP(hAPP(U_7959,hAPP(c_Fun_Ocomp(U_7956,U_7955,U_7956,U_7962),U_7961)),U_7960)
    | ~ c_Fun_Oinj__on(U_7956,U_7956,U_7961,U_7960)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7956),U_7960))
    | ~ c_Finite__Set_Ofolding__image(U_7955,U_7956,U_7957,U_7958,U_7959) ),
    inference(clausify,[status(thm)],[f_1846_2]) ).

fof(f_1847_1,plain,
    ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,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_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_image__INT]) ).

fof(f_1847_2,plain,
    ! [U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964] :
      ( hAPP(c_Set_Oimage(U_7964,U_7965,U_7966),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7964,tc_HOL_Obool)),U_7969),U_7970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7965,tc_HOL_Obool)),U_7969),hAPP(hAPP(c_COMBB(tc_fun(U_7964,tc_HOL_Obool),tc_fun(U_7965,tc_HOL_Obool),U_7968),c_Set_Oimage(U_7964,U_7965,U_7966)),U_7970))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7971),U_7969))
      | ? [U_7963] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7964,tc_HOL_Obool)),hAPP(U_7970,U_7963)),U_7967))
          & hBOOL(hAPP(hAPP(c_member(U_7968),U_7963),U_7969)) )
      | ~ c_Fun_Oinj__on(U_7964,U_7965,U_7966,U_7967) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

fof(f_1847_3,plain,
    ! [U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964] :
      ( hAPP(c_Set_Oimage(U_7964,U_7965,U_7966),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7964,tc_HOL_Obool)),U_7969),U_7970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7965,tc_HOL_Obool)),U_7969),hAPP(hAPP(c_COMBB(tc_fun(U_7964,tc_HOL_Obool),tc_fun(U_7965,tc_HOL_Obool),U_7968),c_Set_Oimage(U_7964,U_7965,U_7966)),U_7970))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7971),U_7969))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7964,tc_HOL_Obool)),hAPP(U_7970,sK197(U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964))),U_7967))
        & hBOOL(hAPP(hAPP(c_member(U_7968),sK197(U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964)),U_7969)) )
      | ~ c_Fun_Oinj__on(U_7964,U_7965,U_7966,U_7967) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_7963,sK197(U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964))],[f_1847_2]) ).

cnf(f_1847_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7968),sK197(U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964)),U_7969))
    | hAPP(c_Set_Oimage(U_7964,U_7965,U_7966),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7964,tc_HOL_Obool)),U_7969),U_7970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7965,tc_HOL_Obool)),U_7969),hAPP(hAPP(c_COMBB(tc_fun(U_7964,tc_HOL_Obool),tc_fun(U_7965,tc_HOL_Obool),U_7968),c_Set_Oimage(U_7964,U_7965,U_7966)),U_7970))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7971),U_7969))
    | ~ c_Fun_Oinj__on(U_7964,U_7965,U_7966,U_7967) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7964,tc_HOL_Obool)),hAPP(U_7970,sK197(U_7971,U_7970,U_7969,U_7968,U_7967,U_7966,U_7965,U_7964))),U_7967))
    | hAPP(c_Set_Oimage(U_7964,U_7965,U_7966),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7964,tc_HOL_Obool)),U_7969),U_7970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7968,tc_fun(U_7965,tc_HOL_Obool)),U_7969),hAPP(hAPP(c_COMBB(tc_fun(U_7964,tc_HOL_Obool),tc_fun(U_7965,tc_HOL_Obool),U_7968),c_Set_Oimage(U_7964,U_7965,U_7966)),U_7970))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7971),U_7969))
    | ~ c_Fun_Oinj__on(U_7964,U_7965,U_7966,U_7967) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

fof(f_1848_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_1848_2,plain,
    ! [U_7973,U_7972] : c_Nitpick_Oint__lcm(U_7972,U_7973) = 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_7972)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7973)))),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

cnf(f_1848_3,plain,
    c_Nitpick_Oint__lcm(U_7972,U_7973) = 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_7972)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7973)))),
    inference(clausify,[status(thm)],[f_1848_2]) ).

fof(f_1849_1,plain,
    ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp]) ).

fof(f_1849_2,plain,
    ! [U_7980,U_7979,U_7978,U_7977,U_7976,U_7975,U_7974] :
      ( hAPP(c_Fun_Othe__inv__into(U_7977,U_7975,U_7979,hAPP(c_Fun_Ocomp(U_7974,U_7975,U_7977,U_7976),U_7978)),U_7980) = hAPP(hAPP(c_Fun_Ocomp(U_7974,U_7977,U_7975,c_Fun_Othe__inv__into(U_7977,U_7974,U_7979,U_7978)),c_Fun_Othe__inv__into(U_7974,U_7975,hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979),U_7976)),U_7980)
      | ~ hBOOL(hAPP(hAPP(c_member(U_7975),U_7980),hAPP(c_Set_Oimage(U_7974,U_7975,U_7976),hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979))))
      | ~ c_Fun_Oinj__on(U_7977,U_7974,U_7978,U_7979)
      | ~ c_Fun_Oinj__on(U_7974,U_7975,U_7976,hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979)) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

cnf(f_1849_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_7977,U_7975,U_7979,hAPP(c_Fun_Ocomp(U_7974,U_7975,U_7977,U_7976),U_7978)),U_7980) = hAPP(hAPP(c_Fun_Ocomp(U_7974,U_7977,U_7975,c_Fun_Othe__inv__into(U_7977,U_7974,U_7979,U_7978)),c_Fun_Othe__inv__into(U_7974,U_7975,hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979),U_7976)),U_7980)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7975),U_7980),hAPP(c_Set_Oimage(U_7974,U_7975,U_7976),hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979))))
    | ~ c_Fun_Oinj__on(U_7977,U_7974,U_7978,U_7979)
    | ~ c_Fun_Oinj__on(U_7974,U_7975,U_7976,hAPP(c_Set_Oimage(U_7977,U_7974,U_7978),U_7979)) ),
    inference(clausify,[status(thm)],[f_1849_2]) ).

fof(f_1850_1,plain,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__into]) ).

fof(f_1850_2,plain,
    ! [U_7986,U_7985,U_7984,U_7983,U_7982,U_7981] :
      ( hBOOL(hAPP(hAPP(c_member(U_7981),hAPP(c_Fun_Othe__inv__into(U_7981,U_7982,U_7984,U_7983),U_7985)),U_7986))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7981,tc_HOL_Obool)),U_7984),U_7986))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7982),U_7985),hAPP(c_Set_Oimage(U_7981,U_7982,U_7983),U_7984)))
      | ~ c_Fun_Oinj__on(U_7981,U_7982,U_7983,U_7984) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

cnf(f_1850_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7981),hAPP(c_Fun_Othe__inv__into(U_7981,U_7982,U_7984,U_7983),U_7985)),U_7986))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7981,tc_HOL_Obool)),U_7984),U_7986))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7982),U_7985),hAPP(c_Set_Oimage(U_7981,U_7982,U_7983),U_7984)))
    | ~ c_Fun_Oinj__on(U_7981,U_7982,U_7983,U_7984) ),
    inference(clausify,[status(thm)],[f_1850_2]) ).

fof(f_1851_1,plain,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),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_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib]) ).

fof(f_1851_2,plain,
    ! [U_7994,U_7993,U_7992,U_7991,U_7990,U_7989,U_7988,U_7987] :
      ( hAPP(hAPP(U_7991,hAPP(hAPP(c_COMBS(U_7988,U_7987,U_7987),hAPP(hAPP(c_COMBB(U_7987,tc_fun(U_7987,U_7987),U_7988),U_7989),U_7993)),U_7994)),U_7992) = hAPP(hAPP(U_7989,hAPP(hAPP(U_7991,U_7993),U_7992)),hAPP(hAPP(U_7991,U_7994),U_7992))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7988),U_7992))
      | ~ c_Finite__Set_Ofolding__image(U_7987,U_7988,U_7989,U_7990,U_7991) ),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

cnf(f_1851_3,plain,
    ( hAPP(hAPP(U_7991,hAPP(hAPP(c_COMBS(U_7988,U_7987,U_7987),hAPP(hAPP(c_COMBB(U_7987,tc_fun(U_7987,U_7987),U_7988),U_7989),U_7993)),U_7994)),U_7992) = hAPP(hAPP(U_7989,hAPP(hAPP(U_7991,U_7993),U_7992)),hAPP(hAPP(U_7991,U_7994),U_7992))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7988),U_7992))
    | ~ c_Finite__Set_Ofolding__image(U_7987,U_7988,U_7989,U_7990,U_7991) ),
    inference(clausify,[status(thm)],[f_1851_2]) ).

fof(f_1852_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f]) ).

fof(f_1852_2,plain,
    ! [U_7999,U_7998,U_7997,U_7996,U_7995] :
      ( hAPP(c_Fun_Othe__inv__into(U_7995,U_7996,U_7998,U_7997),hAPP(U_7997,U_7999)) = U_7999
      | ~ hBOOL(hAPP(hAPP(c_member(U_7995),U_7999),U_7998))
      | ~ c_Fun_Oinj__on(U_7995,U_7996,U_7997,U_7998) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

cnf(f_1852_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_7995,U_7996,U_7998,U_7997),hAPP(U_7997,U_7999)) = U_7999
    | ~ hBOOL(hAPP(hAPP(c_member(U_7995),U_7999),U_7998))
    | ~ c_Fun_Oinj__on(U_7995,U_7996,U_7997,U_7998) ),
    inference(clausify,[status(thm)],[f_1852_2]) ).

fof(f_1853_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | hAPP(V_f_2,V_x_2) != V_y_2
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq]) ).

fof(f_1853_2,plain,
    ! [U_8005,U_8004,U_8003,U_8002,U_8001,U_8000] :
      ( hAPP(c_Fun_Othe__inv__into(U_8000,U_8001,U_8003,U_8002),U_8005) = U_8004
      | ~ hBOOL(hAPP(hAPP(c_member(U_8000),U_8004),U_8003))
      | hAPP(U_8002,U_8004) != U_8005
      | ~ c_Fun_Oinj__on(U_8000,U_8001,U_8002,U_8003) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

cnf(f_1853_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_8000,U_8001,U_8003,U_8002),U_8005) = U_8004
    | ~ hBOOL(hAPP(hAPP(c_member(U_8000),U_8004),U_8003))
    | hAPP(U_8002,U_8004) != U_8005
    | ~ c_Fun_Oinj__on(U_8000,U_8001,U_8002,U_8003) ),
    inference(clausify,[status(thm)],[f_1853_2]) ).

fof(f_1854_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into]) ).

fof(f_1854_2,plain,
    ! [U_8009,U_8008,U_8007,U_8006] :
      ( c_Fun_Oinj__on(U_8007,U_8006,c_Fun_Othe__inv__into(U_8006,U_8007,U_8009,U_8008),hAPP(c_Set_Oimage(U_8006,U_8007,U_8008),U_8009))
      | ~ c_Fun_Oinj__on(U_8006,U_8007,U_8008,U_8009) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

cnf(f_1854_3,plain,
    ( c_Fun_Oinj__on(U_8007,U_8006,c_Fun_Othe__inv__into(U_8006,U_8007,U_8009,U_8008),hAPP(c_Set_Oimage(U_8006,U_8007,U_8008),U_8009))
    | ~ c_Fun_Oinj__on(U_8006,U_8007,U_8008,U_8009) ),
    inference(clausify,[status(thm)],[f_1854_2]) ).

fof(f_1855_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto]) ).

fof(f_1855_2,plain,
    ! [U_8013,U_8012,U_8011,U_8010] :
      ( hAPP(c_Set_Oimage(U_8011,U_8010,c_Fun_Othe__inv__into(U_8010,U_8011,U_8013,U_8012)),hAPP(c_Set_Oimage(U_8010,U_8011,U_8012),U_8013)) = U_8013
      | ~ c_Fun_Oinj__on(U_8010,U_8011,U_8012,U_8013) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

cnf(f_1855_3,plain,
    ( hAPP(c_Set_Oimage(U_8011,U_8010,c_Fun_Othe__inv__into(U_8010,U_8011,U_8013,U_8012)),hAPP(c_Set_Oimage(U_8010,U_8011,U_8012),U_8013)) = U_8013
    | ~ c_Fun_Oinj__on(U_8010,U_8011,U_8012,U_8013) ),
    inference(clausify,[status(thm)],[f_1855_2]) ).

fof(f_1856_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__f__f]) ).

fof(f_1856_2,plain,
    ! [U_8017,U_8016,U_8015,U_8014] :
      ( hAPP(c_Fun_Othe__inv__into(U_8014,U_8015,c_Orderings_Otop__class_Otop(tc_fun(U_8014,tc_HOL_Obool)),U_8016),hAPP(U_8016,U_8017)) = U_8017
      | ~ c_Fun_Oinj__on(U_8014,U_8015,U_8016,c_Orderings_Otop__class_Otop(tc_fun(U_8014,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

cnf(f_1856_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_8014,U_8015,c_Orderings_Otop__class_Otop(tc_fun(U_8014,tc_HOL_Obool)),U_8016),hAPP(U_8016,U_8017)) = U_8017
    | ~ c_Fun_Oinj__on(U_8014,U_8015,U_8016,c_Orderings_Otop__class_Otop(tc_fun(U_8014,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_1856_2]) ).

fof(f_1857_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).

fof(f_1857_2,plain,
    ! [U_8022,U_8021,U_8020,U_8019,U_8018] : hAPP(c_Fun_Othe__inv__into(U_8018,U_8019,U_8020,U_8021),U_8022) = c_HOL_OThe(U_8018,hAPP(hAPP(c_COMBS(U_8018,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8018),c_fconj),hAPP(hAPP(c_COMBC(U_8018,tc_fun(U_8018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8018)),U_8020))),hAPP(hAPP(c_COMBC(U_8018,U_8019,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8019,tc_fun(U_8019,tc_HOL_Obool),U_8018),c_fequal),U_8021)),U_8022))),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

cnf(f_1857_3,plain,
    hAPP(c_Fun_Othe__inv__into(U_8018,U_8019,U_8020,U_8021),U_8022) = c_HOL_OThe(U_8018,hAPP(hAPP(c_COMBS(U_8018,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8018),c_fconj),hAPP(hAPP(c_COMBC(U_8018,tc_fun(U_8018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8018)),U_8020))),hAPP(hAPP(c_COMBC(U_8018,U_8019,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8019,tc_fun(U_8019,tc_HOL_Obool),U_8018),c_fequal),U_8021)),U_8022))),
    inference(clausify,[status(thm)],[f_1857_2]) ).

fof(f_1858_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold]) ).

fof(f_1858_2,plain,
    ! [U_8029,U_8028,U_8027,U_8026,U_8025,U_8024,U_8023] :
      ( hAPP(hAPP(U_8027,U_8029),U_8028) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8023,U_8024,U_8025),U_8029),U_8026),U_8028)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8024),U_8028))
      | ~ c_Finite__Set_Ofolding__image(U_8023,U_8024,U_8025,U_8026,U_8027) ),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

cnf(f_1858_3,plain,
    ( hAPP(hAPP(U_8027,U_8029),U_8028) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8023,U_8024,U_8025),U_8029),U_8026),U_8028)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8024),U_8028))
    | ~ c_Finite__Set_Ofolding__image(U_8023,U_8024,U_8025,U_8026,U_8027) ),
    inference(clausify,[status(thm)],[f_1858_2]) ).

fof(f_1859_1,plain,
    ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f]) ).

fof(f_1859_2,plain,
    ! [U_8034,U_8033,U_8032,U_8031,U_8030] :
      ( hAPP(U_8032,hAPP(c_Fun_Othe__inv__into(U_8030,U_8031,U_8033,U_8032),U_8034)) = U_8034
      | ~ hBOOL(hAPP(hAPP(c_member(U_8031),U_8034),hAPP(c_Set_Oimage(U_8030,U_8031,U_8032),U_8033)))
      | ~ c_Fun_Oinj__on(U_8030,U_8031,U_8032,U_8033) ),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

cnf(f_1859_3,plain,
    ( hAPP(U_8032,hAPP(c_Fun_Othe__inv__into(U_8030,U_8031,U_8033,U_8032),U_8034)) = U_8034
    | ~ hBOOL(hAPP(hAPP(c_member(U_8031),U_8034),hAPP(c_Set_Oimage(U_8030,U_8031,U_8032),U_8033)))
    | ~ c_Fun_Oinj__on(U_8030,U_8031,U_8032,U_8033) ),
    inference(clausify,[status(thm)],[f_1859_2]) ).

fof(f_1860_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J]) ).

fof(f_1860_2,plain,
    ! [U_8040,U_8039,U_8038,U_8037,U_8036] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8039),U_8037) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8040),U_8038)
      | ? [U_8035] :
          ( hAPP(U_8039,U_8035) != hAPP(U_8040,U_8035)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8035)) )
      | ~ c_Nat__Transfer_Onat__set(U_8038)
      | U_8037 != U_8038
      | ~ class_Groups_Ocomm__monoid__mult(U_8036)
      | ~ class_Groups_Ocomm__monoid__add(U_8036) ),
    inference(variable_rename,[status(thm)],[f_1860_1]) ).

fof(f_1860_3,plain,
    ! [U_8040,U_8039,U_8038,U_8037,U_8036] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8039),U_8037) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8040),U_8038)
      | ( hAPP(U_8039,sK198(U_8040,U_8039,U_8038,U_8037,U_8036)) != hAPP(U_8040,sK198(U_8040,U_8039,U_8038,U_8037,U_8036))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_8040,U_8039,U_8038,U_8037,U_8036))) )
      | ~ c_Nat__Transfer_Onat__set(U_8038)
      | U_8037 != U_8038
      | ~ class_Groups_Ocomm__monoid__mult(U_8036)
      | ~ class_Groups_Ocomm__monoid__add(U_8036) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_8035,sK198(U_8040,U_8039,U_8038,U_8037,U_8036))],[f_1860_2]) ).

cnf(f_1860_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK198(U_8040,U_8039,U_8038,U_8037,U_8036)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8039),U_8037) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8040),U_8038)
    | ~ c_Nat__Transfer_Onat__set(U_8038)
    | U_8037 != U_8038
    | ~ class_Groups_Ocomm__monoid__mult(U_8036)
    | ~ class_Groups_Ocomm__monoid__add(U_8036) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

cnf(f_1860_5,plain,
    ( hAPP(U_8039,sK198(U_8040,U_8039,U_8038,U_8037,U_8036)) != hAPP(U_8040,sK198(U_8040,U_8039,U_8038,U_8037,U_8036))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8039),U_8037) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8036),U_8040),U_8038)
    | ~ c_Nat__Transfer_Onat__set(U_8038)
    | U_8037 != U_8038
    | ~ class_Groups_Ocomm__monoid__mult(U_8036)
    | ~ class_Groups_Ocomm__monoid__add(U_8036) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

fof(f_1861_1,plain,
    ! [V_f_2,T_b,T_a,V_S_2] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2))
      | ? [B_A] :
          ( ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) )
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Inter]) ).

fof(f_1861_2,plain,
    ! [U_8045,U_8044,U_8043,U_8042] :
      ( c_Fun_Oinj__on(U_8043,U_8044,U_8045,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8043,tc_HOL_Obool),U_8042))
      | ? [U_8041] :
          ( ~ c_Fun_Oinj__on(U_8043,U_8044,U_8045,U_8041)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8043,tc_HOL_Obool)),U_8041),U_8042)) )
      | U_8042 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8043,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_1861_1]) ).

fof(f_1861_3,plain,
    ! [U_8045,U_8044,U_8043,U_8042] :
      ( c_Fun_Oinj__on(U_8043,U_8044,U_8045,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8043,tc_HOL_Obool),U_8042))
      | ( ~ c_Fun_Oinj__on(U_8043,U_8044,U_8045,sK199(U_8045,U_8044,U_8043,U_8042))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8043,tc_HOL_Obool)),sK199(U_8045,U_8044,U_8043,U_8042)),U_8042)) )
      | U_8042 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8043,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_8041,sK199(U_8045,U_8044,U_8043,U_8042))],[f_1861_2]) ).

cnf(f_1861_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8043,tc_HOL_Obool)),sK199(U_8045,U_8044,U_8043,U_8042)),U_8042))
    | c_Fun_Oinj__on(U_8043,U_8044,U_8045,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8043,tc_HOL_Obool),U_8042))
    | U_8042 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8043,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

cnf(f_1861_5,plain,
    ( ~ c_Fun_Oinj__on(U_8043,U_8044,U_8045,sK199(U_8045,U_8044,U_8043,U_8042))
    | c_Fun_Oinj__on(U_8043,U_8044,U_8045,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8043,tc_HOL_Obool),U_8042))
    | U_8042 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8043,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

fof(f_1862_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).

fof(f_1862_2,plain,
    ! [U_8049,U_8048,U_8047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8047,tc_HOL_Obool),U_8048)),U_8049))
      | U_8048 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8047,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_8046] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),U_8046),U_8049))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8047,tc_HOL_Obool)),U_8046),U_8048)) ) ),
    inference(variable_rename,[status(thm)],[f_1862_1]) ).

fof(f_1862_3,plain,
    ! [U_8049,U_8048,U_8047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8047,tc_HOL_Obool),U_8048)),U_8049))
      | U_8048 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8047,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),sK200(U_8049,U_8048,U_8047)),U_8049))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8047,tc_HOL_Obool)),sK200(U_8049,U_8048,U_8047)),U_8048)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_8046,sK200(U_8049,U_8048,U_8047))],[f_1862_2]) ).

cnf(f_1862_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8047,tc_HOL_Obool)),sK200(U_8049,U_8048,U_8047)),U_8048))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8047,tc_HOL_Obool),U_8048)),U_8049))
    | U_8048 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8047,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1862_3]) ).

cnf(f_1862_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),sK200(U_8049,U_8048,U_8047)),U_8049))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8047,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_8047,tc_HOL_Obool),U_8048)),U_8049))
    | U_8048 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8047,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1862_3]) ).

fof(f_1863_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_1863_2,plain,
    ! [U_8054,U_8053,U_8052] :
      ( ? [U_8051] :
          ( hAPP(U_8053,U_8051) = U_8054
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8051),U_8052)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
      | ? [U_8050] :
          ( ~ 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_8053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8050),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8053,U_8050)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8050),U_8052)) ) ),
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

fof(f_1863_3,plain,
    ! [U_8054,U_8053,U_8052] :
      ( ? [U_8051] :
          ( hAPP(U_8053,U_8051) = U_8054
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8051),U_8052)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
      | ( ~ 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_8053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8053,sK201(U_8054,U_8053,U_8052))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),U_8052)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_8050,sK201(U_8054,U_8053,U_8052))],[f_1863_2]) ).

fof(f_1863_4,plain,
    ! [U_8054,U_8053,U_8052] :
      ( ( hAPP(U_8053,sK202(U_8054,U_8053,U_8052)) = U_8054
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK202(U_8054,U_8053,U_8052)),U_8052)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
      | ( ~ 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_8053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8053,sK201(U_8054,U_8053,U_8052))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),U_8052)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_8051,sK202(U_8054,U_8053,U_8052))],[f_1863_3]) ).

cnf(f_1863_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK202(U_8054,U_8053,U_8052)),U_8052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),U_8052)) ),
    inference(clausify,[status(thm)],[f_1863_4]) ).

cnf(f_1863_6,plain,
    ( hAPP(U_8053,sK202(U_8054,U_8053,U_8052)) = U_8054
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),U_8052)) ),
    inference(clausify,[status(thm)],[f_1863_4]) ).

cnf(f_1863_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK202(U_8054,U_8053,U_8052)),U_8052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
    | ~ 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_8053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8053,sK201(U_8054,U_8053,U_8052))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1863_4]) ).

cnf(f_1863_8,plain,
    ( hAPP(U_8053,sK202(U_8054,U_8053,U_8052)) = U_8054
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8054),hAPP(U_8053,U_8052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8054))
    | ~ 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_8053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK201(U_8054,U_8053,U_8052)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8053,sK201(U_8054,U_8053,U_8052))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1863_4]) ).

fof(f_1864_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_1864_2,plain,
    ! [U_8059,U_8058,U_8057] :
      ( ? [U_8056] :
          ( hAPP(U_8058,U_8056) = U_8059
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8056),U_8057)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
      | ? [U_8055] :
          ( ~ 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_8058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8055),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8058,U_8055)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8055),U_8057)) ) ),
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

fof(f_1864_3,plain,
    ! [U_8059,U_8058,U_8057] :
      ( ? [U_8056] :
          ( hAPP(U_8058,U_8056) = U_8059
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8056),U_8057)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
      | ( ~ 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_8058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8058,sK203(U_8059,U_8058,U_8057))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),U_8057)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_8055,sK203(U_8059,U_8058,U_8057))],[f_1864_2]) ).

fof(f_1864_4,plain,
    ! [U_8059,U_8058,U_8057] :
      ( ( hAPP(U_8058,sK204(U_8059,U_8058,U_8057)) = U_8059
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8059,U_8058,U_8057)),U_8057)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
      | ( ~ 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_8058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8058,sK203(U_8059,U_8058,U_8057))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),U_8057)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_8056,sK204(U_8059,U_8058,U_8057))],[f_1864_3]) ).

cnf(f_1864_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8059,U_8058,U_8057)),U_8057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),U_8057)) ),
    inference(clausify,[status(thm)],[f_1864_4]) ).

cnf(f_1864_6,plain,
    ( hAPP(U_8058,sK204(U_8059,U_8058,U_8057)) = U_8059
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),U_8057)) ),
    inference(clausify,[status(thm)],[f_1864_4]) ).

cnf(f_1864_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8059,U_8058,U_8057)),U_8057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
    | ~ 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_8058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8058,sK203(U_8059,U_8058,U_8057))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1864_4]) ).

cnf(f_1864_8,plain,
    ( hAPP(U_8058,sK204(U_8059,U_8058,U_8057)) = U_8059
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8059),hAPP(U_8058,U_8057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8059))
    | ~ 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_8058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8059,U_8058,U_8057)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8058,sK203(U_8059,U_8058,U_8057))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1864_4]) ).

fof(f_1865_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
      | ? [B_i] :
          ( ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) )
      | V_I_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__INTER]) ).

fof(f_1865_2,plain,
    ! [U_8066,U_8065,U_8064,U_8063,U_8062,U_8061] :
      ( c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8062,tc_fun(U_8063,tc_HOL_Obool)),U_8061),U_8066))
      | ? [U_8060] :
          ( ~ c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(U_8066,U_8060))
          & hBOOL(hAPP(hAPP(c_member(U_8062),U_8060),U_8061)) )
      | U_8061 = c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

fof(f_1865_3,plain,
    ! [U_8066,U_8065,U_8064,U_8063,U_8062,U_8061] :
      ( c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8062,tc_fun(U_8063,tc_HOL_Obool)),U_8061),U_8066))
      | ( ~ c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(U_8066,sK205(U_8066,U_8065,U_8064,U_8063,U_8062,U_8061)))
        & hBOOL(hAPP(hAPP(c_member(U_8062),sK205(U_8066,U_8065,U_8064,U_8063,U_8062,U_8061)),U_8061)) )
      | U_8061 = c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_8060,sK205(U_8066,U_8065,U_8064,U_8063,U_8062,U_8061))],[f_1865_2]) ).

cnf(f_1865_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8062),sK205(U_8066,U_8065,U_8064,U_8063,U_8062,U_8061)),U_8061))
    | c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8062,tc_fun(U_8063,tc_HOL_Obool)),U_8061),U_8066))
    | U_8061 = c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1865_3]) ).

cnf(f_1865_5,plain,
    ( ~ c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(U_8066,sK205(U_8066,U_8065,U_8064,U_8063,U_8062,U_8061)))
    | c_Fun_Oinj__on(U_8063,U_8064,U_8065,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8062,tc_fun(U_8063,tc_HOL_Obool)),U_8061),U_8066))
    | U_8061 = c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1865_3]) ).

fof(f_1866_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_1866_2,plain,
    ! [U_8068,U_8067] :
      ( 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_8067))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8068))))) = 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_8067))),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_8068)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8067)) ),
    inference(variable_rename,[status(thm)],[f_1866_1]) ).

cnf(f_1866_3,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_8067))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8068))))) = 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_8067))),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_8068)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8067)) ),
    inference(clausify,[status(thm)],[f_1866_2]) ).

fof(f_1867_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_1867_2,plain,
    ! [U_8070,U_8069] :
      ( 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_8069))),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_8070))))) != 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_8069)) ),
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

cnf(f_1867_3,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_8069))),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_8070))))) != 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_8069)) ),
    inference(clausify,[status(thm)],[f_1867_2]) ).

fof(f_1868_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_1868_2,plain,
    ! [U_8072,U_8071] :
      ( 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_8071))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8072)))) = 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_8071))),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_8072)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8071)) ),
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

cnf(f_1868_3,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_8071))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8072)))) = 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_8071))),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_8072)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8071)) ),
    inference(clausify,[status(thm)],[f_1868_2]) ).

fof(f_1869_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_1869_2,plain,
    ! [U_8075,U_8074] :
      ( 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_8075),U_8074)
      | ? [U_8073] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8075),U_8073))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8073),U_8074)) ) ),
    inference(variable_rename,[status(thm)],[f_1869_1]) ).

fof(f_1869_3,plain,
    ! [U_8075,U_8074] :
      ( 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_8075),U_8074)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8075),sK206(U_8075,U_8074)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK206(U_8075,U_8074)),U_8074)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_8073,sK206(U_8075,U_8074))],[f_1869_2]) ).

cnf(f_1869_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK206(U_8075,U_8074)),U_8074))
    | 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_8075),U_8074) ),
    inference(clausify,[status(thm)],[f_1869_3]) ).

cnf(f_1869_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8075),sK206(U_8075,U_8074)))
    | 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_8075),U_8074) ),
    inference(clausify,[status(thm)],[f_1869_3]) ).

fof(f_1870_1,plain,
    ! [T_a,V_a_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_CollectI]) ).

fof(f_1870_2,plain,
    ! [U_8078,U_8077,U_8076] :
      ( hBOOL(hAPP(hAPP(c_member(U_8078),U_8077),hAPP(c_Set_OCollect(U_8078),U_8076)))
      | ~ hBOOL(hAPP(U_8076,U_8077)) ),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

cnf(f_1870_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8078),U_8077),hAPP(c_Set_OCollect(U_8078),U_8076)))
    | ~ hBOOL(hAPP(U_8076,U_8077)) ),
    inference(clausify,[status(thm)],[f_1870_2]) ).

fof(f_1871_1,plain,
    ! [V_Q_2,V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).

fof(f_1871_2,plain,
    ! [U_8081,U_8080,U_8079] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),hAPP(hAPP(c_COMBS(U_8079,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8079),c_fconj),U_8080)),U_8081))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),U_8081)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),U_8080))) ) ),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

cnf(f_1871_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),U_8080)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),hAPP(hAPP(c_COMBS(U_8079,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8079),c_fconj),U_8080)),U_8081)))) ),
    inference(clausify,[status(thm)],[f_1871_2]) ).

cnf(f_1871_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),U_8081)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8079),hAPP(c_Set_OCollect(U_8079),hAPP(hAPP(c_COMBS(U_8079,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8079),c_fconj),U_8080)),U_8081)))) ),
    inference(clausify,[status(thm)],[f_1871_2]) ).

fof(f_1872_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_1872_2,plain,
    ! [U_8082] : 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_8082)))),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

cnf(f_1872_3,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_8082)))),
    inference(clausify,[status(thm)],[f_1872_2]) ).

fof(f_1873_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_1873_2,plain,
    ! [U_8083] : 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_8083)))),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

cnf(f_1873_3,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_8083)))),
    inference(clausify,[status(thm)],[f_1873_2]) ).

fof(f_1874_1,plain,
    ! [V_P_2,T_a] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_a),V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).

fof(f_1874_2,plain,
    ! [U_8087,U_8086] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8086,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8086),U_8087)
        | ? [U_8085] : hBOOL(hAPP(U_8087,U_8085)) )
      & ( ! [U_8084] : ~ hBOOL(hAPP(U_8087,U_8084))
        | c_Orderings_Obot__class_Obot(tc_fun(U_8086,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_8086),U_8087) ) ),
    inference(variable_rename,[status(thm)],[f_1874_1]) ).

fof(f_1874_3,plain,
    ( ! [U_8091] :
        ( ! [U_8089] : c_Orderings_Obot__class_Obot(tc_fun(U_8089,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8089),U_8091)
        | ? [U_8085] : hBOOL(hAPP(U_8091,U_8085)) )
    & ! [U_8090] :
        ( ! [U_8088] : c_Orderings_Obot__class_Obot(tc_fun(U_8088,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_8088),U_8090)
        | ! [U_8084] : ~ hBOOL(hAPP(U_8090,U_8084)) ) ),
    inference(miniscope,[status(thm)],[f_1874_2]) ).

fof(f_1874_4,plain,
    ( ! [U_8091] :
        ( ! [U_8089] : c_Orderings_Obot__class_Obot(tc_fun(U_8089,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8089),U_8091)
        | hBOOL(hAPP(U_8091,sK207(U_8091))) )
    & ! [U_8090] :
        ( ! [U_8088] : c_Orderings_Obot__class_Obot(tc_fun(U_8088,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_8088),U_8090)
        | ! [U_8084] : ~ hBOOL(hAPP(U_8090,U_8084)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_8085,sK207(U_8091))],[f_1874_3]) ).

cnf(f_1874_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8088,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_8088),U_8090)
    | ~ hBOOL(hAPP(U_8090,U_8084)) ),
    inference(clausify,[status(thm)],[f_1874_4]) ).

cnf(f_1874_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8089,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8089),U_8091)
    | hBOOL(hAPP(U_8091,sK207(U_8091))) ),
    inference(clausify,[status(thm)],[f_1874_4]) ).

fof(f_1875_1,plain,
    ! [V_P_2,T_a] :
      ( ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | hAPP(c_Set_OCollect(T_a),V_P_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).

fof(f_1875_2,plain,
    ! [U_8095,U_8094] :
      ( ( hAPP(c_Set_OCollect(U_8094),U_8095) = c_Orderings_Obot__class_Obot(tc_fun(U_8094,tc_HOL_Obool))
        | ? [U_8093] : hBOOL(hAPP(U_8095,U_8093)) )
      & ( ! [U_8092] : ~ hBOOL(hAPP(U_8095,U_8092))
        | hAPP(c_Set_OCollect(U_8094),U_8095) != c_Orderings_Obot__class_Obot(tc_fun(U_8094,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

fof(f_1875_3,plain,
    ( ! [U_8099] :
        ( ! [U_8097] : hAPP(c_Set_OCollect(U_8097),U_8099) = c_Orderings_Obot__class_Obot(tc_fun(U_8097,tc_HOL_Obool))
        | ? [U_8093] : hBOOL(hAPP(U_8099,U_8093)) )
    & ! [U_8098] :
        ( ! [U_8096] : hAPP(c_Set_OCollect(U_8096),U_8098) != c_Orderings_Obot__class_Obot(tc_fun(U_8096,tc_HOL_Obool))
        | ! [U_8092] : ~ hBOOL(hAPP(U_8098,U_8092)) ) ),
    inference(miniscope,[status(thm)],[f_1875_2]) ).

fof(f_1875_4,plain,
    ( ! [U_8099] :
        ( ! [U_8097] : hAPP(c_Set_OCollect(U_8097),U_8099) = c_Orderings_Obot__class_Obot(tc_fun(U_8097,tc_HOL_Obool))
        | hBOOL(hAPP(U_8099,sK208(U_8099))) )
    & ! [U_8098] :
        ( ! [U_8096] : hAPP(c_Set_OCollect(U_8096),U_8098) != c_Orderings_Obot__class_Obot(tc_fun(U_8096,tc_HOL_Obool))
        | ! [U_8092] : ~ hBOOL(hAPP(U_8098,U_8092)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_8093,sK208(U_8099))],[f_1875_3]) ).

cnf(f_1875_5,plain,
    ( hAPP(c_Set_OCollect(U_8096),U_8098) != c_Orderings_Obot__class_Obot(tc_fun(U_8096,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_8098,U_8092)) ),
    inference(clausify,[status(thm)],[f_1875_4]) ).

cnf(f_1875_6,plain,
    ( hAPP(c_Set_OCollect(U_8097),U_8099) = c_Orderings_Obot__class_Obot(tc_fun(U_8097,tc_HOL_Obool))
    | hBOOL(hAPP(U_8099,sK208(U_8099))) ),
    inference(clausify,[status(thm)],[f_1875_4]) ).

fof(f_1876_1,plain,
    ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).

fof(f_1876_2,plain,
    ! [U_8101,U_8100] : hAPP(c_Set_OCollect(U_8100),U_8101) = U_8101,
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

cnf(f_1876_3,plain,
    hAPP(c_Set_OCollect(U_8100),U_8101) = U_8101,
    inference(clausify,[status(thm)],[f_1876_2]) ).

fof(f_1877_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).

fof(f_1877_2,plain,
    ! [U_8103,U_8102] : hAPP(c_Set_OCollect(U_8102),hAPP(hAPP(c_COMBC(U_8102,tc_fun(U_8102,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8102)),U_8103)) = U_8103,
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

cnf(f_1877_3,plain,
    hAPP(c_Set_OCollect(U_8102),hAPP(hAPP(c_COMBC(U_8102,tc_fun(U_8102,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8102)),U_8103)) = U_8103,
    inference(clausify,[status(thm)],[f_1877_2]) ).

fof(f_1878_1,plain,
    ! [V_P_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).

fof(f_1878_2,plain,
    ! [U_8106,U_8105,U_8104] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8104),U_8105),hAPP(c_Set_OCollect(U_8104),U_8106)))
        | ~ hBOOL(hAPP(U_8106,U_8105)) )
      & ( hBOOL(hAPP(U_8106,U_8105))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8104),U_8105),hAPP(c_Set_OCollect(U_8104),U_8106))) ) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

fof(f_1878_3,plain,
    ( ! [U_8112,U_8110] :
        ( ! [U_8108] : hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Set_OCollect(U_8108),U_8112)))
        | ~ hBOOL(hAPP(U_8112,U_8110)) )
    & ! [U_8111,U_8109] :
        ( ! [U_8107] : ~ hBOOL(hAPP(hAPP(c_member(U_8107),U_8109),hAPP(c_Set_OCollect(U_8107),U_8111)))
        | hBOOL(hAPP(U_8111,U_8109)) ) ),
    inference(miniscope,[status(thm)],[f_1878_2]) ).

cnf(f_1878_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8107),U_8109),hAPP(c_Set_OCollect(U_8107),U_8111)))
    | hBOOL(hAPP(U_8111,U_8109)) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Set_OCollect(U_8108),U_8112)))
    | ~ hBOOL(hAPP(U_8112,U_8110)) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

fof(f_1879_1,plain,
    ! [V_P_2,V_a_2,T_a] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectD]) ).

fof(f_1879_2,plain,
    ! [U_8115,U_8114,U_8113] :
      ( hBOOL(hAPP(U_8115,U_8114))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),hAPP(c_Set_OCollect(U_8113),U_8115))) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

fof(f_1879_3,plain,
    ! [U_8115,U_8114] :
      ( ! [U_8113] : ~ hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),hAPP(c_Set_OCollect(U_8113),U_8115)))
      | hBOOL(hAPP(U_8115,U_8114)) ),
    inference(miniscope,[status(thm)],[f_1879_2]) ).

cnf(f_1879_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),hAPP(c_Set_OCollect(U_8113),U_8115)))
    | hBOOL(hAPP(U_8115,U_8114)) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

fof(f_1880_1,plain,
    ! [V_P_2,V_a_2,T_a] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectE]) ).

fof(f_1880_2,plain,
    ! [U_8118,U_8117,U_8116] :
      ( hBOOL(hAPP(U_8118,U_8117))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8116),U_8117),hAPP(c_Set_OCollect(U_8116),U_8118))) ),
    inference(variable_rename,[status(thm)],[f_1880_1]) ).

fof(f_1880_3,plain,
    ! [U_8118,U_8117] :
      ( ! [U_8116] : ~ hBOOL(hAPP(hAPP(c_member(U_8116),U_8117),hAPP(c_Set_OCollect(U_8116),U_8118)))
      | hBOOL(hAPP(U_8118,U_8117)) ),
    inference(miniscope,[status(thm)],[f_1880_2]) ).

cnf(f_1880_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8116),U_8117),hAPP(c_Set_OCollect(U_8116),U_8118)))
    | hBOOL(hAPP(U_8118,U_8117)) ),
    inference(clausify,[status(thm)],[f_1880_3]) ).

fof(f_1881_1,plain,
    ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)),
    inference(fof_nnf,[status(thm)],[fact_empty__def]) ).

fof(f_1881_2,plain,
    ! [U_8119] : c_Orderings_Obot__class_Obot(tc_fun(U_8119,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8119),hAPP(c_COMBK(tc_HOL_Obool,U_8119),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_1881_1]) ).

cnf(f_1881_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_8119,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8119),hAPP(c_COMBK(tc_HOL_Obool,U_8119),c_fFalse)),
    inference(clausify,[status(thm)],[f_1881_2]) ).

fof(f_1882_1,plain,
    ! [V_Q_2,V_P_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).

fof(f_1882_2,plain,
    ! [U_8122,U_8121,U_8120] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),hAPP(hAPP(c_COMBS(U_8120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8120),c_fdisj),U_8121)),U_8122))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),U_8122)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),U_8121))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),U_8122)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),U_8121))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8120),hAPP(c_Set_OCollect(U_8120),hAPP(hAPP(c_COMBS(U_8120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8120),c_fdisj),U_8121)),U_8122)))) ) ),
    inference(variable_rename,[status(thm)],[f_1882_1]) ).

fof(f_1882_3,plain,
    ( ! [U_8128,U_8126,U_8124] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),hAPP(hAPP(c_COMBS(U_8124,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8124),c_fdisj),U_8126)),U_8128))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),U_8128)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),U_8126))) )
    & ! [U_8127,U_8125,U_8123] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),U_8127)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),U_8125))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),hAPP(hAPP(c_COMBS(U_8123,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8123),c_fdisj),U_8125)),U_8127)))) ) ),
    inference(miniscope,[status(thm)],[f_1882_2]) ).

cnf(f_1882_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),U_8125)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),hAPP(hAPP(c_COMBS(U_8123,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8123),c_fdisj),U_8125)),U_8127)))) ),
    inference(clausify,[status(thm)],[f_1882_3]) ).

cnf(f_1882_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),U_8127)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8123),hAPP(c_Set_OCollect(U_8123),hAPP(hAPP(c_COMBS(U_8123,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8123),c_fdisj),U_8125)),U_8127)))) ),
    inference(clausify,[status(thm)],[f_1882_3]) ).

cnf(f_1882_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),hAPP(hAPP(c_COMBS(U_8124,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8124),c_fdisj),U_8126)),U_8128))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),U_8128)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8124),hAPP(c_Set_OCollect(U_8124),U_8126))) ),
    inference(clausify,[status(thm)],[f_1882_3]) ).

fof(f_1883_1,plain,
    ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).

fof(f_1883_2,plain,
    ! [U_8131,U_8130,U_8129] : hAPP(hAPP(c_Set_Oinsert(U_8129),U_8130),hAPP(c_Set_OCollect(U_8129),U_8131)) = hAPP(c_Set_OCollect(U_8129),hAPP(hAPP(c_COMBS(U_8129,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8129),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8129),c_fNot),hAPP(hAPP(c_COMBC(U_8129,U_8129,tc_HOL_Obool),c_fequal),U_8130)))),U_8131)),
    inference(variable_rename,[status(thm)],[f_1883_1]) ).

cnf(f_1883_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8129),U_8130),hAPP(c_Set_OCollect(U_8129),U_8131)) = hAPP(c_Set_OCollect(U_8129),hAPP(hAPP(c_COMBS(U_8129,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8129),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8129),c_fNot),hAPP(hAPP(c_COMBC(U_8129,U_8129,tc_HOL_Obool),c_fequal),U_8130)))),U_8131)),
    inference(clausify,[status(thm)],[f_1883_2]) ).

fof(f_1884_1,plain,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).

fof(f_1884_2,plain,
    ! [U_8132] : c_Orderings_Otop__class_Otop(tc_fun(U_8132,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8132),hAPP(c_COMBK(tc_HOL_Obool,U_8132),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

cnf(f_1884_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_8132,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_8132),hAPP(c_COMBK(tc_HOL_Obool,U_8132),c_fTrue)),
    inference(clausify,[status(thm)],[f_1884_2]) ).

fof(f_1885_1,plain,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).

fof(f_1885_2,plain,
    ! [U_8135,U_8134,U_8133] : hAPP(c_Set_OCollect(U_8133),hAPP(hAPP(c_COMBS(U_8133,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8133),c_fdisj),U_8134)),U_8135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8133),U_8134)),hAPP(c_Set_OCollect(U_8133),U_8135)),
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

cnf(f_1885_3,plain,
    hAPP(c_Set_OCollect(U_8133),hAPP(hAPP(c_COMBS(U_8133,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8133),c_fdisj),U_8134)),U_8135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8133),U_8134)),hAPP(c_Set_OCollect(U_8133),U_8135)),
    inference(clausify,[status(thm)],[f_1885_2]) ).

fof(f_1886_1,plain,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).

fof(f_1886_2,plain,
    ! [U_8138,U_8137,U_8136] : hAPP(c_Set_OCollect(U_8136),hAPP(hAPP(c_COMBS(U_8136,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8136),c_fconj),U_8137)),U_8138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8136,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8136),U_8137)),hAPP(c_Set_OCollect(U_8136),U_8138)),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

cnf(f_1886_3,plain,
    hAPP(c_Set_OCollect(U_8136),hAPP(hAPP(c_COMBS(U_8136,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8136),c_fconj),U_8137)),U_8138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8136,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8136),U_8137)),hAPP(c_Set_OCollect(U_8136),U_8138)),
    inference(clausify,[status(thm)],[f_1886_2]) ).

fof(f_1887_1,plain,
    ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(f_1887_2,plain,
    ! [U_8142,U_8141,U_8140,U_8139] : hAPP(c_Set_Ovimage(U_8139,U_8140,U_8141),hAPP(c_Set_OCollect(U_8140),U_8142)) = hAPP(c_Set_OCollect(U_8139),hAPP(hAPP(c_COMBB(U_8140,tc_HOL_Obool,U_8139),U_8142),U_8141)),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

cnf(f_1887_3,plain,
    hAPP(c_Set_Ovimage(U_8139,U_8140,U_8141),hAPP(c_Set_OCollect(U_8140),U_8142)) = hAPP(c_Set_OCollect(U_8139),hAPP(hAPP(c_COMBB(U_8140,tc_HOL_Obool,U_8139),U_8142),U_8141)),
    inference(clausify,[status(thm)],[f_1887_2]) ).

fof(f_1888_1,plain,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr__raw]) ).

fof(f_1888_2,plain,
    ! [U_8145,U_8144,U_8143] : hAPP(hAPP(c_Set_Oinsert(U_8143),U_8144),U_8145) = hAPP(c_Set_OCollect(U_8143),hAPP(hAPP(c_COMBS(U_8143,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8143),c_fdisj),hAPP(hAPP(c_COMBC(U_8143,U_8143,tc_HOL_Obool),c_fequal),U_8144))),hAPP(hAPP(c_COMBC(U_8143,tc_fun(U_8143,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8143)),U_8145))),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

cnf(f_1888_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8143),U_8144),U_8145) = hAPP(c_Set_OCollect(U_8143),hAPP(hAPP(c_COMBS(U_8143,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8143),c_fdisj),hAPP(hAPP(c_COMBC(U_8143,U_8143,tc_HOL_Obool),c_fequal),U_8144))),hAPP(hAPP(c_COMBC(U_8143,tc_fun(U_8143,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8143)),U_8145))),
    inference(clausify,[status(thm)],[f_1888_2]) ).

fof(f_1889_1,plain,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr]) ).

fof(f_1889_2,plain,
    ! [U_8148,U_8147,U_8146] : hAPP(hAPP(c_Set_Oinsert(U_8146),U_8147),U_8148) = hAPP(c_Set_OCollect(U_8146),hAPP(hAPP(c_COMBS(U_8146,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8146),c_fdisj),hAPP(hAPP(c_COMBC(U_8146,U_8146,tc_HOL_Obool),c_fequal),U_8147))),hAPP(hAPP(c_COMBC(U_8146,tc_fun(U_8146,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8146)),U_8148))),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

cnf(f_1889_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8146),U_8147),U_8148) = hAPP(c_Set_OCollect(U_8146),hAPP(hAPP(c_COMBS(U_8146,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8146),c_fdisj),hAPP(hAPP(c_COMBC(U_8146,U_8146,tc_HOL_Obool),c_fequal),U_8147))),hAPP(hAPP(c_COMBC(U_8146,tc_fun(U_8146,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8146)),U_8148))),
    inference(clausify,[status(thm)],[f_1889_2]) ).

fof(f_1890_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__def]) ).

fof(f_1890_2,plain,
    ! [U_8151,U_8150,U_8149] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151) = hAPP(c_Set_OCollect(U_8149),hAPP(hAPP(c_COMBS(U_8149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8149),c_fdisj),hAPP(hAPP(c_COMBC(U_8149,tc_fun(U_8149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8149)),U_8150))),hAPP(hAPP(c_COMBC(U_8149,tc_fun(U_8149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8149)),U_8151))),
    inference(variable_rename,[status(thm)],[f_1890_1]) ).

cnf(f_1890_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8149,tc_HOL_Obool)),U_8150),U_8151) = hAPP(c_Set_OCollect(U_8149),hAPP(hAPP(c_COMBS(U_8149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8149),c_fdisj),hAPP(hAPP(c_COMBC(U_8149,tc_fun(U_8149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8149)),U_8150))),hAPP(hAPP(c_COMBC(U_8149,tc_fun(U_8149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8149)),U_8151))),
    inference(clausify,[status(thm)],[f_1890_2]) ).

fof(f_1891_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__def]) ).

fof(f_1891_2,plain,
    ! [U_8154,U_8153,U_8152] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8154) = hAPP(c_Set_OCollect(U_8152),hAPP(hAPP(c_COMBS(U_8152,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8152),c_fconj),hAPP(hAPP(c_COMBC(U_8152,tc_fun(U_8152,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8152)),U_8153))),hAPP(hAPP(c_COMBC(U_8152,tc_fun(U_8152,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8152)),U_8154))),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

cnf(f_1891_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8152,tc_HOL_Obool)),U_8153),U_8154) = hAPP(c_Set_OCollect(U_8152),hAPP(hAPP(c_COMBS(U_8152,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8152),c_fconj),hAPP(hAPP(c_COMBC(U_8152,tc_fun(U_8152,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8152)),U_8153))),hAPP(hAPP(c_COMBC(U_8152,tc_fun(U_8152,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8152)),U_8154))),
    inference(clausify,[status(thm)],[f_1891_2]) ).

fof(f_1892_1,plain,
    ! [V_P_2,V_A_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))))
        | ~ hBOOL(hAPP(V_P_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(V_P_2,V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).

fof(f_1892_2,plain,
    ! [U_8158,U_8157,U_8156,U_8155] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8155),U_8156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8155,tc_HOL_Obool)),U_8157),hAPP(c_Set_OCollect(U_8155),U_8158))))
        | ~ hBOOL(hAPP(U_8158,U_8156))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8155),U_8156),U_8157)) )
      & ( ( hBOOL(hAPP(U_8158,U_8156))
          & hBOOL(hAPP(hAPP(c_member(U_8155),U_8156),U_8157)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8155),U_8156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8155,tc_HOL_Obool)),U_8157),hAPP(c_Set_OCollect(U_8155),U_8158)))) ) ),
    inference(variable_rename,[status(thm)],[f_1892_1]) ).

fof(f_1892_3,plain,
    ( ! [U_8166,U_8164,U_8162,U_8160] :
        ( hBOOL(hAPP(hAPP(c_member(U_8160),U_8162),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8160,tc_HOL_Obool)),U_8164),hAPP(c_Set_OCollect(U_8160),U_8166))))
        | ~ hBOOL(hAPP(U_8166,U_8162))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8160),U_8162),U_8164)) )
    & ! [U_8165,U_8163,U_8161,U_8159] :
        ( ( hBOOL(hAPP(U_8165,U_8161))
          & hBOOL(hAPP(hAPP(c_member(U_8159),U_8161),U_8163)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8159),U_8161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8159,tc_HOL_Obool)),U_8163),hAPP(c_Set_OCollect(U_8159),U_8165)))) ) ),
    inference(miniscope,[status(thm)],[f_1892_2]) ).

cnf(f_1892_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8159),U_8161),U_8163))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8159),U_8161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8159,tc_HOL_Obool)),U_8163),hAPP(c_Set_OCollect(U_8159),U_8165)))) ),
    inference(clausify,[status(thm)],[f_1892_3]) ).

cnf(f_1892_5,plain,
    ( hBOOL(hAPP(U_8165,U_8161))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8159),U_8161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8159,tc_HOL_Obool)),U_8163),hAPP(c_Set_OCollect(U_8159),U_8165)))) ),
    inference(clausify,[status(thm)],[f_1892_3]) ).

cnf(f_1892_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8160),U_8162),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8160,tc_HOL_Obool)),U_8164),hAPP(c_Set_OCollect(U_8160),U_8166))))
    | ~ hBOOL(hAPP(U_8166,U_8162))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8160),U_8162),U_8164)) ),
    inference(clausify,[status(thm)],[f_1892_3]) ).

fof(f_1893_1,plain,
    ! [T_a,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).

fof(f_1893_2,plain,
    ! [U_8169,U_8168,U_8167] :
      ( ( hAPP(c_Set_OCollect(U_8169),hAPP(hAPP(c_COMBS(U_8169,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8169),c_fconj),hAPP(hAPP(c_COMBC(U_8169,U_8169,tc_HOL_Obool),c_fequal),U_8168))),U_8167)) = c_Orderings_Obot__class_Obot(tc_fun(U_8169,tc_HOL_Obool))
        | hBOOL(hAPP(U_8167,U_8168)) )
      & ( hAPP(c_Set_OCollect(U_8169),hAPP(hAPP(c_COMBS(U_8169,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8169),c_fconj),hAPP(hAPP(c_COMBC(U_8169,U_8169,tc_HOL_Obool),c_fequal),U_8168))),U_8167)) = hAPP(hAPP(c_Set_Oinsert(U_8169),U_8168),c_Orderings_Obot__class_Obot(tc_fun(U_8169,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_8167,U_8168)) ) ),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

fof(f_1893_3,plain,
    ( ! [U_8175,U_8173,U_8171] :
        ( hAPP(c_Set_OCollect(U_8175),hAPP(hAPP(c_COMBS(U_8175,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8175),c_fconj),hAPP(hAPP(c_COMBC(U_8175,U_8175,tc_HOL_Obool),c_fequal),U_8173))),U_8171)) = c_Orderings_Obot__class_Obot(tc_fun(U_8175,tc_HOL_Obool))
        | hBOOL(hAPP(U_8171,U_8173)) )
    & ! [U_8174,U_8172,U_8170] :
        ( hAPP(c_Set_OCollect(U_8174),hAPP(hAPP(c_COMBS(U_8174,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8174),c_fconj),hAPP(hAPP(c_COMBC(U_8174,U_8174,tc_HOL_Obool),c_fequal),U_8172))),U_8170)) = hAPP(hAPP(c_Set_Oinsert(U_8174),U_8172),c_Orderings_Obot__class_Obot(tc_fun(U_8174,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_8170,U_8172)) ) ),
    inference(miniscope,[status(thm)],[f_1893_2]) ).

cnf(f_1893_4,plain,
    ( hAPP(c_Set_OCollect(U_8174),hAPP(hAPP(c_COMBS(U_8174,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8174),c_fconj),hAPP(hAPP(c_COMBC(U_8174,U_8174,tc_HOL_Obool),c_fequal),U_8172))),U_8170)) = hAPP(hAPP(c_Set_Oinsert(U_8174),U_8172),c_Orderings_Obot__class_Obot(tc_fun(U_8174,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_8170,U_8172)) ),
    inference(clausify,[status(thm)],[f_1893_3]) ).

cnf(f_1893_5,plain,
    ( hAPP(c_Set_OCollect(U_8175),hAPP(hAPP(c_COMBS(U_8175,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8175),c_fconj),hAPP(hAPP(c_COMBC(U_8175,U_8175,tc_HOL_Obool),c_fequal),U_8173))),U_8171)) = c_Orderings_Obot__class_Obot(tc_fun(U_8175,tc_HOL_Obool))
    | hBOOL(hAPP(U_8171,U_8173)) ),
    inference(clausify,[status(thm)],[f_1893_3]) ).

fof(f_1894_1,plain,
    ! [T_a,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).

fof(f_1894_2,plain,
    ! [U_8178,U_8177,U_8176] :
      ( ( hAPP(c_Set_OCollect(U_8178),hAPP(hAPP(c_COMBS(U_8178,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8178),c_fconj),hAPP(c_fequal,U_8177))),U_8176)) = c_Orderings_Obot__class_Obot(tc_fun(U_8178,tc_HOL_Obool))
        | hBOOL(hAPP(U_8176,U_8177)) )
      & ( hAPP(c_Set_OCollect(U_8178),hAPP(hAPP(c_COMBS(U_8178,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8178),c_fconj),hAPP(c_fequal,U_8177))),U_8176)) = hAPP(hAPP(c_Set_Oinsert(U_8178),U_8177),c_Orderings_Obot__class_Obot(tc_fun(U_8178,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_8176,U_8177)) ) ),
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

fof(f_1894_3,plain,
    ( ! [U_8184,U_8182,U_8180] :
        ( hAPP(c_Set_OCollect(U_8184),hAPP(hAPP(c_COMBS(U_8184,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8184),c_fconj),hAPP(c_fequal,U_8182))),U_8180)) = c_Orderings_Obot__class_Obot(tc_fun(U_8184,tc_HOL_Obool))
        | hBOOL(hAPP(U_8180,U_8182)) )
    & ! [U_8183,U_8181,U_8179] :
        ( hAPP(c_Set_OCollect(U_8183),hAPP(hAPP(c_COMBS(U_8183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8183),c_fconj),hAPP(c_fequal,U_8181))),U_8179)) = hAPP(hAPP(c_Set_Oinsert(U_8183),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_8179,U_8181)) ) ),
    inference(miniscope,[status(thm)],[f_1894_2]) ).

cnf(f_1894_4,plain,
    ( hAPP(c_Set_OCollect(U_8183),hAPP(hAPP(c_COMBS(U_8183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8183),c_fconj),hAPP(c_fequal,U_8181))),U_8179)) = hAPP(hAPP(c_Set_Oinsert(U_8183),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_8179,U_8181)) ),
    inference(clausify,[status(thm)],[f_1894_3]) ).

cnf(f_1894_5,plain,
    ( hAPP(c_Set_OCollect(U_8184),hAPP(hAPP(c_COMBS(U_8184,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8184),c_fconj),hAPP(c_fequal,U_8182))),U_8180)) = c_Orderings_Obot__class_Obot(tc_fun(U_8184,tc_HOL_Obool))
    | hBOOL(hAPP(U_8180,U_8182)) ),
    inference(clausify,[status(thm)],[f_1894_3]) ).

fof(f_1895_1,plain,
    ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv]) ).

fof(f_1895_2,plain,
    ! [U_8186,U_8185] : hAPP(c_Set_OCollect(U_8185),hAPP(hAPP(c_COMBC(U_8185,U_8185,tc_HOL_Obool),c_fequal),U_8186)) = hAPP(hAPP(c_Set_Oinsert(U_8185),U_8186),c_Orderings_Obot__class_Obot(tc_fun(U_8185,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

cnf(f_1895_3,plain,
    hAPP(c_Set_OCollect(U_8185),hAPP(hAPP(c_COMBC(U_8185,U_8185,tc_HOL_Obool),c_fequal),U_8186)) = hAPP(hAPP(c_Set_Oinsert(U_8185),U_8186),c_Orderings_Obot__class_Obot(tc_fun(U_8185,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1895_2]) ).

fof(f_1896_1,plain,
    ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv2]) ).

fof(f_1896_2,plain,
    ! [U_8188,U_8187] : hAPP(c_Set_OCollect(U_8187),hAPP(c_fequal,U_8188)) = hAPP(hAPP(c_Set_Oinsert(U_8187),U_8188),c_Orderings_Obot__class_Obot(tc_fun(U_8187,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

cnf(f_1896_3,plain,
    hAPP(c_Set_OCollect(U_8187),hAPP(c_fequal,U_8188)) = hAPP(hAPP(c_Set_Oinsert(U_8187),U_8188),c_Orderings_Obot__class_Obot(tc_fun(U_8187,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1896_2]) ).

fof(f_1897_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__diff__eq]) ).

fof(f_1897_2,plain,
    ! [U_8191,U_8190,U_8189] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8189,tc_HOL_Obool)),U_8190),U_8191) = hAPP(c_Set_OCollect(U_8189),hAPP(hAPP(c_COMBS(U_8189,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8189),c_fconj),hAPP(hAPP(c_COMBC(U_8189,tc_fun(U_8189,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8189)),U_8190))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8189),c_fNot),hAPP(hAPP(c_COMBC(U_8189,tc_fun(U_8189,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8189)),U_8191)))),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

cnf(f_1897_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8189,tc_HOL_Obool)),U_8190),U_8191) = hAPP(c_Set_OCollect(U_8189),hAPP(hAPP(c_COMBS(U_8189,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8189),c_fconj),hAPP(hAPP(c_COMBC(U_8189,tc_fun(U_8189,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8189)),U_8190))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8189),c_fNot),hAPP(hAPP(c_COMBC(U_8189,tc_fun(U_8189,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8189)),U_8191)))),
    inference(clausify,[status(thm)],[f_1897_2]) ).

fof(f_1898_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).

fof(f_1898_2,plain,
    ! [U_8193,U_8192] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8192),c_fNot),U_8193))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),c_Orderings_Otop__class_Otop(tc_fun(U_8192,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),c_Orderings_Otop__class_Otop(tc_fun(U_8192,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8192),c_fNot),U_8193)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),U_8193))) ),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

cnf(f_1898_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),c_Orderings_Otop__class_Otop(tc_fun(U_8192,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8192),c_fNot),U_8193))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),U_8193))) ),
    inference(clausify,[status(thm)],[f_1898_2]) ).

cnf(f_1898_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8192),c_fNot),U_8193))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),c_Orderings_Otop__class_Otop(tc_fun(U_8192,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8192),hAPP(c_Set_OCollect(U_8192),U_8193))) ),
    inference(clausify,[status(thm)],[f_1898_2]) ).

fof(f_1899_1,plain,
    ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_insert__def]) ).

fof(f_1899_2,plain,
    ! [U_8196,U_8195,U_8194] : hAPP(hAPP(c_Set_Oinsert(U_8194),U_8195),U_8196) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8194,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8194),hAPP(hAPP(c_COMBC(U_8194,U_8194,tc_HOL_Obool),c_fequal),U_8195))),U_8196),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

cnf(f_1899_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8194),U_8195),U_8196) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8194,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8194),hAPP(hAPP(c_COMBC(U_8194,U_8194,tc_HOL_Obool),c_fequal),U_8195))),U_8196),
    inference(clausify,[status(thm)],[f_1899_2]) ).

fof(f_1900_1,plain,
    ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__def]) ).

fof(f_1900_2,plain,
    ! [U_8200,U_8199,U_8198,U_8197] : hAPP(c_Set_Ovimage(U_8197,U_8198,U_8199),U_8200) = hAPP(c_Set_OCollect(U_8197),hAPP(hAPP(c_COMBC(U_8197,tc_fun(U_8198,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8198,tc_fun(tc_fun(U_8198,tc_HOL_Obool),tc_HOL_Obool),U_8197),c_member(U_8198)),U_8199)),U_8200)),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

cnf(f_1900_3,plain,
    hAPP(c_Set_Ovimage(U_8197,U_8198,U_8199),U_8200) = hAPP(c_Set_OCollect(U_8197),hAPP(hAPP(c_COMBC(U_8197,tc_fun(U_8198,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8198,tc_fun(tc_fun(U_8198,tc_HOL_Obool),tc_HOL_Obool),U_8197),c_member(U_8198)),U_8199)),U_8200)),
    inference(clausify,[status(thm)],[f_1900_2]) ).

fof(f_1901_1,plain,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    inference(fof_nnf,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(f_1901_2,plain,
    ! [U_8202,U_8201] : 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_8201)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8202))))),
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

cnf(f_1901_3,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_8201)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8202))))),
    inference(clausify,[status(thm)],[f_1901_2]) ).

fof(f_1902_1,plain,
    ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).

fof(f_1902_2,plain,
    ! [U_8209,U_8208,U_8207,U_8206,U_8205,U_8204,U_8203] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8204,U_8203),hAPP(hAPP(c_COMBS(U_8204,tc_fun(U_8206,tc_HOL_Obool),U_8203),hAPP(hAPP(c_COMBB(tc_fun(U_8206,U_8203),tc_fun(tc_fun(U_8206,tc_HOL_Obool),U_8203),U_8204),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8206,U_8203)),U_8208)),hAPP(hAPP(c_COMBB(tc_fun(U_8206,tc_HOL_Obool),tc_fun(U_8206,tc_HOL_Obool),U_8204),c_Set_OCollect(U_8206)),hAPP(hAPP(c_COMBB(tc_fun(U_8206,tc_HOL_Obool),tc_fun(U_8206,tc_HOL_Obool),U_8204),hAPP(c_COMBS(U_8206,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8206),c_fconj),hAPP(hAPP(c_COMBC(U_8206,tc_fun(U_8206,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8206)),U_8207)))),U_8209)))),U_8205) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8206,U_8203),hAPP(hAPP(c_COMBS(U_8206,tc_fun(U_8204,tc_HOL_Obool),U_8203),hAPP(hAPP(c_COMBB(tc_fun(U_8204,U_8203),tc_fun(tc_fun(U_8204,tc_HOL_Obool),U_8203),U_8206),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8204,U_8203)),hAPP(c_COMBC(U_8204,U_8206,U_8203),U_8208))),hAPP(hAPP(c_COMBB(tc_fun(U_8204,tc_HOL_Obool),tc_fun(U_8204,tc_HOL_Obool),U_8206),c_Set_OCollect(U_8204)),hAPP(hAPP(c_COMBB(tc_fun(U_8204,tc_HOL_Obool),tc_fun(U_8204,tc_HOL_Obool),U_8206),hAPP(c_COMBS(U_8204,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8204),c_fconj),hAPP(hAPP(c_COMBC(U_8204,tc_fun(U_8204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8204)),U_8205)))),hAPP(c_COMBC(U_8204,U_8206,tc_HOL_Obool),U_8209))))),U_8207)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8206),U_8207))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
      | ~ class_Groups_Ocomm__monoid__add(U_8203) ),
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

cnf(f_1902_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8204,U_8203),hAPP(hAPP(c_COMBS(U_8204,tc_fun(U_8206,tc_HOL_Obool),U_8203),hAPP(hAPP(c_COMBB(tc_fun(U_8206,U_8203),tc_fun(tc_fun(U_8206,tc_HOL_Obool),U_8203),U_8204),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8206,U_8203)),U_8208)),hAPP(hAPP(c_COMBB(tc_fun(U_8206,tc_HOL_Obool),tc_fun(U_8206,tc_HOL_Obool),U_8204),c_Set_OCollect(U_8206)),hAPP(hAPP(c_COMBB(tc_fun(U_8206,tc_HOL_Obool),tc_fun(U_8206,tc_HOL_Obool),U_8204),hAPP(c_COMBS(U_8206,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8206),c_fconj),hAPP(hAPP(c_COMBC(U_8206,tc_fun(U_8206,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8206)),U_8207)))),U_8209)))),U_8205) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8206,U_8203),hAPP(hAPP(c_COMBS(U_8206,tc_fun(U_8204,tc_HOL_Obool),U_8203),hAPP(hAPP(c_COMBB(tc_fun(U_8204,U_8203),tc_fun(tc_fun(U_8204,tc_HOL_Obool),U_8203),U_8206),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8204,U_8203)),hAPP(c_COMBC(U_8204,U_8206,U_8203),U_8208))),hAPP(hAPP(c_COMBB(tc_fun(U_8204,tc_HOL_Obool),tc_fun(U_8204,tc_HOL_Obool),U_8206),c_Set_OCollect(U_8204)),hAPP(hAPP(c_COMBB(tc_fun(U_8204,tc_HOL_Obool),tc_fun(U_8204,tc_HOL_Obool),U_8206),hAPP(c_COMBS(U_8204,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8204),c_fconj),hAPP(hAPP(c_COMBC(U_8204,tc_fun(U_8204,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8204)),U_8205)))),hAPP(c_COMBC(U_8204,U_8206,tc_HOL_Obool),U_8209))))),U_8207)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8206),U_8207))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
    | ~ class_Groups_Ocomm__monoid__add(U_8203) ),
    inference(clausify,[status(thm)],[f_1902_2]) ).

fof(f_1903_1,plain,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))),
    inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).

fof(f_1903_2,plain,
    ! [U_8215,U_8214,U_8213,U_8212,U_8211,U_8210] : hAPP(c_Set_Oimage(U_8210,U_8211,hAPP(hAPP(c_COMBS(U_8210,U_8211,U_8211),hAPP(hAPP(c_COMBS(U_8210,U_8211,tc_fun(U_8211,U_8211)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8211,tc_fun(U_8211,U_8211)),U_8210),c_If(U_8211)),U_8212)),U_8213)),U_8214)),U_8215) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8211,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8210,U_8211,U_8213),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8210,tc_HOL_Obool)),U_8215),hAPP(c_Set_OCollect(U_8210),U_8212)))),hAPP(c_Set_Oimage(U_8210,U_8211,U_8214),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8210,tc_HOL_Obool)),U_8215),hAPP(c_Set_OCollect(U_8210),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8210),c_fNot),U_8212))))),
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

cnf(f_1903_3,plain,
    hAPP(c_Set_Oimage(U_8210,U_8211,hAPP(hAPP(c_COMBS(U_8210,U_8211,U_8211),hAPP(hAPP(c_COMBS(U_8210,U_8211,tc_fun(U_8211,U_8211)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8211,tc_fun(U_8211,U_8211)),U_8210),c_If(U_8211)),U_8212)),U_8213)),U_8214)),U_8215) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8211,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8210,U_8211,U_8213),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8210,tc_HOL_Obool)),U_8215),hAPP(c_Set_OCollect(U_8210),U_8212)))),hAPP(c_Set_Oimage(U_8210,U_8211,U_8214),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8210,tc_HOL_Obool)),U_8215),hAPP(c_Set_OCollect(U_8210),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8210),c_fNot),U_8212))))),
    inference(clausify,[status(thm)],[f_1903_2]) ).

fof(f_1904_1,plain,
    ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__all__eq]) ).

fof(f_1904_2,plain,
    ! [U_8218,U_8217,U_8216] : hAPP(c_Set_OCollect(U_8216),hAPP(hAPP(c_COMBB(tc_fun(U_8217,tc_HOL_Obool),tc_HOL_Obool,U_8216),c_HOL_OAll(U_8217)),U_8218)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8217,tc_fun(U_8216,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8217,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8216,tc_HOL_Obool),tc_fun(U_8216,tc_HOL_Obool),U_8217),c_Set_OCollect(U_8216)),hAPP(c_COMBC(U_8216,U_8217,tc_HOL_Obool),U_8218))),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

cnf(f_1904_3,plain,
    hAPP(c_Set_OCollect(U_8216),hAPP(hAPP(c_COMBB(tc_fun(U_8217,tc_HOL_Obool),tc_HOL_Obool,U_8216),c_HOL_OAll(U_8217)),U_8218)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8217,tc_fun(U_8216,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8217,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8216,tc_HOL_Obool),tc_fun(U_8216,tc_HOL_Obool),U_8217),c_Set_OCollect(U_8216)),hAPP(c_COMBC(U_8216,U_8217,tc_HOL_Obool),U_8218))),
    inference(clausify,[status(thm)],[f_1904_2]) ).

fof(f_1905_1,plain,
    ! [V_n_2,V_f_2,T_a,V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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_1905_2,plain,
    ! [U_8222,U_8221,U_8220,U_8219] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8220),U_8219))
      | U_8219 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8220,U_8221),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_8222))) ),
    inference(variable_rename,[status(thm)],[f_1905_1]) ).

cnf(f_1905_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8220),U_8219))
    | U_8219 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8220,U_8221),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_8222))) ),
    inference(clausify,[status(thm)],[f_1905_2]) ).

fof(f_1906_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).

fof(f_1906_2,plain,
    ! [U_8227,U_8226,U_8225,U_8224,U_8223] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8224,U_8223),U_8226),hAPP(c_Set_OCollect(U_8224),hAPP(hAPP(c_COMBS(U_8224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8224),c_fconj),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8225))),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8227)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8224,U_8223),hAPP(hAPP(c_COMBC(U_8224,U_8223,U_8223),hAPP(hAPP(c_COMBS(U_8224,U_8223,tc_fun(U_8223,U_8223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8223,tc_fun(U_8223,U_8223)),U_8224),c_If(U_8223)),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8227))),U_8226)),c_Groups_Ozero__class_Ozero(U_8223))),U_8225)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225))
      | ~ class_Groups_Ocomm__monoid__add(U_8223) ),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

cnf(f_1906_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8224,U_8223),U_8226),hAPP(c_Set_OCollect(U_8224),hAPP(hAPP(c_COMBS(U_8224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8224),c_fconj),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8225))),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8227)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8224,U_8223),hAPP(hAPP(c_COMBC(U_8224,U_8223,U_8223),hAPP(hAPP(c_COMBS(U_8224,U_8223,tc_fun(U_8223,U_8223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8223,tc_fun(U_8223,U_8223)),U_8224),c_If(U_8223)),hAPP(hAPP(c_COMBC(U_8224,tc_fun(U_8224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8224)),U_8227))),U_8226)),c_Groups_Ozero__class_Ozero(U_8223))),U_8225)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225))
    | ~ class_Groups_Ocomm__monoid__add(U_8223) ),
    inference(clausify,[status(thm)],[f_1906_2]) ).

fof(f_1907_1,plain,
    ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).

fof(f_1907_2,plain,
    ! [U_8233,U_8232,U_8231,U_8230,U_8229,U_8228] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8229,U_8228),U_8231),U_8230) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8232,U_8228),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),U_8228,U_8232),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8229,U_8228),U_8231)),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool),U_8232),c_Set_OCollect(U_8229)),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool),U_8232),hAPP(c_COMBS(U_8229,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8229),c_fconj),hAPP(hAPP(c_COMBC(U_8229,tc_fun(U_8229,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8229)),U_8230)))),hAPP(c_COMBC(U_8229,U_8232,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8232,tc_fun(U_8232,tc_HOL_Obool),U_8229),c_fequal),U_8233)))))),hAPP(c_Set_Oimage(U_8229,U_8232,U_8233),U_8230))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8229),U_8230))
      | ~ class_Groups_Ocomm__monoid__add(U_8228) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

cnf(f_1907_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8229,U_8228),U_8231),U_8230) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8232,U_8228),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),U_8228,U_8232),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8229,U_8228),U_8231)),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool),U_8232),c_Set_OCollect(U_8229)),hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool),U_8232),hAPP(c_COMBS(U_8229,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8229),c_fconj),hAPP(hAPP(c_COMBC(U_8229,tc_fun(U_8229,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8229)),U_8230)))),hAPP(c_COMBC(U_8229,U_8232,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8232,tc_fun(U_8232,tc_HOL_Obool),U_8229),c_fequal),U_8233)))))),hAPP(c_Set_Oimage(U_8229,U_8232,U_8233),U_8230))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8229),U_8230))
    | ~ class_Groups_Ocomm__monoid__add(U_8228) ),
    inference(clausify,[status(thm)],[f_1907_2]) ).

fof(f_1908_1,plain,
    ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))),
    inference(fof_nnf,[status(thm)],[fact_dom__if]) ).

fof(f_1908_2,plain,
    ! [U_8238,U_8237,U_8236,U_8235,U_8234] : c_Map_Odom(U_8234,U_8235,hAPP(hAPP(c_COMBS(U_8234,tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235)),hAPP(hAPP(c_COMBS(U_8234,tc_Option_Ooption(U_8235),tc_fun(tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_8235),tc_fun(tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235))),U_8234),c_If(tc_Option_Ooption(U_8235))),U_8236)),U_8237)),U_8238)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8234,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8234,tc_HOL_Obool)),c_Map_Odom(U_8234,U_8235,U_8237)),hAPP(c_Set_OCollect(U_8234),U_8236))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8234,tc_HOL_Obool)),c_Map_Odom(U_8234,U_8235,U_8238)),hAPP(c_Set_OCollect(U_8234),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8234),c_fNot),U_8236)))),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

cnf(f_1908_3,plain,
    c_Map_Odom(U_8234,U_8235,hAPP(hAPP(c_COMBS(U_8234,tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235)),hAPP(hAPP(c_COMBS(U_8234,tc_Option_Ooption(U_8235),tc_fun(tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_8235),tc_fun(tc_Option_Ooption(U_8235),tc_Option_Ooption(U_8235))),U_8234),c_If(tc_Option_Ooption(U_8235))),U_8236)),U_8237)),U_8238)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8234,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8234,tc_HOL_Obool)),c_Map_Odom(U_8234,U_8235,U_8237)),hAPP(c_Set_OCollect(U_8234),U_8236))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8234,tc_HOL_Obool)),c_Map_Odom(U_8234,U_8235,U_8238)),hAPP(c_Set_OCollect(U_8234),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8234),c_fNot),U_8236)))),
    inference(clausify,[status(thm)],[f_1908_2]) ).

fof(f_1909_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))),
    inference(fof_nnf,[status(thm)],[fact_dom__override__on]) ).

fof(f_1909_2,plain,
    ! [U_8243,U_8242,U_8241,U_8240,U_8239] : c_Map_Odom(U_8239,U_8240,c_Fun_Ooverride__on(U_8239,tc_Option_Ooption(U_8240),U_8241,U_8242,U_8243)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8239,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8239,tc_HOL_Obool)),c_Map_Odom(U_8239,U_8240,U_8241)),hAPP(c_Set_OCollect(U_8239),hAPP(hAPP(c_COMBC(U_8239,tc_fun(U_8239,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8239)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8239,tc_HOL_Obool)),U_8243),c_Map_Odom(U_8239,U_8240,U_8242)))))),hAPP(c_Set_OCollect(U_8239),hAPP(hAPP(c_COMBC(U_8239,tc_fun(U_8239,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8239)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8239,tc_HOL_Obool)),U_8243),c_Map_Odom(U_8239,U_8240,U_8242))))),
    inference(variable_rename,[status(thm)],[f_1909_1]) ).

cnf(f_1909_3,plain,
    c_Map_Odom(U_8239,U_8240,c_Fun_Ooverride__on(U_8239,tc_Option_Ooption(U_8240),U_8241,U_8242,U_8243)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8239,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8239,tc_HOL_Obool)),c_Map_Odom(U_8239,U_8240,U_8241)),hAPP(c_Set_OCollect(U_8239),hAPP(hAPP(c_COMBC(U_8239,tc_fun(U_8239,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8239)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8239,tc_HOL_Obool)),U_8243),c_Map_Odom(U_8239,U_8240,U_8242)))))),hAPP(c_Set_OCollect(U_8239),hAPP(hAPP(c_COMBC(U_8239,tc_fun(U_8239,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8239)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8239,tc_HOL_Obool)),U_8243),c_Map_Odom(U_8239,U_8240,U_8242))))),
    inference(clausify,[status(thm)],[f_1909_2]) ).

fof(f_1910_1,plain,
    ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_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_b),V_T_2))
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).

fof(f_1910_2,plain,
    ! [U_8250,U_8249,U_8248,U_8247,U_8246,U_8245] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_Nat_Onat,U_8245),c_Finite__Set_Ocard(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),c_Set_OCollect(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),hAPP(c_COMBS(U_8247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8247),c_fconj),hAPP(hAPP(c_COMBC(U_8247,tc_fun(U_8247,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8247)),U_8248)))),U_8249)))),U_8246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8250),hAPP(c_Finite__Set_Ocard(U_8247),U_8248))
      | ? [U_8244] :
          ( hAPP(c_Finite__Set_Ocard(U_8245),hAPP(c_Set_OCollect(U_8245),hAPP(hAPP(c_COMBS(U_8245,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8245),c_fconj),hAPP(hAPP(c_COMBC(U_8245,tc_fun(U_8245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8245)),U_8246))),hAPP(hAPP(c_COMBC(U_8245,U_8247,tc_HOL_Obool),U_8249),U_8244)))) != U_8250
          & hBOOL(hAPP(hAPP(c_member(U_8247),U_8244),U_8248)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8245),U_8246)) ),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

fof(f_1910_3,plain,
    ! [U_8250,U_8249,U_8248,U_8247,U_8246,U_8245] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_Nat_Onat,U_8245),c_Finite__Set_Ocard(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),c_Set_OCollect(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),hAPP(c_COMBS(U_8247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8247),c_fconj),hAPP(hAPP(c_COMBC(U_8247,tc_fun(U_8247,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8247)),U_8248)))),U_8249)))),U_8246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8250),hAPP(c_Finite__Set_Ocard(U_8247),U_8248))
      | ( hAPP(c_Finite__Set_Ocard(U_8245),hAPP(c_Set_OCollect(U_8245),hAPP(hAPP(c_COMBS(U_8245,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8245),c_fconj),hAPP(hAPP(c_COMBC(U_8245,tc_fun(U_8245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8245)),U_8246))),hAPP(hAPP(c_COMBC(U_8245,U_8247,tc_HOL_Obool),U_8249),sK209(U_8250,U_8249,U_8248,U_8247,U_8246,U_8245))))) != U_8250
        & hBOOL(hAPP(hAPP(c_member(U_8247),sK209(U_8250,U_8249,U_8248,U_8247,U_8246,U_8245)),U_8248)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8245),U_8246)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_8244,sK209(U_8250,U_8249,U_8248,U_8247,U_8246,U_8245))],[f_1910_2]) ).

cnf(f_1910_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8247),sK209(U_8250,U_8249,U_8248,U_8247,U_8246,U_8245)),U_8248))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_Nat_Onat,U_8245),c_Finite__Set_Ocard(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),c_Set_OCollect(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),hAPP(c_COMBS(U_8247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8247),c_fconj),hAPP(hAPP(c_COMBC(U_8247,tc_fun(U_8247,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8247)),U_8248)))),U_8249)))),U_8246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8250),hAPP(c_Finite__Set_Ocard(U_8247),U_8248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8245),U_8246)) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

cnf(f_1910_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_8245),hAPP(c_Set_OCollect(U_8245),hAPP(hAPP(c_COMBS(U_8245,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8245),c_fconj),hAPP(hAPP(c_COMBC(U_8245,tc_fun(U_8245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8245)),U_8246))),hAPP(hAPP(c_COMBC(U_8245,U_8247,tc_HOL_Obool),U_8249),sK209(U_8250,U_8249,U_8248,U_8247,U_8246,U_8245))))) != U_8250
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_Nat_Onat,U_8245),c_Finite__Set_Ocard(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),c_Set_OCollect(U_8247)),hAPP(hAPP(c_COMBB(tc_fun(U_8247,tc_HOL_Obool),tc_fun(U_8247,tc_HOL_Obool),U_8245),hAPP(c_COMBS(U_8247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8247),c_fconj),hAPP(hAPP(c_COMBC(U_8247,tc_fun(U_8247,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8247)),U_8248)))),U_8249)))),U_8246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8250),hAPP(c_Finite__Set_Ocard(U_8247),U_8248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8245),U_8246)) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

fof(f_1911_1,plain,
    ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2)
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) != hAPP(V_k_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).

fof(f_1911_2,plain,
    ! [U_8257,U_8256,U_8255,U_8254,U_8253,U_8252] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8252,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_Nat_Onat,U_8252),c_Finite__Set_Ocard(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),c_Set_OCollect(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),hAPP(c_COMBS(U_8254,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8254),c_fconj),hAPP(hAPP(c_COMBC(U_8254,tc_fun(U_8254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8254)),U_8255)))),U_8256)))),U_8253) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8254,tc_Nat_Onat),U_8257),U_8255)
      | ? [U_8251] :
          ( hAPP(c_Finite__Set_Ocard(U_8252),hAPP(c_Set_OCollect(U_8252),hAPP(hAPP(c_COMBS(U_8252,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8252),c_fconj),hAPP(hAPP(c_COMBC(U_8252,tc_fun(U_8252,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8252)),U_8253))),hAPP(hAPP(c_COMBC(U_8252,U_8254,tc_HOL_Obool),U_8256),U_8251)))) != hAPP(U_8257,U_8251)
          & hBOOL(hAPP(hAPP(c_member(U_8254),U_8251),U_8255)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8252),U_8253)) ),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ! [U_8257,U_8256,U_8255,U_8254,U_8253,U_8252] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8252,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_Nat_Onat,U_8252),c_Finite__Set_Ocard(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),c_Set_OCollect(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),hAPP(c_COMBS(U_8254,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8254),c_fconj),hAPP(hAPP(c_COMBC(U_8254,tc_fun(U_8254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8254)),U_8255)))),U_8256)))),U_8253) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8254,tc_Nat_Onat),U_8257),U_8255)
      | ( hAPP(c_Finite__Set_Ocard(U_8252),hAPP(c_Set_OCollect(U_8252),hAPP(hAPP(c_COMBS(U_8252,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8252),c_fconj),hAPP(hAPP(c_COMBC(U_8252,tc_fun(U_8252,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8252)),U_8253))),hAPP(hAPP(c_COMBC(U_8252,U_8254,tc_HOL_Obool),U_8256),sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252))))) != hAPP(U_8257,sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252))
        & hBOOL(hAPP(hAPP(c_member(U_8254),sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252)),U_8255)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8252),U_8253)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_8251,sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252))],[f_1911_2]) ).

cnf(f_1911_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8254),sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252)),U_8255))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8252,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_Nat_Onat,U_8252),c_Finite__Set_Ocard(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),c_Set_OCollect(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),hAPP(c_COMBS(U_8254,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8254),c_fconj),hAPP(hAPP(c_COMBC(U_8254,tc_fun(U_8254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8254)),U_8255)))),U_8256)))),U_8253) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8254,tc_Nat_Onat),U_8257),U_8255)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8252),U_8253)) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

cnf(f_1911_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_8252),hAPP(c_Set_OCollect(U_8252),hAPP(hAPP(c_COMBS(U_8252,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8252),c_fconj),hAPP(hAPP(c_COMBC(U_8252,tc_fun(U_8252,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8252)),U_8253))),hAPP(hAPP(c_COMBC(U_8252,U_8254,tc_HOL_Obool),U_8256),sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252))))) != hAPP(U_8257,sK210(U_8257,U_8256,U_8255,U_8254,U_8253,U_8252))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8252,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_Nat_Onat,U_8252),c_Finite__Set_Ocard(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),c_Set_OCollect(U_8254)),hAPP(hAPP(c_COMBB(tc_fun(U_8254,tc_HOL_Obool),tc_fun(U_8254,tc_HOL_Obool),U_8252),hAPP(c_COMBS(U_8254,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8254),c_fconj),hAPP(hAPP(c_COMBC(U_8254,tc_fun(U_8254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8254)),U_8255)))),U_8256)))),U_8253) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8254,tc_Nat_Onat),U_8257),U_8255)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8252),U_8253)) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

fof(f_1912_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).

fof(f_1912_2,plain,
    ! [U_8260,U_8259,U_8258] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8258),U_8260),c_Big__Operators_Olattice__class_OSup__fin(U_8258,U_8259)) = c_Big__Operators_Olattice__class_OSup__fin(U_8258,hAPP(c_Set_OCollect(U_8258),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_HOL_Obool,U_8258),c_HOL_OEx(U_8258)),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_HOL_Obool)),U_8258),c_COMBS(U_8258,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8258),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8258),c_fconj)),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,U_8258),tc_fun(U_8258,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_fun(tc_fun(U_8258,U_8258),tc_fun(U_8258,tc_HOL_Obool)),U_8258),c_COMBB(U_8258,tc_HOL_Obool,U_8258)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8258),U_8260))))),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8258)),U_8259)))))
      | U_8259 = c_Orderings_Obot__class_Obot(tc_fun(U_8258,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8258),U_8259))
      | ~ class_Lattices_Odistrib__lattice(U_8258) ),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

cnf(f_1912_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8258),U_8260),c_Big__Operators_Olattice__class_OSup__fin(U_8258,U_8259)) = c_Big__Operators_Olattice__class_OSup__fin(U_8258,hAPP(c_Set_OCollect(U_8258),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_HOL_Obool,U_8258),c_HOL_OEx(U_8258)),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_HOL_Obool)),U_8258),c_COMBS(U_8258,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_fun(U_8258,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8258),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8258),c_fconj)),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,U_8258),tc_fun(U_8258,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8258,tc_HOL_Obool),tc_fun(tc_fun(U_8258,U_8258),tc_fun(U_8258,tc_HOL_Obool)),U_8258),c_COMBB(U_8258,tc_HOL_Obool,U_8258)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8258),U_8260))))),hAPP(hAPP(c_COMBC(U_8258,tc_fun(U_8258,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8258)),U_8259)))))
    | U_8259 = c_Orderings_Obot__class_Obot(tc_fun(U_8258,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8258),U_8259))
    | ~ class_Lattices_Odistrib__lattice(U_8258) ),
    inference(clausify,[status(thm)],[f_1912_2]) ).

fof(f_1913_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).

fof(f_1913_2,plain,
    ! [U_8262,U_8261] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8261,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_8261,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_8261,tc_HOL_Obool),tc_fun(U_8261,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_8261,tc_HOL_Obool))),U_8262))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8261),U_8262)) ),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

cnf(f_1913_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8261,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_8261,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_8261,tc_HOL_Obool),tc_fun(U_8261,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_8261,tc_HOL_Obool))),U_8262))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8261),U_8262)) ),
    inference(clausify,[status(thm)],[f_1913_2]) ).

fof(f_1914_1,plain,
    ! [V_Q_2,T_b,V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2)))))
          | ? [B_y] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y))))
              & hBOOL(hAPP(V_P_2,B_y)) ) )
        & ( ! [B_y] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y))))
              | ~ hBOOL(hAPP(V_P_2,B_y)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).

fof(f_1914_2,plain,
    ! [U_8268,U_8267,U_8266,U_8265] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268)))))
          | ? [U_8264] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),U_8264))))
              & hBOOL(hAPP(U_8266,U_8264)) ) )
        & ( ! [U_8263] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),U_8263))))
              | ~ hBOOL(hAPP(U_8266,U_8263)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),hAPP(c_Set_OCollect(U_8265),U_8266))) ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

fof(f_1914_3,plain,
    ! [U_8268,U_8267,U_8266,U_8265] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),sK211(U_8268,U_8267,U_8266,U_8265)))))
            & hBOOL(hAPP(U_8266,sK211(U_8268,U_8267,U_8266,U_8265))) ) )
        & ( ! [U_8263] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),U_8263))))
              | ~ hBOOL(hAPP(U_8266,U_8263)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),hAPP(c_Set_OCollect(U_8265),U_8266))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_8264,sK211(U_8268,U_8267,U_8266,U_8265))],[f_1914_2]) ).

cnf(f_1914_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),U_8263))))
    | ~ hBOOL(hAPP(U_8266,U_8263))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),hAPP(c_Set_OCollect(U_8265),U_8266))) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_5,plain,
    ( hBOOL(hAPP(U_8266,sK211(U_8268,U_8267,U_8266,U_8265)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),hAPP(c_Set_OCollect(U_8265),U_8266))) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBC(U_8267,U_8265,tc_HOL_Obool),U_8268),sK211(U_8268,U_8267,U_8266,U_8265)))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8267),hAPP(c_Set_OCollect(U_8267),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_HOL_Obool,U_8267),c_HOL_OEx(U_8265)),hAPP(hAPP(c_COMBB(tc_fun(U_8265,tc_HOL_Obool),tc_fun(U_8265,tc_HOL_Obool),U_8267),hAPP(c_COMBS(U_8265,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8265),c_fconj),U_8266))),U_8268)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),hAPP(c_Set_OCollect(U_8265),U_8266))) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

fof(f_1915_1,plain,
    ! [V_f_2,T_b,V_P_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,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_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).

fof(f_1915_2,plain,
    ! [U_8272,U_8271,U_8270,U_8269] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),hAPP(c_Set_OCollect(U_8271),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_HOL_Obool),tc_HOL_Obool,U_8271),c_HOL_OEx(U_8269)),hAPP(hAPP(c_COMBC(U_8271,tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_HOL_Obool)),U_8271),c_COMBS(U_8269,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8271),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8269),c_fconj)),hAPP(hAPP(c_COMBC(U_8271,tc_fun(U_8269,U_8271),tc_fun(U_8269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8271,tc_HOL_Obool),tc_fun(tc_fun(U_8269,U_8271),tc_fun(U_8269,tc_HOL_Obool)),U_8271),c_COMBB(U_8271,tc_HOL_Obool,U_8269)),c_fequal)),U_8272)))),U_8270)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8269),hAPP(c_Set_OCollect(U_8269),U_8270))) ),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

cnf(f_1915_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),hAPP(c_Set_OCollect(U_8271),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_HOL_Obool),tc_HOL_Obool,U_8271),c_HOL_OEx(U_8269)),hAPP(hAPP(c_COMBC(U_8271,tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_HOL_Obool)),U_8271),c_COMBS(U_8269,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8269,tc_HOL_Obool),tc_fun(U_8269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8271),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8269),c_fconj)),hAPP(hAPP(c_COMBC(U_8271,tc_fun(U_8269,U_8271),tc_fun(U_8269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8271,tc_HOL_Obool),tc_fun(tc_fun(U_8269,U_8271),tc_fun(U_8269,tc_HOL_Obool)),U_8271),c_COMBB(U_8271,tc_HOL_Obool,U_8269)),c_fequal)),U_8272)))),U_8270)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8269),hAPP(c_Set_OCollect(U_8269),U_8270))) ),
    inference(clausify,[status(thm)],[f_1915_2]) ).

fof(f_1916_1,plain,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( hAPP(c_Fun_Ooverride__on(T_a,T_b,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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__in]) ).

fof(f_1916_2,plain,
    ! [U_8278,U_8277,U_8276,U_8275,U_8274,U_8273] :
      ( hAPP(c_Fun_Ooverride__on(U_8273,U_8276,U_8277,U_8278,U_8275),U_8274) = hAPP(U_8278,U_8274)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8273),U_8274),U_8275)) ),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

cnf(f_1916_3,plain,
    ( hAPP(c_Fun_Ooverride__on(U_8273,U_8276,U_8277,U_8278,U_8275),U_8274) = hAPP(U_8278,U_8274)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8273),U_8274),U_8275)) ),
    inference(clausify,[status(thm)],[f_1916_2]) ).

fof(f_1917_1,plain,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( hAPP(c_Fun_Ooverride__on(T_a,T_b,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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__notin]) ).

fof(f_1917_2,plain,
    ! [U_8284,U_8283,U_8282,U_8281,U_8280,U_8279] :
      ( hAPP(c_Fun_Ooverride__on(U_8279,U_8282,U_8283,U_8284,U_8281),U_8280) = hAPP(U_8283,U_8280)
      | hBOOL(hAPP(hAPP(c_member(U_8279),U_8280),U_8281)) ),
    inference(variable_rename,[status(thm)],[f_1917_1]) ).

cnf(f_1917_3,plain,
    ( hAPP(c_Fun_Ooverride__on(U_8279,U_8282,U_8283,U_8284,U_8281),U_8280) = hAPP(U_8283,U_8280)
    | hBOOL(hAPP(hAPP(c_member(U_8279),U_8280),U_8281)) ),
    inference(clausify,[status(thm)],[f_1917_2]) ).

fof(f_1918_1,plain,
    ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_override__on__emptyset]) ).

fof(f_1918_2,plain,
    ! [U_8288,U_8287,U_8286,U_8285] : c_Fun_Ooverride__on(U_8285,U_8286,U_8287,U_8288,c_Orderings_Obot__class_Obot(tc_fun(U_8285,tc_HOL_Obool))) = U_8287,
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

cnf(f_1918_3,plain,
    c_Fun_Ooverride__on(U_8285,U_8286,U_8287,U_8288,c_Orderings_Obot__class_Obot(tc_fun(U_8285,tc_HOL_Obool))) = U_8287,
    inference(clausify,[status(thm)],[f_1918_2]) ).

fof(f_1919_1,plain,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(f_1919_2,plain,
    ! [U_8289] : 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_8289))),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

cnf(f_1919_3,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_8289))),
    inference(clausify,[status(thm)],[f_1919_2]) ).

fof(f_1920_1,plain,
    ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
      ( ( hAPP(c_Fun_Ooverride__on(T_a,T_b,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_a),V_a_2),V_A_2)) )
      & ( hAPP(c_Fun_Ooverride__on(T_a,T_b,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_a),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__def]) ).

fof(f_1920_2,plain,
    ! [U_8295,U_8294,U_8293,U_8292,U_8291,U_8290] :
      ( ( hAPP(c_Fun_Ooverride__on(U_8290,U_8293,U_8294,U_8295,U_8292),U_8291) = hAPP(U_8294,U_8291)
        | hBOOL(hAPP(hAPP(c_member(U_8290),U_8291),U_8292)) )
      & ( hAPP(c_Fun_Ooverride__on(U_8290,U_8293,U_8294,U_8295,U_8292),U_8291) = hAPP(U_8295,U_8291)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8291),U_8292)) ) ),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

fof(f_1920_3,plain,
    ( ! [U_8307,U_8305,U_8303,U_8301,U_8299,U_8297] :
        ( hAPP(c_Fun_Ooverride__on(U_8297,U_8303,U_8305,U_8307,U_8301),U_8299) = hAPP(U_8305,U_8299)
        | hBOOL(hAPP(hAPP(c_member(U_8297),U_8299),U_8301)) )
    & ! [U_8306,U_8304,U_8302,U_8300,U_8298,U_8296] :
        ( hAPP(c_Fun_Ooverride__on(U_8296,U_8302,U_8304,U_8306,U_8300),U_8298) = hAPP(U_8306,U_8298)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8300)) ) ),
    inference(miniscope,[status(thm)],[f_1920_2]) ).

cnf(f_1920_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_8296,U_8302,U_8304,U_8306,U_8300),U_8298) = hAPP(U_8306,U_8298)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8296),U_8298),U_8300)) ),
    inference(clausify,[status(thm)],[f_1920_3]) ).

cnf(f_1920_5,plain,
    ( hAPP(c_Fun_Ooverride__on(U_8297,U_8303,U_8305,U_8307,U_8301),U_8299) = hAPP(U_8305,U_8299)
    | hBOOL(hAPP(hAPP(c_member(U_8297),U_8299),U_8301)) ),
    inference(clausify,[status(thm)],[f_1920_3]) ).

fof(f_1921_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(f_1921_2,plain,
    ! [U_8308] : 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_8308)) = 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_8308),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

cnf(f_1921_3,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_8308)) = 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_8308),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_1921_2]) ).

fof(f_1922_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(f_1922_2,plain,
    ! [U_8309] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_8309) = 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_8309),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

cnf(f_1922_3,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_8309) = 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_8309),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1922_2]) ).

fof(f_1923_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).

fof(f_1923_2,plain,
    ! [U_8312,U_8311,U_8310] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8310),c_Big__Operators_Olattice__class_OInf__fin(U_8310,U_8311)),c_Big__Operators_Olattice__class_OInf__fin(U_8310,U_8312)) = c_Big__Operators_Olattice__class_OInf__fin(U_8310,hAPP(c_Set_OCollect(U_8310),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool,U_8310),c_HOL_OEx(U_8310)),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_HOL_Obool),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool,U_8310),c_HOL_OEx(U_8310))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),tc_fun(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),U_8310),c_COMBS(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_8310,tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBS(U_8310,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8310),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8310),c_fconj))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_fun(U_8310,U_8310)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool)),tc_fun(tc_fun(U_8310,tc_fun(U_8310,U_8310)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),U_8310),c_COMBB(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool),U_8310)),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_fun(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBB(U_8310,tc_HOL_Obool,U_8310)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_8310)))))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8310)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8310),c_fconj),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8310)),U_8311)))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8310)),U_8312)))))))
      | U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8310,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8310),U_8312))
      | U_8311 = c_Orderings_Obot__class_Obot(tc_fun(U_8310,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8310),U_8311))
      | ~ class_Lattices_Odistrib__lattice(U_8310) ),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

cnf(f_1923_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8310),c_Big__Operators_Olattice__class_OInf__fin(U_8310,U_8311)),c_Big__Operators_Olattice__class_OInf__fin(U_8310,U_8312)) = c_Big__Operators_Olattice__class_OInf__fin(U_8310,hAPP(c_Set_OCollect(U_8310),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool,U_8310),c_HOL_OEx(U_8310)),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_HOL_Obool),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool,U_8310),c_HOL_OEx(U_8310))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),tc_fun(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),U_8310),c_COMBS(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_8310,tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool))),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBS(U_8310,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool)),tc_fun(U_8310,tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_8310),hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8310),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8310),c_fconj))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_fun(U_8310,U_8310)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool)),tc_fun(tc_fun(U_8310,tc_fun(U_8310,U_8310)),tc_fun(U_8310,tc_fun(U_8310,tc_HOL_Obool))),U_8310),c_COMBB(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool),U_8310)),hAPP(hAPP(c_COMBB(tc_fun(U_8310,tc_HOL_Obool),tc_fun(tc_fun(U_8310,U_8310),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBB(U_8310,tc_HOL_Obool,U_8310)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_8310)))))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8310,tc_HOL_Obool),tc_fun(U_8310,tc_HOL_Obool)),U_8310),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8310)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8310),c_fconj),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8310)),U_8311)))),hAPP(hAPP(c_COMBC(U_8310,tc_fun(U_8310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8310)),U_8312)))))))
    | U_8312 = c_Orderings_Obot__class_Obot(tc_fun(U_8310,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8310),U_8312))
    | U_8311 = c_Orderings_Obot__class_Obot(tc_fun(U_8310,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8310),U_8311))
    | ~ class_Lattices_Odistrib__lattice(U_8310) ),
    inference(clausify,[status(thm)],[f_1923_2]) ).

fof(f_1924_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).

fof(f_1924_2,plain,
    ! [U_8315,U_8314,U_8313] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8313),U_8315),c_Big__Operators_Olattice__class_OInf__fin(U_8313,U_8314)) = c_Big__Operators_Olattice__class_OInf__fin(U_8313,hAPP(c_Set_OCollect(U_8313),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_HOL_Obool,U_8313),c_HOL_OEx(U_8313)),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_HOL_Obool)),U_8313),c_COMBS(U_8313,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8313),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8313),c_fconj)),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,U_8313),tc_fun(U_8313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_fun(tc_fun(U_8313,U_8313),tc_fun(U_8313,tc_HOL_Obool)),U_8313),c_COMBB(U_8313,tc_HOL_Obool,U_8313)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8313),U_8315))))),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8313)),U_8314)))))
      | U_8314 = c_Orderings_Obot__class_Obot(tc_fun(U_8313,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8313),U_8314))
      | ~ class_Lattices_Odistrib__lattice(U_8313) ),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

cnf(f_1924_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8313),U_8315),c_Big__Operators_Olattice__class_OInf__fin(U_8313,U_8314)) = c_Big__Operators_Olattice__class_OInf__fin(U_8313,hAPP(c_Set_OCollect(U_8313),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_HOL_Obool,U_8313),c_HOL_OEx(U_8313)),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_HOL_Obool)),U_8313),c_COMBS(U_8313,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_fun(U_8313,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8313),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8313),c_fconj)),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,U_8313),tc_fun(U_8313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8313,tc_HOL_Obool),tc_fun(tc_fun(U_8313,U_8313),tc_fun(U_8313,tc_HOL_Obool)),U_8313),c_COMBB(U_8313,tc_HOL_Obool,U_8313)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8313),U_8315))))),hAPP(hAPP(c_COMBC(U_8313,tc_fun(U_8313,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8313)),U_8314)))))
    | U_8314 = c_Orderings_Obot__class_Obot(tc_fun(U_8313,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8313),U_8314))
    | ~ class_Lattices_Odistrib__lattice(U_8313) ),
    inference(clausify,[status(thm)],[f_1924_2]) ).

fof(f_1925_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).

fof(f_1925_2,plain,
    ! [U_8318,U_8317,U_8316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8316),c_Big__Operators_Olattice__class_OSup__fin(U_8316,U_8317)),c_Big__Operators_Olattice__class_OSup__fin(U_8316,U_8318)) = c_Big__Operators_Olattice__class_OSup__fin(U_8316,hAPP(c_Set_OCollect(U_8316),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool,U_8316),c_HOL_OEx(U_8316)),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_HOL_Obool),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool,U_8316),c_HOL_OEx(U_8316))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),tc_fun(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),U_8316),c_COMBS(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_8316,tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBS(U_8316,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8316),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8316),c_fconj))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_fun(U_8316,U_8316)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool)),tc_fun(tc_fun(U_8316,tc_fun(U_8316,U_8316)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),U_8316),c_COMBB(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool),U_8316)),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_fun(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBB(U_8316,tc_HOL_Obool,U_8316)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_8316)))))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8316)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8316),c_fconj),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8317)))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8318)))))))
      | U_8318 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8318))
      | U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
      | ~ class_Lattices_Odistrib__lattice(U_8316) ),
    inference(variable_rename,[status(thm)],[f_1925_1]) ).

cnf(f_1925_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8316),c_Big__Operators_Olattice__class_OSup__fin(U_8316,U_8317)),c_Big__Operators_Olattice__class_OSup__fin(U_8316,U_8318)) = c_Big__Operators_Olattice__class_OSup__fin(U_8316,hAPP(c_Set_OCollect(U_8316),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool,U_8316),c_HOL_OEx(U_8316)),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_HOL_Obool),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool,U_8316),c_HOL_OEx(U_8316))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),tc_fun(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),U_8316),c_COMBS(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_8316,tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool))),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBS(U_8316,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool)),tc_fun(U_8316,tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_8316),hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8316),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8316),c_fconj))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_fun(U_8316,U_8316)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool)),tc_fun(tc_fun(U_8316,tc_fun(U_8316,U_8316)),tc_fun(U_8316,tc_fun(U_8316,tc_HOL_Obool))),U_8316),c_COMBB(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool),U_8316)),hAPP(hAPP(c_COMBB(tc_fun(U_8316,tc_HOL_Obool),tc_fun(tc_fun(U_8316,U_8316),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBB(U_8316,tc_HOL_Obool,U_8316)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_8316)))))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8316,tc_HOL_Obool),tc_fun(U_8316,tc_HOL_Obool)),U_8316),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8316)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8316),c_fconj),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8317)))),hAPP(hAPP(c_COMBC(U_8316,tc_fun(U_8316,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8316)),U_8318)))))))
    | U_8318 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8318))
    | U_8317 = c_Orderings_Obot__class_Obot(tc_fun(U_8316,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8316),U_8317))
    | ~ class_Lattices_Odistrib__lattice(U_8316) ),
    inference(clausify,[status(thm)],[f_1925_2]) ).

fof(f_1926_1,plain,
    ! [V_k_2,V_N_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).

fof(f_1926_2,plain,
    ! [U_8321,U_8320,U_8319] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8319),U_8321),c_Big__Operators_Olinorder__class_OMin(U_8319,U_8320)) = c_Big__Operators_Olinorder__class_OMin(U_8319,hAPP(c_Set_OCollect(U_8319),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_HOL_Obool,U_8319),c_HOL_OEx(U_8319)),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_HOL_Obool)),U_8319),c_COMBS(U_8319,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8319),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8319),c_fconj)),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,U_8319),tc_fun(U_8319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_fun(tc_fun(U_8319,U_8319),tc_fun(U_8319,tc_HOL_Obool)),U_8319),c_COMBB(U_8319,tc_HOL_Obool,U_8319)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_8319),U_8321))))),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8319)),U_8320)))))
      | U_8320 = c_Orderings_Obot__class_Obot(tc_fun(U_8319,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8319),U_8320))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_8319) ),
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

cnf(f_1926_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8319),U_8321),c_Big__Operators_Olinorder__class_OMin(U_8319,U_8320)) = c_Big__Operators_Olinorder__class_OMin(U_8319,hAPP(c_Set_OCollect(U_8319),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_HOL_Obool,U_8319),c_HOL_OEx(U_8319)),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_HOL_Obool)),U_8319),c_COMBS(U_8319,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_fun(U_8319,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8319),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8319),c_fconj)),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,U_8319),tc_fun(U_8319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8319,tc_HOL_Obool),tc_fun(tc_fun(U_8319,U_8319),tc_fun(U_8319,tc_HOL_Obool)),U_8319),c_COMBB(U_8319,tc_HOL_Obool,U_8319)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_8319),U_8321))))),hAPP(hAPP(c_COMBC(U_8319,tc_fun(U_8319,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8319)),U_8320)))))
    | U_8320 = c_Orderings_Obot__class_Obot(tc_fun(U_8319,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8319),U_8320))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_8319) ),
    inference(clausify,[status(thm)],[f_1926_2]) ).

fof(f_1927_1,plain,
    ! [V_k_2,V_N_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).

fof(f_1927_2,plain,
    ! [U_8324,U_8323,U_8322] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8322),U_8324),c_Big__Operators_Olinorder__class_OMax(U_8322,U_8323)) = c_Big__Operators_Olinorder__class_OMax(U_8322,hAPP(c_Set_OCollect(U_8322),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_HOL_Obool,U_8322),c_HOL_OEx(U_8322)),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_HOL_Obool)),U_8322),c_COMBS(U_8322,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8322),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8322),c_fconj)),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,U_8322),tc_fun(U_8322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_fun(tc_fun(U_8322,U_8322),tc_fun(U_8322,tc_HOL_Obool)),U_8322),c_COMBB(U_8322,tc_HOL_Obool,U_8322)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_8322),U_8324))))),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8322)),U_8323)))))
      | U_8323 = c_Orderings_Obot__class_Obot(tc_fun(U_8322,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8322),U_8323))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_8322) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

cnf(f_1927_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8322),U_8324),c_Big__Operators_Olinorder__class_OMax(U_8322,U_8323)) = c_Big__Operators_Olinorder__class_OMax(U_8322,hAPP(c_Set_OCollect(U_8322),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_HOL_Obool,U_8322),c_HOL_OEx(U_8322)),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_HOL_Obool)),U_8322),c_COMBS(U_8322,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_fun(U_8322,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8322),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8322),c_fconj)),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,U_8322),tc_fun(U_8322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8322,tc_HOL_Obool),tc_fun(tc_fun(U_8322,U_8322),tc_fun(U_8322,tc_HOL_Obool)),U_8322),c_COMBB(U_8322,tc_HOL_Obool,U_8322)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_8322),U_8324))))),hAPP(hAPP(c_COMBC(U_8322,tc_fun(U_8322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8322)),U_8323)))))
    | U_8323 = c_Orderings_Obot__class_Obot(tc_fun(U_8322,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8322),U_8323))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_8322) ),
    inference(clausify,[status(thm)],[f_1927_2]) ).

fof(f_1928_1,plain,
    ! [V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | ! [B_n,B_f] : V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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_a,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_a),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image]) ).

fof(f_1928_2,plain,
    ! [U_8330,U_8329] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330))
        | ! [U_8328,U_8327] : U_8330 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8329,U_8327),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_8328))) )
      & ( ? [U_8326,U_8325] : U_8330 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_8329,U_8325),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_8326)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330)) ) ),
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

fof(f_1928_3,plain,
    ( ! [U_8334,U_8332] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8332),U_8334))
        | ! [U_8328,U_8327] : U_8334 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8332,U_8327),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_8328))) )
    & ! [U_8333,U_8331] :
        ( ? [U_8326,U_8325] : U_8333 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_8331,U_8325),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_8326)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8333)) ) ),
    inference(miniscope,[status(thm)],[f_1928_2]) ).

fof(f_1928_4,plain,
    ( ! [U_8334,U_8332] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8332),U_8334))
        | ! [U_8328,U_8327] : U_8334 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8332,U_8327),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_8328))) )
    & ! [U_8333,U_8331] :
        ( ? [U_8325] : U_8333 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_8331,U_8325),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)),sK212(U_8333,U_8331))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8333)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_8326,sK212(U_8333,U_8331))],[f_1928_3]) ).

fof(f_1928_5,plain,
    ( ! [U_8334,U_8332] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8332),U_8334))
        | ! [U_8328,U_8327] : U_8334 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8332,U_8327),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_8328))) )
    & ! [U_8333,U_8331] :
        ( U_8333 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_8331,sK213(U_8333,U_8331)),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)),sK212(U_8333,U_8331))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8333)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_8325,sK213(U_8333,U_8331))],[f_1928_4]) ).

cnf(f_1928_6,plain,
    ( U_8333 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_8331,sK213(U_8333,U_8331)),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)),sK212(U_8333,U_8331))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8331),U_8333)) ),
    inference(clausify,[status(thm)],[f_1928_5]) ).

cnf(f_1928_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8332),U_8334))
    | U_8334 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_8332,U_8327),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_8328))) ),
    inference(clausify,[status(thm)],[f_1928_5]) ).

fof(f_1929_1,plain,
    ! [V_f_2,T_b,V_A_2,T_a] :
      ( ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(f_1929_2,plain,
    ! [U_8339,U_8338,U_8337,U_8336] :
      ( ? [U_8335] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),hAPP(c_Set_OCollect(U_8336),hAPP(hAPP(c_COMBS(U_8336,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8336),c_fconj),hAPP(hAPP(c_COMBC(U_8336,tc_fun(U_8336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8336)),U_8337))),hAPP(hAPP(c_COMBC(U_8336,U_8338,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8338,tc_fun(U_8338,tc_HOL_Obool),U_8336),c_fequal),U_8339)),hAPP(U_8339,U_8335))))))
          & hBOOL(hAPP(hAPP(c_member(U_8336),U_8335),U_8337)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8338),hAPP(c_Set_Oimage(U_8336,U_8338,U_8339),U_8337)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),U_8337)) ),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

fof(f_1929_3,plain,
    ! [U_8339,U_8338,U_8337,U_8336] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),hAPP(c_Set_OCollect(U_8336),hAPP(hAPP(c_COMBS(U_8336,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8336),c_fconj),hAPP(hAPP(c_COMBC(U_8336,tc_fun(U_8336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8336)),U_8337))),hAPP(hAPP(c_COMBC(U_8336,U_8338,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8338,tc_fun(U_8338,tc_HOL_Obool),U_8336),c_fequal),U_8339)),hAPP(U_8339,sK214(U_8339,U_8338,U_8337,U_8336)))))))
        & hBOOL(hAPP(hAPP(c_member(U_8336),sK214(U_8339,U_8338,U_8337,U_8336)),U_8337)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8338),hAPP(c_Set_Oimage(U_8336,U_8338,U_8339),U_8337)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),U_8337)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_8335,sK214(U_8339,U_8338,U_8337,U_8336))],[f_1929_2]) ).

cnf(f_1929_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8336),sK214(U_8339,U_8338,U_8337,U_8336)),U_8337))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8338),hAPP(c_Set_Oimage(U_8336,U_8338,U_8339),U_8337)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),U_8337)) ),
    inference(clausify,[status(thm)],[f_1929_3]) ).

cnf(f_1929_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),hAPP(c_Set_OCollect(U_8336),hAPP(hAPP(c_COMBS(U_8336,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8336),c_fconj),hAPP(hAPP(c_COMBC(U_8336,tc_fun(U_8336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8336)),U_8337))),hAPP(hAPP(c_COMBC(U_8336,U_8338,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8338,tc_fun(U_8338,tc_HOL_Obool),U_8336),c_fequal),U_8339)),hAPP(U_8339,sK214(U_8339,U_8338,U_8337,U_8336)))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8338),hAPP(c_Set_Oimage(U_8336,U_8338,U_8339),U_8337)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8336),U_8337)) ),
    inference(clausify,[status(thm)],[f_1929_3]) ).

fof(f_1930_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_1930_2,plain,
    ! [U_8341,U_8340] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8341)),hAPP(c_Int_Onat,U_8340)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8341),U_8340)),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_8340)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8341)),hAPP(c_Int_Onat,U_8340)) = hAPP(c_Int_Onat,U_8341)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8340)) ) ),
    inference(variable_rename,[status(thm)],[f_1930_1]) ).

fof(f_1930_3,plain,
    ( ! [U_8345,U_8343] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8345)),hAPP(c_Int_Onat,U_8343)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8345),U_8343)),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_8343)) )
    & ! [U_8344,U_8342] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8344)),hAPP(c_Int_Onat,U_8342)) = hAPP(c_Int_Onat,U_8344)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8342)) ) ),
    inference(miniscope,[status(thm)],[f_1930_2]) ).

cnf(f_1930_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8344)),hAPP(c_Int_Onat,U_8342)) = hAPP(c_Int_Onat,U_8344)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8342)) ),
    inference(clausify,[status(thm)],[f_1930_3]) ).

cnf(f_1930_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8345)),hAPP(c_Int_Onat,U_8343)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8345),U_8343)),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_8343)) ),
    inference(clausify,[status(thm)],[f_1930_3]) ).

fof(f_1931_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]) ).

cnf(f_1931_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1931_1]) ).

fof(f_1932_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_1932_2,plain,
    ! [U_8346] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8346))),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

cnf(f_1932_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8346))),
    inference(clausify,[status(thm)],[f_1932_2]) ).

fof(f_1933_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]) ).

cnf(f_1933_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1933_1]) ).

fof(f_1934_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).

fof(f_1934_2,plain,
    ! [U_8348,U_8347] :
      ( c_Big__Operators_Olinorder__class_OMin(U_8347,hAPP(hAPP(c_Set_Oinsert(U_8347),U_8348),c_Orderings_Obot__class_Obot(tc_fun(U_8347,tc_HOL_Obool)))) = U_8348
      | ~ class_Orderings_Olinorder(U_8347) ),
    inference(variable_rename,[status(thm)],[f_1934_1]) ).

cnf(f_1934_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_8347,hAPP(hAPP(c_Set_Oinsert(U_8347),U_8348),c_Orderings_Obot__class_Obot(tc_fun(U_8347,tc_HOL_Obool)))) = U_8348
    | ~ class_Orderings_Olinorder(U_8347) ),
    inference(clausify,[status(thm)],[f_1934_2]) ).

fof(f_1935_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).

fof(f_1935_2,plain,
    ! [U_8350,U_8349] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8349,hAPP(hAPP(c_Set_Oinsert(U_8349),U_8350),c_Orderings_Obot__class_Obot(tc_fun(U_8349,tc_HOL_Obool)))) = U_8350
      | ~ class_Orderings_Olinorder(U_8349) ),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

cnf(f_1935_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8349,hAPP(hAPP(c_Set_Oinsert(U_8349),U_8350),c_Orderings_Obot__class_Obot(tc_fun(U_8349,tc_HOL_Obool)))) = U_8350
    | ~ class_Orderings_Olinorder(U_8349) ),
    inference(clausify,[status(thm)],[f_1935_2]) ).

fof(f_1936_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_1936_2,plain,
    ! [U_8351] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8351))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8351)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8351))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8351)) ) ),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

fof(f_1936_3,plain,
    ( ! [U_8353] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8353))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8353)) )
    & ! [U_8352] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8352))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8352)) ) ),
    inference(miniscope,[status(thm)],[f_1936_2]) ).

cnf(f_1936_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8352))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8352)) ),
    inference(clausify,[status(thm)],[f_1936_3]) ).

cnf(f_1936_5,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8353)) ),
    inference(clausify,[status(thm)],[f_1936_3]) ).

fof(f_1937_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_1937_2,plain,
    ! [U_8354] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8354))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8354),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8354),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8354)) ) ),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

fof(f_1937_3,plain,
    ( ! [U_8356] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8356),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_8355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8355),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8355)) ) ),
    inference(miniscope,[status(thm)],[f_1937_2]) ).

cnf(f_1937_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8355),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8355)) ),
    inference(clausify,[status(thm)],[f_1937_3]) ).

cnf(f_1937_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8356),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1937_3]) ).

fof(f_1938_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_1938_2,plain,
    ! [U_8357] :
      ( hAPP(c_Int_Onat,U_8357) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8357)) ),
    inference(variable_rename,[status(thm)],[f_1938_1]) ).

cnf(f_1938_3,plain,
    ( hAPP(c_Int_Onat,U_8357) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8357)) ),
    inference(clausify,[status(thm)],[f_1938_2]) ).

fof(f_1939_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_1939_2,plain,
    ! [U_8358] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_8358)) = U_8358
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8358)) ),
    inference(variable_rename,[status(thm)],[f_1939_1]) ).

cnf(f_1939_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_8358)) = U_8358
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_8358)) ),
    inference(clausify,[status(thm)],[f_1939_2]) ).

fof(f_1940_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).

fof(f_1940_2,plain,
    ! [U_8361,U_8360,U_8359] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8359),U_8361),c_Big__Operators_Olinorder__class_OMax(U_8359,U_8360)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8359),U_8361),U_8360))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8359),U_8360))
      | ~ class_Orderings_Olinorder(U_8359) ),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

cnf(f_1940_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8359),U_8361),c_Big__Operators_Olinorder__class_OMax(U_8359,U_8360)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8359),U_8361),U_8360))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8359),U_8360))
    | ~ class_Orderings_Olinorder(U_8359) ),
    inference(clausify,[status(thm)],[f_1940_2]) ).

fof(f_1941_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__le]) ).

fof(f_1941_2,plain,
    ! [U_8364,U_8363,U_8362] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8362),c_Big__Operators_Olinorder__class_OMin(U_8362,U_8363)),U_8364))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8362),U_8364),U_8363))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8362),U_8363))
      | ~ class_Orderings_Olinorder(U_8362) ),
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

cnf(f_1941_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8362),c_Big__Operators_Olinorder__class_OMin(U_8362,U_8363)),U_8364))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8362),U_8364),U_8363))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8362),U_8363))
    | ~ class_Orderings_Olinorder(U_8362) ),
    inference(clausify,[status(thm)],[f_1941_2]) ).

fof(f_1942_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__in]) ).

fof(f_1942_2,plain,
    ! [U_8366,U_8365] :
      ( hBOOL(hAPP(hAPP(c_member(U_8365),c_Big__Operators_Olinorder__class_OMax(U_8365,U_8366)),U_8366))
      | U_8366 = c_Orderings_Obot__class_Obot(tc_fun(U_8365,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8365),U_8366))
      | ~ class_Orderings_Olinorder(U_8365) ),
    inference(variable_rename,[status(thm)],[f_1942_1]) ).

cnf(f_1942_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8365),c_Big__Operators_Olinorder__class_OMax(U_8365,U_8366)),U_8366))
    | U_8366 = c_Orderings_Obot__class_Obot(tc_fun(U_8365,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8365),U_8366))
    | ~ class_Orderings_Olinorder(U_8365) ),
    inference(clausify,[status(thm)],[f_1942_2]) ).

fof(f_1943_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__in]) ).

fof(f_1943_2,plain,
    ! [U_8368,U_8367] :
      ( hBOOL(hAPP(hAPP(c_member(U_8367),c_Big__Operators_Olinorder__class_OMin(U_8367,U_8368)),U_8368))
      | U_8368 = c_Orderings_Obot__class_Obot(tc_fun(U_8367,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8367),U_8368))
      | ~ class_Orderings_Olinorder(U_8367) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

cnf(f_1943_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8367),c_Big__Operators_Olinorder__class_OMin(U_8367,U_8368)),U_8368))
    | U_8368 = c_Orderings_Obot__class_Obot(tc_fun(U_8367,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8367),U_8368))
    | ~ class_Orderings_Olinorder(U_8367) ),
    inference(clausify,[status(thm)],[f_1943_2]) ).

fof(f_1944_1,plain,
    ! [V_N_2,V_M_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).

fof(f_1944_2,plain,
    ! [U_8371,U_8370,U_8369] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8369),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8371)),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8370)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8371))
      | U_8370 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8369,tc_HOL_Obool)),U_8370),U_8371))
      | ~ class_Orderings_Olinorder(U_8369) ),
    inference(variable_rename,[status(thm)],[f_1944_1]) ).

cnf(f_1944_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8369),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8371)),c_Big__Operators_Olinorder__class_OMin(U_8369,U_8370)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8369),U_8371))
    | U_8370 = c_Orderings_Obot__class_Obot(tc_fun(U_8369,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8369,tc_HOL_Obool)),U_8370),U_8371))
    | ~ class_Orderings_Olinorder(U_8369) ),
    inference(clausify,[status(thm)],[f_1944_2]) ).

fof(f_1945_1,plain,
    ! [V_N_2,V_M_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).

fof(f_1945_2,plain,
    ! [U_8374,U_8373,U_8372] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8372),c_Big__Operators_Olinorder__class_OMax(U_8372,U_8373)),c_Big__Operators_Olinorder__class_OMax(U_8372,U_8374)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8372),U_8374))
      | U_8373 = c_Orderings_Obot__class_Obot(tc_fun(U_8372,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8372,tc_HOL_Obool)),U_8373),U_8374))
      | ~ class_Orderings_Olinorder(U_8372) ),
    inference(variable_rename,[status(thm)],[f_1945_1]) ).

cnf(f_1945_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8372),c_Big__Operators_Olinorder__class_OMax(U_8372,U_8373)),c_Big__Operators_Olinorder__class_OMax(U_8372,U_8374)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8372),U_8374))
    | U_8373 = c_Orderings_Obot__class_Obot(tc_fun(U_8372,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8372,tc_HOL_Obool)),U_8373),U_8374))
    | ~ class_Orderings_Olinorder(U_8372) ),
    inference(clausify,[status(thm)],[f_1945_2]) ).

fof(f_1946_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).

fof(f_1946_2,plain,
    ! [U_8377,U_8376,U_8375] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_8375,U_8376) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8375),U_8377),c_Big__Operators_Olinorder__class_OMin(U_8375,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_8375,U_8376) = U_8377
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
      | ~ class_Orderings_Olinorder(U_8375) ),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

cnf(f_1946_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_8375,U_8376) = U_8377
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
    | ~ class_Orderings_Olinorder(U_8375) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

cnf(f_1946_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_8375,U_8376) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8375),U_8377),c_Big__Operators_Olinorder__class_OMin(U_8375,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8375,tc_HOL_Obool)),U_8376),hAPP(hAPP(c_Set_Oinsert(U_8375),U_8377),c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8375,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8375),U_8377),U_8376))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8375),U_8376))
    | ~ class_Orderings_Olinorder(U_8375) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

fof(f_1947_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).

fof(f_1947_2,plain,
    ! [U_8380,U_8379,U_8378] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_8378,U_8379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8378),U_8380),c_Big__Operators_Olinorder__class_OMax(U_8378,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_8378,U_8379) = U_8380
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8378),U_8380),U_8379))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
      | ~ class_Orderings_Olinorder(U_8378) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

cnf(f_1947_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8378,U_8379) = U_8380
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8378),U_8380),U_8379))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
    | ~ class_Orderings_Olinorder(U_8378) ),
    inference(clausify,[status(thm)],[f_1947_2]) ).

cnf(f_1947_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8378,U_8379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8378),U_8380),c_Big__Operators_Olinorder__class_OMax(U_8378,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8378,tc_HOL_Obool)),U_8379),hAPP(hAPP(c_Set_Oinsert(U_8378),U_8380),c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8378),U_8380),U_8379))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8378),U_8379))
    | ~ class_Orderings_Olinorder(U_8378) ),
    inference(clausify,[status(thm)],[f_1947_2]) ).

fof(f_1948_1,plain,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),V_P_2)),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_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).

fof(f_1948_2,plain,
    ! [U_8386,U_8385,U_8384,U_8383,U_8382,U_8381] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),hAPP(hAPP(c_COMBS(U_8382,U_8381,U_8381),hAPP(hAPP(c_COMBS(U_8382,U_8381,tc_fun(U_8381,U_8381)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8381,tc_fun(U_8381,U_8381)),U_8382),c_If(U_8381)),U_8384)),U_8385)),U_8386)),U_8383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),U_8385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8382,tc_HOL_Obool)),U_8383),hAPP(c_Set_OCollect(U_8382),U_8384)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),U_8386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8382,tc_HOL_Obool)),U_8383),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8382,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8382),U_8384)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8382),U_8383))
      | ~ class_Groups_Ocomm__monoid__add(U_8381) ),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

cnf(f_1948_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),hAPP(hAPP(c_COMBS(U_8382,U_8381,U_8381),hAPP(hAPP(c_COMBS(U_8382,U_8381,tc_fun(U_8381,U_8381)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8381,tc_fun(U_8381,U_8381)),U_8382),c_If(U_8381)),U_8384)),U_8385)),U_8386)),U_8383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),U_8385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8382,tc_HOL_Obool)),U_8383),hAPP(c_Set_OCollect(U_8382),U_8384)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8382,U_8381),U_8386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8382,tc_HOL_Obool)),U_8383),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8382,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8382),U_8384)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8382),U_8383))
    | ~ class_Groups_Ocomm__monoid__add(U_8381) ),
    inference(clausify,[status(thm)],[f_1948_2]) ).

fof(f_1949_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).

fof(f_1949_2,plain,
    ! [U_8391,U_8390,U_8389,U_8388,U_8387] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8388,U_8387),U_8391),U_8389) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8387),hAPP(U_8391,U_8390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8388,U_8387),U_8391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8388,tc_HOL_Obool)),U_8389),hAPP(hAPP(c_Set_Oinsert(U_8388),U_8390),c_Orderings_Obot__class_Obot(tc_fun(U_8388,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8388),U_8390),U_8389))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8388),U_8389))
      | ~ class_Groups_Ocomm__monoid__mult(U_8387) ),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

cnf(f_1949_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8388,U_8387),U_8391),U_8389) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8387),hAPP(U_8391,U_8390)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8388,U_8387),U_8391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8388,tc_HOL_Obool)),U_8389),hAPP(hAPP(c_Set_Oinsert(U_8388),U_8390),c_Orderings_Obot__class_Obot(tc_fun(U_8388,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8388),U_8390),U_8389))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8388),U_8389))
    | ~ class_Groups_Ocomm__monoid__mult(U_8387) ),
    inference(clausify,[status(thm)],[f_1949_2]) ).

fof(f_1950_1,plain,
    ! [V_k_2,V_C_2,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))
      | ? [B_c1] :
          ( ? [B_c2] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
              & B_c1 != B_c2
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) )
      | ? [B_c] :
          ( hAPP(c_Finite__Set_Ocard(T_a),B_c) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__partition]) ).

fof(f_1950_2,plain,
    ! [U_8397,U_8396,U_8395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
      | ? [U_8394] :
          ( ? [U_8393] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),U_8394),U_8393) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
              & U_8394 != U_8393
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8393),U_8396)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8394),U_8396)) )
      | ? [U_8392] :
          ( hAPP(c_Finite__Set_Ocard(U_8395),U_8392) != U_8397
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8392),U_8396)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

fof(f_1950_3,plain,
    ! [U_8397,U_8396,U_8395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
      | ? [U_8394] :
          ( ? [U_8393] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),U_8394),U_8393) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
              & U_8394 != U_8393
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8393),U_8396)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8394),U_8396)) )
      | ( hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_8392,sK215(U_8397,U_8396,U_8395))],[f_1950_2]) ).

fof(f_1950_4,plain,
    ! [U_8397,U_8396,U_8395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
      | ( ? [U_8393] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),U_8393) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
            & sK216(U_8397,U_8396,U_8395) != U_8393
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),U_8393),U_8396)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),U_8396)) )
      | ( hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_8394,sK216(U_8397,U_8396,U_8395))],[f_1950_3]) ).

fof(f_1950_5,plain,
    ! [U_8397,U_8396,U_8395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),sK217(U_8397,U_8396,U_8395)) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
        & sK216(U_8397,U_8396,U_8395) != sK217(U_8397,U_8396,U_8395)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK217(U_8397,U_8396,U_8395)),U_8396))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),U_8396)) )
      | ( hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_8393,sK217(U_8397,U_8396,U_8395))],[f_1950_4]) ).

cnf(f_1950_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),U_8396))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK217(U_8397,U_8396,U_8395)),U_8396))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_8,plain,
    ( sK216(U_8397,U_8396,U_8395) != sK217(U_8397,U_8396,U_8395)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),sK217(U_8397,U_8396,U_8395)) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK215(U_8397,U_8396,U_8395)),U_8396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),U_8396))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8395,tc_HOL_Obool)),sK217(U_8397,U_8396,U_8395)),U_8396))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_12,plain,
    ( sK216(U_8397,U_8396,U_8395) != sK217(U_8397,U_8396,U_8395)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8395,tc_HOL_Obool)),sK216(U_8397,U_8396,U_8395)),sK217(U_8397,U_8396,U_8395)) != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8397),hAPP(c_Finite__Set_Ocard(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) = hAPP(c_Finite__Set_Ocard(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396))
    | hAPP(c_Finite__Set_Ocard(U_8395),sK215(U_8397,U_8396,U_8395)) != U_8397
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8395),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_8395,tc_HOL_Obool),U_8396)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8395,tc_HOL_Obool)),U_8396)) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

fof(f_1951_1,plain,
    ! [V_A_2,T_a] :
      ( c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inj__uminus]) ).

fof(f_1951_2,plain,
    ! [U_8399,U_8398] :
      ( c_Fun_Oinj__on(U_8398,U_8398,c_Groups_Ouminus__class_Ouminus(U_8398),U_8399)
      | ~ class_Groups_Oordered__ab__group__add(U_8398) ),
    inference(variable_rename,[status(thm)],[f_1951_1]) ).

cnf(f_1951_3,plain,
    ( c_Fun_Oinj__on(U_8398,U_8398,c_Groups_Ouminus__class_Ouminus(U_8398),U_8399)
    | ~ class_Groups_Oordered__ab__group__add(U_8398) ),
    inference(clausify,[status(thm)],[f_1951_2]) ).

fof(f_1952_1,plain,
    ! [V_A_2,V_c_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ComplI]) ).

fof(f_1952_2,plain,
    ! [U_8402,U_8401,U_8400] :
      ( hBOOL(hAPP(hAPP(c_member(U_8400),U_8401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8400,tc_HOL_Obool)),U_8402)))
      | hBOOL(hAPP(hAPP(c_member(U_8400),U_8401),U_8402)) ),
    inference(variable_rename,[status(thm)],[f_1952_1]) ).

cnf(f_1952_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8400),U_8401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8400,tc_HOL_Obool)),U_8402)))
    | hBOOL(hAPP(hAPP(c_member(U_8400),U_8401),U_8402)) ),
    inference(clausify,[status(thm)],[f_1952_2]) ).

fof(f_1953_1,plain,
    ! [T_a] :
      ( c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a)
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__max]) ).

fof(f_1953_2,plain,
    ! [U_8403] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8403) = c_Orderings_Oord__class_Omax(U_8403)
      | ~ class_Orderings_Olinorder(U_8403)
      | ~ class_Lattices_Osemilattice__sup(U_8403) ),
    inference(variable_rename,[status(thm)],[f_1953_1]) ).

cnf(f_1953_3,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_8403) = c_Orderings_Oord__class_Omax(U_8403)
    | ~ class_Orderings_Olinorder(U_8403)
    | ~ class_Lattices_Osemilattice__sup(U_8403) ),
    inference(clausify,[status(thm)],[f_1953_2]) ).

fof(f_1954_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_1954_2,plain,
    ! [U_8404] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8404) = U_8404,
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

cnf(f_1954_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8404) = U_8404,
    inference(clausify,[status(thm)],[f_1954_2]) ).

fof(f_1955_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_1955_2,plain,
    ! [U_8405] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8405),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8405,
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

cnf(f_1955_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8405),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8405,
    inference(clausify,[status(thm)],[f_1955_2]) ).

fof(f_1956_1,plain,
    ! [T_a] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a)
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__min]) ).

fof(f_1956_2,plain,
    ! [U_8406] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_8406) = c_Orderings_Oord__class_Omin(U_8406)
      | ~ class_Orderings_Olinorder(U_8406)
      | ~ class_Lattices_Osemilattice__inf(U_8406) ),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

cnf(f_1956_3,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_8406) = c_Orderings_Oord__class_Omin(U_8406)
    | ~ class_Orderings_Olinorder(U_8406)
    | ~ class_Lattices_Osemilattice__inf(U_8406) ),
    inference(clausify,[status(thm)],[f_1956_2]) ).

fof(f_1957_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_1957_2,plain,
    ! [U_8407] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

cnf(f_1957_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1957_2]) ).

fof(f_1958_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_1958_2,plain,
    ! [U_8408] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8408),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1958_1]) ).

cnf(f_1958_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8408),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1958_2]) ).

fof(f_1959_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_1959_2,plain,
    ! [U_8410,U_8409] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8409)),hAPP(c_Nat_OSuc,U_8410)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8409),U_8410)),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

cnf(f_1959_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8409)),hAPP(c_Nat_OSuc,U_8410)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8409),U_8410)),
    inference(clausify,[status(thm)],[f_1959_2]) ).

fof(f_1960_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_1960_2,plain,
    ! [U_8412,U_8411] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8411)),hAPP(c_Nat_OSuc,U_8412)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8411),U_8412)),
    inference(variable_rename,[status(thm)],[f_1960_1]) ).

cnf(f_1960_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8411)),hAPP(c_Nat_OSuc,U_8412)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8411),U_8412)),
    inference(clausify,[status(thm)],[f_1960_2]) ).

fof(f_1961_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).

fof(f_1961_2,plain,
    ! [U_8415,U_8414,U_8413] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8413,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8413,tc_HOL_Obool)),U_8415)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8413,tc_HOL_Obool)),U_8414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8413,tc_HOL_Obool)),U_8414),U_8415)) ),
    inference(variable_rename,[status(thm)],[f_1961_1]) ).

cnf(f_1961_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8413,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8413,tc_HOL_Obool)),U_8415)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8413,tc_HOL_Obool)),U_8414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8413,tc_HOL_Obool)),U_8414),U_8415)) ),
    inference(clausify,[status(thm)],[f_1961_2]) ).

fof(f_1962_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).

fof(f_1962_2,plain,
    ! [U_8418,U_8417,U_8416] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8416,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8416,tc_HOL_Obool)),U_8417)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8416,tc_HOL_Obool)),U_8418)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8416,tc_HOL_Obool)),U_8418),U_8417)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8416,tc_HOL_Obool)),U_8418),U_8417))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8416,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8416,tc_HOL_Obool)),U_8417)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8416,tc_HOL_Obool)),U_8418))) ) ),
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

fof(f_1962_3,plain,
    ( ! [U_8424,U_8422,U_8420] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8420,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8420,tc_HOL_Obool)),U_8422)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8420,tc_HOL_Obool)),U_8424)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8420,tc_HOL_Obool)),U_8424),U_8422)) )
    & ! [U_8423,U_8421,U_8419] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8419,tc_HOL_Obool)),U_8423),U_8421))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8419,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8419,tc_HOL_Obool)),U_8421)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8419,tc_HOL_Obool)),U_8423))) ) ),
    inference(miniscope,[status(thm)],[f_1962_2]) ).

cnf(f_1962_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8419,tc_HOL_Obool)),U_8423),U_8421))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8419,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8419,tc_HOL_Obool)),U_8421)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8419,tc_HOL_Obool)),U_8423))) ),
    inference(clausify,[status(thm)],[f_1962_3]) ).

cnf(f_1962_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8420,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8420,tc_HOL_Obool)),U_8422)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8420,tc_HOL_Obool)),U_8424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8420,tc_HOL_Obool)),U_8424),U_8422)) ),
    inference(clausify,[status(thm)],[f_1962_3]) ).

fof(f_1963_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_1963_2,plain,
    ! [U_8428,U_8427,U_8426,U_8425] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8425),U_8426),U_8427)),U_8428) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),U_8426),U_8428)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),U_8427),U_8428))
      | ~ class_Groups_Oordered__ab__group__add(U_8425) ),
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

cnf(f_1963_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8425),U_8426),U_8427)),U_8428) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),U_8426),U_8428)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8425),U_8427),U_8428))
    | ~ class_Groups_Oordered__ab__group__add(U_8425) ),
    inference(clausify,[status(thm)],[f_1963_2]) ).

fof(f_1964_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_a)
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).

fof(f_1964_2,plain,
    ! [U_8432,U_8431,U_8430,U_8429] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8429),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8430,tc_Nat_Onat),U_8431),U_8432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8430,U_8429),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8429,U_8430),c_Nat_Osemiring__1__class_Oof__nat(U_8429)),U_8431)),U_8432)
      | ~ class_Rings_Osemiring__1(U_8429)
      | ~ class_Groups_Ocomm__monoid__mult(U_8429) ),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

cnf(f_1964_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8429),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8430,tc_Nat_Onat),U_8431),U_8432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8430,U_8429),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8429,U_8430),c_Nat_Osemiring__1__class_Oof__nat(U_8429)),U_8431)),U_8432)
    | ~ class_Rings_Osemiring__1(U_8429)
    | ~ class_Groups_Ocomm__monoid__mult(U_8429) ),
    inference(clausify,[status(thm)],[f_1964_2]) ).

fof(f_1965_1,plain,
    ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),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_1965_2,plain,
    ! [U_8435,U_8434,U_8433] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8433,tc_Nat_Onat),U_8434),U_8435)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8433,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8433),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8434)),U_8435),
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

cnf(f_1965_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8433,tc_Nat_Onat),U_8434),U_8435)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8433,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8433),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8434)),U_8435),
    inference(clausify,[status(thm)],[f_1965_2]) ).

fof(f_1966_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_1966_2,plain,
    ! [U_8437,U_8436] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8436),hAPP(c_Groups_Ouminus__class_Ouminus(U_8436),U_8437)) = U_8437
      | ~ class_Groups_Ogroup__add(U_8436) ),
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

cnf(f_1966_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8436),hAPP(c_Groups_Ouminus__class_Ouminus(U_8436),U_8437)) = U_8437
    | ~ class_Groups_Ogroup__add(U_8436) ),
    inference(clausify,[status(thm)],[f_1966_2]) ).

fof(f_1967_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_1967_2,plain,
    ! [U_8440,U_8439,U_8438] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8438),U_8439),U_8440)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8438),hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),U_8439)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),U_8440))
      | ~ class_Groups_Olinordered__ab__group__add(U_8438) ),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

cnf(f_1967_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8438),U_8439),U_8440)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8438),hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),U_8439)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8438),U_8440))
    | ~ class_Groups_Olinordered__ab__group__add(U_8438) ),
    inference(clausify,[status(thm)],[f_1967_2]) ).

fof(f_1968_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_1968_2,plain,
    ! [U_8443,U_8442,U_8441] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8441),U_8442),U_8443)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8441),hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),U_8442)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),U_8443))
      | ~ class_Groups_Olinordered__ab__group__add(U_8441) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

cnf(f_1968_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8441),U_8442),U_8443)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8441),hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),U_8442)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8441),U_8443))
    | ~ class_Groups_Olinordered__ab__group__add(U_8441) ),
    inference(clausify,[status(thm)],[f_1968_2]) ).

fof(f_1969_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
          | V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) )
        & ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).

fof(f_1969_2,plain,
    ! [U_8446,U_8445,U_8444] :
      ( ( ( U_8445 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8446)
          | U_8446 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8445) )
        & ( U_8446 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8445)
          | U_8445 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8446) ) )
      | ~ class_Groups_Ogroup__add(U_8444) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

cnf(f_1969_3,plain,
    ( U_8446 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8445)
    | U_8445 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8446)
    | ~ class_Groups_Ogroup__add(U_8444) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

cnf(f_1969_4,plain,
    ( U_8445 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8446)
    | U_8446 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8444),U_8445)
    | ~ class_Groups_Ogroup__add(U_8444) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

fof(f_1970_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) != V_a_2 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) != V_b_2 ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).

fof(f_1970_2,plain,
    ! [U_8449,U_8448,U_8447] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8448) = U_8449
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8449) != U_8448 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8449) = U_8448
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8448) != U_8449 ) )
      | ~ class_Groups_Ogroup__add(U_8447) ),
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

cnf(f_1970_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8449) = U_8448
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8448) != U_8449
    | ~ class_Groups_Ogroup__add(U_8447) ),
    inference(clausify,[status(thm)],[f_1970_2]) ).

cnf(f_1970_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8448) = U_8449
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8447),U_8449) != U_8448
    | ~ class_Groups_Ogroup__add(U_8447) ),
    inference(clausify,[status(thm)],[f_1970_2]) ).

fof(f_1971_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).

fof(f_1971_2,plain,
    ! [U_8452,U_8451,U_8450] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8451) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8452)
          | U_8451 != U_8452 )
        & ( U_8451 = U_8452
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8451) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8452) ) )
      | ~ class_Groups_Ogroup__add(U_8450) ),
    inference(variable_rename,[status(thm)],[f_1971_1]) ).

cnf(f_1971_3,plain,
    ( U_8451 = U_8452
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8451) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8452)
    | ~ class_Groups_Ogroup__add(U_8450) ),
    inference(clausify,[status(thm)],[f_1971_2]) ).

cnf(f_1971_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8451) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8450),U_8452)
    | U_8451 != U_8452
    | ~ class_Groups_Ogroup__add(U_8450) ),
    inference(clausify,[status(thm)],[f_1971_2]) ).

fof(f_1972_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_double__complement]) ).

fof(f_1972_2,plain,
    ! [U_8454,U_8453] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),U_8454)) = U_8454,
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

cnf(f_1972_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),U_8454)) = U_8454,
    inference(clausify,[status(thm)],[f_1972_2]) ).

fof(f_1973_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_1973_2,plain,
    ! [U_8456,U_8455] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8455),hAPP(c_Groups_Ouminus__class_Ouminus(U_8455),U_8456)) = U_8456
      | ~ class_Lattices_Oboolean__algebra(U_8455) ),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

cnf(f_1973_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8455),hAPP(c_Groups_Ouminus__class_Ouminus(U_8455),U_8456)) = U_8456
    | ~ class_Lattices_Oboolean__algebra(U_8455) ),
    inference(clausify,[status(thm)],[f_1973_2]) ).

fof(f_1974_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem]) ).

fof(f_1974_2,plain,
    ! [U_8458,U_8457] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8457),U_8458),U_8458) = U_8458
      | ~ class_Orderings_Olinorder(U_8457) ),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

cnf(f_1974_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8457),U_8458),U_8458) = U_8458
    | ~ class_Orderings_Olinorder(U_8457) ),
    inference(clausify,[status(thm)],[f_1974_2]) ).

fof(f_1975_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_1975_2,plain,
    ! [U_8460,U_8459] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8459),U_8460),U_8460) = U_8460
      | ~ class_Orderings_Olinorder(U_8459) ),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

cnf(f_1975_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8459),U_8460),U_8460) = U_8460
    | ~ class_Orderings_Olinorder(U_8459) ),
    inference(clausify,[status(thm)],[f_1975_2]) ).

fof(f_1976_1,plain,
    ! [V_x_2,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).

fof(f_1976_2,plain,
    ! [U_8464,U_8463,U_8462,U_8461] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8462,U_8461)),U_8463),U_8464) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8461),hAPP(U_8463,U_8464))
      | ~ class_Groups_Ouminus(U_8461) ),
    inference(variable_rename,[status(thm)],[f_1976_1]) ).

cnf(f_1976_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8462,U_8461)),U_8463),U_8464) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8461),hAPP(U_8463,U_8464))
    | ~ class_Groups_Ouminus(U_8461) ),
    inference(clausify,[status(thm)],[f_1976_2]) ).

fof(f_1977_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_1977_2,plain,
    ! [U_8467,U_8466,U_8465] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8465),U_8466),U_8467) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8465),U_8467),U_8466)
      | ~ class_Orderings_Olinorder(U_8465) ),
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

cnf(f_1977_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8465),U_8466),U_8467) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8465),U_8467),U_8466)
    | ~ class_Orderings_Olinorder(U_8465) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

fof(f_1978_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_1978_2,plain,
    ! [U_8470,U_8469,U_8468] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8468),U_8469),U_8470) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8468),U_8470),U_8469)
      | ~ class_Orderings_Olinorder(U_8468) ),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

cnf(f_1978_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8468),U_8469),U_8470) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8468),U_8470),U_8469)
    | ~ class_Orderings_Olinorder(U_8468) ),
    inference(clausify,[status(thm)],[f_1978_2]) ).

fof(f_1979_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_1979_2,plain,
    ! [U_8473,U_8472,U_8471] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8471),U_8472),U_8473) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8471),U_8473),U_8472)
      | ~ class_Orderings_Olinorder(U_8471) ),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

cnf(f_1979_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8471),U_8472),U_8473) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8471),U_8473),U_8472)
    | ~ class_Orderings_Olinorder(U_8471) ),
    inference(clausify,[status(thm)],[f_1979_2]) ).

fof(f_1980_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_1980_2,plain,
    ! [U_8476,U_8475,U_8474] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8476) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8476),U_8475)
      | ~ class_Orderings_Olinorder(U_8474) ),
    inference(variable_rename,[status(thm)],[f_1980_1]) ).

cnf(f_1980_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8476) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8476),U_8475)
    | ~ class_Orderings_Olinorder(U_8474) ),
    inference(clausify,[status(thm)],[f_1980_2]) ).

fof(f_1981_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_1981_2,plain,
    ! [U_8479,U_8478,U_8477] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8477),U_8478),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8477),U_8478),U_8479)) = U_8478
      | ~ class_Orderings_Olinorder(U_8477) ),
    inference(variable_rename,[status(thm)],[f_1981_1]) ).

cnf(f_1981_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8477),U_8478),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8477),U_8478),U_8479)) = U_8478
    | ~ class_Orderings_Olinorder(U_8477) ),
    inference(clausify,[status(thm)],[f_1981_2]) ).

fof(f_1982_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_1982_2,plain,
    ! [U_8482,U_8481,U_8480] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8480),U_8481),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8480),U_8481),U_8482)) = U_8481
      | ~ class_Orderings_Olinorder(U_8480) ),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

cnf(f_1982_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8480),U_8481),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8480),U_8481),U_8482)) = U_8481
    | ~ class_Orderings_Olinorder(U_8480) ),
    inference(clausify,[status(thm)],[f_1982_2]) ).

fof(f_1983_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_1983_2,plain,
    ! [U_8485,U_8484,U_8483] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8485)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8485)
      | ~ class_Orderings_Olinorder(U_8483) ),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

cnf(f_1983_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8485)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8483),U_8484),U_8485)
    | ~ class_Orderings_Olinorder(U_8483) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

fof(f_1984_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_1984_2,plain,
    ! [U_8488,U_8487,U_8486] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),U_8488)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),U_8488)
      | ~ class_Orderings_Olinorder(U_8486) ),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

cnf(f_1984_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),U_8488)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8486),U_8487),U_8488)
    | ~ class_Orderings_Olinorder(U_8486) ),
    inference(clausify,[status(thm)],[f_1984_2]) ).

fof(f_1985_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_1985_2,plain,
    ! [U_8491,U_8490,U_8489] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),U_8491)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),U_8491)
      | ~ class_Orderings_Olinorder(U_8489) ),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

cnf(f_1985_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),U_8491)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8489),U_8490),U_8491)
    | ~ class_Orderings_Olinorder(U_8489) ),
    inference(clausify,[status(thm)],[f_1985_2]) ).

fof(f_1986_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_1986_2,plain,
    ! [U_8494,U_8493,U_8492] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),U_8494)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),U_8494)
      | ~ class_Orderings_Olinorder(U_8492) ),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

cnf(f_1986_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),U_8494)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8493),U_8494)
    | ~ class_Orderings_Olinorder(U_8492) ),
    inference(clausify,[status(thm)],[f_1986_2]) ).

fof(f_1987_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_1987_2,plain,
    ! [U_8498,U_8497,U_8496,U_8495] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8496),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8497),U_8498)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8496),U_8498))
      | ~ class_Orderings_Olinorder(U_8495) ),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

cnf(f_1987_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8496),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8497),U_8498)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8495),U_8496),U_8498))
    | ~ class_Orderings_Olinorder(U_8495) ),
    inference(clausify,[status(thm)],[f_1987_2]) ).

fof(f_1988_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_1988_2,plain,
    ! [U_8502,U_8501,U_8500,U_8499] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),U_8502)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),U_8502))
      | ~ class_Orderings_Olinorder(U_8499) ),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

cnf(f_1988_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),U_8502)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8501),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8499),U_8500),U_8502))
    | ~ class_Orderings_Olinorder(U_8499) ),
    inference(clausify,[status(thm)],[f_1988_2]) ).

fof(f_1989_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_1989_2,plain,
    ! [U_8506,U_8505,U_8504,U_8503] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8504),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8505),U_8506)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8504),U_8506))
      | ~ class_Orderings_Olinorder(U_8503) ),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

cnf(f_1989_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8504),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8505),U_8506)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8503),U_8504),U_8506))
    | ~ class_Orderings_Olinorder(U_8503) ),
    inference(clausify,[status(thm)],[f_1989_2]) ).

fof(f_1990_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_1990_2,plain,
    ! [U_8510,U_8509,U_8508,U_8507] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8508),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8509),U_8510)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8509),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8508),U_8510))
      | ~ class_Orderings_Olinorder(U_8507) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

cnf(f_1990_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8508),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8509),U_8510)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8509),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8507),U_8508),U_8510))
    | ~ class_Orderings_Olinorder(U_8507) ),
    inference(clausify,[status(thm)],[f_1990_2]) ).

fof(f_1991_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_1991_2,plain,
    ! [U_8514,U_8513,U_8512,U_8511] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8511),U_8513),U_8514)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8511),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8513)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8514))
      | ~ class_Orderings_Olinorder(U_8511) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

cnf(f_1991_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8511),U_8513),U_8514)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8511),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8513)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8511),U_8512),U_8514))
    | ~ class_Orderings_Olinorder(U_8511) ),
    inference(clausify,[status(thm)],[f_1991_2]) ).

fof(f_1992_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_1992_2,plain,
    ! [U_8518,U_8517,U_8516,U_8515] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8515),U_8517),U_8518)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8515),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),U_8517)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),U_8518))
      | ~ class_Orderings_Olinorder(U_8515) ),
    inference(variable_rename,[status(thm)],[f_1992_1]) ).

cnf(f_1992_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8515),U_8517),U_8518)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8515),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),U_8517)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8515),U_8516),U_8518))
    | ~ class_Orderings_Olinorder(U_8515) ),
    inference(clausify,[status(thm)],[f_1992_2]) ).

fof(f_1993_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,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_a,tc_HOL_Obool)),V_A_2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).

fof(f_1993_2,plain,
    ! [U_8521,U_8520,U_8519] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8519,tc_HOL_Obool)),U_8520) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8519,tc_HOL_Obool)),U_8521)
        | U_8520 != U_8521 )
      & ( U_8520 = U_8521
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8519,tc_HOL_Obool)),U_8520) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8519,tc_HOL_Obool)),U_8521) ) ),
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

fof(f_1993_3,plain,
    ( ! [U_8527,U_8525] :
        ( ! [U_8523] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8523,tc_HOL_Obool)),U_8525) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8523,tc_HOL_Obool)),U_8527)
        | U_8525 != U_8527 )
    & ! [U_8526,U_8524] :
        ( ! [U_8522] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8522,tc_HOL_Obool)),U_8524) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8522,tc_HOL_Obool)),U_8526)
        | U_8524 = U_8526 ) ),
    inference(miniscope,[status(thm)],[f_1993_2]) ).

cnf(f_1993_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8522,tc_HOL_Obool)),U_8524) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8522,tc_HOL_Obool)),U_8526)
    | U_8524 = U_8526 ),
    inference(clausify,[status(thm)],[f_1993_3]) ).

cnf(f_1993_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8523,tc_HOL_Obool)),U_8525) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8523,tc_HOL_Obool)),U_8527)
    | U_8525 != U_8527 ),
    inference(clausify,[status(thm)],[f_1993_3]) ).

fof(f_1994_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) ) )
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).

fof(f_1994_2,plain,
    ! [U_8530,U_8529,U_8528] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8529) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8530)
          | U_8529 != U_8530 )
        & ( U_8529 = U_8530
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8529) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8530) ) )
      | ~ class_Lattices_Oboolean__algebra(U_8528) ),
    inference(variable_rename,[status(thm)],[f_1994_1]) ).

cnf(f_1994_3,plain,
    ( U_8529 = U_8530
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8529) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8530)
    | ~ class_Lattices_Oboolean__algebra(U_8528) ),
    inference(clausify,[status(thm)],[f_1994_2]) ).

cnf(f_1994_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8529) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8528),U_8530)
    | U_8529 != U_8530
    | ~ class_Lattices_Oboolean__algebra(U_8528) ),
    inference(clausify,[status(thm)],[f_1994_2]) ).

fof(f_1995_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_1995_2,plain,
    ! [U_8534,U_8533,U_8532,U_8531] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8532),U_8533)),U_8534) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8532),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8533),U_8534))
      | ~ class_Orderings_Olinorder(U_8531) ),
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

cnf(f_1995_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8532),U_8533)),U_8534) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8532),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8531),U_8533),U_8534))
    | ~ class_Orderings_Olinorder(U_8531) ),
    inference(clausify,[status(thm)],[f_1995_2]) ).

fof(f_1996_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_1996_2,plain,
    ! [U_8538,U_8537,U_8536,U_8535] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8536),U_8537)),U_8538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8536),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8537),U_8538))
      | ~ class_Orderings_Olinorder(U_8535) ),
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

cnf(f_1996_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8536),U_8537)),U_8538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8536),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8535),U_8537),U_8538))
    | ~ class_Orderings_Olinorder(U_8535) ),
    inference(clausify,[status(thm)],[f_1996_2]) ).

fof(f_1997_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_1997_2,plain,
    ! [U_8542,U_8541,U_8540,U_8539] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8540),U_8541)),U_8542) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8540),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8541),U_8542))
      | ~ class_Orderings_Olinorder(U_8539) ),
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

cnf(f_1997_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8540),U_8541)),U_8542) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8540),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8539),U_8541),U_8542))
    | ~ class_Orderings_Olinorder(U_8539) ),
    inference(clausify,[status(thm)],[f_1997_2]) ).

fof(f_1998_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_1998_2,plain,
    ! [U_8546,U_8545,U_8544,U_8543] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8544),U_8545)),U_8546) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8544),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8545),U_8546))
      | ~ class_Orderings_Olinorder(U_8543) ),
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

cnf(f_1998_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8544),U_8545)),U_8546) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8544),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8543),U_8545),U_8546))
    | ~ class_Orderings_Olinorder(U_8543) ),
    inference(clausify,[status(thm)],[f_1998_2]) ).

fof(f_1999_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_1999_2,plain,
    ! [U_8550,U_8549,U_8548,U_8547] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8547),U_8548),U_8549)),U_8550) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8547),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8548),U_8550)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8549),U_8550))
      | ~ class_Orderings_Olinorder(U_8547) ),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

cnf(f_1999_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8547),U_8548),U_8549)),U_8550) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8547),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8548),U_8550)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8547),U_8549),U_8550))
    | ~ class_Orderings_Olinorder(U_8547) ),
    inference(clausify,[status(thm)],[f_1999_2]) ).

fof(f_2000_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_2000_2,plain,
    ! [U_8554,U_8553,U_8552,U_8551] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),U_8552),U_8554)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),U_8553),U_8554))
      | ~ class_Orderings_Olinorder(U_8551) ),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

cnf(f_2000_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),U_8552),U_8553)),U_8554) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8551),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),U_8552),U_8554)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8551),U_8553),U_8554))
    | ~ class_Orderings_Olinorder(U_8551) ),
    inference(clausify,[status(thm)],[f_2000_2]) ).

fof(f_2001_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_2001_2,plain,
    ! [U_8556,U_8555] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8556) = U_8556
      | ~ class_Orderings_Olinorder(U_8555) ),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

cnf(f_2001_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8555),U_8556),U_8556) = U_8556
    | ~ class_Orderings_Olinorder(U_8555) ),
    inference(clausify,[status(thm)],[f_2001_2]) ).

fof(f_2002_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_2002_2,plain,
    ! [U_8558,U_8557] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8557),U_8558),U_8558) = U_8558
      | ~ class_Orderings_Olinorder(U_8557) ),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

cnf(f_2002_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8557),U_8558),U_8558) = U_8558
    | ~ class_Orderings_Olinorder(U_8557) ),
    inference(clausify,[status(thm)],[f_2002_2]) ).

fof(f_2003_1,plain,
    ! [V_x_2,V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).

fof(f_2003_2,plain,
    ! [U_8562,U_8561,U_8560,U_8559] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8560,U_8559)),U_8561),U_8562) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8559),hAPP(U_8561,U_8562))
      | ~ class_Groups_Ouminus(U_8559) ),
    inference(variable_rename,[status(thm)],[f_2003_1]) ).

cnf(f_2003_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8560,U_8559)),U_8561),U_8562) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8559),hAPP(U_8561,U_8562))
    | ~ class_Groups_Ouminus(U_8559) ),
    inference(clausify,[status(thm)],[f_2003_2]) ).

fof(f_2004_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_2004_2,plain,
    ! [U_8566,U_8565,U_8564,U_8563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8563),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8563),U_8565),U_8566))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8563),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),U_8565)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),U_8566))))
      | ~ class_Orderings_Olinorder(U_8563) ),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

cnf(f_2004_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8563),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8563),U_8565),U_8566))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8563),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),U_8565)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8563),U_8564),U_8566))))
    | ~ class_Orderings_Olinorder(U_8563) ),
    inference(clausify,[status(thm)],[f_2004_2]) ).

fof(f_2005_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_2005_2,plain,
    ! [U_8570,U_8569,U_8568,U_8567] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8567),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8567),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),U_8569)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),U_8570))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8567),U_8569),U_8570))))
      | ~ class_Orderings_Olinorder(U_8567) ),
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

cnf(f_2005_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8567),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8567),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),U_8569)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),U_8570))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8567),U_8568),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8567),U_8569),U_8570))))
    | ~ class_Orderings_Olinorder(U_8567) ),
    inference(clausify,[status(thm)],[f_2005_2]) ).

fof(f_2006_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_2006_2,plain,
    ! [U_8574,U_8573,U_8572,U_8571] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8571),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8571),U_8574),U_8572)),U_8573))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8571),U_8572),U_8573))
      | ~ class_Orderings_Olinorder(U_8571) ),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

cnf(f_2006_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8571),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8571),U_8574),U_8572)),U_8573))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8571),U_8572),U_8573))
    | ~ class_Orderings_Olinorder(U_8571) ),
    inference(clausify,[status(thm)],[f_2006_2]) ).

fof(f_2007_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_2007_2,plain,
    ! [U_8578,U_8577,U_8576,U_8575] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8575),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8575),U_8576),U_8578)),U_8577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8575),U_8576),U_8577))
      | ~ class_Orderings_Olinorder(U_8575) ),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

cnf(f_2007_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8575),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8575),U_8576),U_8578)),U_8577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8575),U_8576),U_8577))
    | ~ class_Orderings_Olinorder(U_8575) ),
    inference(clausify,[status(thm)],[f_2007_2]) ).

fof(f_2008_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).

fof(f_2008_2,plain,
    ! [U_8582,U_8581,U_8580,U_8579] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8579),U_8580),U_8581)),U_8582))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8580),U_8582)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8580),U_8582))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8579),U_8580),U_8581)),U_8582)) ) )
      | ~ class_Orderings_Olinorder(U_8579) ),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

cnf(f_2008_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8580),U_8582))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8579),U_8580),U_8581)),U_8582))
    | ~ class_Orderings_Olinorder(U_8579) ),
    inference(clausify,[status(thm)],[f_2008_2]) ).

cnf(f_2008_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8580),U_8582))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8579),U_8580),U_8581)),U_8582))
    | ~ class_Orderings_Olinorder(U_8579) ),
    inference(clausify,[status(thm)],[f_2008_2]) ).

cnf(f_2008_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8579),U_8580),U_8581)),U_8582))
    | ~ class_Orderings_Olinorder(U_8579) ),
    inference(clausify,[status(thm)],[f_2008_2]) ).

fof(f_2009_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).

fof(f_2009_2,plain,
    ! [U_8586,U_8585,U_8584,U_8583] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8583),U_8585),U_8586)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8586))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8586))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8583),U_8585),U_8586))) ) )
      | ~ class_Orderings_Olinorder(U_8583) ),
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

cnf(f_2009_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8583),U_8585),U_8586)))
    | ~ class_Orderings_Olinorder(U_8583) ),
    inference(clausify,[status(thm)],[f_2009_2]) ).

cnf(f_2009_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8586))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8583),U_8585),U_8586)))
    | ~ class_Orderings_Olinorder(U_8583) ),
    inference(clausify,[status(thm)],[f_2009_2]) ).

cnf(f_2009_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8583),U_8585),U_8586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8586))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585))
    | ~ class_Orderings_Olinorder(U_8583) ),
    inference(clausify,[status(thm)],[f_2009_2]) ).

fof(f_2010_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).

fof(f_2010_2,plain,
    ! [U_8589,U_8588,U_8587] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8588)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8589)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),U_8589),U_8588)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),U_8589),U_8588))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8588)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8589))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8587) ),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

cnf(f_2010_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),U_8589),U_8588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8588)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8589)))
    | ~ class_Groups_Oordered__ab__group__add(U_8587) ),
    inference(clausify,[status(thm)],[f_2010_2]) ).

cnf(f_2010_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8588)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8587),U_8589)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8587),U_8589),U_8588))
    | ~ class_Groups_Oordered__ab__group__add(U_8587) ),
    inference(clausify,[status(thm)],[f_2010_2]) ).

fof(f_2011_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).

fof(f_2011_2,plain,
    ! [U_8592,U_8591,U_8590] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8591)),U_8592))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8592)),U_8591)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8592)),U_8591))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8591)),U_8592)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8590) ),
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

cnf(f_2011_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8592)),U_8591))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8591)),U_8592))
    | ~ class_Groups_Oordered__ab__group__add(U_8590) ),
    inference(clausify,[status(thm)],[f_2011_2]) ).

cnf(f_2011_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8591)),U_8592))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8590),hAPP(c_Groups_Ouminus__class_Ouminus(U_8590),U_8592)),U_8591))
    | ~ class_Groups_Oordered__ab__group__add(U_8590) ),
    inference(clausify,[status(thm)],[f_2011_2]) ).

fof(f_2012_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).

fof(f_2012_2,plain,
    ! [U_8595,U_8594,U_8593] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8594),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8595)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8595),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8594))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8595),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8594)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8594),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8595))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8593) ),
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

cnf(f_2012_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8595),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8594)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8594),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8595)))
    | ~ class_Groups_Oordered__ab__group__add(U_8593) ),
    inference(clausify,[status(thm)],[f_2012_2]) ).

cnf(f_2012_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8594),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8595)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8593),U_8595),hAPP(c_Groups_Ouminus__class_Ouminus(U_8593),U_8594)))
    | ~ class_Groups_Oordered__ab__group__add(U_8593) ),
    inference(clausify,[status(thm)],[f_2012_2]) ).

fof(f_2013_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_2013_2,plain,
    ! [U_8599,U_8598,U_8597,U_8596] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8596),U_8597),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8596),U_8599),U_8598)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8596),U_8597),U_8598))
      | ~ class_Orderings_Olinorder(U_8596) ),
    inference(variable_rename,[status(thm)],[f_2013_1]) ).

cnf(f_2013_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8596),U_8597),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8596),U_8599),U_8598)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8596),U_8597),U_8598))
    | ~ class_Orderings_Olinorder(U_8596) ),
    inference(clausify,[status(thm)],[f_2013_2]) ).

fof(f_2014_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_2014_2,plain,
    ! [U_8603,U_8602,U_8601,U_8600] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8600),U_8601),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8600),U_8602),U_8603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8600),U_8601),U_8602))
      | ~ class_Orderings_Olinorder(U_8600) ),
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

cnf(f_2014_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8600),U_8601),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8600),U_8602),U_8603)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8600),U_8601),U_8602))
    | ~ class_Orderings_Olinorder(U_8600) ),
    inference(clausify,[status(thm)],[f_2014_2]) ).

fof(f_2015_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).

fof(f_2015_2,plain,
    ! [U_8607,U_8606,U_8605,U_8604] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8604),U_8605),U_8606)),U_8607))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8606),U_8607))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8605),U_8607)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8606),U_8607))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8605),U_8607)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8604),U_8605),U_8606)),U_8607)) ) )
      | ~ class_Orderings_Olinorder(U_8604) ),
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

cnf(f_2015_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8605),U_8607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8604),U_8605),U_8606)),U_8607))
    | ~ class_Orderings_Olinorder(U_8604) ),
    inference(clausify,[status(thm)],[f_2015_2]) ).

cnf(f_2015_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8606),U_8607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8604),U_8605),U_8606)),U_8607))
    | ~ class_Orderings_Olinorder(U_8604) ),
    inference(clausify,[status(thm)],[f_2015_2]) ).

cnf(f_2015_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8604),U_8605),U_8606)),U_8607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8606),U_8607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8604),U_8605),U_8607))
    | ~ class_Orderings_Olinorder(U_8604) ),
    inference(clausify,[status(thm)],[f_2015_2]) ).

fof(f_2016_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).

fof(f_2016_2,plain,
    ! [U_8611,U_8610,U_8609,U_8608] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8608),U_8610),U_8611)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8611))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8610)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8611))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8610))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8608),U_8610),U_8611))) ) )
      | ~ class_Orderings_Olinorder(U_8608) ),
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

cnf(f_2016_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8611))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8608),U_8610),U_8611)))
    | ~ class_Orderings_Olinorder(U_8608) ),
    inference(clausify,[status(thm)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8608),U_8610),U_8611)))
    | ~ class_Orderings_Olinorder(U_8608) ),
    inference(clausify,[status(thm)],[f_2016_2]) ).

cnf(f_2016_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),U_8611))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8608),U_8609),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8608),U_8610),U_8611)))
    | ~ class_Orderings_Olinorder(U_8608) ),
    inference(clausify,[status(thm)],[f_2016_2]) ).

fof(f_2017_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) != V_a_2 ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).

fof(f_2017_2,plain,
    ! [U_8613,U_8612] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613) = U_8613
          | U_8613 != c_Groups_Ozero__class_Ozero(U_8612) )
        & ( U_8613 = c_Groups_Ozero__class_Ozero(U_8612)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613) != U_8613 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_8612) ),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

cnf(f_2017_3,plain,
    ( U_8613 = c_Groups_Ozero__class_Ozero(U_8612)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613) != U_8613
    | ~ class_Groups_Olinordered__ab__group__add(U_8612) ),
    inference(clausify,[status(thm)],[f_2017_2]) ).

cnf(f_2017_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613) = U_8613
    | U_8613 != c_Groups_Ozero__class_Ozero(U_8612)
    | ~ class_Groups_Olinordered__ab__group__add(U_8612) ),
    inference(clausify,[status(thm)],[f_2017_2]) ).

fof(f_2018_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).

fof(f_2018_2,plain,
    ! [U_8615,U_8614] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8614),U_8615) = c_Groups_Ozero__class_Ozero(U_8614)
          | U_8615 != c_Groups_Ozero__class_Ozero(U_8614) )
        & ( U_8615 = c_Groups_Ozero__class_Ozero(U_8614)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_8614),U_8615) != c_Groups_Ozero__class_Ozero(U_8614) ) )
      | ~ class_Groups_Ogroup__add(U_8614) ),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

cnf(f_2018_3,plain,
    ( U_8615 = c_Groups_Ozero__class_Ozero(U_8614)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_8614),U_8615) != c_Groups_Ozero__class_Ozero(U_8614)
    | ~ class_Groups_Ogroup__add(U_8614) ),
    inference(clausify,[status(thm)],[f_2018_2]) ).

cnf(f_2018_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8614),U_8615) = c_Groups_Ozero__class_Ozero(U_8614)
    | U_8615 != c_Groups_Ozero__class_Ozero(U_8614)
    | ~ class_Groups_Ogroup__add(U_8614) ),
    inference(clausify,[status(thm)],[f_2018_2]) ).

fof(f_2019_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).

fof(f_2019_2,plain,
    ! [U_8617,U_8616] :
      ( ( ( U_8617 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),U_8617)
          | U_8617 != c_Groups_Ozero__class_Ozero(U_8616) )
        & ( U_8617 = c_Groups_Ozero__class_Ozero(U_8616)
          | U_8617 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),U_8617) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_8616) ),
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

cnf(f_2019_3,plain,
    ( U_8617 = c_Groups_Ozero__class_Ozero(U_8616)
    | U_8617 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),U_8617)
    | ~ class_Groups_Olinordered__ab__group__add(U_8616) ),
    inference(clausify,[status(thm)],[f_2019_2]) ).

cnf(f_2019_4,plain,
    ( U_8617 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),U_8617)
    | U_8617 != c_Groups_Ozero__class_Ozero(U_8616)
    | ~ class_Groups_Olinordered__ab__group__add(U_8616) ),
    inference(clausify,[status(thm)],[f_2019_2]) ).

fof(f_2020_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
          | c_Groups_Ozero__class_Ozero(T_a) != V_a_2 )
        & ( c_Groups_Ozero__class_Ozero(T_a) = V_a_2
          | c_Groups_Ozero__class_Ozero(T_a) != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).

fof(f_2020_2,plain,
    ! [U_8619,U_8618] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_8618) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8618),U_8619)
          | c_Groups_Ozero__class_Ozero(U_8618) != U_8619 )
        & ( c_Groups_Ozero__class_Ozero(U_8618) = U_8619
          | c_Groups_Ozero__class_Ozero(U_8618) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8618),U_8619) ) )
      | ~ class_Groups_Ogroup__add(U_8618) ),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

cnf(f_2020_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_8618) = U_8619
    | c_Groups_Ozero__class_Ozero(U_8618) != hAPP(c_Groups_Ouminus__class_Ouminus(U_8618),U_8619)
    | ~ class_Groups_Ogroup__add(U_8618) ),
    inference(clausify,[status(thm)],[f_2020_2]) ).

cnf(f_2020_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_8618) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8618),U_8619)
    | c_Groups_Ozero__class_Ozero(U_8618) != U_8619
    | ~ class_Groups_Ogroup__add(U_8618) ),
    inference(clausify,[status(thm)],[f_2020_2]) ).

fof(f_2021_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_2021_2,plain,
    ! [U_8620] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8620),c_Groups_Ozero__class_Ozero(U_8620)) = c_Groups_Ozero__class_Ozero(U_8620)
      | ~ class_Groups_Ogroup__add(U_8620) ),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

cnf(f_2021_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8620),c_Groups_Ozero__class_Ozero(U_8620)) = c_Groups_Ozero__class_Ozero(U_8620)
    | ~ class_Groups_Ogroup__add(U_8620) ),
    inference(clausify,[status(thm)],[f_2021_2]) ).

fof(f_2022_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_2022_2,plain,
    ! [U_8624,U_8623,U_8622,U_8621] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),U_8624))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),U_8623)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8621),U_8623),U_8624)))
      | ~ class_Orderings_Olinorder(U_8621) ),
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

cnf(f_2022_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),U_8623))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8621),U_8623),U_8624)))
    | ~ class_Orderings_Olinorder(U_8621) ),
    inference(clausify,[status(thm)],[f_2022_2]) ).

cnf(f_2022_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),U_8624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8621),U_8622),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8621),U_8623),U_8624)))
    | ~ class_Orderings_Olinorder(U_8621) ),
    inference(clausify,[status(thm)],[f_2022_2]) ).

fof(f_2023_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_2023_2,plain,
    ! [U_8629,U_8628,U_8627,U_8626,U_8625] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8625),U_8626),U_8628)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8625),U_8627),U_8629)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),U_8628),U_8629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),U_8626),U_8627))
      | ~ class_Orderings_Olinorder(U_8625) ),
    inference(variable_rename,[status(thm)],[f_2023_1]) ).

cnf(f_2023_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8625),U_8626),U_8628)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8625),U_8627),U_8629)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),U_8628),U_8629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8625),U_8626),U_8627))
    | ~ class_Orderings_Olinorder(U_8625) ),
    inference(clausify,[status(thm)],[f_2023_2]) ).

fof(f_2024_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_2024_2,plain,
    ! [U_8633,U_8632,U_8631,U_8630] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8630),U_8632),U_8633)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),U_8633))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),U_8632))
      | ~ class_Orderings_Olinorder(U_8630) ),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

cnf(f_2024_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8630),U_8632),U_8633)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),U_8633))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8630),U_8631),U_8632))
    | ~ class_Orderings_Olinorder(U_8630) ),
    inference(clausify,[status(thm)],[f_2024_2]) ).

fof(f_2025_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_2025_2,plain,
    ! [U_8637,U_8636,U_8635,U_8634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8634),U_8636),U_8637)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),U_8637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),U_8636))
      | ~ class_Orderings_Olinorder(U_8634) ),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

cnf(f_2025_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8634),U_8636),U_8637)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),U_8637))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8634),U_8635),U_8636))
    | ~ class_Orderings_Olinorder(U_8634) ),
    inference(clausify,[status(thm)],[f_2025_2]) ).

fof(f_2026_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_2026_2,plain,
    ! [U_8640,U_8639,U_8638] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8638),U_8640),U_8639) = U_8639
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8638),U_8639),U_8640))
      | ~ class_Orderings_Olinorder(U_8638) ),
    inference(variable_rename,[status(thm)],[f_2026_1]) ).

cnf(f_2026_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8638),U_8640),U_8639) = U_8639
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8638),U_8639),U_8640))
    | ~ class_Orderings_Olinorder(U_8638) ),
    inference(clausify,[status(thm)],[f_2026_2]) ).

fof(f_2027_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_2027_2,plain,
    ! [U_8643,U_8642,U_8641] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8641),U_8642),U_8643) = U_8642
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8641),U_8642),U_8643))
      | ~ class_Orderings_Olinorder(U_8641) ),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

cnf(f_2027_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8641),U_8642),U_8643) = U_8642
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8641),U_8642),U_8643))
    | ~ class_Orderings_Olinorder(U_8641) ),
    inference(clausify,[status(thm)],[f_2027_2]) ).

fof(f_2028_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_2028_2,plain,
    ! [U_8647,U_8646,U_8645,U_8644] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8644),U_8647),U_8645)),U_8646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),U_8645),U_8646))
      | ~ class_Orderings_Olinorder(U_8644) ),
    inference(variable_rename,[status(thm)],[f_2028_1]) ).

cnf(f_2028_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8644),U_8647),U_8645)),U_8646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8644),U_8645),U_8646))
    | ~ class_Orderings_Olinorder(U_8644) ),
    inference(clausify,[status(thm)],[f_2028_2]) ).

fof(f_2029_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_2029_2,plain,
    ! [U_8651,U_8650,U_8649,U_8648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8648),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8648),U_8649),U_8651)),U_8650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8648),U_8649),U_8650))
      | ~ class_Orderings_Olinorder(U_8648) ),
    inference(variable_rename,[status(thm)],[f_2029_1]) ).

cnf(f_2029_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8648),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8648),U_8649),U_8651)),U_8650))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8648),U_8649),U_8650))
    | ~ class_Orderings_Olinorder(U_8648) ),
    inference(clausify,[status(thm)],[f_2029_2]) ).

fof(f_2030_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).

fof(f_2030_2,plain,
    ! [U_8655,U_8654,U_8653,U_8652] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8652),U_8653),U_8654)),U_8655))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8654),U_8655))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8653),U_8655)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8654),U_8655))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8653),U_8655))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8652),U_8653),U_8654)),U_8655)) ) )
      | ~ class_Orderings_Olinorder(U_8652) ),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

cnf(f_2030_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8654),U_8655))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8653),U_8655))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8652),U_8653),U_8654)),U_8655))
    | ~ class_Orderings_Olinorder(U_8652) ),
    inference(clausify,[status(thm)],[f_2030_2]) ).

cnf(f_2030_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8653),U_8655))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8652),U_8653),U_8654)),U_8655))
    | ~ class_Orderings_Olinorder(U_8652) ),
    inference(clausify,[status(thm)],[f_2030_2]) ).

cnf(f_2030_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),U_8654),U_8655))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8652),U_8653),U_8654)),U_8655))
    | ~ class_Orderings_Olinorder(U_8652) ),
    inference(clausify,[status(thm)],[f_2030_2]) ).

fof(f_2031_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).

fof(f_2031_2,plain,
    ! [U_8659,U_8658,U_8657,U_8656] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),U_8658),U_8659)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8659))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8658)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8659))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8658)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),U_8658),U_8659))) ) )
      | ~ class_Orderings_Olinorder(U_8656) ),
    inference(variable_rename,[status(thm)],[f_2031_1]) ).

cnf(f_2031_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),U_8658),U_8659)))
    | ~ class_Orderings_Olinorder(U_8656) ),
    inference(clausify,[status(thm)],[f_2031_2]) ).

cnf(f_2031_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),U_8658),U_8659)))
    | ~ class_Orderings_Olinorder(U_8656) ),
    inference(clausify,[status(thm)],[f_2031_2]) ).

cnf(f_2031_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),U_8658),U_8659)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8656),U_8657),U_8658))
    | ~ class_Orderings_Olinorder(U_8656) ),
    inference(clausify,[status(thm)],[f_2031_2]) ).

fof(f_2032_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).

fof(f_2032_2,plain,
    ! [U_8662,U_8661,U_8660] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8660),U_8661),U_8662))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8660),U_8661),U_8662) != U_8661 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8660),U_8661),U_8662) = U_8661
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8660),U_8661),U_8662)) ) )
      | ~ class_Orderings_Olinorder(U_8660) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

cnf(f_2032_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8660),U_8661),U_8662) = U_8661
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8660),U_8661),U_8662))
    | ~ class_Orderings_Olinorder(U_8660) ),
    inference(clausify,[status(thm)],[f_2032_2]) ).

cnf(f_2032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8660),U_8661),U_8662))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8660),U_8661),U_8662) != U_8661
    | ~ class_Orderings_Olinorder(U_8660) ),
    inference(clausify,[status(thm)],[f_2032_2]) ).

fof(f_2033_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_2033_2,plain,
    ! [U_8665,U_8664,U_8663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8663),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8663),U_8664),U_8665)),U_8665))
      | ~ class_Orderings_Olinorder(U_8663) ),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

cnf(f_2033_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8663),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8663),U_8664),U_8665)),U_8665))
    | ~ class_Orderings_Olinorder(U_8663) ),
    inference(clausify,[status(thm)],[f_2033_2]) ).

fof(f_2034_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_2034_2,plain,
    ! [U_8668,U_8667,U_8666] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8666),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8666),U_8667),U_8668)),U_8667))
      | ~ class_Orderings_Olinorder(U_8666) ),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

cnf(f_2034_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8666),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8666),U_8667),U_8668)),U_8667))
    | ~ class_Orderings_Olinorder(U_8666) ),
    inference(clausify,[status(thm)],[f_2034_2]) ).

fof(f_2035_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_2035_2,plain,
    ! [U_8671,U_8670,U_8669] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8669),hAPP(c_Groups_Ouminus__class_Ouminus(U_8669),U_8671)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8669),U_8670)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8669),U_8670),U_8671))
      | ~ class_Lattices_Oboolean__algebra(U_8669) ),
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

cnf(f_2035_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8669),hAPP(c_Groups_Ouminus__class_Ouminus(U_8669),U_8671)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8669),U_8670)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8669),U_8670),U_8671))
    | ~ class_Lattices_Oboolean__algebra(U_8669) ),
    inference(clausify,[status(thm)],[f_2035_2]) ).

fof(f_2036_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) ) )
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).

fof(f_2036_2,plain,
    ! [U_8674,U_8673,U_8672] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8674)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),U_8674),U_8673)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),U_8674),U_8673))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8674))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_8672) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

cnf(f_2036_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),U_8674),U_8673))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8674)))
    | ~ class_Lattices_Oboolean__algebra(U_8672) ),
    inference(clausify,[status(thm)],[f_2036_2]) ).

cnf(f_2036_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8672),U_8674)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8672),U_8674),U_8673))
    | ~ class_Lattices_Oboolean__algebra(U_8672) ),
    inference(clausify,[status(thm)],[f_2036_2]) ).

fof(f_2037_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_2037_2,plain,
    ! [U_8677,U_8676,U_8675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8675),hAPP(c_Groups_Ouminus__class_Ouminus(U_8675),U_8677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8675),U_8676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8675),U_8676),U_8677))
      | ~ class_Groups_Oordered__ab__group__add(U_8675) ),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

cnf(f_2037_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8675),hAPP(c_Groups_Ouminus__class_Ouminus(U_8675),U_8677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8675),U_8676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8675),U_8676),U_8677))
    | ~ class_Groups_Oordered__ab__group__add(U_8675) ),
    inference(clausify,[status(thm)],[f_2037_2]) ).

fof(f_2038_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).

fof(f_2038_2,plain,
    ! [U_8680,U_8679,U_8678] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8679)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8680)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),U_8680),U_8679)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),U_8680),U_8679))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8679)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8680))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8678) ),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

cnf(f_2038_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),U_8680),U_8679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8679)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8680)))
    | ~ class_Groups_Oordered__ab__group__add(U_8678) ),
    inference(clausify,[status(thm)],[f_2038_2]) ).

cnf(f_2038_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8679)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8678),U_8680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8678),U_8680),U_8679))
    | ~ class_Groups_Oordered__ab__group__add(U_8678) ),
    inference(clausify,[status(thm)],[f_2038_2]) ).

fof(f_2039_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).

fof(f_2039_2,plain,
    ! [U_8683,U_8682,U_8681] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8682)),U_8683))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8683)),U_8682)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8683)),U_8682))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8682)),U_8683)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8681) ),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

cnf(f_2039_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8683)),U_8682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8682)),U_8683))
    | ~ class_Groups_Oordered__ab__group__add(U_8681) ),
    inference(clausify,[status(thm)],[f_2039_2]) ).

cnf(f_2039_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8682)),U_8683))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Ouminus__class_Ouminus(U_8681),U_8683)),U_8682))
    | ~ class_Groups_Oordered__ab__group__add(U_8681) ),
    inference(clausify,[status(thm)],[f_2039_2]) ).

fof(f_2040_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).

fof(f_2040_2,plain,
    ! [U_8686,U_8685,U_8684] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8685),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8686)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8686),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8685))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8686),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8685)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8685),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8686))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8684) ),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

cnf(f_2040_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8686),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8685),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8686)))
    | ~ class_Groups_Oordered__ab__group__add(U_8684) ),
    inference(clausify,[status(thm)],[f_2040_2]) ).

cnf(f_2040_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8685),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8684),U_8686),hAPP(c_Groups_Ouminus__class_Ouminus(U_8684),U_8685)))
    | ~ class_Groups_Oordered__ab__group__add(U_8684) ),
    inference(clausify,[status(thm)],[f_2040_2]) ).

fof(f_2041_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_2041_2,plain,
    ! [U_8690,U_8689,U_8688,U_8687] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),U_8689),U_8690))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),U_8688),U_8690)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8687),U_8688),U_8689)),U_8690))
      | ~ class_Orderings_Olinorder(U_8687) ),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

cnf(f_2041_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),U_8688),U_8690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8687),U_8688),U_8689)),U_8690))
    | ~ class_Orderings_Olinorder(U_8687) ),
    inference(clausify,[status(thm)],[f_2041_2]) ).

cnf(f_2041_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),U_8689),U_8690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8687),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8687),U_8688),U_8689)),U_8690))
    | ~ class_Orderings_Olinorder(U_8687) ),
    inference(clausify,[status(thm)],[f_2041_2]) ).

fof(f_2042_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_2042_2,plain,
    ! [U_8695,U_8694,U_8693,U_8692,U_8691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8691),U_8692),U_8694)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8691),U_8693),U_8695)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),U_8694),U_8695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),U_8692),U_8693))
      | ~ class_Orderings_Olinorder(U_8691) ),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

cnf(f_2042_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8691),U_8692),U_8694)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8691),U_8693),U_8695)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),U_8694),U_8695))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),U_8692),U_8693))
    | ~ class_Orderings_Olinorder(U_8691) ),
    inference(clausify,[status(thm)],[f_2042_2]) ).

fof(f_2043_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_2043_2,plain,
    ! [U_8699,U_8698,U_8697,U_8696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8696),U_8697),U_8699)),U_8698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),U_8699),U_8698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),U_8697),U_8698))
      | ~ class_Orderings_Olinorder(U_8696) ),
    inference(variable_rename,[status(thm)],[f_2043_1]) ).

cnf(f_2043_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8696),U_8697),U_8699)),U_8698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),U_8699),U_8698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8696),U_8697),U_8698))
    | ~ class_Orderings_Olinorder(U_8696) ),
    inference(clausify,[status(thm)],[f_2043_2]) ).

fof(f_2044_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_2044_2,plain,
    ! [U_8703,U_8702,U_8701,U_8700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8700),U_8701),U_8703)),U_8702))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),U_8703),U_8702))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),U_8701),U_8702))
      | ~ class_Orderings_Olinorder(U_8700) ),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

cnf(f_2044_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8700),U_8701),U_8703)),U_8702))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),U_8703),U_8702))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8700),U_8701),U_8702))
    | ~ class_Orderings_Olinorder(U_8700) ),
    inference(clausify,[status(thm)],[f_2044_2]) ).

fof(f_2045_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_2045_2,plain,
    ! [U_8706,U_8705,U_8704] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8704),U_8706),U_8705) = U_8706
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8704),U_8705),U_8706))
      | ~ class_Orderings_Olinorder(U_8704) ),
    inference(variable_rename,[status(thm)],[f_2045_1]) ).

cnf(f_2045_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8704),U_8706),U_8705) = U_8706
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8704),U_8705),U_8706))
    | ~ class_Orderings_Olinorder(U_8704) ),
    inference(clausify,[status(thm)],[f_2045_2]) ).

fof(f_2046_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_2046_2,plain,
    ! [U_8709,U_8708,U_8707] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8707),U_8708),U_8709) = U_8709
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8707),U_8708),U_8709))
      | ~ class_Orderings_Olinorder(U_8707) ),
    inference(variable_rename,[status(thm)],[f_2046_1]) ).

cnf(f_2046_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8707),U_8708),U_8709) = U_8709
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8707),U_8708),U_8709))
    | ~ class_Orderings_Olinorder(U_8707) ),
    inference(clausify,[status(thm)],[f_2046_2]) ).

fof(f_2047_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_2047_2,plain,
    ! [U_8713,U_8712,U_8711,U_8710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),U_8713),U_8712)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),U_8712))
      | ~ class_Orderings_Olinorder(U_8710) ),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

cnf(f_2047_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8710),U_8713),U_8712)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),U_8712))
    | ~ class_Orderings_Olinorder(U_8710) ),
    inference(clausify,[status(thm)],[f_2047_2]) ).

fof(f_2048_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_2048_2,plain,
    ! [U_8717,U_8716,U_8715,U_8714] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8714),U_8716),U_8717)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716))
      | ~ class_Orderings_Olinorder(U_8714) ),
    inference(variable_rename,[status(thm)],[f_2048_1]) ).

cnf(f_2048_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8714),U_8716),U_8717)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716))
    | ~ class_Orderings_Olinorder(U_8714) ),
    inference(clausify,[status(thm)],[f_2048_2]) ).

fof(f_2049_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).

fof(f_2049_2,plain,
    ! [U_8721,U_8720,U_8719,U_8718] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8718),U_8719),U_8720)),U_8721))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8720),U_8721))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8719),U_8721)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8720),U_8721))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8719),U_8721)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8718),U_8719),U_8720)),U_8721)) ) )
      | ~ class_Orderings_Olinorder(U_8718) ),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

cnf(f_2049_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8719),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8718),U_8719),U_8720)),U_8721))
    | ~ class_Orderings_Olinorder(U_8718) ),
    inference(clausify,[status(thm)],[f_2049_2]) ).

cnf(f_2049_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8720),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8718),U_8719),U_8720)),U_8721))
    | ~ class_Orderings_Olinorder(U_8718) ),
    inference(clausify,[status(thm)],[f_2049_2]) ).

cnf(f_2049_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8718),U_8719),U_8720)),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8720),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8718),U_8719),U_8721))
    | ~ class_Orderings_Olinorder(U_8718) ),
    inference(clausify,[status(thm)],[f_2049_2]) ).

fof(f_2050_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).

fof(f_2050_2,plain,
    ! [U_8725,U_8724,U_8723,U_8722] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8722),U_8724),U_8725)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8725))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8724)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8725))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8724))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8722),U_8724),U_8725))) ) )
      | ~ class_Orderings_Olinorder(U_8722) ),
    inference(variable_rename,[status(thm)],[f_2050_1]) ).

cnf(f_2050_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8722),U_8724),U_8725)))
    | ~ class_Orderings_Olinorder(U_8722) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

cnf(f_2050_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8724))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8722),U_8724),U_8725)))
    | ~ class_Orderings_Olinorder(U_8722) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

cnf(f_2050_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),U_8725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8722),U_8723),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8722),U_8724),U_8725)))
    | ~ class_Orderings_Olinorder(U_8722) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

fof(f_2051_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).

fof(f_2051_2,plain,
    ! [U_8728,U_8727,U_8726] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8726),U_8727),U_8728))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8726),U_8727),U_8728) != U_8728 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8726),U_8727),U_8728) = U_8728
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8726),U_8727),U_8728)) ) )
      | ~ class_Orderings_Olinorder(U_8726) ),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

cnf(f_2051_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8726),U_8727),U_8728) = U_8728
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8726),U_8727),U_8728))
    | ~ class_Orderings_Olinorder(U_8726) ),
    inference(clausify,[status(thm)],[f_2051_2]) ).

cnf(f_2051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8726),U_8727),U_8728))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8726),U_8727),U_8728) != U_8728
    | ~ class_Orderings_Olinorder(U_8726) ),
    inference(clausify,[status(thm)],[f_2051_2]) ).

fof(f_2052_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_2052_2,plain,
    ! [U_8731,U_8730,U_8729] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8729),U_8730),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8729),U_8731),U_8730)))
      | ~ class_Orderings_Olinorder(U_8729) ),
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

cnf(f_2052_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8729),U_8730),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8729),U_8731),U_8730)))
    | ~ class_Orderings_Olinorder(U_8729) ),
    inference(clausify,[status(thm)],[f_2052_2]) ).

fof(f_2053_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_2053_2,plain,
    ! [U_8734,U_8733,U_8732] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8732),U_8733),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8732),U_8733),U_8734)))
      | ~ class_Orderings_Olinorder(U_8732) ),
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

cnf(f_2053_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8732),U_8733),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8732),U_8733),U_8734)))
    | ~ class_Orderings_Olinorder(U_8732) ),
    inference(clausify,[status(thm)],[f_2053_2]) ).

fof(f_2054_1,plain,
    ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),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_2054_2,plain,
    ! [U_8737,U_8736,U_8735] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8735,tc_Nat_Onat),U_8736),U_8737) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8735,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8735),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8736)),U_8737)),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

cnf(f_2054_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8735,tc_Nat_Onat),U_8736),U_8737) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8735,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8735),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8736)),U_8737)),
    inference(clausify,[status(thm)],[f_2054_2]) ).

fof(f_2055_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).

fof(f_2055_2,plain,
    ! [U_8742,U_8741,U_8740,U_8739,U_8738] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8738,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,U_8739),U_8740)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,U_8741),U_8742)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8738),U_8739),U_8741)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8738),U_8740),U_8742))
      | ~ class_Orderings_Olinorder(U_8738) ),
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

cnf(f_2055_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8738,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,U_8739),U_8740)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,U_8741),U_8742)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8738,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8738),U_8739),U_8741)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8738),U_8740),U_8742))
    | ~ class_Orderings_Olinorder(U_8738) ),
    inference(clausify,[status(thm)],[f_2055_2]) ).

fof(f_2056_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).

fof(f_2056_2,plain,
    ! [U_8747,U_8746,U_8745,U_8744,U_8743] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8743,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,U_8744,U_8745)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,U_8746,U_8747)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8743),U_8744),U_8746),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8743),U_8745),U_8747))
      | ~ class_Orderings_Olinorder(U_8743) ),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

cnf(f_2056_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8743,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,U_8744,U_8745)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,U_8746,U_8747)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8743,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8743),U_8744),U_8746),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8743),U_8745),U_8747))
    | ~ class_Orderings_Olinorder(U_8743) ),
    inference(clausify,[status(thm)],[f_2056_2]) ).

fof(f_2057_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).

fof(f_2057_2,plain,
    ! [U_8752,U_8751,U_8750,U_8749,U_8748] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8748,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,U_8749,U_8750)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,U_8751,U_8752)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8748),U_8749),U_8751),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8748),U_8750),U_8752))
      | ~ class_Orderings_Olinorder(U_8748) ),
    inference(variable_rename,[status(thm)],[f_2057_1]) ).

cnf(f_2057_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8748,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,U_8749,U_8750)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,U_8751,U_8752)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8748,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8748),U_8749),U_8751),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8748),U_8750),U_8752))
    | ~ class_Orderings_Olinorder(U_8748) ),
    inference(clausify,[status(thm)],[f_2057_2]) ).

fof(f_2058_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).

fof(f_2058_2,plain,
    ! [U_8757,U_8756,U_8755,U_8754,U_8753] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8753,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8753,U_8754,U_8755)),c_SetInterval_Oord__class_OatLeastAtMost(U_8753,U_8756,U_8757)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8753,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8753),U_8754),U_8756),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8753),U_8755),U_8757))
      | ~ class_Orderings_Olinorder(U_8753) ),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

cnf(f_2058_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8753,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8753,U_8754,U_8755)),c_SetInterval_Oord__class_OatLeastAtMost(U_8753,U_8756,U_8757)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8753,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8753),U_8754),U_8756),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8753),U_8755),U_8757))
    | ~ class_Orderings_Olinorder(U_8753) ),
    inference(clausify,[status(thm)],[f_2058_2]) ).

fof(f_2059_1,plain,
    ! [V_A_2,V_c_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).

fof(f_2059_2,plain,
    ! [U_8760,U_8759,U_8758] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8758,tc_HOL_Obool)),U_8760)))
        | hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),U_8760)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),U_8760))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8758,tc_HOL_Obool)),U_8760))) ) ),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

fof(f_2059_3,plain,
    ( ! [U_8766,U_8764,U_8762] :
        ( hBOOL(hAPP(hAPP(c_member(U_8762),U_8764),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8762,tc_HOL_Obool)),U_8766)))
        | hBOOL(hAPP(hAPP(c_member(U_8762),U_8764),U_8766)) )
    & ! [U_8765,U_8763,U_8761] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8761),U_8763),U_8765))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8761),U_8763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8761,tc_HOL_Obool)),U_8765))) ) ),
    inference(miniscope,[status(thm)],[f_2059_2]) ).

cnf(f_2059_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8761),U_8763),U_8765))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8761),U_8763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8761,tc_HOL_Obool)),U_8765))) ),
    inference(clausify,[status(thm)],[f_2059_3]) ).

cnf(f_2059_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8762),U_8764),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8762,tc_HOL_Obool)),U_8766)))
    | hBOOL(hAPP(hAPP(c_member(U_8762),U_8764),U_8766)) ),
    inference(clausify,[status(thm)],[f_2059_3]) ).

fof(f_2060_1,plain,
    ! [V_A_2,V_c_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplD]) ).

fof(f_2060_2,plain,
    ! [U_8769,U_8768,U_8767] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8767),U_8768),U_8769))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8767),U_8768),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8767,tc_HOL_Obool)),U_8769))) ),
    inference(variable_rename,[status(thm)],[f_2060_1]) ).

cnf(f_2060_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8767),U_8768),U_8769))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8767),U_8768),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8767,tc_HOL_Obool)),U_8769))) ),
    inference(clausify,[status(thm)],[f_2060_2]) ).

fof(f_2061_1,plain,
    ! [V_A_2,V_c_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplE]) ).

fof(f_2061_2,plain,
    ! [U_8772,U_8771,U_8770] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8770),U_8771),U_8772))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8770),U_8771),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8770,tc_HOL_Obool)),U_8772))) ),
    inference(variable_rename,[status(thm)],[f_2061_1]) ).

cnf(f_2061_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8770),U_8771),U_8772))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8770),U_8771),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8770,tc_HOL_Obool)),U_8772))) ),
    inference(clausify,[status(thm)],[f_2061_2]) ).

fof(f_2062_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_2062_2,plain,
    ! [U_8776,U_8775,U_8774,U_8773] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8773),U_8774),U_8775)),U_8776) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),U_8774),U_8776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),U_8775),U_8776))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8773) ),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

cnf(f_2062_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8773),U_8774),U_8775)),U_8776) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),U_8774),U_8776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8773),U_8775),U_8776))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8773) ),
    inference(clausify,[status(thm)],[f_2062_2]) ).

fof(f_2063_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
            & V_a_2 != V_b_2 ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
          | V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).

fof(f_2063_2,plain,
    ! [U_8779,U_8778,U_8777] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8778),U_8778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8779),U_8779)
          | ( U_8778 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8777),U_8779)
            & U_8778 != U_8779 ) )
        & ( U_8778 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8777),U_8779)
          | U_8778 = U_8779
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8778),U_8778) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8779),U_8779) ) )
      | ~ class_Rings_Oidom(U_8777) ),
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

cnf(f_2063_3,plain,
    ( U_8778 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8777),U_8779)
    | U_8778 = U_8779
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8778),U_8778) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8779),U_8779)
    | ~ class_Rings_Oidom(U_8777) ),
    inference(clausify,[status(thm)],[f_2063_2]) ).

cnf(f_2063_4,plain,
    ( U_8778 != U_8779
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8778),U_8778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8779),U_8779)
    | ~ class_Rings_Oidom(U_8777) ),
    inference(clausify,[status(thm)],[f_2063_2]) ).

cnf(f_2063_5,plain,
    ( U_8778 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8777),U_8779)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8778),U_8778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8777),U_8779),U_8779)
    | ~ class_Rings_Oidom(U_8777) ),
    inference(clausify,[status(thm)],[f_2063_2]) ).

fof(f_2064_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_2064_2,plain,
    ! [U_8782,U_8781,U_8780] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8780),hAPP(c_Groups_Ouminus__class_Ouminus(U_8780),U_8781)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8780),U_8782)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8780),U_8781),U_8782)
      | ~ class_Rings_Oring(U_8780) ),
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

cnf(f_2064_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8780),hAPP(c_Groups_Ouminus__class_Ouminus(U_8780),U_8781)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8780),U_8782)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8780),U_8781),U_8782)
    | ~ class_Rings_Oring(U_8780) ),
    inference(clausify,[status(thm)],[f_2064_2]) ).

fof(f_2065_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_2065_2,plain,
    ! [U_8785,U_8784,U_8783] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8783),hAPP(c_Groups_Ouminus__class_Ouminus(U_8783),U_8784)),U_8785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8783),U_8784),hAPP(c_Groups_Ouminus__class_Ouminus(U_8783),U_8785))
      | ~ class_Rings_Oring(U_8783) ),
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

cnf(f_2065_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8783),hAPP(c_Groups_Ouminus__class_Ouminus(U_8783),U_8784)),U_8785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8783),U_8784),hAPP(c_Groups_Ouminus__class_Ouminus(U_8783),U_8785))
    | ~ class_Rings_Oring(U_8783) ),
    inference(clausify,[status(thm)],[f_2065_2]) ).

fof(f_2066_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_2066_2,plain,
    ! [U_8788,U_8787,U_8786] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8786),U_8787),U_8788)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8786),hAPP(c_Groups_Ouminus__class_Ouminus(U_8786),U_8787)),U_8788)
      | ~ class_Rings_Oring(U_8786) ),
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

cnf(f_2066_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8786),U_8787),U_8788)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8786),hAPP(c_Groups_Ouminus__class_Ouminus(U_8786),U_8787)),U_8788)
    | ~ class_Rings_Oring(U_8786) ),
    inference(clausify,[status(thm)],[f_2066_2]) ).

fof(f_2067_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_2067_2,plain,
    ! [U_8791,U_8790,U_8789] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8789),U_8790),U_8791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8789),U_8790),hAPP(c_Groups_Ouminus__class_Ouminus(U_8789),U_8791))
      | ~ class_Rings_Oring(U_8789) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

cnf(f_2067_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8789),U_8790),U_8791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8789),U_8790),hAPP(c_Groups_Ouminus__class_Ouminus(U_8789),U_8791))
    | ~ class_Rings_Oring(U_8789) ),
    inference(clausify,[status(thm)],[f_2067_2]) ).

fof(f_2068_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_2068_2,plain,
    ! [U_8794,U_8793,U_8792] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8792),U_8793),U_8794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8792),hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),U_8793)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),U_8794))
      | ~ class_Groups_Oab__group__add(U_8792) ),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

cnf(f_2068_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8792),U_8793),U_8794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8792),hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),U_8793)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8792),U_8794))
    | ~ class_Groups_Oab__group__add(U_8792) ),
    inference(clausify,[status(thm)],[f_2068_2]) ).

fof(f_2069_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_2069_2,plain,
    ! [U_8797,U_8796,U_8795] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8795),U_8796),U_8797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8795),hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),U_8797)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),U_8796))
      | ~ class_Groups_Ogroup__add(U_8795) ),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

cnf(f_2069_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8795),U_8796),U_8797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8795),hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),U_8797)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8795),U_8796))
    | ~ class_Groups_Ogroup__add(U_8795) ),
    inference(clausify,[status(thm)],[f_2069_2]) ).

fof(f_2070_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_2070_2,plain,
    ! [U_8800,U_8799,U_8798] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8798),U_8799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8798),hAPP(c_Groups_Ouminus__class_Ouminus(U_8798),U_8799)),U_8800)) = U_8800
      | ~ class_Groups_Ogroup__add(U_8798) ),
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

cnf(f_2070_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8798),U_8799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8798),hAPP(c_Groups_Ouminus__class_Ouminus(U_8798),U_8799)),U_8800)) = U_8800
    | ~ class_Groups_Ogroup__add(U_8798) ),
    inference(clausify,[status(thm)],[f_2070_2]) ).

fof(f_2071_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_2071_2,plain,
    ! [U_8803,U_8802,U_8801] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8801),hAPP(c_Groups_Ouminus__class_Ouminus(U_8801),U_8802)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8801),U_8802),U_8803)) = U_8803
      | ~ class_Groups_Ogroup__add(U_8801) ),
    inference(variable_rename,[status(thm)],[f_2071_1]) ).

cnf(f_2071_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8801),hAPP(c_Groups_Ouminus__class_Ouminus(U_8801),U_8802)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8801),U_8802),U_8803)) = U_8803
    | ~ class_Groups_Ogroup__add(U_8801) ),
    inference(clausify,[status(thm)],[f_2071_2]) ).

fof(f_2072_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_2072_2,plain,
    ! [U_8807,U_8806,U_8805,U_8804] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),U_8805),U_8806)),U_8807) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),U_8805),U_8807)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),U_8806),U_8807))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8804) ),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

cnf(f_2072_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),U_8805),U_8806)),U_8807) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),U_8805),U_8807)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8804),U_8806),U_8807))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8804) ),
    inference(clausify,[status(thm)],[f_2072_2]) ).

fof(f_2073_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_2073_2,plain,
    ! [U_8811,U_8810,U_8809,U_8808] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8808),U_8809),U_8810)),U_8811) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8808),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),U_8809),U_8811)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),U_8810),U_8811))
      | ~ class_Groups_Oordered__ab__group__add(U_8808) ),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

cnf(f_2073_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8808),U_8809),U_8810)),U_8811) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8808),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),U_8809),U_8811)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8808),U_8810),U_8811))
    | ~ class_Groups_Oordered__ab__group__add(U_8808) ),
    inference(clausify,[status(thm)],[f_2073_2]) ).

fof(f_2074_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_2074_2,plain,
    ! [U_8814,U_8813,U_8812] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8812),U_8813),U_8814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8812),U_8814),U_8813)
      | ~ class_Groups_Oab__group__add(U_8812) ),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

cnf(f_2074_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8812),U_8813),U_8814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8812),U_8814),U_8813)
    | ~ class_Groups_Oab__group__add(U_8812) ),
    inference(clausify,[status(thm)],[f_2074_2]) ).

fof(f_2075_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_2075_2,plain,
    ! [U_8817,U_8816,U_8815] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8815),U_8816)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8817),U_8816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8815),U_8817)),U_8816),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

cnf(f_2075_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8815),U_8816)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8817),U_8816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8815),U_8817)),U_8816),
    inference(clausify,[status(thm)],[f_2075_2]) ).

fof(f_2076_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_2076_2,plain,
    ! [U_8819,U_8818] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8818),hAPP(c_Groups_Ouminus__class_Ouminus(U_8818),U_8819)) = hAPP(c_Groups_Oabs__class_Oabs(U_8818),U_8819)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8818) ),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

cnf(f_2076_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8818),hAPP(c_Groups_Ouminus__class_Ouminus(U_8818),U_8819)) = hAPP(c_Groups_Oabs__class_Oabs(U_8818),U_8819)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8818) ),
    inference(clausify,[status(thm)],[f_2076_2]) ).

fof(f_2077_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Compl]) ).

fof(f_2077_2,plain,
    ! [U_8823,U_8822,U_8821,U_8820] : hAPP(c_Set_Ovimage(U_8820,U_8821,U_8822),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8821,tc_HOL_Obool)),U_8823)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8820,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_8820,U_8821,U_8822),U_8823)),
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

cnf(f_2077_3,plain,
    hAPP(c_Set_Ovimage(U_8820,U_8821,U_8822),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8821,tc_HOL_Obool)),U_8823)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8820,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_8820,U_8821,U_8822),U_8823)),
    inference(clausify,[status(thm)],[f_2077_2]) ).

fof(f_2078_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).

fof(f_2078_2,plain,
    ! [U_8828,U_8827,U_8826,U_8825,U_8824] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),hAPP(hAPP(c_COMBS(U_8825,U_8824,U_8824),hAPP(hAPP(c_COMBB(U_8824,tc_fun(U_8824,U_8824),U_8825),c_Groups_Otimes__class_Otimes(U_8824)),U_8826)),U_8827)),U_8828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8824),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),U_8826),U_8828)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),U_8827),U_8828))
      | ~ class_Groups_Ocomm__monoid__mult(U_8824) ),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

cnf(f_2078_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),hAPP(hAPP(c_COMBS(U_8825,U_8824,U_8824),hAPP(hAPP(c_COMBB(U_8824,tc_fun(U_8824,U_8824),U_8825),c_Groups_Otimes__class_Otimes(U_8824)),U_8826)),U_8827)),U_8828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8824),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),U_8826),U_8828)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8825,U_8824),U_8827),U_8828))
    | ~ class_Groups_Ocomm__monoid__mult(U_8824) ),
    inference(clausify,[status(thm)],[f_2078_2]) ).

fof(f_2079_1,plain,
    ! [V_A_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).

fof(f_2079_2,plain,
    ! [U_8831,U_8830,U_8829] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8830,U_8829),hAPP(c_COMBK(U_8829,U_8830),c_Groups_Oone__class_Oone(U_8829))),U_8831) = c_Groups_Oone__class_Oone(U_8829)
      | ~ class_Groups_Ocomm__monoid__mult(U_8829) ),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

cnf(f_2079_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8830,U_8829),hAPP(c_COMBK(U_8829,U_8830),c_Groups_Oone__class_Oone(U_8829))),U_8831) = c_Groups_Oone__class_Oone(U_8829)
    | ~ class_Groups_Ocomm__monoid__mult(U_8829) ),
    inference(clausify,[status(thm)],[f_2079_2]) ).

fof(f_2080_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).

fof(f_2080_2,plain,
    ! [U_8835,U_8834,U_8833,U_8832] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8832),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8833,U_8832),U_8834),U_8835)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8833,U_8832),hAPP(hAPP(c_COMBB(U_8832,U_8832,U_8833),c_Groups_Oabs__class_Oabs(U_8832)),U_8834)),U_8835)
      | ~ class_Fields_Olinordered__field(U_8832) ),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

cnf(f_2080_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8832),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8833,U_8832),U_8834),U_8835)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8833,U_8832),hAPP(hAPP(c_COMBB(U_8832,U_8832,U_8833),c_Groups_Oabs__class_Oabs(U_8832)),U_8834)),U_8835)
    | ~ class_Fields_Olinordered__field(U_8832) ),
    inference(clausify,[status(thm)],[f_2080_2]) ).

fof(f_2081_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).

fof(f_2081_2,plain,
    ! [U_8836] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_8836,U_8836,c_Orderings_Oord__class_Omax(U_8836))
      | ~ class_Orderings_Olinorder(U_8836) ),
    inference(variable_rename,[status(thm)],[f_2081_1]) ).

cnf(f_2081_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_8836,U_8836,c_Orderings_Oord__class_Omax(U_8836))
    | ~ class_Orderings_Olinorder(U_8836) ),
    inference(clausify,[status(thm)],[f_2081_2]) ).

fof(f_2082_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).

fof(f_2082_2,plain,
    ! [U_8837] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_8837,U_8837,c_Orderings_Oord__class_Omin(U_8837))
      | ~ class_Orderings_Olinorder(U_8837) ),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

cnf(f_2082_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_8837,U_8837,c_Orderings_Oord__class_Omin(U_8837))
    | ~ class_Orderings_Olinorder(U_8837) ),
    inference(clausify,[status(thm)],[f_2082_2]) ).

fof(f_2083_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).

fof(f_2083_2,plain,
    ! [U_8841,U_8840,U_8839,U_8838] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8839,U_8838),hAPP(hAPP(c_COMBB(U_8838,U_8838,U_8839),c_Groups_Ouminus__class_Ouminus(U_8838)),U_8840)),U_8841) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8838),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8839,U_8838),U_8840),U_8841))
      | ~ class_Groups_Oab__group__add(U_8838) ),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

cnf(f_2083_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8839,U_8838),hAPP(hAPP(c_COMBB(U_8838,U_8838,U_8839),c_Groups_Ouminus__class_Ouminus(U_8838)),U_8840)),U_8841) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8838),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8839,U_8838),U_8840),U_8841))
    | ~ class_Groups_Oab__group__add(U_8838) ),
    inference(clausify,[status(thm)],[f_2083_2]) ).

fof(f_2084_1,plain,
    ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).

fof(f_2084_2,plain,
    ! [U_8843,U_8842] : hAPP(c_Set_OCollect(U_8842),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8842),c_fNot),U_8843)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8842,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8842),U_8843)),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

cnf(f_2084_3,plain,
    hAPP(c_Set_OCollect(U_8842),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8842),c_fNot),U_8843)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8842,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8842),U_8843)),
    inference(clausify,[status(thm)],[f_2084_2]) ).

fof(f_2085_1,plain,
    ! [V_A_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).

fof(f_2085_2,plain,
    ! [U_8846,U_8845,U_8844] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8844),U_8845),U_8846) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8844),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8844,tc_Int_Oint),U_8845),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8846))
      | ~ class_Groups_Ocomm__monoid__mult(U_8844)
      | ~ class_Groups_Ocomm__monoid__add(U_8844) ),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

cnf(f_2085_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8844),U_8845),U_8846) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8844),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8844,tc_Int_Oint),U_8845),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8846))
    | ~ class_Groups_Ocomm__monoid__mult(U_8844)
    | ~ class_Groups_Ocomm__monoid__add(U_8844) ),
    inference(clausify,[status(thm)],[f_2085_2]) ).

fof(f_2086_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
      | ! [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).

fof(f_2086_2,plain,
    ! [U_8851,U_8850,U_8849,U_8848] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8849,U_8848),U_8851),U_8850) = c_Groups_Ozero__class_Ozero(U_8848)
      | ! [U_8847] :
          ( hAPP(U_8851,U_8847) != c_Groups_Ozero__class_Ozero(U_8848)
          | ~ hBOOL(hAPP(hAPP(c_member(U_8849),U_8847),U_8850)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8849),U_8850))
      | ~ class_Rings_Ocomm__semiring__1(U_8848) ),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

cnf(f_2086_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8849,U_8848),U_8851),U_8850) = c_Groups_Ozero__class_Ozero(U_8848)
    | hAPP(U_8851,U_8847) != c_Groups_Ozero__class_Ozero(U_8848)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8849),U_8847),U_8850))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8849),U_8850))
    | ~ class_Rings_Ocomm__semiring__1(U_8848) ),
    inference(clausify,[status(thm)],[f_2086_2]) ).

fof(f_2087_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ! [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b)
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Rings_Ono__zero__divisors(T_b)
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).

fof(f_2087_2,plain,
    ! [U_8857,U_8856,U_8855,U_8854] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) = c_Groups_Ozero__class_Ozero(U_8854)
          | ! [U_8853] :
              ( hAPP(U_8857,U_8853) != c_Groups_Ozero__class_Ozero(U_8854)
              | ~ hBOOL(hAPP(hAPP(c_member(U_8855),U_8853),U_8856)) ) )
        & ( ? [U_8852] :
              ( hAPP(U_8857,U_8852) = c_Groups_Ozero__class_Ozero(U_8854)
              & hBOOL(hAPP(hAPP(c_member(U_8855),U_8852),U_8856)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) != c_Groups_Ozero__class_Ozero(U_8854) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8855),U_8856))
      | ~ class_Rings_Ono__zero__divisors(U_8854)
      | ~ class_Rings_Ocomm__semiring__1(U_8854) ),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

fof(f_2087_3,plain,
    ! [U_8857,U_8856,U_8855,U_8854] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) = c_Groups_Ozero__class_Ozero(U_8854)
          | ! [U_8853] :
              ( hAPP(U_8857,U_8853) != c_Groups_Ozero__class_Ozero(U_8854)
              | ~ hBOOL(hAPP(hAPP(c_member(U_8855),U_8853),U_8856)) ) )
        & ( ( hAPP(U_8857,sK218(U_8857,U_8856,U_8855,U_8854)) = c_Groups_Ozero__class_Ozero(U_8854)
            & hBOOL(hAPP(hAPP(c_member(U_8855),sK218(U_8857,U_8856,U_8855,U_8854)),U_8856)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) != c_Groups_Ozero__class_Ozero(U_8854) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8855),U_8856))
      | ~ class_Rings_Ono__zero__divisors(U_8854)
      | ~ class_Rings_Ocomm__semiring__1(U_8854) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_8852,sK218(U_8857,U_8856,U_8855,U_8854))],[f_2087_2]) ).

cnf(f_2087_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8855),sK218(U_8857,U_8856,U_8855,U_8854)),U_8856))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) != c_Groups_Ozero__class_Ozero(U_8854)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8855),U_8856))
    | ~ class_Rings_Ono__zero__divisors(U_8854)
    | ~ class_Rings_Ocomm__semiring__1(U_8854) ),
    inference(clausify,[status(thm)],[f_2087_3]) ).

cnf(f_2087_5,plain,
    ( hAPP(U_8857,sK218(U_8857,U_8856,U_8855,U_8854)) = c_Groups_Ozero__class_Ozero(U_8854)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) != c_Groups_Ozero__class_Ozero(U_8854)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8855),U_8856))
    | ~ class_Rings_Ono__zero__divisors(U_8854)
    | ~ class_Rings_Ocomm__semiring__1(U_8854) ),
    inference(clausify,[status(thm)],[f_2087_3]) ).

cnf(f_2087_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8855,U_8854),U_8857),U_8856) = c_Groups_Ozero__class_Ozero(U_8854)
    | hAPP(U_8857,U_8853) != c_Groups_Ozero__class_Ozero(U_8854)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8855),U_8853),U_8856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8855),U_8856))
    | ~ class_Rings_Ono__zero__divisors(U_8854)
    | ~ class_Rings_Ocomm__semiring__1(U_8854) ),
    inference(clausify,[status(thm)],[f_2087_3]) ).

fof(f_2088_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).

fof(f_2088_2,plain,
    ! [U_8860,U_8859,U_8858] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8859,U_8858),U_8860),c_Orderings_Obot__class_Obot(tc_fun(U_8859,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8858)
      | ~ class_Groups_Ocomm__monoid__mult(U_8858) ),
    inference(variable_rename,[status(thm)],[f_2088_1]) ).

cnf(f_2088_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8859,U_8858),U_8860),c_Orderings_Obot__class_Obot(tc_fun(U_8859,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8858)
    | ~ class_Groups_Ocomm__monoid__mult(U_8858) ),
    inference(clausify,[status(thm)],[f_2088_2]) ).

fof(f_2089_1,plain,
    ! [V_g_2,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).

fof(f_2089_2,plain,
    ! [U_8863,U_8862,U_8861] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8862,U_8861),U_8863),c_Orderings_Obot__class_Obot(tc_fun(U_8862,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8861)
      | ~ class_Groups_Ocomm__monoid__mult(U_8861) ),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

cnf(f_2089_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8862,U_8861),U_8863),c_Orderings_Obot__class_Obot(tc_fun(U_8862,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8861)
    | ~ class_Groups_Ocomm__monoid__mult(U_8861) ),
    inference(clausify,[status(thm)],[f_2089_2]) ).

fof(f_2090_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(f_2090_2,plain,
    ! [U_8867,U_8866,U_8865,U_8864] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8865,U_8864),U_8867),U_8866) = c_Groups_Oone__class_Oone(U_8864)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8865),U_8866))
      | ~ class_Groups_Ocomm__monoid__mult(U_8864) ),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

cnf(f_2090_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8865,U_8864),U_8867),U_8866) = c_Groups_Oone__class_Oone(U_8864)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8865),U_8866))
    | ~ class_Groups_Ocomm__monoid__mult(U_8864) ),
    inference(clausify,[status(thm)],[f_2090_2]) ).

fof(f_2091_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).

fof(f_2091_2,plain,
    ! [U_8871,U_8870,U_8869,U_8868] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8869,U_8868),U_8871),U_8870) = c_Groups_Oone__class_Oone(U_8868)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8869),U_8870))
      | ~ class_Groups_Ocomm__monoid__mult(U_8868) ),
    inference(variable_rename,[status(thm)],[f_2091_1]) ).

cnf(f_2091_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8869,U_8868),U_8871),U_8870) = c_Groups_Oone__class_Oone(U_8868)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_8869),U_8870))
    | ~ class_Groups_Ocomm__monoid__mult(U_8868) ),
    inference(clausify,[status(thm)],[f_2091_2]) ).

fof(f_2092_1,plain,
    ! [V_f_2,V_F_2,T_a] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,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_a),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_a),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).

fof(f_2092_2,plain,
    ! [U_8876,U_8875,U_8874] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_8873] :
              ( hAPP(U_8876,U_8873) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_8874),U_8873),U_8875)) ) )
        & ( ! [U_8872] :
              ( hAPP(U_8876,U_8872) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_8874),U_8872),U_8875)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) ),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

fof(f_2092_3,plain,
    ! [U_8876,U_8875,U_8874] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_8876,sK219(U_8876,U_8875,U_8874)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_8874),sK219(U_8876,U_8875,U_8874)),U_8875)) ) )
        & ( ! [U_8872] :
              ( hAPP(U_8876,U_8872) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_8874),U_8872),U_8875)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_8873,sK219(U_8876,U_8875,U_8874))],[f_2092_2]) ).

cnf(f_2092_4,plain,
    ( hAPP(U_8876,U_8872) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8874),U_8872),U_8875))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) ),
    inference(clausify,[status(thm)],[f_2092_3]) ).

cnf(f_2092_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8874),sK219(U_8876,U_8875,U_8874)),U_8875))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) ),
    inference(clausify,[status(thm)],[f_2092_3]) ).

cnf(f_2092_6,plain,
    ( hAPP(U_8876,sK219(U_8876,U_8875,U_8874)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8874,tc_Nat_Onat),U_8876),U_8875) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8874),U_8875)) ),
    inference(clausify,[status(thm)],[f_2092_3]) ).

fof(f_2093_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).

fof(f_2093_2,plain,
    ! [U_8878,U_8877] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),c_Groups_Ozero__class_Ozero(U_8877)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8877),U_8878)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),U_8878),c_Groups_Ozero__class_Ozero(U_8877))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),U_8878),c_Groups_Ozero__class_Ozero(U_8877)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),c_Groups_Ozero__class_Ozero(U_8877)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8877),U_8878))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8877) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

cnf(f_2093_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),U_8878),c_Groups_Ozero__class_Ozero(U_8877)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),c_Groups_Ozero__class_Ozero(U_8877)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8877),U_8878)))
    | ~ class_Groups_Oordered__ab__group__add(U_8877) ),
    inference(clausify,[status(thm)],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),c_Groups_Ozero__class_Ozero(U_8877)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8877),U_8878)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8877),U_8878),c_Groups_Ozero__class_Ozero(U_8877)))
    | ~ class_Groups_Oordered__ab__group__add(U_8877) ),
    inference(clausify,[status(thm)],[f_2093_2]) ).

fof(f_2094_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).

fof(f_2094_2,plain,
    ! [U_8880,U_8879] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),hAPP(c_Groups_Ouminus__class_Ouminus(U_8879),U_8880)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),c_Groups_Ozero__class_Ozero(U_8879))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),c_Groups_Ozero__class_Ozero(U_8879)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),hAPP(c_Groups_Ouminus__class_Ouminus(U_8879),U_8880))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_8879) ),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

cnf(f_2094_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),c_Groups_Ozero__class_Ozero(U_8879)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),hAPP(c_Groups_Ouminus__class_Ouminus(U_8879),U_8880)))
    | ~ class_Groups_Olinordered__ab__group__add(U_8879) ),
    inference(clausify,[status(thm)],[f_2094_2]) ).

cnf(f_2094_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),hAPP(c_Groups_Ouminus__class_Ouminus(U_8879),U_8880)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8879),U_8880),c_Groups_Ozero__class_Ozero(U_8879)))
    | ~ class_Groups_Olinordered__ab__group__add(U_8879) ),
    inference(clausify,[status(thm)],[f_2094_2]) ).

fof(f_2095_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),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_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).

fof(f_2095_2,plain,
    ! [U_8882,U_8881] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),c_Groups_Ozero__class_Ozero(U_8881)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),c_Groups_Ozero__class_Ozero(U_8881)),U_8882)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),c_Groups_Ozero__class_Ozero(U_8881)),U_8882))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),c_Groups_Ozero__class_Ozero(U_8881))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8881) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

cnf(f_2095_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),c_Groups_Ozero__class_Ozero(U_8881)),U_8882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),c_Groups_Ozero__class_Ozero(U_8881)))
    | ~ class_Groups_Oordered__ab__group__add(U_8881) ),
    inference(clausify,[status(thm)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),c_Groups_Ozero__class_Ozero(U_8881)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8881),c_Groups_Ozero__class_Ozero(U_8881)),U_8882))
    | ~ class_Groups_Oordered__ab__group__add(U_8881) ),
    inference(clausify,[status(thm)],[f_2095_2]) ).

fof(f_2096_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).

fof(f_2096_2,plain,
    ! [U_8884,U_8883] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),hAPP(c_Groups_Ouminus__class_Ouminus(U_8883),U_8884)),U_8884))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),c_Groups_Ozero__class_Ozero(U_8883)),U_8884)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),c_Groups_Ozero__class_Ozero(U_8883)),U_8884))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),hAPP(c_Groups_Ouminus__class_Ouminus(U_8883),U_8884)),U_8884)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_8883) ),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

cnf(f_2096_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),c_Groups_Ozero__class_Ozero(U_8883)),U_8884))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),hAPP(c_Groups_Ouminus__class_Ouminus(U_8883),U_8884)),U_8884))
    | ~ class_Groups_Olinordered__ab__group__add(U_8883) ),
    inference(clausify,[status(thm)],[f_2096_2]) ).

cnf(f_2096_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),hAPP(c_Groups_Ouminus__class_Ouminus(U_8883),U_8884)),U_8884))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8883),c_Groups_Ozero__class_Ozero(U_8883)),U_8884))
    | ~ class_Groups_Olinordered__ab__group__add(U_8883) ),
    inference(clausify,[status(thm)],[f_2096_2]) ).

fof(f_2097_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).

fof(f_2097_2,plain,
    ! [U_8886,U_8885] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),c_Groups_Ozero__class_Ozero(U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8885),U_8886)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),U_8886),c_Groups_Ozero__class_Ozero(U_8885))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),U_8886),c_Groups_Ozero__class_Ozero(U_8885)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),c_Groups_Ozero__class_Ozero(U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8885),U_8886))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8885) ),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

cnf(f_2097_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),U_8886),c_Groups_Ozero__class_Ozero(U_8885)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),c_Groups_Ozero__class_Ozero(U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8885),U_8886)))
    | ~ class_Groups_Oordered__ab__group__add(U_8885) ),
    inference(clausify,[status(thm)],[f_2097_2]) ).

cnf(f_2097_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),c_Groups_Ozero__class_Ozero(U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8885),U_8886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8885),U_8886),c_Groups_Ozero__class_Ozero(U_8885)))
    | ~ class_Groups_Oordered__ab__group__add(U_8885) ),
    inference(clausify,[status(thm)],[f_2097_2]) ).

fof(f_2098_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),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_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).

fof(f_2098_2,plain,
    ! [U_8888,U_8887] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),c_Groups_Ozero__class_Ozero(U_8887)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),c_Groups_Ozero__class_Ozero(U_8887)),U_8888)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),c_Groups_Ozero__class_Ozero(U_8887)),U_8888))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),c_Groups_Ozero__class_Ozero(U_8887))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_8887) ),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

cnf(f_2098_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),c_Groups_Ozero__class_Ozero(U_8887)),U_8888))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),c_Groups_Ozero__class_Ozero(U_8887)))
    | ~ class_Groups_Oordered__ab__group__add(U_8887) ),
    inference(clausify,[status(thm)],[f_2098_2]) ).

cnf(f_2098_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),c_Groups_Ozero__class_Ozero(U_8887)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8887),c_Groups_Ozero__class_Ozero(U_8887)),U_8888))
    | ~ class_Groups_Oordered__ab__group__add(U_8887) ),
    inference(clausify,[status(thm)],[f_2098_2]) ).

fof(f_2099_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).

fof(f_2099_2,plain,
    ! [U_8890,U_8889] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),hAPP(c_Groups_Ouminus__class_Ouminus(U_8889),U_8890)),U_8890))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),c_Groups_Ozero__class_Ozero(U_8889)),U_8890)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),c_Groups_Ozero__class_Ozero(U_8889)),U_8890))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),hAPP(c_Groups_Ouminus__class_Ouminus(U_8889),U_8890)),U_8890)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_8889) ),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

cnf(f_2099_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),c_Groups_Ozero__class_Ozero(U_8889)),U_8890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),hAPP(c_Groups_Ouminus__class_Ouminus(U_8889),U_8890)),U_8890))
    | ~ class_Groups_Olinordered__ab__group__add(U_8889) ),
    inference(clausify,[status(thm)],[f_2099_2]) ).

cnf(f_2099_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),hAPP(c_Groups_Ouminus__class_Ouminus(U_8889),U_8890)),U_8890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8889),c_Groups_Ozero__class_Ozero(U_8889)),U_8890))
    | ~ class_Groups_Olinordered__ab__group__add(U_8889) ),
    inference(clausify,[status(thm)],[f_2099_2]) ).

fof(f_2100_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).

fof(f_2100_2,plain,
    ! [U_8892,U_8891] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),hAPP(c_Groups_Ouminus__class_Ouminus(U_8891),U_8892)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),c_Groups_Ozero__class_Ozero(U_8891))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),c_Groups_Ozero__class_Ozero(U_8891)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),hAPP(c_Groups_Ouminus__class_Ouminus(U_8891),U_8892))) ) )
      | ~ class_Rings_Olinordered__idom(U_8891) ),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

cnf(f_2100_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),c_Groups_Ozero__class_Ozero(U_8891)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),hAPP(c_Groups_Ouminus__class_Ouminus(U_8891),U_8892)))
    | ~ class_Rings_Olinordered__idom(U_8891) ),
    inference(clausify,[status(thm)],[f_2100_2]) ).

cnf(f_2100_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),hAPP(c_Groups_Ouminus__class_Ouminus(U_8891),U_8892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8891),U_8892),c_Groups_Ozero__class_Ozero(U_8891)))
    | ~ class_Rings_Olinordered__idom(U_8891) ),
    inference(clausify,[status(thm)],[f_2100_2]) ).

fof(f_2101_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_2101_2,plain,
    ! [U_8895,U_8894,U_8893] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8893),U_8894) = U_8895
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8893),U_8894),U_8895) != c_Groups_Ozero__class_Ozero(U_8893)
      | ~ class_Groups_Ogroup__add(U_8893) ),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

cnf(f_2101_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8893),U_8894) = U_8895
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8893),U_8894),U_8895) != c_Groups_Ozero__class_Ozero(U_8893)
    | ~ class_Groups_Ogroup__add(U_8893) ),
    inference(clausify,[status(thm)],[f_2101_2]) ).

fof(f_2102_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_2102_2,plain,
    ! [U_8897,U_8896] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8896),hAPP(c_Groups_Ouminus__class_Ouminus(U_8896),U_8897)),U_8897) = c_Groups_Ozero__class_Ozero(U_8896)
      | ~ class_Groups_Oab__group__add(U_8896) ),
    inference(variable_rename,[status(thm)],[f_2102_1]) ).

cnf(f_2102_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8896),hAPP(c_Groups_Ouminus__class_Ouminus(U_8896),U_8897)),U_8897) = c_Groups_Ozero__class_Ozero(U_8896)
    | ~ class_Groups_Oab__group__add(U_8896) ),
    inference(clausify,[status(thm)],[f_2102_2]) ).

fof(f_2103_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_2103_2,plain,
    ! [U_8899,U_8898] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8898),hAPP(c_Groups_Ouminus__class_Ouminus(U_8898),U_8899)),U_8899) = c_Groups_Ozero__class_Ozero(U_8898)
      | ~ class_Groups_Ogroup__add(U_8898) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

cnf(f_2103_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8898),hAPP(c_Groups_Ouminus__class_Ouminus(U_8898),U_8899)),U_8899) = c_Groups_Ozero__class_Ozero(U_8898)
    | ~ class_Groups_Ogroup__add(U_8898) ),
    inference(clausify,[status(thm)],[f_2103_2]) ).

fof(f_2104_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).

fof(f_2104_2,plain,
    ! [U_8902,U_8901,U_8900] :
      ( ( ( U_8901 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8900),U_8902)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8900),U_8901),U_8902) != c_Groups_Ozero__class_Ozero(U_8900) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8900),U_8901),U_8902) = c_Groups_Ozero__class_Ozero(U_8900)
          | U_8901 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8900),U_8902) ) )
      | ~ class_Groups_Ogroup__add(U_8900) ),
    inference(variable_rename,[status(thm)],[f_2104_1]) ).

cnf(f_2104_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8900),U_8901),U_8902) = c_Groups_Ozero__class_Ozero(U_8900)
    | U_8901 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8900),U_8902)
    | ~ class_Groups_Ogroup__add(U_8900) ),
    inference(clausify,[status(thm)],[f_2104_2]) ).

cnf(f_2104_4,plain,
    ( U_8901 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8900),U_8902)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8900),U_8901),U_8902) != c_Groups_Ozero__class_Ozero(U_8900)
    | ~ class_Groups_Ogroup__add(U_8900) ),
    inference(clausify,[status(thm)],[f_2104_2]) ).

fof(f_2105_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_2105_2,plain,
    ! [U_8904,U_8903] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8903),U_8904),hAPP(c_Groups_Ouminus__class_Ouminus(U_8903),U_8904)) = c_Groups_Ozero__class_Ozero(U_8903)
      | ~ class_Groups_Ogroup__add(U_8903) ),
    inference(variable_rename,[status(thm)],[f_2105_1]) ).

cnf(f_2105_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8903),U_8904),hAPP(c_Groups_Ouminus__class_Ouminus(U_8903),U_8904)) = c_Groups_Ozero__class_Ozero(U_8903)
    | ~ class_Groups_Ogroup__add(U_8903) ),
    inference(clausify,[status(thm)],[f_2105_2]) ).

fof(f_2106_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_2106_2,plain,
    ! [U_8906,U_8905] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8905),c_Groups_Ozero__class_Ozero(U_8905)),U_8906) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8905),U_8906)
      | ~ class_Groups_Ogroup__add(U_8905) ),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

cnf(f_2106_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8905),c_Groups_Ozero__class_Ozero(U_8905)),U_8906) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8905),U_8906)
    | ~ class_Groups_Ogroup__add(U_8905) ),
    inference(clausify,[status(thm)],[f_2106_2]) ).

fof(f_2107_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_2107_2,plain,
    ! [U_8909,U_8908,U_8907] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8907),U_8908),U_8909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8907),U_8908),hAPP(c_Groups_Ouminus__class_Ouminus(U_8907),U_8909))
      | ~ class_Rings_Ocomm__ring__1(U_8907) ),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

cnf(f_2107_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8907),U_8908),U_8909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8907),U_8908),hAPP(c_Groups_Ouminus__class_Ouminus(U_8907),U_8909))
    | ~ class_Rings_Ocomm__ring__1(U_8907) ),
    inference(clausify,[status(thm)],[f_2107_2]) ).

fof(f_2108_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_2108_2,plain,
    ! [U_8912,U_8911,U_8910] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8910),U_8911),hAPP(c_Groups_Ouminus__class_Ouminus(U_8910),U_8912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8910),U_8911),U_8912)
      | ~ class_Groups_Ogroup__add(U_8910) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

cnf(f_2108_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8910),U_8911),hAPP(c_Groups_Ouminus__class_Ouminus(U_8910),U_8912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8910),U_8911),U_8912)
    | ~ class_Groups_Ogroup__add(U_8910) ),
    inference(clausify,[status(thm)],[f_2108_2]) ).

fof(f_2109_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_2109_2,plain,
    ! [U_8915,U_8914,U_8913] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8913),U_8914),U_8915) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8913),U_8914),hAPP(c_Groups_Ouminus__class_Ouminus(U_8913),U_8915))
      | ~ class_Groups_Oab__group__add(U_8913) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

cnf(f_2109_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8913),U_8914),U_8915) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8913),U_8914),hAPP(c_Groups_Ouminus__class_Ouminus(U_8913),U_8915))
    | ~ class_Groups_Oab__group__add(U_8913) ),
    inference(clausify,[status(thm)],[f_2109_2]) ).

fof(f_2110_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_2110_2,plain,
    ! [U_8918,U_8917,U_8916] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8916),U_8917),U_8918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8916),U_8917),hAPP(c_Groups_Ouminus__class_Ouminus(U_8916),U_8918))
      | ~ class_Groups_Ogroup__add(U_8916) ),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

cnf(f_2110_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8916),U_8917),U_8918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8916),U_8917),hAPP(c_Groups_Ouminus__class_Ouminus(U_8916),U_8918))
    | ~ class_Groups_Ogroup__add(U_8916) ),
    inference(clausify,[status(thm)],[f_2110_2]) ).

fof(f_2111_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
          | ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
            & V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
        & ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
          | V_x_2 = c_Groups_Oone__class_Oone(T_a)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).

fof(f_2111_2,plain,
    ! [U_8920,U_8919] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8919),U_8920),U_8920) = c_Groups_Oone__class_Oone(U_8919)
          | ( U_8920 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8919),c_Groups_Oone__class_Oone(U_8919))
            & U_8920 != c_Groups_Oone__class_Oone(U_8919) ) )
        & ( U_8920 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8919),c_Groups_Oone__class_Oone(U_8919))
          | U_8920 = c_Groups_Oone__class_Oone(U_8919)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8919),U_8920),U_8920) != c_Groups_Oone__class_Oone(U_8919) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_8919) ),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

cnf(f_2111_3,plain,
    ( U_8920 = hAPP(c_Groups_Ouminus__class_Ouminus(U_8919),c_Groups_Oone__class_Oone(U_8919))
    | U_8920 = c_Groups_Oone__class_Oone(U_8919)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8919),U_8920),U_8920) != c_Groups_Oone__class_Oone(U_8919)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_8919) ),
    inference(clausify,[status(thm)],[f_2111_2]) ).

cnf(f_2111_4,plain,
    ( U_8920 != c_Groups_Oone__class_Oone(U_8919)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8919),U_8920),U_8920) = c_Groups_Oone__class_Oone(U_8919)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_8919) ),
    inference(clausify,[status(thm)],[f_2111_2]) ).

cnf(f_2111_5,plain,
    ( U_8920 != hAPP(c_Groups_Ouminus__class_Ouminus(U_8919),c_Groups_Oone__class_Oone(U_8919))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8919),U_8920),U_8920) = c_Groups_Oone__class_Oone(U_8919)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_8919) ),
    inference(clausify,[status(thm)],[f_2111_2]) ).

fof(f_2112_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_2112_2,plain,
    ! [U_8922,U_8921] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8921),U_8922) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8921),hAPP(c_Groups_Ouminus__class_Ouminus(U_8921),c_Groups_Oone__class_Oone(U_8921))),U_8922)
      | ~ class_Rings_Ocomm__ring__1(U_8921) ),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

cnf(f_2112_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8921),U_8922) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8921),hAPP(c_Groups_Ouminus__class_Ouminus(U_8921),c_Groups_Oone__class_Oone(U_8921))),U_8922)
    | ~ class_Rings_Ocomm__ring__1(U_8921) ),
    inference(clausify,[status(thm)],[f_2112_2]) ).

fof(f_2113_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_2113_2,plain,
    ! [U_8924,U_8923] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8923),U_8924),hAPP(c_Groups_Ouminus__class_Ouminus(U_8923),U_8924)) = c_Orderings_Obot__class_Obot(U_8923)
      | ~ class_Lattices_Oboolean__algebra(U_8923) ),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

cnf(f_2113_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8923),U_8924),hAPP(c_Groups_Ouminus__class_Ouminus(U_8923),U_8924)) = c_Orderings_Obot__class_Obot(U_8923)
    | ~ class_Lattices_Oboolean__algebra(U_8923) ),
    inference(clausify,[status(thm)],[f_2113_2]) ).

fof(f_2114_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_2114_2,plain,
    ! [U_8926,U_8925] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8925),hAPP(c_Groups_Ouminus__class_Ouminus(U_8925),U_8926)),U_8926) = c_Orderings_Obot__class_Obot(U_8925)
      | ~ class_Lattices_Oboolean__algebra(U_8925) ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

cnf(f_2114_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8925),hAPP(c_Groups_Ouminus__class_Ouminus(U_8925),U_8926)),U_8926) = c_Orderings_Obot__class_Obot(U_8925)
    | ~ class_Lattices_Oboolean__algebra(U_8925) ),
    inference(clausify,[status(thm)],[f_2114_2]) ).

fof(f_2115_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_2115_2,plain,
    ! [U_8929,U_8928,U_8927] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8927),U_8928),U_8929) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8927),U_8928),hAPP(c_Groups_Ouminus__class_Ouminus(U_8927),U_8929))
      | ~ class_Lattices_Oboolean__algebra(U_8927) ),
    inference(variable_rename,[status(thm)],[f_2115_1]) ).

cnf(f_2115_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8927),U_8928),U_8929) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8927),U_8928),hAPP(c_Groups_Ouminus__class_Ouminus(U_8927),U_8929))
    | ~ class_Lattices_Oboolean__algebra(U_8927) ),
    inference(clausify,[status(thm)],[f_2115_2]) ).

fof(f_2116_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_2116_2,plain,
    ! [U_8930] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8930),c_Orderings_Otop__class_Otop(U_8930)) = c_Orderings_Obot__class_Obot(U_8930)
      | ~ class_Lattices_Oboolean__algebra(U_8930) ),
    inference(variable_rename,[status(thm)],[f_2116_1]) ).

cnf(f_2116_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8930),c_Orderings_Otop__class_Otop(U_8930)) = c_Orderings_Obot__class_Obot(U_8930)
    | ~ class_Lattices_Oboolean__algebra(U_8930) ),
    inference(clausify,[status(thm)],[f_2116_2]) ).

fof(f_2117_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_2117_2,plain,
    ! [U_8931] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8931),c_Orderings_Obot__class_Obot(U_8931)) = c_Orderings_Otop__class_Otop(U_8931)
      | ~ class_Lattices_Oboolean__algebra(U_8931) ),
    inference(variable_rename,[status(thm)],[f_2117_1]) ).

cnf(f_2117_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8931),c_Orderings_Obot__class_Obot(U_8931)) = c_Orderings_Otop__class_Otop(U_8931)
    | ~ class_Lattices_Oboolean__algebra(U_8931) ),
    inference(clausify,[status(thm)],[f_2117_2]) ).

fof(f_2118_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_2118_2,plain,
    ! [U_8934,U_8933,U_8932] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8932),U_8933),U_8934)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8932),hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),U_8933)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),U_8934))
      | ~ class_Lattices_Oboolean__algebra(U_8932) ),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

cnf(f_2118_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8932),U_8933),U_8934)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8932),hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),U_8933)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8932),U_8934))
    | ~ class_Lattices_Oboolean__algebra(U_8932) ),
    inference(clausify,[status(thm)],[f_2118_2]) ).

fof(f_2119_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_2119_2,plain,
    ! [U_8937,U_8936,U_8935] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8935),U_8936),U_8937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8935),hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),U_8936)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),U_8937))
      | ~ class_Lattices_Oboolean__algebra(U_8935) ),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

cnf(f_2119_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8935),U_8936),U_8937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8935),hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),U_8936)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8935),U_8937))
    | ~ class_Lattices_Oboolean__algebra(U_8935) ),
    inference(clausify,[status(thm)],[f_2119_2]) ).

fof(f_2120_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_2120_2,plain,
    ! [U_8939,U_8938] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8938),hAPP(c_Groups_Ouminus__class_Ouminus(U_8938),U_8939)),U_8939) = c_Orderings_Otop__class_Otop(U_8938)
      | ~ class_Lattices_Oboolean__algebra(U_8938) ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

cnf(f_2120_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8938),hAPP(c_Groups_Ouminus__class_Ouminus(U_8938),U_8939)),U_8939) = c_Orderings_Otop__class_Otop(U_8938)
    | ~ class_Lattices_Oboolean__algebra(U_8938) ),
    inference(clausify,[status(thm)],[f_2120_2]) ).

fof(f_2121_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_2121_2,plain,
    ! [U_8941,U_8940] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8940),U_8941),hAPP(c_Groups_Ouminus__class_Ouminus(U_8940),U_8941)) = c_Orderings_Otop__class_Otop(U_8940)
      | ~ class_Lattices_Oboolean__algebra(U_8940) ),
    inference(variable_rename,[status(thm)],[f_2121_1]) ).

cnf(f_2121_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8940),U_8941),hAPP(c_Groups_Ouminus__class_Ouminus(U_8940),U_8941)) = c_Orderings_Otop__class_Otop(U_8940)
    | ~ class_Lattices_Oboolean__algebra(U_8940) ),
    inference(clausify,[status(thm)],[f_2121_2]) ).

fof(f_2122_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_2122_2,plain,
    ! [U_8943,U_8942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8942),hAPP(c_Groups_Ouminus__class_Ouminus(U_8942),U_8943)),hAPP(c_Groups_Oabs__class_Oabs(U_8942),U_8943)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8942) ),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

cnf(f_2122_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8942),hAPP(c_Groups_Ouminus__class_Ouminus(U_8942),U_8943)),hAPP(c_Groups_Oabs__class_Oabs(U_8942),U_8943)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8942) ),
    inference(clausify,[status(thm)],[f_2122_2]) ).

fof(f_2123_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).

fof(f_2123_2,plain,
    ! [U_8946,U_8945,U_8944] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Oabs__class_Oabs(U_8944),U_8945)),U_8946))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Ouminus__class_Ouminus(U_8944),U_8945)),U_8946))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),U_8945),U_8946)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Ouminus__class_Ouminus(U_8944),U_8945)),U_8946))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),U_8945),U_8946)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Oabs__class_Oabs(U_8944),U_8945)),U_8946)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8944) ),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

cnf(f_2123_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),U_8945),U_8946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Oabs__class_Oabs(U_8944),U_8945)),U_8946))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8944) ),
    inference(clausify,[status(thm)],[f_2123_2]) ).

cnf(f_2123_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Ouminus__class_Ouminus(U_8944),U_8945)),U_8946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Oabs__class_Oabs(U_8944),U_8945)),U_8946))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8944) ),
    inference(clausify,[status(thm)],[f_2123_2]) ).

cnf(f_2123_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Oabs__class_Oabs(U_8944),U_8945)),U_8946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),hAPP(c_Groups_Ouminus__class_Ouminus(U_8944),U_8945)),U_8946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8944),U_8945),U_8946))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8944) ),
    inference(clausify,[status(thm)],[f_2123_2]) ).

fof(f_2124_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_2124_2,plain,
    ! [U_8949,U_8948,U_8947] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),hAPP(c_Groups_Oabs__class_Oabs(U_8947),U_8948)),U_8949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),hAPP(c_Groups_Ouminus__class_Ouminus(U_8947),U_8948)),U_8949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),U_8948),U_8949))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8947) ),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

cnf(f_2124_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),hAPP(c_Groups_Oabs__class_Oabs(U_8947),U_8948)),U_8949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),hAPP(c_Groups_Ouminus__class_Ouminus(U_8947),U_8948)),U_8949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8947),U_8948),U_8949))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8947) ),
    inference(clausify,[status(thm)],[f_2124_2]) ).

fof(f_2125_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_2125_2,plain,
    ! [U_8952,U_8951,U_8950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8950),hAPP(c_Groups_Ouminus__class_Ouminus(U_8950),U_8951)),U_8952))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8950),hAPP(c_Groups_Oabs__class_Oabs(U_8950),U_8951)),U_8952))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8950) ),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

cnf(f_2125_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8950),hAPP(c_Groups_Ouminus__class_Ouminus(U_8950),U_8951)),U_8952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8950),hAPP(c_Groups_Oabs__class_Oabs(U_8950),U_8951)),U_8952))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8950) ),
    inference(clausify,[status(thm)],[f_2125_2]) ).

fof(f_2126_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).

fof(f_2126_2,plain,
    ! [U_8955,U_8954,U_8953] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Oabs__class_Oabs(U_8953),U_8954)),U_8955))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Ouminus__class_Ouminus(U_8953),U_8954)),U_8955))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),U_8954),U_8955)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Ouminus__class_Ouminus(U_8953),U_8954)),U_8955))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),U_8954),U_8955)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Oabs__class_Oabs(U_8953),U_8954)),U_8955)) ) )
      | ~ class_Rings_Olinordered__idom(U_8953) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

cnf(f_2126_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),U_8954),U_8955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Oabs__class_Oabs(U_8953),U_8954)),U_8955))
    | ~ class_Rings_Olinordered__idom(U_8953) ),
    inference(clausify,[status(thm)],[f_2126_2]) ).

cnf(f_2126_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Ouminus__class_Ouminus(U_8953),U_8954)),U_8955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Oabs__class_Oabs(U_8953),U_8954)),U_8955))
    | ~ class_Rings_Olinordered__idom(U_8953) ),
    inference(clausify,[status(thm)],[f_2126_2]) ).

cnf(f_2126_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Oabs__class_Oabs(U_8953),U_8954)),U_8955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),hAPP(c_Groups_Ouminus__class_Ouminus(U_8953),U_8954)),U_8955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8953),U_8954),U_8955))
    | ~ class_Rings_Olinordered__idom(U_8953) ),
    inference(clausify,[status(thm)],[f_2126_2]) ).

fof(f_2127_1,plain,
    ! [V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).

fof(f_2127_2,plain,
    ! [U_8957,U_8956] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8956,tc_HOL_Obool)),U_8957)))
        | U_8957 != c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)) )
      & ( U_8957 = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8956,tc_HOL_Obool)),U_8957))) ) ),
    inference(variable_rename,[status(thm)],[f_2127_1]) ).

fof(f_2127_3,plain,
    ( ! [U_8961,U_8959] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8959,tc_HOL_Obool)),U_8961),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8959,tc_HOL_Obool)),U_8961)))
        | U_8961 != c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool)) )
    & ! [U_8960,U_8958] :
        ( U_8960 = c_Orderings_Obot__class_Obot(tc_fun(U_8958,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8958,tc_HOL_Obool)),U_8960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8958,tc_HOL_Obool)),U_8960))) ) ),
    inference(miniscope,[status(thm)],[f_2127_2]) ).

cnf(f_2127_4,plain,
    ( U_8960 = c_Orderings_Obot__class_Obot(tc_fun(U_8958,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8958,tc_HOL_Obool)),U_8960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8958,tc_HOL_Obool)),U_8960))) ),
    inference(clausify,[status(thm)],[f_2127_3]) ).

cnf(f_2127_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8959,tc_HOL_Obool)),U_8961),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8959,tc_HOL_Obool)),U_8961)))
    | U_8961 != c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2127_3]) ).

fof(f_2128_1,plain,
    ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(f_2128_2,plain,
    ! [U_8962] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8962,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8962,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

cnf(f_2128_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8962,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8962,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2128_2]) ).

fof(f_2129_1,plain,
    ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).

fof(f_2129_2,plain,
    ! [U_8963] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8963,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_8963,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

cnf(f_2129_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8963,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_8963,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2129_2]) ).

fof(f_2130_1,plain,
    ! [V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).

fof(f_2130_2,plain,
    ! [U_8965,U_8964] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8964,tc_HOL_Obool)),U_8965)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),c_Orderings_Otop__class_Otop(tc_fun(U_8964,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),c_Orderings_Otop__class_Otop(tc_fun(U_8964,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8964,tc_HOL_Obool)),U_8965))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),U_8965)) ),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

cnf(f_2130_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),c_Orderings_Otop__class_Otop(tc_fun(U_8964,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8964,tc_HOL_Obool)),U_8965)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),U_8965)) ),
    inference(clausify,[status(thm)],[f_2130_2]) ).

cnf(f_2130_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8964,tc_HOL_Obool)),U_8965)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),c_Orderings_Otop__class_Otop(tc_fun(U_8964,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8964),U_8965)) ),
    inference(clausify,[status(thm)],[f_2130_2]) ).

fof(f_2131_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).

fof(f_2131_2,plain,
    ! [U_8967,U_8966] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8966,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8966,tc_HOL_Obool)),U_8967)),U_8967) = c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

cnf(f_2131_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8966,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8966,tc_HOL_Obool)),U_8967)),U_8967) = c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2131_2]) ).

fof(f_2132_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).

fof(f_2132_2,plain,
    ! [U_8969,U_8968] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8968,tc_HOL_Obool)),U_8969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8968,tc_HOL_Obool)),U_8969)) = c_Orderings_Obot__class_Obot(tc_fun(U_8968,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

cnf(f_2132_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8968,tc_HOL_Obool)),U_8969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8968,tc_HOL_Obool)),U_8969)) = c_Orderings_Obot__class_Obot(tc_fun(U_8968,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2132_2]) ).

fof(f_2133_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).

fof(f_2133_2,plain,
    ! [U_8972,U_8971,U_8970] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8970),U_8972),U_8971) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8970),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8970,tc_Nat_Onat),U_8972),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8971))
      | ~ c_Nat__Transfer_Onat__set(U_8971)
      | ~ class_Groups_Ocomm__monoid__mult(U_8970)
      | ~ class_Groups_Ocomm__monoid__add(U_8970) ),
    inference(variable_rename,[status(thm)],[f_2133_1]) ).

cnf(f_2133_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8970),U_8972),U_8971) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8970),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8970,tc_Nat_Onat),U_8972),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8971))
    | ~ c_Nat__Transfer_Onat__set(U_8971)
    | ~ class_Groups_Ocomm__monoid__mult(U_8970)
    | ~ class_Groups_Ocomm__monoid__add(U_8970) ),
    inference(clausify,[status(thm)],[f_2133_2]) ).

fof(f_2134_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_2134_2,plain,
    ! [U_8974,U_8973] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8973),U_8974)),U_8974) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8973),U_8974),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

cnf(f_2134_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8973),U_8974)),U_8974) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8973),U_8974),
    inference(clausify,[status(thm)],[f_2134_2]) ).

fof(f_2135_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).

fof(f_2135_2,plain,
    ! [U_8976,U_8975] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8975,tc_HOL_Obool)),U_8976)),U_8976) = c_Orderings_Otop__class_Otop(tc_fun(U_8975,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2135_1]) ).

cnf(f_2135_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8975,tc_HOL_Obool)),U_8976)),U_8976) = c_Orderings_Otop__class_Otop(tc_fun(U_8975,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2135_2]) ).

fof(f_2136_1,plain,
    ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).

fof(f_2136_2,plain,
    ! [U_8978,U_8977] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8977,tc_HOL_Obool)),U_8978),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8977,tc_HOL_Obool)),U_8978)) = c_Orderings_Otop__class_Otop(tc_fun(U_8977,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

cnf(f_2136_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8977,tc_HOL_Obool)),U_8978),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8977,tc_HOL_Obool)),U_8978)) = c_Orderings_Otop__class_Otop(tc_fun(U_8977,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2136_2]) ).

fof(f_2137_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).

fof(f_2137_2,plain,
    ! [U_8981,U_8980,U_8979] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8979,tc_HOL_Obool)),U_8980),U_8981)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8979,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),U_8980)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),U_8981)),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

cnf(f_2137_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8979,tc_HOL_Obool)),U_8980),U_8981)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8979,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),U_8980)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8979,tc_HOL_Obool)),U_8981)),
    inference(clausify,[status(thm)],[f_2137_2]) ).

fof(f_2138_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).

fof(f_2138_2,plain,
    ! [U_8984,U_8983,U_8982] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8982,tc_HOL_Obool)),U_8983),U_8984)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8982,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),U_8983)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),U_8984)),
    inference(variable_rename,[status(thm)],[f_2138_1]) ).

cnf(f_2138_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8982,tc_HOL_Obool)),U_8983),U_8984)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8982,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),U_8983)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8982,tc_HOL_Obool)),U_8984)),
    inference(clausify,[status(thm)],[f_2138_2]) ).

fof(f_2139_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).

fof(f_2139_2,plain,
    ! [U_8987,U_8986,U_8985] :
      ( hAPP(c_Set_Oimage(U_8985,U_8985,c_Groups_Ouminus__class_Ouminus(U_8985)),c_SetInterval_Oord__class_OatLeastAtMost(U_8985,U_8986,U_8987)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8985,hAPP(c_Groups_Ouminus__class_Ouminus(U_8985),U_8987),hAPP(c_Groups_Ouminus__class_Ouminus(U_8985),U_8986))
      | ~ class_Groups_Oordered__ab__group__add(U_8985) ),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

cnf(f_2139_3,plain,
    ( hAPP(c_Set_Oimage(U_8985,U_8985,c_Groups_Ouminus__class_Ouminus(U_8985)),c_SetInterval_Oord__class_OatLeastAtMost(U_8985,U_8986,U_8987)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8985,hAPP(c_Groups_Ouminus__class_Ouminus(U_8985),U_8987),hAPP(c_Groups_Ouminus__class_Ouminus(U_8985),U_8986))
    | ~ class_Groups_Oordered__ab__group__add(U_8985) ),
    inference(clausify,[status(thm)],[f_2139_2]) ).

fof(f_2140_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(f_2140_2,plain,
    ! [U_8989,U_8988] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8988,tc_HOL_Obool)),U_8989) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),U_8989),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

cnf(f_2140_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8988,tc_HOL_Obool)),U_8989) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),U_8989),
    inference(clausify,[status(thm)],[f_2140_2]) ).

fof(f_2141_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).

fof(f_2141_2,plain,
    ! [U_8992,U_8991,U_8990] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8990,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8990,tc_HOL_Obool)),U_8991)),U_8992),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

cnf(f_2141_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8990,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8990,tc_HOL_Obool)),U_8991)),U_8992),
    inference(clausify,[status(thm)],[f_2141_2]) ).

fof(f_2142_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).

fof(f_2142_2,plain,
    ! [U_8995,U_8994,U_8993] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8993,tc_HOL_Obool)),U_8994),U_8995) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8993,tc_HOL_Obool)),U_8994),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8993,tc_HOL_Obool)),U_8995)),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

cnf(f_2142_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8993,tc_HOL_Obool)),U_8994),U_8995) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8993,tc_HOL_Obool)),U_8994),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8993,tc_HOL_Obool)),U_8995)),
    inference(clausify,[status(thm)],[f_2142_2]) ).

fof(f_2143_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).

fof(f_2143_2,plain,
    ! [U_8998,U_8997,U_8996] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8996,tc_HOL_Obool)),U_8997),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8996,tc_HOL_Obool)),U_8998)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8996,tc_HOL_Obool)),U_8997),U_8998),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

cnf(f_2143_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8996,tc_HOL_Obool)),U_8997),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8996,tc_HOL_Obool)),U_8998)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8996,tc_HOL_Obool)),U_8997),U_8998),
    inference(clausify,[status(thm)],[f_2143_2]) ).

fof(f_2144_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).

fof(f_2144_2,plain,
    ! [U_9003,U_9002,U_9001,U_9000,U_8999] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),hAPP(hAPP(c_COMBS(U_9000,U_8999,U_8999),hAPP(hAPP(c_COMBB(U_8999,tc_fun(U_8999,U_8999),U_9000),c_Groups_Otimes__class_Otimes(U_8999)),U_9002)),U_9003)),U_9001) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8999),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),U_9002),U_9001)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),U_9003),U_9001))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9000),U_9001))
      | ~ class_Groups_Ocomm__monoid__mult(U_8999) ),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

cnf(f_2144_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),hAPP(hAPP(c_COMBS(U_9000,U_8999,U_8999),hAPP(hAPP(c_COMBB(U_8999,tc_fun(U_8999,U_8999),U_9000),c_Groups_Otimes__class_Otimes(U_8999)),U_9002)),U_9003)),U_9001) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8999),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),U_9002),U_9001)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9000,U_8999),U_9003),U_9001))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9000),U_9001))
    | ~ class_Groups_Ocomm__monoid__mult(U_8999) ),
    inference(clausify,[status(thm)],[f_2144_2]) ).

fof(f_2145_1,plain,
    ! [V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).

fof(f_2145_2,plain,
    ! [U_9005,U_9004] :
      ( hBOOL(hAPP(hAPP(c_member(U_9004),hAPP(c_Groups_Ouminus__class_Ouminus(U_9004),U_9005)),c_Int_Oring__1__class_OInts(U_9004)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9004),U_9005),c_Int_Oring__1__class_OInts(U_9004)))
      | ~ class_Rings_Oring__1(U_9004) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

cnf(f_2145_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9004),hAPP(c_Groups_Ouminus__class_Ouminus(U_9004),U_9005)),c_Int_Oring__1__class_OInts(U_9004)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9004),U_9005),c_Int_Oring__1__class_OInts(U_9004)))
    | ~ class_Rings_Oring__1(U_9004) ),
    inference(clausify,[status(thm)],[f_2145_2]) ).

fof(f_2146_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).

fof(f_2146_2,plain,
    ! [U_9008,U_9007,U_9006] :
      ( hAPP(c_Set_Oimage(U_9006,U_9006,c_Groups_Ouminus__class_Ouminus(U_9006)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9006,U_9007,U_9008)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9006,hAPP(c_Groups_Ouminus__class_Ouminus(U_9006),U_9008),hAPP(c_Groups_Ouminus__class_Ouminus(U_9006),U_9007))
      | ~ class_Groups_Oordered__ab__group__add(U_9006) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

cnf(f_2146_3,plain,
    ( hAPP(c_Set_Oimage(U_9006,U_9006,c_Groups_Ouminus__class_Ouminus(U_9006)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9006,U_9007,U_9008)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9006,hAPP(c_Groups_Ouminus__class_Ouminus(U_9006),U_9008),hAPP(c_Groups_Ouminus__class_Ouminus(U_9006),U_9007))
    | ~ class_Groups_Oordered__ab__group__add(U_9006) ),
    inference(clausify,[status(thm)],[f_2146_2]) ).

fof(f_2147_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).

fof(f_2147_2,plain,
    ! [U_9010,U_9009] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9009,tc_HOL_Obool)),U_9010) = hAPP(c_Set_OCollect(U_9009),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9009),c_fNot),hAPP(hAPP(c_COMBC(U_9009,tc_fun(U_9009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9009)),U_9010))),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

cnf(f_2147_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9009,tc_HOL_Obool)),U_9010) = hAPP(c_Set_OCollect(U_9009),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9009),c_fNot),hAPP(hAPP(c_COMBC(U_9009,tc_fun(U_9009,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9009)),U_9010))),
    inference(clausify,[status(thm)],[f_2147_2]) ).

fof(f_2148_1,plain,
    ! [V_k_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).

fof(f_2148_2,plain,
    ! [U_9012,U_9011] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9011,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9011),U_9012)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_9011),U_9012)
      | ~ class_Orderings_Olinorder(U_9011) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

cnf(f_2148_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9011,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9011),U_9012)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_9011),U_9012)
    | ~ class_Orderings_Olinorder(U_9011) ),
    inference(clausify,[status(thm)],[f_2148_2]) ).

fof(f_2149_1,plain,
    ! [V_k_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).

fof(f_2149_2,plain,
    ! [U_9014,U_9013] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9013,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9013),U_9014)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_9013),U_9014)
      | ~ class_Orderings_Olinorder(U_9013) ),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

cnf(f_2149_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9013,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9013),U_9014)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_9013),U_9014)
    | ~ class_Orderings_Olinorder(U_9013) ),
    inference(clausify,[status(thm)],[f_2149_2]) ).

fof(f_2150_1,plain,
    ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).

fof(f_2150_2,plain,
    ! [U_9017,U_9016,U_9015] : hAPP(c_Set_OCollect(U_9015),hAPP(hAPP(c_COMBS(U_9015,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9015),c_fimplies),U_9016)),U_9017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9015,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9015,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9015),U_9016))),hAPP(c_Set_OCollect(U_9015),U_9017)),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

cnf(f_2150_3,plain,
    hAPP(c_Set_OCollect(U_9015),hAPP(hAPP(c_COMBS(U_9015,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9015),c_fimplies),U_9016)),U_9017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9015,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9015,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9015),U_9016))),hAPP(c_Set_OCollect(U_9015),U_9017)),
    inference(clausify,[status(thm)],[f_2150_2]) ).

fof(f_2151_1,plain,
    ! [V_k_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).

fof(f_2151_2,plain,
    ! [U_9019,U_9018] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9018,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9018),U_9019)) = hAPP(c_SetInterval_Oord__class_OatMost(U_9018),U_9019)
      | ~ class_Orderings_Olinorder(U_9018) ),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

cnf(f_2151_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9018,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9018),U_9019)) = hAPP(c_SetInterval_Oord__class_OatMost(U_9018),U_9019)
    | ~ class_Orderings_Olinorder(U_9018) ),
    inference(clausify,[status(thm)],[f_2151_2]) ).

fof(f_2152_1,plain,
    ! [V_k_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).

fof(f_2152_2,plain,
    ! [U_9021,U_9020] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9020,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_9020),U_9021)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9020),U_9021)
      | ~ class_Orderings_Olinorder(U_9020) ),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

cnf(f_2152_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9020,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_9020),U_9021)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9020),U_9021)
    | ~ class_Orderings_Olinorder(U_9020) ),
    inference(clausify,[status(thm)],[f_2152_2]) ).

fof(f_2153_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).

fof(f_2153_2,plain,
    ! [U_9025,U_9024,U_9023,U_9022] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9022,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9023,tc_fun(U_9022,tc_HOL_Obool)),U_9024),U_9025)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9023,tc_fun(U_9022,tc_HOL_Obool)),U_9024),hAPP(hAPP(c_COMBB(tc_fun(U_9022,tc_HOL_Obool),tc_fun(U_9022,tc_HOL_Obool),U_9023),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9022,tc_HOL_Obool))),U_9025)),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

cnf(f_2153_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9022,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9023,tc_fun(U_9022,tc_HOL_Obool)),U_9024),U_9025)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9023,tc_fun(U_9022,tc_HOL_Obool)),U_9024),hAPP(hAPP(c_COMBB(tc_fun(U_9022,tc_HOL_Obool),tc_fun(U_9022,tc_HOL_Obool),U_9023),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9022,tc_HOL_Obool))),U_9025)),
    inference(clausify,[status(thm)],[f_2153_2]) ).

fof(f_2154_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).

fof(f_2154_2,plain,
    ! [U_9029,U_9028,U_9027,U_9026] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9026,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9027,tc_fun(U_9026,tc_HOL_Obool)),U_9028),U_9029)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9027,tc_fun(U_9026,tc_HOL_Obool)),U_9028),hAPP(hAPP(c_COMBB(tc_fun(U_9026,tc_HOL_Obool),tc_fun(U_9026,tc_HOL_Obool),U_9027),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9026,tc_HOL_Obool))),U_9029)),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

cnf(f_2154_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9026,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9027,tc_fun(U_9026,tc_HOL_Obool)),U_9028),U_9029)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9027,tc_fun(U_9026,tc_HOL_Obool)),U_9028),hAPP(hAPP(c_COMBB(tc_fun(U_9026,tc_HOL_Obool),tc_fun(U_9026,tc_HOL_Obool),U_9027),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9026,tc_HOL_Obool))),U_9029)),
    inference(clausify,[status(thm)],[f_2154_2]) ).

fof(f_2155_1,plain,
    ! [V_f_2,V_S_2,T_a] :
      ( ( ( 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_a,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_a),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_a),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_a,tc_Nat_Onat),V_f_2),V_S_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).

fof(f_2155_2,plain,
    ! [U_9034,U_9033,U_9032] :
      ( ( ( 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_9032,tc_Nat_Onat),U_9034),U_9033)))
          | ? [U_9031] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,U_9031)))
              & hBOOL(hAPP(hAPP(c_member(U_9032),U_9031),U_9033)) ) )
        & ( ! [U_9030] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,U_9030)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9032),U_9030),U_9033)) )
          | ~ 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_9032,tc_Nat_Onat),U_9034),U_9033))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9032),U_9033)) ),
    inference(variable_rename,[status(thm)],[f_2155_1]) ).

fof(f_2155_3,plain,
    ! [U_9034,U_9033,U_9032] :
      ( ( ( 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_9032,tc_Nat_Onat),U_9034),U_9033)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,sK220(U_9034,U_9033,U_9032))))
            & hBOOL(hAPP(hAPP(c_member(U_9032),sK220(U_9034,U_9033,U_9032)),U_9033)) ) )
        & ( ! [U_9030] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,U_9030)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9032),U_9030),U_9033)) )
          | ~ 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_9032,tc_Nat_Onat),U_9034),U_9033))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9032),U_9033)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_9031,sK220(U_9034,U_9033,U_9032))],[f_2155_2]) ).

cnf(f_2155_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,U_9030)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9032),U_9030),U_9033))
    | ~ 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_9032,tc_Nat_Onat),U_9034),U_9033)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9032),U_9033)) ),
    inference(clausify,[status(thm)],[f_2155_3]) ).

cnf(f_2155_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9032),sK220(U_9034,U_9033,U_9032)),U_9033))
    | 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_9032,tc_Nat_Onat),U_9034),U_9033)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9032),U_9033)) ),
    inference(clausify,[status(thm)],[f_2155_3]) ).

cnf(f_2155_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9034,sK220(U_9034,U_9033,U_9032))))
    | 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_9032,tc_Nat_Onat),U_9034),U_9033)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9032),U_9033)) ),
    inference(clausify,[status(thm)],[f_2155_3]) ).

fof(f_2156_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex]) ).

fof(f_2156_2,plain,
    ! [U_9040,U_9039,U_9038,U_9037,U_9036,U_9035] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9037,U_9035),U_9040),hAPP(c_Set_Oimage(U_9036,U_9037,U_9038),U_9039)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9036,U_9035),hAPP(c_Fun_Ocomp(U_9037,U_9035,U_9036,U_9040),U_9038)),U_9039)
      | ~ c_Fun_Oinj__on(U_9036,U_9037,U_9038,U_9039)
      | ~ class_Groups_Ocomm__monoid__mult(U_9035) ),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

cnf(f_2156_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9037,U_9035),U_9040),hAPP(c_Set_Oimage(U_9036,U_9037,U_9038),U_9039)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9036,U_9035),hAPP(c_Fun_Ocomp(U_9037,U_9035,U_9036,U_9040),U_9038)),U_9039)
    | ~ c_Fun_Oinj__on(U_9036,U_9037,U_9038,U_9039)
    | ~ class_Groups_Ocomm__monoid__mult(U_9035) ),
    inference(clausify,[status(thm)],[f_2156_2]) ).

fof(f_2157_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2)
      | V_g_2 != hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
      | V_B_2 != hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong]) ).

fof(f_2157_2,plain,
    ! [U_9048,U_9047,U_9046,U_9045,U_9044,U_9043,U_9042,U_9041] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9043,U_9041),U_9048),U_9046) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9042,U_9041),U_9047),U_9045)
      | U_9047 != hAPP(c_Fun_Ocomp(U_9043,U_9041,U_9042,U_9048),U_9044)
      | U_9046 != hAPP(c_Set_Oimage(U_9042,U_9043,U_9044),U_9045)
      | ~ c_Fun_Oinj__on(U_9042,U_9043,U_9044,U_9045)
      | ~ class_Groups_Ocomm__monoid__mult(U_9041) ),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

cnf(f_2157_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9043,U_9041),U_9048),U_9046) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9042,U_9041),U_9047),U_9045)
    | U_9047 != hAPP(c_Fun_Ocomp(U_9043,U_9041,U_9042,U_9048),U_9044)
    | U_9046 != hAPP(c_Set_Oimage(U_9042,U_9043,U_9044),U_9045)
    | ~ c_Fun_Oinj__on(U_9042,U_9043,U_9044,U_9045)
    | ~ class_Groups_Ocomm__monoid__mult(U_9041) ),
    inference(clausify,[status(thm)],[f_2157_2]) ).

fof(f_2158_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_2158_2,plain,
    ! [U_9050,U_9049] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9049),U_9050) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9049),U_9050)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9049),U_9050),c_Groups_Ozero__class_Ozero(U_9049)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_9049) ),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

cnf(f_2158_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9049),U_9050) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9049),U_9050)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9049),U_9050),c_Groups_Ozero__class_Ozero(U_9049)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_9049) ),
    inference(clausify,[status(thm)],[f_2158_2]) ).

fof(f_2159_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_2159_2,plain,
    ! [U_9052,U_9051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9051),hAPP(c_Groups_Ouminus__class_Ouminus(U_9051),hAPP(c_Groups_Oabs__class_Oabs(U_9051),U_9052))),c_Groups_Ozero__class_Ozero(U_9051)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_9051) ),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

cnf(f_2159_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9051),hAPP(c_Groups_Ouminus__class_Ouminus(U_9051),hAPP(c_Groups_Oabs__class_Oabs(U_9051),U_9052))),c_Groups_Ozero__class_Ozero(U_9051)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_9051) ),
    inference(clausify,[status(thm)],[f_2159_2]) ).

fof(f_2160_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_2160_2,plain,
    ! [U_9054,U_9053] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_9053),U_9054) = U_9054
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9053),U_9054),c_Groups_Ozero__class_Ozero(U_9053))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_9053),U_9054) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9053),U_9054)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9053),U_9054),c_Groups_Ozero__class_Ozero(U_9053))) ) )
      | ~ class_Groups_Oabs__if(U_9053) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

cnf(f_2160_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9053),U_9054) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9053),U_9054)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9053),U_9054),c_Groups_Ozero__class_Ozero(U_9053)))
    | ~ class_Groups_Oabs__if(U_9053) ),
    inference(clausify,[status(thm)],[f_2160_2]) ).

cnf(f_2160_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9053),U_9054) = U_9054
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9053),U_9054),c_Groups_Ozero__class_Ozero(U_9053)))
    | ~ class_Groups_Oabs__if(U_9053) ),
    inference(clausify,[status(thm)],[f_2160_2]) ).

fof(f_2161_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_2161_2,plain,
    ! [U_9056,U_9055] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9055),U_9056) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9055),U_9056)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9055),U_9056),c_Groups_Ozero__class_Ozero(U_9055)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_9055) ),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

cnf(f_2161_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9055),U_9056) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9055),U_9056)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9055),U_9056),c_Groups_Ozero__class_Ozero(U_9055)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_9055) ),
    inference(clausify,[status(thm)],[f_2161_2]) ).

fof(f_2162_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_2162_2,plain,
    ! [U_9058,U_9057] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_9057),hAPP(c_Nat_OSuc,U_9058)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9058),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_9058)),U_9057),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

cnf(f_2162_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_9057),hAPP(c_Nat_OSuc,U_9058)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9058),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_9058)),U_9057),
    inference(clausify,[status(thm)],[f_2162_2]) ).

fof(f_2163_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_2163_2,plain,
    ! [U_9060,U_9059] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9059)),U_9060) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9059),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_9059)),U_9060),
    inference(variable_rename,[status(thm)],[f_2163_1]) ).

cnf(f_2163_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9059)),U_9060) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9059),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_9059)),U_9060),
    inference(clausify,[status(thm)],[f_2163_2]) ).

fof(f_2164_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).

fof(f_2164_2,plain,
    ! [U_9065,U_9064,U_9063,U_9062,U_9061] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9062,U_9061),hAPP(hAPP(c_COMBC(U_9062,U_9061,U_9061),hAPP(hAPP(c_COMBS(U_9062,U_9061,tc_fun(U_9061,U_9061)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9061,tc_fun(U_9061,U_9061)),U_9062),c_If(U_9061)),hAPP(hAPP(c_COMBC(U_9062,U_9062,tc_HOL_Obool),c_fequal),U_9064))),U_9065)),c_Groups_Oone__class_Oone(U_9061))),U_9063) = c_Groups_Oone__class_Oone(U_9061)
          | hBOOL(hAPP(hAPP(c_member(U_9062),U_9064),U_9063)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9062,U_9061),hAPP(hAPP(c_COMBC(U_9062,U_9061,U_9061),hAPP(hAPP(c_COMBS(U_9062,U_9061,tc_fun(U_9061,U_9061)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9061,tc_fun(U_9061,U_9061)),U_9062),c_If(U_9061)),hAPP(hAPP(c_COMBC(U_9062,U_9062,tc_HOL_Obool),c_fequal),U_9064))),U_9065)),c_Groups_Oone__class_Oone(U_9061))),U_9063) = hAPP(U_9065,U_9064)
          | ~ hBOOL(hAPP(hAPP(c_member(U_9062),U_9064),U_9063)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9062),U_9063))
      | ~ class_Groups_Ocomm__monoid__mult(U_9061) ),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

cnf(f_2164_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9062,U_9061),hAPP(hAPP(c_COMBC(U_9062,U_9061,U_9061),hAPP(hAPP(c_COMBS(U_9062,U_9061,tc_fun(U_9061,U_9061)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9061,tc_fun(U_9061,U_9061)),U_9062),c_If(U_9061)),hAPP(hAPP(c_COMBC(U_9062,U_9062,tc_HOL_Obool),c_fequal),U_9064))),U_9065)),c_Groups_Oone__class_Oone(U_9061))),U_9063) = hAPP(U_9065,U_9064)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9062),U_9064),U_9063))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9062),U_9063))
    | ~ class_Groups_Ocomm__monoid__mult(U_9061) ),
    inference(clausify,[status(thm)],[f_2164_2]) ).

cnf(f_2164_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9062,U_9061),hAPP(hAPP(c_COMBC(U_9062,U_9061,U_9061),hAPP(hAPP(c_COMBS(U_9062,U_9061,tc_fun(U_9061,U_9061)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9061,tc_fun(U_9061,U_9061)),U_9062),c_If(U_9061)),hAPP(hAPP(c_COMBC(U_9062,U_9062,tc_HOL_Obool),c_fequal),U_9064))),U_9065)),c_Groups_Oone__class_Oone(U_9061))),U_9063) = c_Groups_Oone__class_Oone(U_9061)
    | hBOOL(hAPP(hAPP(c_member(U_9062),U_9064),U_9063))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9062),U_9063))
    | ~ class_Groups_Ocomm__monoid__mult(U_9061) ),
    inference(clausify,[status(thm)],[f_2164_2]) ).

fof(f_2165_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).

fof(f_2165_2,plain,
    ! [U_9070,U_9069,U_9068,U_9067,U_9066] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9067,U_9066),hAPP(hAPP(c_COMBC(U_9067,U_9066,U_9066),hAPP(hAPP(c_COMBS(U_9067,U_9066,tc_fun(U_9066,U_9066)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9066,tc_fun(U_9066,U_9066)),U_9067),c_If(U_9066)),hAPP(c_fequal,U_9069))),U_9070)),c_Groups_Oone__class_Oone(U_9066))),U_9068) = c_Groups_Oone__class_Oone(U_9066)
          | hBOOL(hAPP(hAPP(c_member(U_9067),U_9069),U_9068)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9067,U_9066),hAPP(hAPP(c_COMBC(U_9067,U_9066,U_9066),hAPP(hAPP(c_COMBS(U_9067,U_9066,tc_fun(U_9066,U_9066)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9066,tc_fun(U_9066,U_9066)),U_9067),c_If(U_9066)),hAPP(c_fequal,U_9069))),U_9070)),c_Groups_Oone__class_Oone(U_9066))),U_9068) = hAPP(U_9070,U_9069)
          | ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9069),U_9068)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9067),U_9068))
      | ~ class_Groups_Ocomm__monoid__mult(U_9066) ),
    inference(variable_rename,[status(thm)],[f_2165_1]) ).

cnf(f_2165_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9067,U_9066),hAPP(hAPP(c_COMBC(U_9067,U_9066,U_9066),hAPP(hAPP(c_COMBS(U_9067,U_9066,tc_fun(U_9066,U_9066)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9066,tc_fun(U_9066,U_9066)),U_9067),c_If(U_9066)),hAPP(c_fequal,U_9069))),U_9070)),c_Groups_Oone__class_Oone(U_9066))),U_9068) = hAPP(U_9070,U_9069)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9069),U_9068))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9067),U_9068))
    | ~ class_Groups_Ocomm__monoid__mult(U_9066) ),
    inference(clausify,[status(thm)],[f_2165_2]) ).

cnf(f_2165_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9067,U_9066),hAPP(hAPP(c_COMBC(U_9067,U_9066,U_9066),hAPP(hAPP(c_COMBS(U_9067,U_9066,tc_fun(U_9066,U_9066)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9066,tc_fun(U_9066,U_9066)),U_9067),c_If(U_9066)),hAPP(c_fequal,U_9069))),U_9070)),c_Groups_Oone__class_Oone(U_9066))),U_9068) = c_Groups_Oone__class_Oone(U_9066)
    | hBOOL(hAPP(hAPP(c_member(U_9067),U_9069),U_9068))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9067),U_9068))
    | ~ class_Groups_Ocomm__monoid__mult(U_9066) ),
    inference(clausify,[status(thm)],[f_2165_2]) ).

fof(f_2166_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).

fof(f_2166_2,plain,
    ! [U_9073,U_9072,U_9071] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9073) = c_Orderings_Obot__class_Obot(tc_fun(U_9071,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9072),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9071,tc_HOL_Obool)),U_9073))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9071,tc_HOL_Obool)),U_9072),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9071,tc_HOL_Obool)),U_9073)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9071,tc_HOL_Obool)),U_9072),U_9073) != c_Orderings_Obot__class_Obot(tc_fun(U_9071,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

fof(f_2166_3,plain,
    ( ! [U_9079,U_9077,U_9075] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9075,tc_HOL_Obool)),U_9077),U_9079) = c_Orderings_Obot__class_Obot(tc_fun(U_9075,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9075,tc_HOL_Obool)),U_9077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9075,tc_HOL_Obool)),U_9079))) )
    & ! [U_9078,U_9076,U_9074] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9074,tc_HOL_Obool)),U_9076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9074,tc_HOL_Obool)),U_9078)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9074,tc_HOL_Obool)),U_9076),U_9078) != c_Orderings_Obot__class_Obot(tc_fun(U_9074,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2166_2]) ).

cnf(f_2166_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9074,tc_HOL_Obool)),U_9076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9074,tc_HOL_Obool)),U_9078)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9074,tc_HOL_Obool)),U_9076),U_9078) != c_Orderings_Obot__class_Obot(tc_fun(U_9074,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2166_3]) ).

cnf(f_2166_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9075,tc_HOL_Obool)),U_9077),U_9079) = c_Orderings_Obot__class_Obot(tc_fun(U_9075,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9075,tc_HOL_Obool)),U_9077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9075,tc_HOL_Obool)),U_9079))) ),
    inference(clausify,[status(thm)],[f_2166_3]) ).

fof(f_2167_1,plain,
    ! [V_A_2,V_f_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))))
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).

fof(f_2167_2,plain,
    ! [U_9083,U_9082,U_9081,U_9080] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9081,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9081,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),U_9083))),hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9080,tc_HOL_Obool)),U_9083))))
      | hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),c_Orderings_Otop__class_Otop(tc_fun(U_9080,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_9081,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

cnf(f_2167_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9081,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9081,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),U_9083))),hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9080,tc_HOL_Obool)),U_9083))))
    | hAPP(c_Set_Oimage(U_9080,U_9081,U_9082),c_Orderings_Otop__class_Otop(tc_fun(U_9080,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_9081,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2167_2]) ).

fof(f_2168_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).

fof(f_2168_2,plain,
    ! [U_9087,U_9086,U_9085,U_9084] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_9084,U_9084,c_Orderings_Oord__class_Omax(U_9084)),U_9086),hAPP(hAPP(c_Set_Oinsert(U_9084),U_9087),U_9085)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9084),U_9087),hAPP(hAPP(c_Finite__Set_Ofold(U_9084,U_9084,c_Orderings_Oord__class_Omax(U_9084)),U_9086),U_9085))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9084),U_9085))
      | ~ class_Orderings_Olinorder(U_9084) ),
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

cnf(f_2168_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_9084,U_9084,c_Orderings_Oord__class_Omax(U_9084)),U_9086),hAPP(hAPP(c_Set_Oinsert(U_9084),U_9087),U_9085)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9084),U_9087),hAPP(hAPP(c_Finite__Set_Ofold(U_9084,U_9084,c_Orderings_Oord__class_Omax(U_9084)),U_9086),U_9085))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9084),U_9085))
    | ~ class_Orderings_Olinorder(U_9084) ),
    inference(clausify,[status(thm)],[f_2168_2]) ).

fof(f_2169_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).

fof(f_2169_2,plain,
    ! [U_9091,U_9090,U_9089,U_9088] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_9088,U_9088,c_Orderings_Oord__class_Omin(U_9088)),U_9090),hAPP(hAPP(c_Set_Oinsert(U_9088),U_9091),U_9089)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9088),U_9091),hAPP(hAPP(c_Finite__Set_Ofold(U_9088,U_9088,c_Orderings_Oord__class_Omin(U_9088)),U_9090),U_9089))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9088),U_9089))
      | ~ class_Orderings_Olinorder(U_9088) ),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

cnf(f_2169_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_9088,U_9088,c_Orderings_Oord__class_Omin(U_9088)),U_9090),hAPP(hAPP(c_Set_Oinsert(U_9088),U_9091),U_9089)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9088),U_9091),hAPP(hAPP(c_Finite__Set_Ofold(U_9088,U_9088,c_Orderings_Oord__class_Omin(U_9088)),U_9090),U_9089))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9088),U_9089))
    | ~ class_Orderings_Olinorder(U_9088) ),
    inference(clausify,[status(thm)],[f_2169_2]) ).

fof(f_2170_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).

fof(f_2170_2,plain,
    ! [U_9094,U_9093,U_9092] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9092),U_9094),c_Big__Operators_Olinorder__class_OMax(U_9092,U_9093)) = c_Big__Operators_Olinorder__class_OMax(U_9092,U_9093)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9092),U_9094),U_9093))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9092),U_9093))
      | ~ class_Orderings_Olinorder(U_9092) ),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

cnf(f_2170_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9092),U_9094),c_Big__Operators_Olinorder__class_OMax(U_9092,U_9093)) = c_Big__Operators_Olinorder__class_OMax(U_9092,U_9093)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9092),U_9094),U_9093))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9092),U_9093))
    | ~ class_Orderings_Olinorder(U_9092) ),
    inference(clausify,[status(thm)],[f_2170_2]) ).

fof(f_2171_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).

fof(f_2171_2,plain,
    ! [U_9097,U_9096,U_9095] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9095),U_9097),c_Big__Operators_Olinorder__class_OMin(U_9095,U_9096)) = c_Big__Operators_Olinorder__class_OMin(U_9095,U_9096)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9095),U_9097),U_9096))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9095),U_9096))
      | ~ class_Orderings_Olinorder(U_9095) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

cnf(f_2171_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9095),U_9097),c_Big__Operators_Olinorder__class_OMin(U_9095,U_9096)) = c_Big__Operators_Olinorder__class_OMin(U_9095,U_9096)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9095),U_9097),U_9096))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9095),U_9096))
    | ~ class_Orderings_Olinorder(U_9095) ),
    inference(clausify,[status(thm)],[f_2171_2]) ).

fof(f_2172_1,plain,
    ! [V_d_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).

fof(f_2172_2,plain,
    ! [U_9101,U_9100,U_9099,U_9098] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9098,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9098,U_9099,U_9100)),hAPP(c_SetInterval_Oord__class_OatMost(U_9098),U_9101)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9098,U_9099,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9098),U_9100),U_9101))
      | ~ class_Orderings_Olinorder(U_9098) ),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

cnf(f_2172_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9098,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9098,U_9099,U_9100)),hAPP(c_SetInterval_Oord__class_OatMost(U_9098),U_9101)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9098,U_9099,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9098),U_9100),U_9101))
    | ~ class_Orderings_Olinorder(U_9098) ),
    inference(clausify,[status(thm)],[f_2172_2]) ).

fof(f_2173_1,plain,
    ! [V_d_2,V_c_2,V_b_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).

fof(f_2173_2,plain,
    ! [U_9105,U_9104,U_9103,U_9102] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_9102),U_9103)),c_SetInterval_Oord__class_OatLeastAtMost(U_9102,U_9104,U_9105)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9102,U_9104,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9102),U_9103),U_9105))
      | ~ class_Orderings_Olinorder(U_9102) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

cnf(f_2173_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_9102),U_9103)),c_SetInterval_Oord__class_OatLeastAtMost(U_9102,U_9104,U_9105)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9102,U_9104,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9102),U_9103),U_9105))
    | ~ class_Orderings_Olinorder(U_9102) ),
    inference(clausify,[status(thm)],[f_2173_2]) ).

fof(f_2174_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).

fof(f_2174_2,plain,
    ! [U_9108,U_9107,U_9106] :
      ( hAPP(c_Set_Oimage(U_9106,U_9106,c_Groups_Ouminus__class_Ouminus(U_9106)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_9106,U_9107),U_9108)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9106,hAPP(c_Groups_Ouminus__class_Ouminus(U_9106),U_9108),hAPP(c_Groups_Ouminus__class_Ouminus(U_9106),U_9107))
      | ~ class_Groups_Oordered__ab__group__add(U_9106) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

cnf(f_2174_3,plain,
    ( hAPP(c_Set_Oimage(U_9106,U_9106,c_Groups_Ouminus__class_Ouminus(U_9106)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_9106,U_9107),U_9108)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9106,hAPP(c_Groups_Ouminus__class_Ouminus(U_9106),U_9108),hAPP(c_Groups_Ouminus__class_Ouminus(U_9106),U_9107))
    | ~ class_Groups_Oordered__ab__group__add(U_9106) ),
    inference(clausify,[status(thm)],[f_2174_2]) ).

fof(f_2175_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).

fof(f_2175_2,plain,
    ! [U_9111,U_9110,U_9109] :
      ( hAPP(c_Set_Oimage(U_9109,U_9109,c_Groups_Ouminus__class_Ouminus(U_9109)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9109,U_9110,U_9111)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_9109,hAPP(c_Groups_Ouminus__class_Ouminus(U_9109),U_9111)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9109),U_9110))
      | ~ class_Groups_Oordered__ab__group__add(U_9109) ),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

cnf(f_2175_3,plain,
    ( hAPP(c_Set_Oimage(U_9109,U_9109,c_Groups_Ouminus__class_Ouminus(U_9109)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9109,U_9110,U_9111)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_9109,hAPP(c_Groups_Ouminus__class_Ouminus(U_9109),U_9111)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9109),U_9110))
    | ~ class_Groups_Oordered__ab__group__add(U_9109) ),
    inference(clausify,[status(thm)],[f_2175_2]) ).

fof(f_2176_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).

fof(f_2176_2,plain,
    ! [U_9115,U_9114,U_9113,U_9112] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9112,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9112,U_9113,U_9114)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9112),U_9115)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9112,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9112),U_9113),U_9115),U_9114)
      | ~ class_Orderings_Olinorder(U_9112) ),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

cnf(f_2176_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9112,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9112,U_9113,U_9114)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9112),U_9115)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9112,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9112),U_9113),U_9115),U_9114)
    | ~ class_Orderings_Olinorder(U_9112) ),
    inference(clausify,[status(thm)],[f_2176_2]) ).

fof(f_2177_1,plain,
    ! [V_d_2,V_c_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).

fof(f_2177_2,plain,
    ! [U_9119,U_9118,U_9117,U_9116] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9116),U_9117)),c_SetInterval_Oord__class_OatLeastAtMost(U_9116,U_9118,U_9119)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9116,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9116),U_9117),U_9118),U_9119)
      | ~ class_Orderings_Olinorder(U_9116) ),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

cnf(f_2177_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9116),U_9117)),c_SetInterval_Oord__class_OatLeastAtMost(U_9116,U_9118,U_9119)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9116,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9116),U_9117),U_9118),U_9119)
    | ~ class_Orderings_Olinorder(U_9116) ),
    inference(clausify,[status(thm)],[f_2177_2]) ).

fof(f_2178_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).

fof(f_2178_2,plain,
    ! [U_9121,U_9120] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9120,U_9121) = hAPP(c_Finite__Set_Ofold1(U_9120,c_Orderings_Oord__class_Omax(U_9120)),U_9121)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9120),U_9121))
      | ~ class_Orderings_Olinorder(U_9120) ),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

cnf(f_2178_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9120,U_9121) = hAPP(c_Finite__Set_Ofold1(U_9120,c_Orderings_Oord__class_Omax(U_9120)),U_9121)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9120),U_9121))
    | ~ class_Orderings_Olinorder(U_9120) ),
    inference(clausify,[status(thm)],[f_2178_2]) ).

fof(f_2179_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).

fof(f_2179_2,plain,
    ! [U_9123,U_9122] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9122,U_9123) = hAPP(c_Finite__Set_Ofold1(U_9122,c_Orderings_Oord__class_Omin(U_9122)),U_9123)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9122),U_9123))
      | ~ class_Orderings_Olinorder(U_9122) ),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

cnf(f_2179_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9122,U_9123) = hAPP(c_Finite__Set_Ofold1(U_9122,c_Orderings_Oord__class_Omin(U_9122)),U_9123)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9122),U_9123))
    | ~ class_Orderings_Olinorder(U_9122) ),
    inference(clausify,[status(thm)],[f_2179_2]) ).

fof(f_2180_1,plain,
    ! [V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).

fof(f_2180_2,plain,
    ! [U_9125,U_9124] :
      ( hAPP(c_Set_Oimage(U_9124,U_9124,c_Groups_Ouminus__class_Ouminus(U_9124)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9124),U_9125)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9124),hAPP(c_Groups_Ouminus__class_Ouminus(U_9124),U_9125))
      | ~ class_Groups_Oordered__ab__group__add(U_9124) ),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

cnf(f_2180_3,plain,
    ( hAPP(c_Set_Oimage(U_9124,U_9124,c_Groups_Ouminus__class_Ouminus(U_9124)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9124),U_9125)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9124),hAPP(c_Groups_Ouminus__class_Ouminus(U_9124),U_9125))
    | ~ class_Groups_Oordered__ab__group__add(U_9124) ),
    inference(clausify,[status(thm)],[f_2180_2]) ).

fof(f_2181_1,plain,
    ! [V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).

fof(f_2181_2,plain,
    ! [U_9127,U_9126] :
      ( hAPP(c_Set_Oimage(U_9126,U_9126,c_Groups_Ouminus__class_Ouminus(U_9126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9126),U_9127)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_9126),hAPP(c_Groups_Ouminus__class_Ouminus(U_9126),U_9127))
      | ~ class_Groups_Oordered__ab__group__add(U_9126) ),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

cnf(f_2181_3,plain,
    ( hAPP(c_Set_Oimage(U_9126,U_9126,c_Groups_Ouminus__class_Ouminus(U_9126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_9126),U_9127)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_9126),hAPP(c_Groups_Ouminus__class_Ouminus(U_9126),U_9127))
    | ~ class_Groups_Oordered__ab__group__add(U_9126) ),
    inference(clausify,[status(thm)],[f_2181_2]) ).

fof(f_2182_1,plain,
    ! [V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).

fof(f_2182_2,plain,
    ! [U_9129,U_9128] :
      ( hAPP(c_Set_Oimage(U_9128,U_9128,c_Groups_Ouminus__class_Ouminus(U_9128)),hAPP(c_SetInterval_Oord__class_OatMost(U_9128),U_9129)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_9128),hAPP(c_Groups_Ouminus__class_Ouminus(U_9128),U_9129))
      | ~ class_Groups_Oordered__ab__group__add(U_9128) ),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

cnf(f_2182_3,plain,
    ( hAPP(c_Set_Oimage(U_9128,U_9128,c_Groups_Ouminus__class_Ouminus(U_9128)),hAPP(c_SetInterval_Oord__class_OatMost(U_9128),U_9129)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_9128),hAPP(c_Groups_Ouminus__class_Ouminus(U_9128),U_9129))
    | ~ class_Groups_Oordered__ab__group__add(U_9128) ),
    inference(clausify,[status(thm)],[f_2182_2]) ).

fof(f_2183_1,plain,
    ! [V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).

fof(f_2183_2,plain,
    ! [U_9131,U_9130] :
      ( hAPP(c_Set_Oimage(U_9130,U_9130,c_Groups_Ouminus__class_Ouminus(U_9130)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9130),U_9131)) = hAPP(c_SetInterval_Oord__class_OatMost(U_9130),hAPP(c_Groups_Ouminus__class_Ouminus(U_9130),U_9131))
      | ~ class_Groups_Oordered__ab__group__add(U_9130) ),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

cnf(f_2183_3,plain,
    ( hAPP(c_Set_Oimage(U_9130,U_9130,c_Groups_Ouminus__class_Ouminus(U_9130)),hAPP(c_SetInterval_Oord__class_OatLeast(U_9130),U_9131)) = hAPP(c_SetInterval_Oord__class_OatMost(U_9130),hAPP(c_Groups_Ouminus__class_Ouminus(U_9130),U_9131))
    | ~ class_Groups_Oordered__ab__group__add(U_9130) ),
    inference(clausify,[status(thm)],[f_2183_2]) ).

fof(f_2184_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).

fof(f_2184_2,plain,
    ! [U_9136,U_9135,U_9134,U_9133,U_9132] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9133,U_9132),U_9136),hAPP(hAPP(c_Set_Oinsert(U_9133),U_9135),U_9134)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9132),hAPP(U_9136,U_9135)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9133,U_9132),U_9136),U_9134))
      | hBOOL(hAPP(hAPP(c_member(U_9133),U_9135),U_9134))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9133),U_9134))
      | ~ class_Groups_Ocomm__monoid__mult(U_9132) ),
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

cnf(f_2184_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9133,U_9132),U_9136),hAPP(hAPP(c_Set_Oinsert(U_9133),U_9135),U_9134)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9132),hAPP(U_9136,U_9135)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9133,U_9132),U_9136),U_9134))
    | hBOOL(hAPP(hAPP(c_member(U_9133),U_9135),U_9134))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9133),U_9134))
    | ~ class_Groups_Ocomm__monoid__mult(U_9132) ),
    inference(clausify,[status(thm)],[f_2184_2]) ).

fof(f_2185_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).

fof(f_2185_2,plain,
    ! [U_9141,U_9140,U_9139,U_9138,U_9137] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9138,U_9137),U_9141),hAPP(hAPP(c_Set_Oinsert(U_9138),U_9140),U_9139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9137),hAPP(U_9141,U_9140)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9138,U_9137),U_9141),U_9139))
      | hBOOL(hAPP(hAPP(c_member(U_9138),U_9140),U_9139))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9138),U_9139))
      | ~ class_Groups_Ocomm__monoid__mult(U_9137) ),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

cnf(f_2185_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9138,U_9137),U_9141),hAPP(hAPP(c_Set_Oinsert(U_9138),U_9140),U_9139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9137),hAPP(U_9141,U_9140)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9138,U_9137),U_9141),U_9139))
    | hBOOL(hAPP(hAPP(c_member(U_9138),U_9140),U_9139))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9138),U_9139))
    | ~ class_Groups_Ocomm__monoid__mult(U_9137) ),
    inference(clausify,[status(thm)],[f_2185_2]) ).

fof(f_2186_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).

fof(f_2186_2,plain,
    ! [U_9146,U_9145,U_9144,U_9143,U_9142] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),U_9144)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),U_9145))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9143),U_9145))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9143),U_9144))
      | ~ class_Groups_Ocomm__monoid__mult(U_9142) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

cnf(f_2186_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9142),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),U_9144)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9143,U_9142),U_9146),U_9145))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9143),U_9145))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9143),U_9144))
    | ~ class_Groups_Ocomm__monoid__mult(U_9142) ),
    inference(clausify,[status(thm)],[f_2186_2]) ).

fof(f_2187_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).

fof(f_2187_2,plain,
    ! [U_9151,U_9150,U_9149,U_9148,U_9147] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9147),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9148,tc_HOL_Obool)),U_9149),U_9150))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9148,tc_HOL_Obool)),U_9149),U_9150))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9147),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),U_9149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),U_9150))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9148),U_9150))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9148),U_9149))
      | ~ class_Groups_Ocomm__monoid__mult(U_9147) ),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

cnf(f_2187_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9147),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9148,tc_HOL_Obool)),U_9149),U_9150))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9148,tc_HOL_Obool)),U_9149),U_9150))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9147),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),U_9149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9148,U_9147),U_9151),U_9150))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9148),U_9150))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9148),U_9149))
    | ~ class_Groups_Ocomm__monoid__mult(U_9147) ),
    inference(clausify,[status(thm)],[f_2187_2]) ).

fof(f_2188_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex]) ).

fof(f_2188_2,plain,
    ! [U_9156,U_9155,U_9154,U_9153,U_9152] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9153,U_9152),U_9156),hAPP(c_Set_Oimage(U_9153,U_9153,U_9155),U_9154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9153,U_9152),hAPP(c_Fun_Ocomp(U_9153,U_9152,U_9153,U_9156),U_9155)),U_9154)
      | ~ c_Fun_Oinj__on(U_9153,U_9153,U_9155,U_9154)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9153),U_9154))
      | ~ class_Groups_Ocomm__monoid__mult(U_9152) ),
    inference(variable_rename,[status(thm)],[f_2188_1]) ).

cnf(f_2188_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9153,U_9152),U_9156),hAPP(c_Set_Oimage(U_9153,U_9153,U_9155),U_9154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9153,U_9152),hAPP(c_Fun_Ocomp(U_9153,U_9152,U_9153,U_9156),U_9155)),U_9154)
    | ~ c_Fun_Oinj__on(U_9153,U_9153,U_9155,U_9154)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9153),U_9154))
    | ~ class_Groups_Ocomm__monoid__mult(U_9152) ),
    inference(clausify,[status(thm)],[f_2188_2]) ).

fof(f_2189_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).

fof(f_2189_2,plain,
    ! [U_9160,U_9159,U_9158,U_9157] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9158,U_9157),U_9160),U_9159) = c_Groups_Oone__class_Oone(U_9157)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9158),U_9159)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9158,U_9157),U_9160),U_9159) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9157,U_9158,c_Groups_Otimes__class_Otimes(U_9157)),U_9160),c_Groups_Oone__class_Oone(U_9157)),U_9159)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9158),U_9159)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_9157) ),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

cnf(f_2189_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9158,U_9157),U_9160),U_9159) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9157,U_9158,c_Groups_Otimes__class_Otimes(U_9157)),U_9160),c_Groups_Oone__class_Oone(U_9157)),U_9159)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9158),U_9159))
    | ~ class_Groups_Ocomm__monoid__mult(U_9157) ),
    inference(clausify,[status(thm)],[f_2189_2]) ).

cnf(f_2189_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9158,U_9157),U_9160),U_9159) = c_Groups_Oone__class_Oone(U_9157)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9158),U_9159))
    | ~ class_Groups_Ocomm__monoid__mult(U_9157) ),
    inference(clausify,[status(thm)],[f_2189_2]) ).

fof(f_2190_1,plain,
    ! [V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).

fof(f_2190_2,plain,
    ! [U_9164,U_9163,U_9162,U_9161] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9162,U_9161),U_9164),U_9163) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9161,U_9162,c_Groups_Otimes__class_Otimes(U_9161)),U_9164),c_Groups_Oone__class_Oone(U_9161)),U_9163)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9162),U_9163))
      | ~ class_Groups_Ocomm__monoid__mult(U_9161) ),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

cnf(f_2190_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9162,U_9161),U_9164),U_9163) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9161,U_9162,c_Groups_Otimes__class_Otimes(U_9161)),U_9164),c_Groups_Oone__class_Oone(U_9161)),U_9163)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9162),U_9163))
    | ~ class_Groups_Ocomm__monoid__mult(U_9161) ),
    inference(clausify,[status(thm)],[f_2190_2]) ).

fof(f_2191_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_2191_2,plain,
    ! [U_9167,U_9166,U_9165] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9165),U_9166) = U_9167
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9165),U_9166),U_9167) != c_Orderings_Otop__class_Otop(U_9165)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9165),U_9166),U_9167) != c_Orderings_Obot__class_Obot(U_9165)
      | ~ class_Lattices_Oboolean__algebra(U_9165) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

cnf(f_2191_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9165),U_9166) = U_9167
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9165),U_9166),U_9167) != c_Orderings_Otop__class_Otop(U_9165)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9165),U_9166),U_9167) != c_Orderings_Obot__class_Obot(U_9165)
    | ~ class_Lattices_Oboolean__algebra(U_9165) ),
    inference(clausify,[status(thm)],[f_2191_2]) ).

fof(f_2192_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_2192_2,plain,
    ! [U_9169,U_9168] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_9168),hAPP(c_Nat_OSuc,U_9169)) = 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_9169)),U_9168),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

cnf(f_2192_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_9168),hAPP(c_Nat_OSuc,U_9169)) = 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_9169)),U_9168),
    inference(clausify,[status(thm)],[f_2192_2]) ).

fof(f_2193_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_2193_2,plain,
    ! [U_9171,U_9170] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9170)),U_9171) = 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_9170)),U_9171),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

cnf(f_2193_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9170)),U_9171) = 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_9170)),U_9171),
    inference(clausify,[status(thm)],[f_2193_2]) ).

fof(f_2194_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).

fof(f_2194_2,plain,
    ! [U_9175,U_9174,U_9173,U_9172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9172),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9172),U_9174),U_9175)),hAPP(hAPP(c_Finite__Set_Ofold(U_9172,U_9172,c_Orderings_Oord__class_Omax(U_9172)),U_9175),U_9173)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9173))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9172),U_9173))
      | ~ class_Orderings_Olinorder(U_9172) ),
    inference(variable_rename,[status(thm)],[f_2194_1]) ).

cnf(f_2194_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9172),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9172),U_9174),U_9175)),hAPP(hAPP(c_Finite__Set_Ofold(U_9172,U_9172,c_Orderings_Oord__class_Omax(U_9172)),U_9175),U_9173)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9172),U_9174),U_9173))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9172),U_9173))
    | ~ class_Orderings_Olinorder(U_9172) ),
    inference(clausify,[status(thm)],[f_2194_2]) ).

fof(f_2195_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).

fof(f_2195_2,plain,
    ! [U_9179,U_9178,U_9177,U_9176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9176),hAPP(hAPP(c_Finite__Set_Ofold(U_9176,U_9176,c_Orderings_Oord__class_Omin(U_9176)),U_9179),U_9177)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9176),U_9178),U_9179)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9176),U_9178),U_9177))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9176),U_9177))
      | ~ class_Orderings_Olinorder(U_9176) ),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

cnf(f_2195_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9176),hAPP(hAPP(c_Finite__Set_Ofold(U_9176,U_9176,c_Orderings_Oord__class_Omin(U_9176)),U_9179),U_9177)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9176),U_9178),U_9179)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9176),U_9178),U_9177))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9176),U_9177))
    | ~ class_Orderings_Olinorder(U_9176) ),
    inference(clausify,[status(thm)],[f_2195_2]) ).

fof(f_2196_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).

fof(f_2196_2,plain,
    ! [U_9182,U_9181,U_9180] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9180),hAPP(c_Finite__Set_Ofold1(U_9180,c_Orderings_Oord__class_Omin(U_9180)),U_9181)),U_9182))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9180),U_9182),U_9181))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9180),U_9181))
      | ~ class_Orderings_Olinorder(U_9180) ),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

cnf(f_2196_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9180),hAPP(c_Finite__Set_Ofold1(U_9180,c_Orderings_Oord__class_Omin(U_9180)),U_9181)),U_9182))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9180),U_9182),U_9181))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9180),U_9181))
    | ~ class_Orderings_Olinorder(U_9180) ),
    inference(clausify,[status(thm)],[f_2196_2]) ).

fof(f_2197_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).

fof(f_2197_2,plain,
    ! [U_9187,U_9186,U_9185] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187))
          | ! [U_9184] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),U_9184),U_9187))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9185),U_9184),U_9186)) ) )
        & ( ? [U_9183] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),U_9183),U_9187))
              & hBOOL(hAPP(hAPP(c_member(U_9185),U_9183),U_9186)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187)) ) )
      | U_9186 = c_Orderings_Obot__class_Obot(tc_fun(U_9185,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9185),U_9186))
      | ~ class_Orderings_Olinorder(U_9185) ),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

fof(f_2197_3,plain,
    ! [U_9187,U_9186,U_9185] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187))
          | ! [U_9184] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),U_9184),U_9187))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9185),U_9184),U_9186)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),sK221(U_9187,U_9186,U_9185)),U_9187))
            & hBOOL(hAPP(hAPP(c_member(U_9185),sK221(U_9187,U_9186,U_9185)),U_9186)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187)) ) )
      | U_9186 = c_Orderings_Obot__class_Obot(tc_fun(U_9185,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9185),U_9186))
      | ~ class_Orderings_Olinorder(U_9185) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_9183,sK221(U_9187,U_9186,U_9185))],[f_2197_2]) ).

cnf(f_2197_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9185),sK221(U_9187,U_9186,U_9185)),U_9186))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187))
    | U_9186 = c_Orderings_Obot__class_Obot(tc_fun(U_9185,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9185),U_9186))
    | ~ class_Orderings_Olinorder(U_9185) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

cnf(f_2197_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),sK221(U_9187,U_9186,U_9185)),U_9187))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187))
    | U_9186 = c_Orderings_Obot__class_Obot(tc_fun(U_9185,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9185),U_9186))
    | ~ class_Orderings_Olinorder(U_9185) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

cnf(f_2197_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),hAPP(c_Finite__Set_Ofold1(U_9185,c_Orderings_Oord__class_Omin(U_9185)),U_9186)),U_9187))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9185),U_9184),U_9187))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9185),U_9184),U_9186))
    | U_9186 = c_Orderings_Obot__class_Obot(tc_fun(U_9185,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9185),U_9186))
    | ~ class_Orderings_Olinorder(U_9185) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

fof(f_2198_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).

fof(f_2198_2,plain,
    ! [U_9192,U_9191,U_9190] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191)))
          | ? [U_9189] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),U_9189))
              & hBOOL(hAPP(hAPP(c_member(U_9190),U_9189),U_9191)) ) )
        & ( ! [U_9188] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),U_9188))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9190),U_9188),U_9191)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191))) ) )
      | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9190,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9190),U_9191))
      | ~ class_Orderings_Olinorder(U_9190) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

fof(f_2198_3,plain,
    ! [U_9192,U_9191,U_9190] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),sK222(U_9192,U_9191,U_9190)))
            & hBOOL(hAPP(hAPP(c_member(U_9190),sK222(U_9192,U_9191,U_9190)),U_9191)) ) )
        & ( ! [U_9188] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),U_9188))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9190),U_9188),U_9191)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191))) ) )
      | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9190,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9190),U_9191))
      | ~ class_Orderings_Olinorder(U_9190) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_9189,sK222(U_9192,U_9191,U_9190))],[f_2198_2]) ).

cnf(f_2198_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),U_9188))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9190),U_9188),U_9191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191)))
    | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9190),U_9191))
    | ~ class_Orderings_Olinorder(U_9190) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9190),sK222(U_9192,U_9191,U_9190)),U_9191))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191)))
    | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9190),U_9191))
    | ~ class_Orderings_Olinorder(U_9190) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),sK222(U_9192,U_9191,U_9190)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9190),U_9192),hAPP(c_Finite__Set_Ofold1(U_9190,c_Orderings_Oord__class_Omin(U_9190)),U_9191)))
    | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9190),U_9191))
    | ~ class_Orderings_Olinorder(U_9190) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

fof(f_2199_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).

fof(f_2199_2,plain,
    ! [U_9197,U_9196,U_9195] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196)))
          | ? [U_9194] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),U_9194))
              & hBOOL(hAPP(hAPP(c_member(U_9195),U_9194),U_9196)) ) )
        & ( ! [U_9193] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),U_9193))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9195),U_9193),U_9196)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196))) ) )
      | U_9196 = c_Orderings_Obot__class_Obot(tc_fun(U_9195,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9195),U_9196))
      | ~ class_Orderings_Olinorder(U_9195) ),
    inference(variable_rename,[status(thm)],[f_2199_1]) ).

fof(f_2199_3,plain,
    ! [U_9197,U_9196,U_9195] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),sK223(U_9197,U_9196,U_9195)))
            & hBOOL(hAPP(hAPP(c_member(U_9195),sK223(U_9197,U_9196,U_9195)),U_9196)) ) )
        & ( ! [U_9193] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),U_9193))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9195),U_9193),U_9196)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196))) ) )
      | U_9196 = c_Orderings_Obot__class_Obot(tc_fun(U_9195,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9195),U_9196))
      | ~ class_Orderings_Olinorder(U_9195) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_9194,sK223(U_9197,U_9196,U_9195))],[f_2199_2]) ).

cnf(f_2199_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),U_9193))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9195),U_9193),U_9196))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196)))
    | U_9196 = c_Orderings_Obot__class_Obot(tc_fun(U_9195,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9195),U_9196))
    | ~ class_Orderings_Olinorder(U_9195) ),
    inference(clausify,[status(thm)],[f_2199_3]) ).

cnf(f_2199_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9195),sK223(U_9197,U_9196,U_9195)),U_9196))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196)))
    | U_9196 = c_Orderings_Obot__class_Obot(tc_fun(U_9195,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9195),U_9196))
    | ~ class_Orderings_Olinorder(U_9195) ),
    inference(clausify,[status(thm)],[f_2199_3]) ).

cnf(f_2199_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),sK223(U_9197,U_9196,U_9195)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9195),U_9197),hAPP(c_Finite__Set_Ofold1(U_9195,c_Orderings_Oord__class_Omin(U_9195)),U_9196)))
    | U_9196 = c_Orderings_Obot__class_Obot(tc_fun(U_9195,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9195),U_9196))
    | ~ class_Orderings_Olinorder(U_9195) ),
    inference(clausify,[status(thm)],[f_2199_3]) ).

fof(f_2200_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).

fof(f_2200_2,plain,
    ! [U_9202,U_9201,U_9200] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202))
          | ! [U_9199] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),U_9199),U_9202))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9200),U_9199),U_9201)) ) )
        & ( ? [U_9198] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),U_9198),U_9202))
              & hBOOL(hAPP(hAPP(c_member(U_9200),U_9198),U_9201)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202)) ) )
      | U_9201 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9200),U_9201))
      | ~ class_Orderings_Olinorder(U_9200) ),
    inference(variable_rename,[status(thm)],[f_2200_1]) ).

fof(f_2200_3,plain,
    ! [U_9202,U_9201,U_9200] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202))
          | ! [U_9199] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),U_9199),U_9202))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9200),U_9199),U_9201)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),sK224(U_9202,U_9201,U_9200)),U_9202))
            & hBOOL(hAPP(hAPP(c_member(U_9200),sK224(U_9202,U_9201,U_9200)),U_9201)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202)) ) )
      | U_9201 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9200),U_9201))
      | ~ class_Orderings_Olinorder(U_9200) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_9198,sK224(U_9202,U_9201,U_9200))],[f_2200_2]) ).

cnf(f_2200_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9200),sK224(U_9202,U_9201,U_9200)),U_9201))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202))
    | U_9201 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9200),U_9201))
    | ~ class_Orderings_Olinorder(U_9200) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),sK224(U_9202,U_9201,U_9200)),U_9202))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202))
    | U_9201 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9200),U_9201))
    | ~ class_Orderings_Olinorder(U_9200) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),hAPP(c_Finite__Set_Ofold1(U_9200,c_Orderings_Oord__class_Omin(U_9200)),U_9201)),U_9202))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9200),U_9199),U_9202))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9200),U_9199),U_9201))
    | U_9201 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9200),U_9201))
    | ~ class_Orderings_Olinorder(U_9200) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

fof(f_2201_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).

fof(f_2201_2,plain,
    ! [U_9205,U_9204,U_9203] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9203,hAPP(hAPP(c_Set_Oinsert(U_9203),U_9205),U_9204)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9203),U_9205),c_Big__Operators_Olinorder__class_OMax(U_9203,U_9204))
      | U_9204 = c_Orderings_Obot__class_Obot(tc_fun(U_9203,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9203),U_9204))
      | ~ class_Orderings_Olinorder(U_9203) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

cnf(f_2201_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9203,hAPP(hAPP(c_Set_Oinsert(U_9203),U_9205),U_9204)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9203),U_9205),c_Big__Operators_Olinorder__class_OMax(U_9203,U_9204))
    | U_9204 = c_Orderings_Obot__class_Obot(tc_fun(U_9203,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9203),U_9204))
    | ~ class_Orderings_Olinorder(U_9203) ),
    inference(clausify,[status(thm)],[f_2201_2]) ).

fof(f_2202_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).

fof(f_2202_2,plain,
    ! [U_9208,U_9207,U_9206] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9206,hAPP(hAPP(c_Set_Oinsert(U_9206),U_9208),U_9207)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9206),U_9208),c_Big__Operators_Olinorder__class_OMin(U_9206,U_9207))
      | U_9207 = c_Orderings_Obot__class_Obot(tc_fun(U_9206,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9206),U_9207))
      | ~ class_Orderings_Olinorder(U_9206) ),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

cnf(f_2202_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9206,hAPP(hAPP(c_Set_Oinsert(U_9206),U_9208),U_9207)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9206),U_9208),c_Big__Operators_Olinorder__class_OMin(U_9206,U_9207))
    | U_9207 = c_Orderings_Obot__class_Obot(tc_fun(U_9206,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9206),U_9207))
    | ~ class_Orderings_Olinorder(U_9206) ),
    inference(clausify,[status(thm)],[f_2202_2]) ).

fof(f_2203_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).

fof(f_2203_2,plain,
    ! [U_9211,U_9210,U_9209] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9209),c_Big__Operators_Olinorder__class_OMax(U_9209,U_9211)),c_Big__Operators_Olinorder__class_OMax(U_9209,U_9210)) = c_Big__Operators_Olinorder__class_OMax(U_9209,U_9210)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9209,tc_HOL_Obool)),U_9211),U_9210))
      | U_9211 = c_Orderings_Obot__class_Obot(tc_fun(U_9209,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),U_9210))
      | ~ class_Orderings_Olinorder(U_9209) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

cnf(f_2203_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9209),c_Big__Operators_Olinorder__class_OMax(U_9209,U_9211)),c_Big__Operators_Olinorder__class_OMax(U_9209,U_9210)) = c_Big__Operators_Olinorder__class_OMax(U_9209,U_9210)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9209,tc_HOL_Obool)),U_9211),U_9210))
    | U_9211 = c_Orderings_Obot__class_Obot(tc_fun(U_9209,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),U_9210))
    | ~ class_Orderings_Olinorder(U_9209) ),
    inference(clausify,[status(thm)],[f_2203_2]) ).

fof(f_2204_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).

fof(f_2204_2,plain,
    ! [U_9214,U_9213,U_9212] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9212),c_Big__Operators_Olinorder__class_OMin(U_9212,U_9214)),c_Big__Operators_Olinorder__class_OMin(U_9212,U_9213)) = c_Big__Operators_Olinorder__class_OMin(U_9212,U_9213)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9212,tc_HOL_Obool)),U_9214),U_9213))
      | U_9214 = c_Orderings_Obot__class_Obot(tc_fun(U_9212,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213))
      | ~ class_Orderings_Olinorder(U_9212) ),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

cnf(f_2204_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9212),c_Big__Operators_Olinorder__class_OMin(U_9212,U_9214)),c_Big__Operators_Olinorder__class_OMin(U_9212,U_9213)) = c_Big__Operators_Olinorder__class_OMin(U_9212,U_9213)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9212,tc_HOL_Obool)),U_9214),U_9213))
    | U_9214 = c_Orderings_Obot__class_Obot(tc_fun(U_9212,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213))
    | ~ class_Orderings_Olinorder(U_9212) ),
    inference(clausify,[status(thm)],[f_2204_2]) ).

fof(f_2205_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset]) ).

fof(f_2205_2,plain,
    ! [U_9218,U_9217,U_9216,U_9215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9216,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9215,U_9216,U_9217),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9215,tc_HOL_Obool)),U_9218))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9216,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9215,U_9216,U_9217),U_9218))))
      | ~ c_Fun_Oinj__on(U_9215,U_9216,U_9217,c_Orderings_Otop__class_Otop(tc_fun(U_9215,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

cnf(f_2205_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9216,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9215,U_9216,U_9217),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9215,tc_HOL_Obool)),U_9218))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9216,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9215,U_9216,U_9217),U_9218))))
    | ~ c_Fun_Oinj__on(U_9215,U_9216,U_9217,c_Orderings_Otop__class_Otop(tc_fun(U_9215,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2205_2]) ).

fof(f_2206_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).

fof(f_2206_2,plain,
    ! [U_9221,U_9220,U_9219] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9219,tc_HOL_Obool)),U_9220),U_9221)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9219),c_Big__Operators_Olinorder__class_OMax(U_9219,U_9220)),c_Big__Operators_Olinorder__class_OMax(U_9219,U_9221))
      | U_9221 = c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),U_9221))
      | U_9220 = c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),U_9220))
      | ~ class_Orderings_Olinorder(U_9219) ),
    inference(variable_rename,[status(thm)],[f_2206_1]) ).

cnf(f_2206_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9219,tc_HOL_Obool)),U_9220),U_9221)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9219),c_Big__Operators_Olinorder__class_OMax(U_9219,U_9220)),c_Big__Operators_Olinorder__class_OMax(U_9219,U_9221))
    | U_9221 = c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),U_9221))
    | U_9220 = c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),U_9220))
    | ~ class_Orderings_Olinorder(U_9219) ),
    inference(clausify,[status(thm)],[f_2206_2]) ).

fof(f_2207_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).

fof(f_2207_2,plain,
    ! [U_9224,U_9223,U_9222] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9222,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9222,tc_HOL_Obool)),U_9223),U_9224)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9222),c_Big__Operators_Olinorder__class_OMin(U_9222,U_9223)),c_Big__Operators_Olinorder__class_OMin(U_9222,U_9224))
      | U_9224 = c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9222),U_9224))
      | U_9223 = c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9222),U_9223))
      | ~ class_Orderings_Olinorder(U_9222) ),
    inference(variable_rename,[status(thm)],[f_2207_1]) ).

cnf(f_2207_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9222,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9222,tc_HOL_Obool)),U_9223),U_9224)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9222),c_Big__Operators_Olinorder__class_OMin(U_9222,U_9223)),c_Big__Operators_Olinorder__class_OMin(U_9222,U_9224))
    | U_9224 = c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9222),U_9224))
    | U_9223 = c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9222),U_9223))
    | ~ class_Orderings_Olinorder(U_9222) ),
    inference(clausify,[status(thm)],[f_2207_2]) ).

fof(f_2208_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).

fof(f_2208_2,plain,
    ! [U_9227,U_9226,U_9225] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9225,hAPP(hAPP(c_Set_Oinsert(U_9225),U_9227),U_9226)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9225,U_9225,c_Orderings_Oord__class_Omax(U_9225)),U_9227),U_9226)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9225),U_9226))
      | ~ class_Orderings_Olinorder(U_9225) ),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

cnf(f_2208_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9225,hAPP(hAPP(c_Set_Oinsert(U_9225),U_9227),U_9226)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9225,U_9225,c_Orderings_Oord__class_Omax(U_9225)),U_9227),U_9226)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9225),U_9226))
    | ~ class_Orderings_Olinorder(U_9225) ),
    inference(clausify,[status(thm)],[f_2208_2]) ).

fof(f_2209_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).

fof(f_2209_2,plain,
    ! [U_9230,U_9229,U_9228] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9228,hAPP(hAPP(c_Set_Oinsert(U_9228),U_9230),U_9229)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9228,U_9228,c_Orderings_Oord__class_Omin(U_9228)),U_9230),U_9229)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9228),U_9229))
      | ~ class_Orderings_Olinorder(U_9228) ),
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

cnf(f_2209_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9228,hAPP(hAPP(c_Set_Oinsert(U_9228),U_9230),U_9229)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9228,U_9228,c_Orderings_Oord__class_Omin(U_9228)),U_9230),U_9229)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9228),U_9229))
    | ~ class_Orderings_Olinorder(U_9228) ),
    inference(clausify,[status(thm)],[f_2209_2]) ).

fof(f_2210_1,plain,
    ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] :
      ( ( ( ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) ) )
        | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
      & ( ( ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
            | hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).

fof(f_2210_2,plain,
    ! [U_9236,U_9235,U_9234,U_9233,U_9232,U_9231] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_9235,U_9231,hAPP(hAPP(c_COMBC(U_9235,U_9231,U_9231),hAPP(hAPP(c_COMBC(U_9235,U_9231,tc_fun(U_9231,U_9231)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9231,tc_fun(U_9231,U_9231)),U_9235),c_If(U_9231)),hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),U_9236))),U_9232)),U_9234)),U_9233) = c_Orderings_Obot__class_Obot(tc_fun(U_9235,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_9231),U_9234),U_9233)) )
          & ( hAPP(c_Set_Ovimage(U_9235,U_9231,hAPP(hAPP(c_COMBC(U_9235,U_9231,U_9231),hAPP(hAPP(c_COMBC(U_9235,U_9231,tc_fun(U_9231,U_9231)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9231,tc_fun(U_9231,U_9231)),U_9235),c_If(U_9231)),hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),U_9236))),U_9232)),U_9234)),U_9233) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9235,tc_HOL_Obool)),U_9236)
            | ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9234),U_9233)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_9231),U_9232),U_9233)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_9235,U_9231,hAPP(hAPP(c_COMBC(U_9235,U_9231,U_9231),hAPP(hAPP(c_COMBC(U_9235,U_9231,tc_fun(U_9231,U_9231)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9231,tc_fun(U_9231,U_9231)),U_9235),c_If(U_9231)),hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),U_9236))),U_9232)),U_9234)),U_9233) = U_9236
            | hBOOL(hAPP(hAPP(c_member(U_9231),U_9234),U_9233)) )
          & ( hAPP(c_Set_Ovimage(U_9235,U_9231,hAPP(hAPP(c_COMBC(U_9235,U_9231,U_9231),hAPP(hAPP(c_COMBC(U_9235,U_9231,tc_fun(U_9231,U_9231)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9231,tc_fun(U_9231,U_9231)),U_9235),c_If(U_9231)),hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),U_9236))),U_9232)),U_9234)),U_9233) = c_Orderings_Otop__class_Otop(tc_fun(U_9235,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9234),U_9233)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9231),U_9232),U_9233)) ) ),
    inference(variable_rename,[status(thm)],[f_2210_1]) ).

fof(f_2210_3,plain,
    ( ! [U_9248,U_9246,U_9244,U_9242,U_9240,U_9238] :
        ( ( ( hAPP(c_Set_Ovimage(U_9246,U_9238,hAPP(hAPP(c_COMBC(U_9246,U_9238,U_9238),hAPP(hAPP(c_COMBC(U_9246,U_9238,tc_fun(U_9238,U_9238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9238,tc_fun(U_9238,U_9238)),U_9246),c_If(U_9238)),hAPP(hAPP(c_COMBC(U_9246,tc_fun(U_9246,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9246)),U_9248))),U_9240)),U_9244)),U_9242) = c_Orderings_Obot__class_Obot(tc_fun(U_9246,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_9238),U_9244),U_9242)) )
          & ( hAPP(c_Set_Ovimage(U_9246,U_9238,hAPP(hAPP(c_COMBC(U_9246,U_9238,U_9238),hAPP(hAPP(c_COMBC(U_9246,U_9238,tc_fun(U_9238,U_9238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9238,tc_fun(U_9238,U_9238)),U_9246),c_If(U_9238)),hAPP(hAPP(c_COMBC(U_9246,tc_fun(U_9246,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9246)),U_9248))),U_9240)),U_9244)),U_9242) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9246,tc_HOL_Obool)),U_9248)
            | ~ hBOOL(hAPP(hAPP(c_member(U_9238),U_9244),U_9242)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_9238),U_9240),U_9242)) )
    & ! [U_9247,U_9245,U_9243,U_9241,U_9239,U_9237] :
        ( ( ( hAPP(c_Set_Ovimage(U_9245,U_9237,hAPP(hAPP(c_COMBC(U_9245,U_9237,U_9237),hAPP(hAPP(c_COMBC(U_9245,U_9237,tc_fun(U_9237,U_9237)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9237,tc_fun(U_9237,U_9237)),U_9245),c_If(U_9237)),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9245)),U_9247))),U_9239)),U_9243)),U_9241) = U_9247
            | hBOOL(hAPP(hAPP(c_member(U_9237),U_9243),U_9241)) )
          & ( hAPP(c_Set_Ovimage(U_9245,U_9237,hAPP(hAPP(c_COMBC(U_9245,U_9237,U_9237),hAPP(hAPP(c_COMBC(U_9245,U_9237,tc_fun(U_9237,U_9237)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9237,tc_fun(U_9237,U_9237)),U_9245),c_If(U_9237)),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9245)),U_9247))),U_9239)),U_9243)),U_9241) = c_Orderings_Otop__class_Otop(tc_fun(U_9245,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9237),U_9243),U_9241)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9237),U_9239),U_9241)) ) ),
    inference(miniscope,[status(thm)],[f_2210_2]) ).

cnf(f_2210_4,plain,
    ( hAPP(c_Set_Ovimage(U_9245,U_9237,hAPP(hAPP(c_COMBC(U_9245,U_9237,U_9237),hAPP(hAPP(c_COMBC(U_9245,U_9237,tc_fun(U_9237,U_9237)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9237,tc_fun(U_9237,U_9237)),U_9245),c_If(U_9237)),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9245)),U_9247))),U_9239)),U_9243)),U_9241) = c_Orderings_Otop__class_Otop(tc_fun(U_9245,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9237),U_9243),U_9241))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9237),U_9239),U_9241)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_5,plain,
    ( hAPP(c_Set_Ovimage(U_9245,U_9237,hAPP(hAPP(c_COMBC(U_9245,U_9237,U_9237),hAPP(hAPP(c_COMBC(U_9245,U_9237,tc_fun(U_9237,U_9237)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9237,tc_fun(U_9237,U_9237)),U_9245),c_If(U_9237)),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9245,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9245)),U_9247))),U_9239)),U_9243)),U_9241) = U_9247
    | hBOOL(hAPP(hAPP(c_member(U_9237),U_9243),U_9241))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9237),U_9239),U_9241)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_6,plain,
    ( hAPP(c_Set_Ovimage(U_9246,U_9238,hAPP(hAPP(c_COMBC(U_9246,U_9238,U_9238),hAPP(hAPP(c_COMBC(U_9246,U_9238,tc_fun(U_9238,U_9238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9238,tc_fun(U_9238,U_9238)),U_9246),c_If(U_9238)),hAPP(hAPP(c_COMBC(U_9246,tc_fun(U_9246,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9246)),U_9248))),U_9240)),U_9244)),U_9242) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9246,tc_HOL_Obool)),U_9248)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9238),U_9244),U_9242))
    | hBOOL(hAPP(hAPP(c_member(U_9238),U_9240),U_9242)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_7,plain,
    ( hAPP(c_Set_Ovimage(U_9246,U_9238,hAPP(hAPP(c_COMBC(U_9246,U_9238,U_9238),hAPP(hAPP(c_COMBC(U_9246,U_9238,tc_fun(U_9238,U_9238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9238,tc_fun(U_9238,U_9238)),U_9246),c_If(U_9238)),hAPP(hAPP(c_COMBC(U_9246,tc_fun(U_9246,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9246)),U_9248))),U_9240)),U_9244)),U_9242) = c_Orderings_Obot__class_Obot(tc_fun(U_9246,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9238),U_9244),U_9242))
    | hBOOL(hAPP(hAPP(c_member(U_9238),U_9240),U_9242)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

fof(f_2211_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).

fof(f_2211_2,plain,
    ! [U_9253,U_9252,U_9251,U_9250,U_9249] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9250,U_9249),U_9252),hAPP(hAPP(c_Set_Oinsert(U_9250),U_9253),U_9251)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9249),hAPP(U_9252,U_9253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9250,U_9249),U_9252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9250,tc_HOL_Obool)),U_9251),hAPP(hAPP(c_Set_Oinsert(U_9250),U_9253),c_Orderings_Obot__class_Obot(tc_fun(U_9250,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9250),U_9251))
      | ~ class_Groups_Ocomm__monoid__mult(U_9249) ),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

cnf(f_2211_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9250,U_9249),U_9252),hAPP(hAPP(c_Set_Oinsert(U_9250),U_9253),U_9251)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9249),hAPP(U_9252,U_9253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9250,U_9249),U_9252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9250,tc_HOL_Obool)),U_9251),hAPP(hAPP(c_Set_Oinsert(U_9250),U_9253),c_Orderings_Obot__class_Obot(tc_fun(U_9250,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9250),U_9251))
    | ~ class_Groups_Ocomm__monoid__mult(U_9249) ),
    inference(clausify,[status(thm)],[f_2211_2]) ).

fof(f_2212_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).

fof(f_2212_2,plain,
    ! [U_9258,U_9257,U_9256,U_9255,U_9254] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9254),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),U_9256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),U_9257))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9257) != c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9257))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9256))
      | ~ class_Groups_Ocomm__monoid__mult(U_9254) ),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

cnf(f_2212_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9254),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),U_9256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9255,U_9254),U_9258),U_9257))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9255,tc_HOL_Obool)),U_9256),U_9257) != c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9257))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9256))
    | ~ class_Groups_Ocomm__monoid__mult(U_9254) ),
    inference(clausify,[status(thm)],[f_2212_2]) ).

fof(f_2213_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).

fof(f_2213_2,plain,
    ! [U_9263,U_9262,U_9261,U_9260,U_9259] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9260,tc_HOL_Obool)),U_9261),U_9262)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9259),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),U_9261)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),U_9262))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9260,tc_HOL_Obool)),U_9261),U_9262) != c_Orderings_Obot__class_Obot(tc_fun(U_9260,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),U_9262))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),U_9261))
      | ~ class_Groups_Ocomm__monoid__mult(U_9259) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

cnf(f_2213_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9260,tc_HOL_Obool)),U_9261),U_9262)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9259),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),U_9261)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9260,U_9259),U_9263),U_9262))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9260,tc_HOL_Obool)),U_9261),U_9262) != c_Orderings_Obot__class_Obot(tc_fun(U_9260,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),U_9262))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),U_9261))
    | ~ class_Groups_Ocomm__monoid__mult(U_9259) ),
    inference(clausify,[status(thm)],[f_2213_2]) ).

fof(f_2214_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).

fof(f_2214_2,plain,
    ! [U_9266,U_9265,U_9264] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9264,hAPP(hAPP(c_Set_Oinsert(U_9264),U_9266),U_9265)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9264),U_9266),c_Big__Operators_Olinorder__class_OMax(U_9264,U_9265))
      | U_9265 = c_Orderings_Obot__class_Obot(tc_fun(U_9264,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9264),U_9266),U_9265))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),U_9265))
      | ~ class_Orderings_Olinorder(U_9264) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

cnf(f_2214_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9264,hAPP(hAPP(c_Set_Oinsert(U_9264),U_9266),U_9265)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9264),U_9266),c_Big__Operators_Olinorder__class_OMax(U_9264,U_9265))
    | U_9265 = c_Orderings_Obot__class_Obot(tc_fun(U_9264,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9264),U_9266),U_9265))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),U_9265))
    | ~ class_Orderings_Olinorder(U_9264) ),
    inference(clausify,[status(thm)],[f_2214_2]) ).

fof(f_2215_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).

fof(f_2215_2,plain,
    ! [U_9269,U_9268,U_9267] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9267,hAPP(hAPP(c_Set_Oinsert(U_9267),U_9269),U_9268)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9267),U_9269),c_Big__Operators_Olinorder__class_OMin(U_9267,U_9268))
      | U_9268 = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9267),U_9269),U_9268))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9267),U_9268))
      | ~ class_Orderings_Olinorder(U_9267) ),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

cnf(f_2215_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9267,hAPP(hAPP(c_Set_Oinsert(U_9267),U_9269),U_9268)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9267),U_9269),c_Big__Operators_Olinorder__class_OMin(U_9267,U_9268))
    | U_9268 = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9267),U_9269),U_9268))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9267),U_9268))
    | ~ class_Orderings_Olinorder(U_9267) ),
    inference(clausify,[status(thm)],[f_2215_2]) ).

fof(f_2216_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).

fof(f_2216_2,plain,
    ! [U_9272,U_9271,U_9270] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9270),hAPP(c_Finite__Set_Ofold1(U_9270,c_Orderings_Oord__class_Omin(U_9270)),U_9272)),hAPP(c_Finite__Set_Ofold1(U_9270,c_Orderings_Oord__class_Omin(U_9270)),U_9271)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9270),U_9272))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9270,tc_HOL_Obool)),U_9271),U_9272))
      | U_9271 = c_Orderings_Obot__class_Obot(tc_fun(U_9270,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_9270) ),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

cnf(f_2216_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9270),hAPP(c_Finite__Set_Ofold1(U_9270,c_Orderings_Oord__class_Omin(U_9270)),U_9272)),hAPP(c_Finite__Set_Ofold1(U_9270,c_Orderings_Oord__class_Omin(U_9270)),U_9271)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9270),U_9272))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9270,tc_HOL_Obool)),U_9271),U_9272))
    | U_9271 = c_Orderings_Obot__class_Obot(tc_fun(U_9270,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_9270) ),
    inference(clausify,[status(thm)],[f_2216_2]) ).

fof(f_2217_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).

fof(f_2217_2,plain,
    ! [U_9275,U_9274,U_9273] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),U_9274)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9273),U_9275),c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),U_9274)) = U_9275
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9273),U_9274))
      | ~ class_Orderings_Olinorder(U_9273) ),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

cnf(f_2217_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),U_9274)) = U_9275
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9273),U_9274))
    | ~ class_Orderings_Olinorder(U_9273) ),
    inference(clausify,[status(thm)],[f_2217_2]) ).

cnf(f_2217_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),U_9274)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9273),U_9275),c_Big__Operators_Olinorder__class_OMax(U_9273,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9273,tc_HOL_Obool)),U_9274),hAPP(hAPP(c_Set_Oinsert(U_9273),U_9275),c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9273),U_9274))
    | ~ class_Orderings_Olinorder(U_9273) ),
    inference(clausify,[status(thm)],[f_2217_2]) ).

fof(f_2218_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).

fof(f_2218_2,plain,
    ! [U_9278,U_9277,U_9276] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9276),c_Big__Operators_Olinorder__class_OMax(U_9276,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278))),c_Big__Operators_Olinorder__class_OMax(U_9276,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9276),c_Big__Operators_Olinorder__class_OMax(U_9276,U_9277)),c_Big__Operators_Olinorder__class_OMax(U_9276,U_9278))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278) = c_Orderings_Obot__class_Obot(tc_fun(U_9276,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9278))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9277))
      | ~ class_Orderings_Olinorder(U_9276) ),
    inference(variable_rename,[status(thm)],[f_2218_1]) ).

cnf(f_2218_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9276),c_Big__Operators_Olinorder__class_OMax(U_9276,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278))),c_Big__Operators_Olinorder__class_OMax(U_9276,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9276),c_Big__Operators_Olinorder__class_OMax(U_9276,U_9277)),c_Big__Operators_Olinorder__class_OMax(U_9276,U_9278))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278) = c_Orderings_Obot__class_Obot(tc_fun(U_9276,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9278))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9277))
    | ~ class_Orderings_Olinorder(U_9276) ),
    inference(clausify,[status(thm)],[f_2218_2]) ).

fof(f_2219_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).

fof(f_2219_2,plain,
    ! [U_9281,U_9280,U_9279] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9279,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9279,tc_HOL_Obool)),U_9280),U_9281)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9279),c_Big__Operators_Olinorder__class_OMax(U_9279,U_9280)),c_Big__Operators_Olinorder__class_OMax(U_9279,U_9281))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9279,tc_HOL_Obool)),U_9280),U_9281) != c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
      | U_9281 = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9281))
      | U_9280 = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9280))
      | ~ class_Orderings_Olinorder(U_9279) ),
    inference(variable_rename,[status(thm)],[f_2219_1]) ).

cnf(f_2219_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9279,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9279,tc_HOL_Obool)),U_9280),U_9281)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9279),c_Big__Operators_Olinorder__class_OMax(U_9279,U_9280)),c_Big__Operators_Olinorder__class_OMax(U_9279,U_9281))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9279,tc_HOL_Obool)),U_9280),U_9281) != c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
    | U_9281 = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9281))
    | U_9280 = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9280))
    | ~ class_Orderings_Olinorder(U_9279) ),
    inference(clausify,[status(thm)],[f_2219_2]) ).

fof(f_2220_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).

fof(f_2220_2,plain,
    ! [U_9284,U_9283,U_9282] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),U_9283)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9282),U_9284),c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),U_9283)) = U_9284
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9282),U_9283))
      | ~ class_Orderings_Olinorder(U_9282) ),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

cnf(f_2220_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),U_9283)) = U_9284
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9282),U_9283))
    | ~ class_Orderings_Olinorder(U_9282) ),
    inference(clausify,[status(thm)],[f_2220_2]) ).

cnf(f_2220_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),U_9283)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9282),U_9284),c_Big__Operators_Olinorder__class_OMin(U_9282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9282,tc_HOL_Obool)),U_9283),hAPP(hAPP(c_Set_Oinsert(U_9282),U_9284),c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9282,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9282),U_9283))
    | ~ class_Orderings_Olinorder(U_9282) ),
    inference(clausify,[status(thm)],[f_2220_2]) ).

fof(f_2221_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).

fof(f_2221_2,plain,
    ! [U_9287,U_9286,U_9285] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9285),c_Big__Operators_Olinorder__class_OMin(U_9285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287))),c_Big__Operators_Olinorder__class_OMin(U_9285,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9285),c_Big__Operators_Olinorder__class_OMin(U_9285,U_9286)),c_Big__Operators_Olinorder__class_OMin(U_9285,U_9287))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287) = c_Orderings_Obot__class_Obot(tc_fun(U_9285,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9285),U_9287))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9285),U_9286))
      | ~ class_Orderings_Olinorder(U_9285) ),
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

cnf(f_2221_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9285),c_Big__Operators_Olinorder__class_OMin(U_9285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287))),c_Big__Operators_Olinorder__class_OMin(U_9285,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9285),c_Big__Operators_Olinorder__class_OMin(U_9285,U_9286)),c_Big__Operators_Olinorder__class_OMin(U_9285,U_9287))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9285,tc_HOL_Obool)),U_9286),U_9287) = c_Orderings_Obot__class_Obot(tc_fun(U_9285,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9285),U_9287))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9285),U_9286))
    | ~ class_Orderings_Olinorder(U_9285) ),
    inference(clausify,[status(thm)],[f_2221_2]) ).

fof(f_2222_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).

fof(f_2222_2,plain,
    ! [U_9290,U_9289,U_9288] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9288,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9290)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9288),c_Big__Operators_Olinorder__class_OMin(U_9288,U_9289)),c_Big__Operators_Olinorder__class_OMin(U_9288,U_9290))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9290) != c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
      | U_9290 = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9288),U_9290))
      | U_9289 = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9288),U_9289))
      | ~ class_Orderings_Olinorder(U_9288) ),
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

cnf(f_2222_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9288,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9290)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9288),c_Big__Operators_Olinorder__class_OMin(U_9288,U_9289)),c_Big__Operators_Olinorder__class_OMin(U_9288,U_9290))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9290) != c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
    | U_9290 = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9288),U_9290))
    | U_9289 = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9288),U_9289))
    | ~ class_Orderings_Olinorder(U_9288) ),
    inference(clausify,[status(thm)],[f_2222_2]) ).

fof(f_2223_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(f_2223_2,plain,
    ! [U_9293,U_9292,U_9291] :
      ( c_Big__Operators_Olinorder__class_OMax(U_9291,hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),U_9292)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9291,U_9291,c_Orderings_Oord__class_Omax(U_9291)),U_9293),U_9292)
      | hBOOL(hAPP(hAPP(c_member(U_9291),U_9293),U_9292))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9291),U_9292))
      | ~ class_Orderings_Olinorder(U_9291) ),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

cnf(f_2223_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_9291,hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),U_9292)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9291,U_9291,c_Orderings_Oord__class_Omax(U_9291)),U_9293),U_9292)
    | hBOOL(hAPP(hAPP(c_member(U_9291),U_9293),U_9292))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9291),U_9292))
    | ~ class_Orderings_Olinorder(U_9291) ),
    inference(clausify,[status(thm)],[f_2223_2]) ).

fof(f_2224_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(f_2224_2,plain,
    ! [U_9296,U_9295,U_9294] :
      ( c_Big__Operators_Olinorder__class_OMin(U_9294,hAPP(hAPP(c_Set_Oinsert(U_9294),U_9296),U_9295)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9294,U_9294,c_Orderings_Oord__class_Omin(U_9294)),U_9296),U_9295)
      | hBOOL(hAPP(hAPP(c_member(U_9294),U_9296),U_9295))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9294),U_9295))
      | ~ class_Orderings_Olinorder(U_9294) ),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

cnf(f_2224_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_9294,hAPP(hAPP(c_Set_Oinsert(U_9294),U_9296),U_9295)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9294,U_9294,c_Orderings_Oord__class_Omin(U_9294)),U_9296),U_9295)
    | hBOOL(hAPP(hAPP(c_member(U_9294),U_9296),U_9295))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9294),U_9295))
    | ~ class_Orderings_Olinorder(U_9294) ),
    inference(clausify,[status(thm)],[f_2224_2]) ).

fof(f_2225_1,plain,
    ! [V_S_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).

fof(f_2225_2,plain,
    ! [U_9298,U_9297] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9297),c_Big__Operators_Olinorder__class_OMax(U_9297,U_9298)) = c_Big__Operators_Olinorder__class_OMin(U_9297,hAPP(c_Set_Oimage(U_9297,U_9297,c_Groups_Ouminus__class_Ouminus(U_9297)),U_9298))
      | U_9298 = c_Orderings_Obot__class_Obot(tc_fun(U_9297,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9297),U_9298))
      | ~ class_Groups_Olinordered__ab__group__add(U_9297) ),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

cnf(f_2225_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9297),c_Big__Operators_Olinorder__class_OMax(U_9297,U_9298)) = c_Big__Operators_Olinorder__class_OMin(U_9297,hAPP(c_Set_Oimage(U_9297,U_9297,c_Groups_Ouminus__class_Ouminus(U_9297)),U_9298))
    | U_9298 = c_Orderings_Obot__class_Obot(tc_fun(U_9297,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9297),U_9298))
    | ~ class_Groups_Olinordered__ab__group__add(U_9297) ),
    inference(clausify,[status(thm)],[f_2225_2]) ).

fof(f_2226_1,plain,
    ! [V_S_2,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).

fof(f_2226_2,plain,
    ! [U_9300,U_9299] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9299),c_Big__Operators_Olinorder__class_OMin(U_9299,U_9300)) = c_Big__Operators_Olinorder__class_OMax(U_9299,hAPP(c_Set_Oimage(U_9299,U_9299,c_Groups_Ouminus__class_Ouminus(U_9299)),U_9300))
      | U_9300 = c_Orderings_Obot__class_Obot(tc_fun(U_9299,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9299),U_9300))
      | ~ class_Groups_Olinordered__ab__group__add(U_9299) ),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

cnf(f_2226_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9299),c_Big__Operators_Olinorder__class_OMin(U_9299,U_9300)) = c_Big__Operators_Olinorder__class_OMax(U_9299,hAPP(c_Set_Oimage(U_9299,U_9299,c_Groups_Ouminus__class_Ouminus(U_9299)),U_9300))
    | U_9300 = c_Orderings_Obot__class_Obot(tc_fun(U_9299,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9299),U_9300))
    | ~ class_Groups_Olinordered__ab__group__add(U_9299) ),
    inference(clausify,[status(thm)],[f_2226_2]) ).

fof(f_2227_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dual__min]) ).

fof(f_2227_2,plain,
    ! [U_9301] :
      ( c_Orderings_Oord_Omin(U_9301,hAPP(c_COMBC(U_9301,U_9301,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_9301))) = c_Orderings_Oord__class_Omax(U_9301)
      | ~ class_Orderings_Olinorder(U_9301) ),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

cnf(f_2227_3,plain,
    ( c_Orderings_Oord_Omin(U_9301,hAPP(c_COMBC(U_9301,U_9301,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_9301))) = c_Orderings_Oord__class_Omax(U_9301)
    | ~ class_Orderings_Olinorder(U_9301) ),
    inference(clausify,[status(thm)],[f_2227_2]) ).

fof(f_2228_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dual__max]) ).

fof(f_2228_2,plain,
    ! [U_9302] :
      ( c_Orderings_Oord_Omax(U_9302,hAPP(c_COMBC(U_9302,U_9302,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_9302))) = c_Orderings_Oord__class_Omin(U_9302)
      | ~ class_Orderings_Olinorder(U_9302) ),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

cnf(f_2228_3,plain,
    ( c_Orderings_Oord_Omax(U_9302,hAPP(c_COMBC(U_9302,U_9302,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_9302))) = c_Orderings_Oord__class_Omin(U_9302)
    | ~ class_Orderings_Olinorder(U_9302) ),
    inference(clausify,[status(thm)],[f_2228_2]) ).

fof(f_2229_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).

fof(f_2229_2,plain,
    ! [U_9303] :
      ( c_Orderings_Oord__class_Omax(U_9303) = c_Orderings_Oord_Omax(U_9303,c_Orderings_Oord__class_Oless__eq(U_9303))
      | ~ class_Orderings_Oord(U_9303) ),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

cnf(f_2229_3,plain,
    ( c_Orderings_Oord__class_Omax(U_9303) = c_Orderings_Oord_Omax(U_9303,c_Orderings_Oord__class_Oless__eq(U_9303))
    | ~ class_Orderings_Oord(U_9303) ),
    inference(clausify,[status(thm)],[f_2229_2]) ).

fof(f_2230_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).

fof(f_2230_2,plain,
    ! [U_9304] :
      ( c_Orderings_Oord__class_Omin(U_9304) = c_Orderings_Oord_Omin(U_9304,c_Orderings_Oord__class_Oless__eq(U_9304))
      | ~ class_Orderings_Oord(U_9304) ),
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

cnf(f_2230_3,plain,
    ( c_Orderings_Oord__class_Omin(U_9304) = c_Orderings_Oord_Omin(U_9304,c_Orderings_Oord__class_Oless__eq(U_9304))
    | ~ class_Orderings_Oord(U_9304) ),
    inference(clausify,[status(thm)],[f_2230_2]) ).

fof(f_2231_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).

fof(f_2231_2,plain,
    ! [U_9307,U_9306,U_9305] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9305),c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),U_9306)),c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),U_9307)) = c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),hAPP(c_Set_OCollect(U_9305),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool,U_9305),c_HOL_OEx(U_9305)),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_HOL_Obool),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool,U_9305),c_HOL_OEx(U_9305))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),tc_fun(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),U_9305),c_COMBS(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9305,tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBS(U_9305,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9305),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9305),c_fconj))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_fun(U_9305,U_9305)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool)),tc_fun(tc_fun(U_9305,tc_fun(U_9305,U_9305)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),U_9305),c_COMBB(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool),U_9305)),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBB(U_9305,tc_HOL_Obool,U_9305)),c_fequal))),c_Orderings_Oord__class_Omin(U_9305)))))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9305)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9305),c_fconj),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305)),U_9306)))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305)),U_9307)))))))
      | U_9307 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9305),U_9307))
      | U_9306 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9305),U_9306))
      | ~ class_Orderings_Olinorder(U_9305) ),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

cnf(f_2231_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9305),c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),U_9306)),c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),U_9307)) = c_Big__Operators_Olattice_OSup__fin(U_9305,c_Orderings_Oord__class_Omax(U_9305),hAPP(c_Set_OCollect(U_9305),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool,U_9305),c_HOL_OEx(U_9305)),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_HOL_Obool),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool,U_9305),c_HOL_OEx(U_9305))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),tc_fun(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),U_9305),c_COMBS(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9305,tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool))),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBS(U_9305,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool)),tc_fun(U_9305,tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9305),hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9305),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9305),c_fconj))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_fun(U_9305,U_9305)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool)),tc_fun(tc_fun(U_9305,tc_fun(U_9305,U_9305)),tc_fun(U_9305,tc_fun(U_9305,tc_HOL_Obool))),U_9305),c_COMBB(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool),U_9305)),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(tc_fun(U_9305,U_9305),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBB(U_9305,tc_HOL_Obool,U_9305)),c_fequal))),c_Orderings_Oord__class_Omin(U_9305)))))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool)),U_9305),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9305)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9305),c_fconj),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305)),U_9306)))),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305)),U_9307)))))))
    | U_9307 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9305),U_9307))
    | U_9306 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9305),U_9306))
    | ~ class_Orderings_Olinorder(U_9305) ),
    inference(clausify,[status(thm)],[f_2231_2]) ).

fof(f_2232_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_2232_2,plain,
    ! [U_9309,U_9308] : 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_9308))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9309))),
    inference(variable_rename,[status(thm)],[f_2232_1]) ).

cnf(f_2232_3,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_9308))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9309))),
    inference(clausify,[status(thm)],[f_2232_2]) ).

fof(f_2233_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_2233_2,plain,
    ! [U_9311,U_9310] : 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_9310)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9311))),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

cnf(f_2233_3,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_9310)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9311))),
    inference(clausify,[status(thm)],[f_2233_2]) ).

fof(f_2234_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_2234_2,plain,
    ! [U_9313,U_9312] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9312)),U_9313) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9312),U_9313)),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

cnf(f_2234_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9312)),U_9313) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9312),U_9313)),
    inference(clausify,[status(thm)],[f_2234_2]) ).

fof(f_2235_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]) ).

cnf(f_2235_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(clausify,[status(thm)],[f_2235_1]) ).

fof(f_2236_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]) ).

cnf(f_2236_2,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2236_1]) ).

fof(f_2237_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]) ).

cnf(f_2237_2,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2237_1]) ).

fof(f_2238_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_2238_2,plain,
    ! [U_9315,U_9314] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9314),U_9315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9314)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9315)),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

cnf(f_2238_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9314),U_9315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9314)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9315)),
    inference(clausify,[status(thm)],[f_2238_2]) ).

fof(f_2239_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_2239_2,plain,
    ! [U_9316] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9316)),U_9316) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

cnf(f_2239_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9316)),U_9316) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2239_2]) ).

fof(f_2240_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_2240_2,plain,
    ! [U_9318,U_9317] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9317)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9318)
        | U_9318 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9317 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_9318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9317 = 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_9317)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9318) ) ),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

fof(f_2240_3,plain,
    ( ! [U_9322,U_9320] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9322)
        | U_9322 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_9321,U_9319] :
        ( ( U_9321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9319 = 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_9319)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9321) ) ),
    inference(miniscope,[status(thm)],[f_2240_2]) ).

cnf(f_2240_4,plain,
    ( U_9319 = 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_9319)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9321) ),
    inference(clausify,[status(thm)],[f_2240_3]) ).

cnf(f_2240_5,plain,
    ( U_9321 = 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_9319)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9321) ),
    inference(clausify,[status(thm)],[f_2240_3]) ).

cnf(f_2240_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9322)
    | U_9322 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_9320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2240_3]) ).

fof(f_2241_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_2241_2,plain,
    ! [U_9324,U_9323] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9323)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9324)))),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

cnf(f_2241_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9323)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9324)))),
    inference(clausify,[status(thm)],[f_2241_2]) ).

fof(f_2242_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_2242_2,plain,
    ! [U_9326,U_9325] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9325),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9326)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9325),U_9326),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

cnf(f_2242_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9325),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9326)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9325),U_9326),
    inference(clausify,[status(thm)],[f_2242_2]) ).

fof(f_2243_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_2243_2,plain,
    ! [U_9328,U_9327] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9327),U_9328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9327),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9328)),
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

cnf(f_2243_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9327),U_9328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9327),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9328)),
    inference(clausify,[status(thm)],[f_2243_2]) ).

fof(f_2244_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_2244_2,plain,
    ! [U_9330,U_9329] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9329)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9330))))
        | U_9330 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9329 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_9330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9329 = 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_9329)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9330)))) ) ),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

fof(f_2244_3,plain,
    ( ! [U_9334,U_9332] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9332)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9334))))
        | U_9334 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_9333,U_9331] :
        ( ( U_9333 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9331 = 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_9331)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9333)))) ) ),
    inference(miniscope,[status(thm)],[f_2244_2]) ).

cnf(f_2244_4,plain,
    ( U_9331 = 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_9331)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9333)))) ),
    inference(clausify,[status(thm)],[f_2244_3]) ).

cnf(f_2244_5,plain,
    ( U_9333 = 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_9331)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9333)))) ),
    inference(clausify,[status(thm)],[f_2244_3]) ).

cnf(f_2244_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_9332)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9334))))
    | U_9334 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_9332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2244_3]) ).

fof(f_2245_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_2245_2,plain,
    ! [U_9335] : 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_9335))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2245_1]) ).

cnf(f_2245_3,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_9335))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2245_2]) ).

fof(f_2246_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_2246_2,plain,
    ! [U_9336] : 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_9336))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

cnf(f_2246_3,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_9336))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2246_2]) ).

fof(f_2247_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_2247_2,plain,
    ! [U_9337] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9337) = U_9337
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9337),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9337) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9337)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9337),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2247_1]) ).

fof(f_2247_3,plain,
    ( ! [U_9339] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9339) = U_9339
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9339),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_9338] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9338) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9338)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9338),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2247_2]) ).

cnf(f_2247_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9338) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9338)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9338),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

cnf(f_2247_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9339) = U_9339
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9339),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

fof(f_2248_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_2248_2,plain,
    ! [U_9340] : 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_9340))))),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

cnf(f_2248_3,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_9340))))),
    inference(clausify,[status(thm)],[f_2248_2]) ).

fof(f_2249_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).

fof(f_2249_2,plain,
    ! [U_9343,U_9342,U_9341] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9341),U_9343),c_Big__Operators_Olattice_OSup__fin(U_9341,c_Orderings_Oord__class_Omax(U_9341),U_9342)) = c_Big__Operators_Olattice_OSup__fin(U_9341,c_Orderings_Oord__class_Omax(U_9341),U_9342)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9341),U_9343),U_9342))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9341),U_9342))
      | ~ class_Orderings_Olinorder(U_9341) ),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

cnf(f_2249_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9341),U_9343),c_Big__Operators_Olattice_OSup__fin(U_9341,c_Orderings_Oord__class_Omax(U_9341),U_9342)) = c_Big__Operators_Olattice_OSup__fin(U_9341,c_Orderings_Oord__class_Omax(U_9341),U_9342)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9341),U_9343),U_9342))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9341),U_9342))
    | ~ class_Orderings_Olinorder(U_9341) ),
    inference(clausify,[status(thm)],[f_2249_2]) ).

fof(f_2250_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).

fof(f_2250_2,plain,
    ! [U_9345,U_9344] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9344,c_Orderings_Oord__class_Omax(U_9344),hAPP(hAPP(c_Set_Oinsert(U_9344),U_9345),c_Orderings_Obot__class_Obot(tc_fun(U_9344,tc_HOL_Obool)))) = U_9345
      | ~ class_Orderings_Olinorder(U_9344) ),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

cnf(f_2250_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9344,c_Orderings_Oord__class_Omax(U_9344),hAPP(hAPP(c_Set_Oinsert(U_9344),U_9345),c_Orderings_Obot__class_Obot(tc_fun(U_9344,tc_HOL_Obool)))) = U_9345
    | ~ class_Orderings_Olinorder(U_9344) ),
    inference(clausify,[status(thm)],[f_2250_2]) ).

fof(f_2251_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).

fof(f_2251_2,plain,
    ! [U_9347,U_9346] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9346,c_Orderings_Oord__class_Omax(U_9346),U_9347) = hAPP(c_Finite__Set_Ofold1(U_9346,c_Orderings_Oord__class_Omax(U_9346)),U_9347)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9346),U_9347))
      | ~ class_Orderings_Olinorder(U_9346) ),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

cnf(f_2251_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9346,c_Orderings_Oord__class_Omax(U_9346),U_9347) = hAPP(c_Finite__Set_Ofold1(U_9346,c_Orderings_Oord__class_Omax(U_9346)),U_9347)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9346),U_9347))
    | ~ class_Orderings_Olinorder(U_9346) ),
    inference(clausify,[status(thm)],[f_2251_2]) ).

fof(f_2252_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_2252_2,plain,
    ! [U_9348] : ~ 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_9348))))),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

cnf(f_2252_3,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_9348))))),
    inference(clausify,[status(thm)],[f_2252_2]) ).

fof(f_2253_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_2253_2,plain,
    ! [U_9349] : 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_9349)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

cnf(f_2253_3,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_9349)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2253_2]) ).

fof(f_2254_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).

fof(f_2254_2,plain,
    ! [U_9352,U_9351,U_9350] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9350,c_Orderings_Oord__class_Omax(U_9350),hAPP(hAPP(c_Set_Oinsert(U_9350),U_9352),U_9351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9350),U_9352),c_Big__Operators_Olattice_OSup__fin(U_9350,c_Orderings_Oord__class_Omax(U_9350),U_9351))
      | U_9351 = c_Orderings_Obot__class_Obot(tc_fun(U_9350,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9350),U_9351))
      | ~ class_Orderings_Olinorder(U_9350) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

cnf(f_2254_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9350,c_Orderings_Oord__class_Omax(U_9350),hAPP(hAPP(c_Set_Oinsert(U_9350),U_9352),U_9351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9350),U_9352),c_Big__Operators_Olattice_OSup__fin(U_9350,c_Orderings_Oord__class_Omax(U_9350),U_9351))
    | U_9351 = c_Orderings_Obot__class_Obot(tc_fun(U_9350,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9350),U_9351))
    | ~ class_Orderings_Olinorder(U_9350) ),
    inference(clausify,[status(thm)],[f_2254_2]) ).

fof(f_2255_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).

fof(f_2255_2,plain,
    ! [U_9355,U_9354,U_9353] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9353),c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9355)),c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9354)) = c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9354)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),U_9355),U_9354))
      | U_9355 = c_Orderings_Obot__class_Obot(tc_fun(U_9353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9353),U_9354))
      | ~ class_Orderings_Olinorder(U_9353) ),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

cnf(f_2255_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9353),c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9355)),c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9354)) = c_Big__Operators_Olattice_OSup__fin(U_9353,c_Orderings_Oord__class_Omax(U_9353),U_9354)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),U_9355),U_9354))
    | U_9355 = c_Orderings_Obot__class_Obot(tc_fun(U_9353,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9353),U_9354))
    | ~ class_Orderings_Olinorder(U_9353) ),
    inference(clausify,[status(thm)],[f_2255_2]) ).

fof(f_2256_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).

fof(f_2256_2,plain,
    ! [U_9358,U_9357,U_9356] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9356),U_9358),c_Big__Operators_Olattice_OSup__fin(U_9356,c_Orderings_Oord__class_Omax(U_9356),U_9357)) = U_9358
      | ~ hBOOL(hAPP(hAPP(c_member(U_9356),U_9358),U_9357))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9356),U_9357))
      | ~ class_Orderings_Olinorder(U_9356) ),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

cnf(f_2256_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9356),U_9358),c_Big__Operators_Olattice_OSup__fin(U_9356,c_Orderings_Oord__class_Omax(U_9356),U_9357)) = U_9358
    | ~ hBOOL(hAPP(hAPP(c_member(U_9356),U_9358),U_9357))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9356),U_9357))
    | ~ class_Orderings_Olinorder(U_9356) ),
    inference(clausify,[status(thm)],[f_2256_2]) ).

fof(f_2257_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).

fof(f_2257_2,plain,
    ! [U_9361,U_9360,U_9359] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9359,tc_HOL_Obool)),U_9360),U_9361)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9359),c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),U_9360)),c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),U_9361))
      | U_9361 = c_Orderings_Obot__class_Obot(tc_fun(U_9359,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9359),U_9361))
      | U_9360 = c_Orderings_Obot__class_Obot(tc_fun(U_9359,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9359),U_9360))
      | ~ class_Orderings_Olinorder(U_9359) ),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

cnf(f_2257_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9359,tc_HOL_Obool)),U_9360),U_9361)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9359),c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),U_9360)),c_Big__Operators_Olattice_OSup__fin(U_9359,c_Orderings_Oord__class_Omax(U_9359),U_9361))
    | U_9361 = c_Orderings_Obot__class_Obot(tc_fun(U_9359,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9359),U_9361))
    | U_9360 = c_Orderings_Obot__class_Obot(tc_fun(U_9359,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9359),U_9360))
    | ~ class_Orderings_Olinorder(U_9359) ),
    inference(clausify,[status(thm)],[f_2257_2]) ).

fof(f_2258_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).

fof(f_2258_2,plain,
    ! [U_9364,U_9363,U_9362] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9362,c_Orderings_Oord__class_Omax(U_9362),hAPP(hAPP(c_Set_Oinsert(U_9362),U_9364),U_9363)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9362,U_9362,c_Orderings_Oord__class_Omax(U_9362)),U_9364),U_9363)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9362),U_9363))
      | ~ class_Orderings_Olinorder(U_9362) ),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

cnf(f_2258_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9362,c_Orderings_Oord__class_Omax(U_9362),hAPP(hAPP(c_Set_Oinsert(U_9362),U_9364),U_9363)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9362,U_9362,c_Orderings_Oord__class_Omax(U_9362)),U_9364),U_9363)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9362),U_9363))
    | ~ class_Orderings_Olinorder(U_9362) ),
    inference(clausify,[status(thm)],[f_2258_2]) ).

fof(f_2259_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_2259_2,plain,
    ! [U_9366,U_9365] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9365),U_9366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9365))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9366)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9365),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

cnf(f_2259_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9365),U_9366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9365))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9366)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9365),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2259_2]) ).

fof(f_2260_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(f_2260_2,plain,
    ! [U_9369,U_9368,U_9367] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9367,c_Orderings_Oord__class_Omax(U_9367),hAPP(hAPP(c_Set_Oinsert(U_9367),U_9369),U_9368)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9367),U_9369),c_Big__Operators_Olattice_OSup__fin(U_9367,c_Orderings_Oord__class_Omax(U_9367),U_9368))
      | U_9368 = c_Orderings_Obot__class_Obot(tc_fun(U_9367,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9367),U_9369),U_9368))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9367),U_9368))
      | ~ class_Orderings_Olinorder(U_9367) ),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

cnf(f_2260_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9367,c_Orderings_Oord__class_Omax(U_9367),hAPP(hAPP(c_Set_Oinsert(U_9367),U_9369),U_9368)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9367),U_9369),c_Big__Operators_Olattice_OSup__fin(U_9367,c_Orderings_Oord__class_Omax(U_9367),U_9368))
    | U_9368 = c_Orderings_Obot__class_Obot(tc_fun(U_9367,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9367),U_9369),U_9368))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9367),U_9368))
    | ~ class_Orderings_Olinorder(U_9367) ),
    inference(clausify,[status(thm)],[f_2260_2]) ).

fof(f_2261_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).

fof(f_2261_2,plain,
    ! [U_9372,U_9371,U_9370] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),U_9371)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9370),U_9372),c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),U_9371)) = U_9372
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9370),U_9371))
      | ~ class_Orderings_Olinorder(U_9370) ),
    inference(variable_rename,[status(thm)],[f_2261_1]) ).

cnf(f_2261_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),U_9371)) = U_9372
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9370),U_9371))
    | ~ class_Orderings_Olinorder(U_9370) ),
    inference(clausify,[status(thm)],[f_2261_2]) ).

cnf(f_2261_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),U_9371)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9370),U_9372),c_Big__Operators_Olattice_OSup__fin(U_9370,c_Orderings_Oord__class_Omax(U_9370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9370,tc_HOL_Obool)),U_9371),hAPP(hAPP(c_Set_Oinsert(U_9370),U_9372),c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9370,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9370),U_9371))
    | ~ class_Orderings_Olinorder(U_9370) ),
    inference(clausify,[status(thm)],[f_2261_2]) ).

fof(f_2262_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).

fof(f_2262_2,plain,
    ! [U_9375,U_9374,U_9373] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9373,tc_HOL_Obool)),U_9374),U_9375)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9373),c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),U_9374)),c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),U_9375))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9373,tc_HOL_Obool)),U_9374),U_9375) != c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
      | U_9375 = c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9373),U_9375))
      | U_9374 = c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9373),U_9374))
      | ~ class_Orderings_Olinorder(U_9373) ),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

cnf(f_2262_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9373,tc_HOL_Obool)),U_9374),U_9375)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9373),c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),U_9374)),c_Big__Operators_Olattice_OSup__fin(U_9373,c_Orderings_Oord__class_Omax(U_9373),U_9375))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9373,tc_HOL_Obool)),U_9374),U_9375) != c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
    | U_9375 = c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9373),U_9375))
    | U_9374 = c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9373),U_9374))
    | ~ class_Orderings_Olinorder(U_9373) ),
    inference(clausify,[status(thm)],[f_2262_2]) ).

fof(f_2263_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).

fof(f_2263_2,plain,
    ! [U_9378,U_9377,U_9376] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9376),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378))),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9376),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),U_9377)),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),U_9378))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378) = c_Orderings_Obot__class_Obot(tc_fun(U_9376,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9376),U_9378))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9376),U_9377))
      | ~ class_Orderings_Olinorder(U_9376) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

cnf(f_2263_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9376),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378))),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9376),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),U_9377)),c_Big__Operators_Olattice_OSup__fin(U_9376,c_Orderings_Oord__class_Omax(U_9376),U_9378))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9377),U_9378) = c_Orderings_Obot__class_Obot(tc_fun(U_9376,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9376),U_9378))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9376),U_9377))
    | ~ class_Orderings_Olinorder(U_9376) ),
    inference(clausify,[status(thm)],[f_2263_2]) ).

fof(f_2264_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(f_2264_2,plain,
    ! [U_9381,U_9380,U_9379] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9379,c_Orderings_Oord__class_Omax(U_9379),hAPP(hAPP(c_Set_Oinsert(U_9379),U_9381),U_9380)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9379,U_9379,c_Orderings_Oord__class_Omax(U_9379)),U_9381),U_9380)
      | hBOOL(hAPP(hAPP(c_member(U_9379),U_9381),U_9380))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9379),U_9380))
      | ~ class_Orderings_Olinorder(U_9379) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

cnf(f_2264_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9379,c_Orderings_Oord__class_Omax(U_9379),hAPP(hAPP(c_Set_Oinsert(U_9379),U_9381),U_9380)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9379,U_9379,c_Orderings_Oord__class_Omax(U_9379)),U_9381),U_9380)
    | hBOOL(hAPP(hAPP(c_member(U_9379),U_9381),U_9380))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9379),U_9380))
    | ~ class_Orderings_Olinorder(U_9379) ),
    inference(clausify,[status(thm)],[f_2264_2]) ).

fof(f_2265_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).

fof(f_2265_2,plain,
    ! [U_9384,U_9383,U_9382] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),U_9383) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9382),U_9384),c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),U_9383) = U_9384
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9382),U_9384),U_9383))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9382),U_9383))
      | ~ class_Orderings_Olinorder(U_9382) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

cnf(f_2265_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),U_9383) = U_9384
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9382),U_9384),U_9383))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9382),U_9383))
    | ~ class_Orderings_Olinorder(U_9382) ),
    inference(clausify,[status(thm)],[f_2265_2]) ).

cnf(f_2265_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),U_9383) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9382),U_9384),c_Big__Operators_Olattice_OSup__fin(U_9382,c_Orderings_Oord__class_Omax(U_9382),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9382,tc_HOL_Obool)),U_9383),hAPP(hAPP(c_Set_Oinsert(U_9382),U_9384),c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9382,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9382),U_9384),U_9383))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9382),U_9383))
    | ~ class_Orderings_Olinorder(U_9382) ),
    inference(clausify,[status(thm)],[f_2265_2]) ).

fof(f_2266_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).

fof(f_2266_2,plain,
    ! [U_9387,U_9386,U_9385] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9385),U_9387),c_Big__Operators_Olattice_OSup__fin(U_9385,c_Orderings_Oord__class_Omax(U_9385),U_9386)) = c_Big__Operators_Olattice_OSup__fin(U_9385,c_Orderings_Oord__class_Omax(U_9385),hAPP(c_Set_OCollect(U_9385),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_HOL_Obool,U_9385),c_HOL_OEx(U_9385)),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_HOL_Obool)),U_9385),c_COMBS(U_9385,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9385),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9385),c_fconj)),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,U_9385),tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_fun(tc_fun(U_9385,U_9385),tc_fun(U_9385,tc_HOL_Obool)),U_9385),c_COMBB(U_9385,tc_HOL_Obool,U_9385)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9385),U_9387))))),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9385)),U_9386)))))
      | U_9386 = c_Orderings_Obot__class_Obot(tc_fun(U_9385,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9386))
      | ~ class_Orderings_Olinorder(U_9385) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

cnf(f_2266_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9385),U_9387),c_Big__Operators_Olattice_OSup__fin(U_9385,c_Orderings_Oord__class_Omax(U_9385),U_9386)) = c_Big__Operators_Olattice_OSup__fin(U_9385,c_Orderings_Oord__class_Omax(U_9385),hAPP(c_Set_OCollect(U_9385),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_HOL_Obool,U_9385),c_HOL_OEx(U_9385)),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_HOL_Obool)),U_9385),c_COMBS(U_9385,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_fun(U_9385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9385),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9385),c_fconj)),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,U_9385),tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9385,tc_HOL_Obool),tc_fun(tc_fun(U_9385,U_9385),tc_fun(U_9385,tc_HOL_Obool)),U_9385),c_COMBB(U_9385,tc_HOL_Obool,U_9385)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9385),U_9387))))),hAPP(hAPP(c_COMBC(U_9385,tc_fun(U_9385,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9385)),U_9386)))))
    | U_9386 = c_Orderings_Obot__class_Obot(tc_fun(U_9385,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9386))
    | ~ class_Orderings_Olinorder(U_9385) ),
    inference(clausify,[status(thm)],[f_2266_2]) ).

fof(f_2267_1,plain,
    ! [V_f_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),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_a),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).

fof(f_2267_2,plain,
    ! [U_9391,U_9390,U_9389] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Int_Oint),U_9391),U_9390) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9389),c_Int_Onat),U_9391)),U_9390))
      | ? [U_9388] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9391,U_9388))
          & hBOOL(hAPP(hAPP(c_member(U_9389),U_9388),U_9390)) ) ),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

fof(f_2267_3,plain,
    ! [U_9391,U_9390,U_9389] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Int_Oint),U_9391),U_9390) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9389),c_Int_Onat),U_9391)),U_9390))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9391,sK225(U_9391,U_9390,U_9389)))
        & hBOOL(hAPP(hAPP(c_member(U_9389),sK225(U_9391,U_9390,U_9389)),U_9390)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_9388,sK225(U_9391,U_9390,U_9389))],[f_2267_2]) ).

cnf(f_2267_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9389),sK225(U_9391,U_9390,U_9389)),U_9390))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Int_Oint),U_9391),U_9390) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9389),c_Int_Onat),U_9391)),U_9390)) ),
    inference(clausify,[status(thm)],[f_2267_3]) ).

cnf(f_2267_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9391,sK225(U_9391,U_9390,U_9389)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Int_Oint),U_9391),U_9390) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9389),c_Int_Onat),U_9391)),U_9390)) ),
    inference(clausify,[status(thm)],[f_2267_3]) ).

fof(f_2268_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).

fof(f_2268_2,plain,
    ! [U_9394,U_9393,U_9392] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9392),U_9394),c_Big__Operators_Olattice_OInf__fin(U_9392,c_Orderings_Oord__class_Omin(U_9392),U_9393)) = c_Big__Operators_Olattice_OInf__fin(U_9392,c_Orderings_Oord__class_Omin(U_9392),hAPP(c_Set_OCollect(U_9392),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_HOL_Obool,U_9392),c_HOL_OEx(U_9392)),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_HOL_Obool)),U_9392),c_COMBS(U_9392,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9392),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9392),c_fconj)),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,U_9392),tc_fun(U_9392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_fun(tc_fun(U_9392,U_9392),tc_fun(U_9392,tc_HOL_Obool)),U_9392),c_COMBB(U_9392,tc_HOL_Obool,U_9392)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9392),U_9394))))),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9392)),U_9393)))))
      | U_9393 = c_Orderings_Obot__class_Obot(tc_fun(U_9392,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9392),U_9393))
      | ~ class_Orderings_Olinorder(U_9392) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

cnf(f_2268_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9392),U_9394),c_Big__Operators_Olattice_OInf__fin(U_9392,c_Orderings_Oord__class_Omin(U_9392),U_9393)) = c_Big__Operators_Olattice_OInf__fin(U_9392,c_Orderings_Oord__class_Omin(U_9392),hAPP(c_Set_OCollect(U_9392),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_HOL_Obool,U_9392),c_HOL_OEx(U_9392)),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_HOL_Obool)),U_9392),c_COMBS(U_9392,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_fun(U_9392,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9392),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9392),c_fconj)),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,U_9392),tc_fun(U_9392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9392,tc_HOL_Obool),tc_fun(tc_fun(U_9392,U_9392),tc_fun(U_9392,tc_HOL_Obool)),U_9392),c_COMBB(U_9392,tc_HOL_Obool,U_9392)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9392),U_9394))))),hAPP(hAPP(c_COMBC(U_9392,tc_fun(U_9392,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9392)),U_9393)))))
    | U_9393 = c_Orderings_Obot__class_Obot(tc_fun(U_9392,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9392),U_9393))
    | ~ class_Orderings_Olinorder(U_9392) ),
    inference(clausify,[status(thm)],[f_2268_2]) ).

fof(f_2269_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).

fof(f_2269_2,plain,
    ! [U_9397,U_9396,U_9395] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9395),c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),U_9396)),c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),U_9397)) = c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),hAPP(c_Set_OCollect(U_9395),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool,U_9395),c_HOL_OEx(U_9395)),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_HOL_Obool),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool,U_9395),c_HOL_OEx(U_9395))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),tc_fun(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),U_9395),c_COMBS(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9395,tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBS(U_9395,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9395),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9395),c_fconj))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_fun(U_9395,U_9395)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool)),tc_fun(tc_fun(U_9395,tc_fun(U_9395,U_9395)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),U_9395),c_COMBB(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool),U_9395)),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_fun(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBB(U_9395,tc_HOL_Obool,U_9395)),c_fequal))),c_Orderings_Oord__class_Omax(U_9395)))))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9395)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9395),c_fconj),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9395)),U_9396)))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9395)),U_9397)))))))
      | U_9397 = c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9395),U_9397))
      | U_9396 = c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9395),U_9396))
      | ~ class_Orderings_Olinorder(U_9395) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

cnf(f_2269_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9395),c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),U_9396)),c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),U_9397)) = c_Big__Operators_Olattice_OInf__fin(U_9395,c_Orderings_Oord__class_Omin(U_9395),hAPP(c_Set_OCollect(U_9395),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool,U_9395),c_HOL_OEx(U_9395)),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_HOL_Obool),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool,U_9395),c_HOL_OEx(U_9395))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),tc_fun(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),U_9395),c_COMBS(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9395,tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool))),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBS(U_9395,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool)),tc_fun(U_9395,tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9395),hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9395),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9395),c_fconj))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_fun(U_9395,U_9395)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool)),tc_fun(tc_fun(U_9395,tc_fun(U_9395,U_9395)),tc_fun(U_9395,tc_fun(U_9395,tc_HOL_Obool))),U_9395),c_COMBB(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool),U_9395)),hAPP(hAPP(c_COMBB(tc_fun(U_9395,tc_HOL_Obool),tc_fun(tc_fun(U_9395,U_9395),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBB(U_9395,tc_HOL_Obool,U_9395)),c_fequal))),c_Orderings_Oord__class_Omax(U_9395)))))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_fun(U_9395,tc_HOL_Obool)),U_9395),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9395)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9395),c_fconj),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9395)),U_9396)))),hAPP(hAPP(c_COMBC(U_9395,tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9395)),U_9397)))))))
    | U_9397 = c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9395),U_9397))
    | U_9396 = c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9395),U_9396))
    | ~ class_Orderings_Olinorder(U_9395) ),
    inference(clausify,[status(thm)],[f_2269_2]) ).

fof(f_2270_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).

fof(f_2270_2,plain,
    ! [U_9401,U_9400] :
      ( hBOOL(hAPP(hAPP(c_member(U_9400),c_Big__Operators_Olattice_OSup__fin(U_9400,c_Orderings_Oord__class_Omax(U_9400),U_9401)),U_9401))
      | ? [U_9399,U_9398] : ~ hBOOL(hAPP(hAPP(c_member(U_9400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9400),U_9399),U_9398)),hAPP(hAPP(c_Set_Oinsert(U_9400),U_9399),hAPP(hAPP(c_Set_Oinsert(U_9400),U_9398),c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))))))
      | U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9400),U_9401))
      | ~ class_Orderings_Olinorder(U_9400) ),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

fof(f_2270_3,plain,
    ! [U_9401,U_9400] :
      ( hBOOL(hAPP(hAPP(c_member(U_9400),c_Big__Operators_Olattice_OSup__fin(U_9400,c_Orderings_Oord__class_Omax(U_9400),U_9401)),U_9401))
      | ? [U_9398] : ~ hBOOL(hAPP(hAPP(c_member(U_9400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9400),sK226(U_9401,U_9400)),U_9398)),hAPP(hAPP(c_Set_Oinsert(U_9400),sK226(U_9401,U_9400)),hAPP(hAPP(c_Set_Oinsert(U_9400),U_9398),c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))))))
      | U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9400),U_9401))
      | ~ class_Orderings_Olinorder(U_9400) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_9399,sK226(U_9401,U_9400))],[f_2270_2]) ).

fof(f_2270_4,plain,
    ! [U_9401,U_9400] :
      ( hBOOL(hAPP(hAPP(c_member(U_9400),c_Big__Operators_Olattice_OSup__fin(U_9400,c_Orderings_Oord__class_Omax(U_9400),U_9401)),U_9401))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9400),sK226(U_9401,U_9400)),sK227(U_9401,U_9400))),hAPP(hAPP(c_Set_Oinsert(U_9400),sK226(U_9401,U_9400)),hAPP(hAPP(c_Set_Oinsert(U_9400),sK227(U_9401,U_9400)),c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))))))
      | U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9400),U_9401))
      | ~ class_Orderings_Olinorder(U_9400) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_9398,sK227(U_9401,U_9400))],[f_2270_3]) ).

cnf(f_2270_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9400),c_Big__Operators_Olattice_OSup__fin(U_9400,c_Orderings_Oord__class_Omax(U_9400),U_9401)),U_9401))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9400),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9400),sK226(U_9401,U_9400)),sK227(U_9401,U_9400))),hAPP(hAPP(c_Set_Oinsert(U_9400),sK226(U_9401,U_9400)),hAPP(hAPP(c_Set_Oinsert(U_9400),sK227(U_9401,U_9400)),c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))))))
    | U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9400),U_9401))
    | ~ class_Orderings_Olinorder(U_9400) ),
    inference(clausify,[status(thm)],[f_2270_4]) ).

fof(f_2271_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_2271_2,plain,
    ! [U_9402] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9402)) = U_9402,
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

cnf(f_2271_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9402)) = U_9402,
    inference(clausify,[status(thm)],[f_2271_2]) ).

fof(f_2272_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).

fof(f_2272_2,plain,
    ! [U_9405,U_9404,U_9403] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9403),U_9405),c_Big__Operators_Olattice_OInf__fin(U_9403,c_Orderings_Oord__class_Omin(U_9403),U_9404)) = c_Big__Operators_Olattice_OInf__fin(U_9403,c_Orderings_Oord__class_Omin(U_9403),U_9404)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9403),U_9405),U_9404))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9403),U_9404))
      | ~ class_Orderings_Olinorder(U_9403) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

cnf(f_2272_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9403),U_9405),c_Big__Operators_Olattice_OInf__fin(U_9403,c_Orderings_Oord__class_Omin(U_9403),U_9404)) = c_Big__Operators_Olattice_OInf__fin(U_9403,c_Orderings_Oord__class_Omin(U_9403),U_9404)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9403),U_9405),U_9404))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9403),U_9404))
    | ~ class_Orderings_Olinorder(U_9403) ),
    inference(clausify,[status(thm)],[f_2272_2]) ).

fof(f_2273_1,plain,
    ! [V_x_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).

fof(f_2273_2,plain,
    ! [U_9407,U_9406] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9406,c_Orderings_Oord__class_Omin(U_9406),hAPP(hAPP(c_Set_Oinsert(U_9406),U_9407),c_Orderings_Obot__class_Obot(tc_fun(U_9406,tc_HOL_Obool)))) = U_9407
      | ~ class_Orderings_Olinorder(U_9406) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

cnf(f_2273_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9406,c_Orderings_Oord__class_Omin(U_9406),hAPP(hAPP(c_Set_Oinsert(U_9406),U_9407),c_Orderings_Obot__class_Obot(tc_fun(U_9406,tc_HOL_Obool)))) = U_9407
    | ~ class_Orderings_Olinorder(U_9406) ),
    inference(clausify,[status(thm)],[f_2273_2]) ).

fof(f_2274_1,plain,
    ! [V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).

fof(f_2274_2,plain,
    ! [U_9409,U_9408] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9408,c_Orderings_Oord__class_Omin(U_9408),U_9409) = hAPP(c_Finite__Set_Ofold1(U_9408,c_Orderings_Oord__class_Omin(U_9408)),U_9409)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9408),U_9409))
      | ~ class_Orderings_Olinorder(U_9408) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

cnf(f_2274_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9408,c_Orderings_Oord__class_Omin(U_9408),U_9409) = hAPP(c_Finite__Set_Ofold1(U_9408,c_Orderings_Oord__class_Omin(U_9408)),U_9409)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9408),U_9409))
    | ~ class_Orderings_Olinorder(U_9408) ),
    inference(clausify,[status(thm)],[f_2274_2]) ).

fof(f_2275_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).

fof(f_2275_2,plain,
    ! [U_9412,U_9411,U_9410] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9410,c_Orderings_Oord__class_Omin(U_9410),hAPP(hAPP(c_Set_Oinsert(U_9410),U_9412),U_9411)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9410),U_9412),c_Big__Operators_Olattice_OInf__fin(U_9410,c_Orderings_Oord__class_Omin(U_9410),U_9411))
      | U_9411 = c_Orderings_Obot__class_Obot(tc_fun(U_9410,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9410),U_9411))
      | ~ class_Orderings_Olinorder(U_9410) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

cnf(f_2275_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9410,c_Orderings_Oord__class_Omin(U_9410),hAPP(hAPP(c_Set_Oinsert(U_9410),U_9412),U_9411)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9410),U_9412),c_Big__Operators_Olattice_OInf__fin(U_9410,c_Orderings_Oord__class_Omin(U_9410),U_9411))
    | U_9411 = c_Orderings_Obot__class_Obot(tc_fun(U_9410,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9410),U_9411))
    | ~ class_Orderings_Olinorder(U_9410) ),
    inference(clausify,[status(thm)],[f_2275_2]) ).

fof(f_2276_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).

fof(f_2276_2,plain,
    ! [U_9415,U_9414,U_9413] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9413),c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9415)),c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9414)) = c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9414)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9413,tc_HOL_Obool)),U_9415),U_9414))
      | U_9415 = c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9413),U_9414))
      | ~ class_Orderings_Olinorder(U_9413) ),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

cnf(f_2276_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9413),c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9415)),c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9414)) = c_Big__Operators_Olattice_OInf__fin(U_9413,c_Orderings_Oord__class_Omin(U_9413),U_9414)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9413,tc_HOL_Obool)),U_9415),U_9414))
    | U_9415 = c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9413),U_9414))
    | ~ class_Orderings_Olinorder(U_9413) ),
    inference(clausify,[status(thm)],[f_2276_2]) ).

fof(f_2277_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).

fof(f_2277_2,plain,
    ! [U_9418,U_9417,U_9416] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9416),U_9418),c_Big__Operators_Olattice_OInf__fin(U_9416,c_Orderings_Oord__class_Omin(U_9416),U_9417)) = U_9418
      | ~ hBOOL(hAPP(hAPP(c_member(U_9416),U_9418),U_9417))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9416),U_9417))
      | ~ class_Orderings_Olinorder(U_9416) ),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

cnf(f_2277_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9416),U_9418),c_Big__Operators_Olattice_OInf__fin(U_9416,c_Orderings_Oord__class_Omin(U_9416),U_9417)) = U_9418
    | ~ hBOOL(hAPP(hAPP(c_member(U_9416),U_9418),U_9417))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9416),U_9417))
    | ~ class_Orderings_Olinorder(U_9416) ),
    inference(clausify,[status(thm)],[f_2277_2]) ).

fof(f_2278_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).

fof(f_2278_2,plain,
    ! [U_9421,U_9420,U_9419] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9419,tc_HOL_Obool)),U_9420),U_9421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9419),c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),U_9420)),c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),U_9421))
      | U_9421 = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9419),U_9421))
      | U_9420 = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9419),U_9420))
      | ~ class_Orderings_Olinorder(U_9419) ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

cnf(f_2278_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9419,tc_HOL_Obool)),U_9420),U_9421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9419),c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),U_9420)),c_Big__Operators_Olattice_OInf__fin(U_9419,c_Orderings_Oord__class_Omin(U_9419),U_9421))
    | U_9421 = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9419),U_9421))
    | U_9420 = c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9419),U_9420))
    | ~ class_Orderings_Olinorder(U_9419) ),
    inference(clausify,[status(thm)],[f_2278_2]) ).

fof(f_2279_1,plain,
    ! [V_a_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).

fof(f_2279_2,plain,
    ! [U_9424,U_9423,U_9422] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9422,c_Orderings_Oord__class_Omin(U_9422),hAPP(hAPP(c_Set_Oinsert(U_9422),U_9424),U_9423)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9422,U_9422,c_Orderings_Oord__class_Omin(U_9422)),U_9424),U_9423)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9422),U_9423))
      | ~ class_Orderings_Olinorder(U_9422) ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

cnf(f_2279_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9422,c_Orderings_Oord__class_Omin(U_9422),hAPP(hAPP(c_Set_Oinsert(U_9422),U_9424),U_9423)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9422,U_9422,c_Orderings_Oord__class_Omin(U_9422)),U_9424),U_9423)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9422),U_9423))
    | ~ class_Orderings_Olinorder(U_9422) ),
    inference(clausify,[status(thm)],[f_2279_2]) ).

fof(f_2280_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(f_2280_2,plain,
    ! [U_9427,U_9426,U_9425] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9425,c_Orderings_Oord__class_Omin(U_9425),hAPP(hAPP(c_Set_Oinsert(U_9425),U_9427),U_9426)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9425),U_9427),c_Big__Operators_Olattice_OInf__fin(U_9425,c_Orderings_Oord__class_Omin(U_9425),U_9426))
      | U_9426 = c_Orderings_Obot__class_Obot(tc_fun(U_9425,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9425),U_9427),U_9426))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9425),U_9426))
      | ~ class_Orderings_Olinorder(U_9425) ),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

cnf(f_2280_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9425,c_Orderings_Oord__class_Omin(U_9425),hAPP(hAPP(c_Set_Oinsert(U_9425),U_9427),U_9426)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9425),U_9427),c_Big__Operators_Olattice_OInf__fin(U_9425,c_Orderings_Oord__class_Omin(U_9425),U_9426))
    | U_9426 = c_Orderings_Obot__class_Obot(tc_fun(U_9425,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9425),U_9427),U_9426))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9425),U_9426))
    | ~ class_Orderings_Olinorder(U_9425) ),
    inference(clausify,[status(thm)],[f_2280_2]) ).

fof(f_2281_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).

fof(f_2281_2,plain,
    ! [U_9430,U_9429,U_9428] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),U_9429)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9428),U_9430),c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),U_9429)) = U_9430
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9428),U_9429))
      | ~ class_Orderings_Olinorder(U_9428) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

cnf(f_2281_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),U_9429)) = U_9430
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9428),U_9429))
    | ~ class_Orderings_Olinorder(U_9428) ),
    inference(clausify,[status(thm)],[f_2281_2]) ).

cnf(f_2281_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),U_9429)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9428),U_9430),c_Big__Operators_Olattice_OInf__fin(U_9428,c_Orderings_Oord__class_Omin(U_9428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9428,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_Set_Oinsert(U_9428),U_9430),c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9428,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9428),U_9429))
    | ~ class_Orderings_Olinorder(U_9428) ),
    inference(clausify,[status(thm)],[f_2281_2]) ).

fof(f_2282_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).

fof(f_2282_2,plain,
    ! [U_9433,U_9432,U_9431] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9431),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433))),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9431),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),U_9432)),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),U_9433))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433) = c_Orderings_Obot__class_Obot(tc_fun(U_9431,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9431),U_9433))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9431),U_9432))
      | ~ class_Orderings_Olinorder(U_9431) ),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

cnf(f_2282_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9431),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433))),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9431),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),U_9432)),c_Big__Operators_Olattice_OInf__fin(U_9431,c_Orderings_Oord__class_Omin(U_9431),U_9433))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),U_9432),U_9433) = c_Orderings_Obot__class_Obot(tc_fun(U_9431,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9431),U_9433))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9431),U_9432))
    | ~ class_Orderings_Olinorder(U_9431) ),
    inference(clausify,[status(thm)],[f_2282_2]) ).

fof(f_2283_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).

fof(f_2283_2,plain,
    ! [U_9436,U_9435,U_9434] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9434),c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),U_9435)),c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),U_9436))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436) != c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
      | U_9436 = c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9434),U_9436))
      | U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9434),U_9435))
      | ~ class_Orderings_Olinorder(U_9434) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

cnf(f_2283_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9434),c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),U_9435)),c_Big__Operators_Olattice_OInf__fin(U_9434,c_Orderings_Oord__class_Omin(U_9434),U_9436))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9434,tc_HOL_Obool)),U_9435),U_9436) != c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
    | U_9436 = c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9434),U_9436))
    | U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9434,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9434),U_9435))
    | ~ class_Orderings_Olinorder(U_9434) ),
    inference(clausify,[status(thm)],[f_2283_2]) ).

fof(f_2284_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(f_2284_2,plain,
    ! [U_9439,U_9438,U_9437] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9437,c_Orderings_Oord__class_Omin(U_9437),hAPP(hAPP(c_Set_Oinsert(U_9437),U_9439),U_9438)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9437,U_9437,c_Orderings_Oord__class_Omin(U_9437)),U_9439),U_9438)
      | hBOOL(hAPP(hAPP(c_member(U_9437),U_9439),U_9438))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9437),U_9438))
      | ~ class_Orderings_Olinorder(U_9437) ),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

cnf(f_2284_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9437,c_Orderings_Oord__class_Omin(U_9437),hAPP(hAPP(c_Set_Oinsert(U_9437),U_9439),U_9438)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9437,U_9437,c_Orderings_Oord__class_Omin(U_9437)),U_9439),U_9438)
    | hBOOL(hAPP(hAPP(c_member(U_9437),U_9439),U_9438))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9437),U_9438))
    | ~ class_Orderings_Olinorder(U_9437) ),
    inference(clausify,[status(thm)],[f_2284_2]) ).

fof(f_2285_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).

fof(f_2285_2,plain,
    ! [U_9442,U_9441,U_9440] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),U_9441) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9440),U_9442),c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),U_9441) = U_9442
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9440),U_9442),U_9441))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9440),U_9441))
      | ~ class_Orderings_Olinorder(U_9440) ),
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

cnf(f_2285_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),U_9441) = U_9442
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9440),U_9442),U_9441))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9440),U_9441))
    | ~ class_Orderings_Olinorder(U_9440) ),
    inference(clausify,[status(thm)],[f_2285_2]) ).

cnf(f_2285_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),U_9441) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9440),U_9442),c_Big__Operators_Olattice_OInf__fin(U_9440,c_Orderings_Oord__class_Omin(U_9440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9440,tc_HOL_Obool)),U_9441),hAPP(hAPP(c_Set_Oinsert(U_9440),U_9442),c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9440,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9440),U_9442),U_9441))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9440),U_9441))
    | ~ class_Orderings_Olinorder(U_9440) ),
    inference(clausify,[status(thm)],[f_2285_2]) ).

fof(f_2286_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).

fof(f_2286_2,plain,
    ! [U_9444,U_9443] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9443),c_Big__Operators_Olattice_OInf__fin(U_9443,c_Orderings_Oord__class_Omin(U_9443),U_9444)),c_Big__Operators_Olattice_OSup__fin(U_9443,c_Orderings_Oord__class_Omax(U_9443),U_9444)))
      | U_9444 = c_Orderings_Obot__class_Obot(tc_fun(U_9443,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9443),U_9444))
      | ~ class_Orderings_Olinorder(U_9443) ),
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

cnf(f_2286_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9443),c_Big__Operators_Olattice_OInf__fin(U_9443,c_Orderings_Oord__class_Omin(U_9443),U_9444)),c_Big__Operators_Olattice_OSup__fin(U_9443,c_Orderings_Oord__class_Omax(U_9443),U_9444)))
    | U_9444 = c_Orderings_Obot__class_Obot(tc_fun(U_9443,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9443),U_9444))
    | ~ class_Orderings_Olinorder(U_9443) ),
    inference(clausify,[status(thm)],[f_2286_2]) ).

fof(f_2287_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).

fof(f_2287_2,plain,
    ! [U_9448,U_9447] :
      ( hBOOL(hAPP(hAPP(c_member(U_9447),c_Big__Operators_Olattice_OInf__fin(U_9447,c_Orderings_Oord__class_Omin(U_9447),U_9448)),U_9448))
      | ? [U_9446,U_9445] : ~ hBOOL(hAPP(hAPP(c_member(U_9447),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9447),U_9446),U_9445)),hAPP(hAPP(c_Set_Oinsert(U_9447),U_9446),hAPP(hAPP(c_Set_Oinsert(U_9447),U_9445),c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))))))
      | U_9448 = c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9447),U_9448))
      | ~ class_Orderings_Olinorder(U_9447) ),
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

fof(f_2287_3,plain,
    ! [U_9448,U_9447] :
      ( hBOOL(hAPP(hAPP(c_member(U_9447),c_Big__Operators_Olattice_OInf__fin(U_9447,c_Orderings_Oord__class_Omin(U_9447),U_9448)),U_9448))
      | ? [U_9445] : ~ hBOOL(hAPP(hAPP(c_member(U_9447),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9447),sK228(U_9448,U_9447)),U_9445)),hAPP(hAPP(c_Set_Oinsert(U_9447),sK228(U_9448,U_9447)),hAPP(hAPP(c_Set_Oinsert(U_9447),U_9445),c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))))))
      | U_9448 = c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9447),U_9448))
      | ~ class_Orderings_Olinorder(U_9447) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_9446,sK228(U_9448,U_9447))],[f_2287_2]) ).

fof(f_2287_4,plain,
    ! [U_9448,U_9447] :
      ( hBOOL(hAPP(hAPP(c_member(U_9447),c_Big__Operators_Olattice_OInf__fin(U_9447,c_Orderings_Oord__class_Omin(U_9447),U_9448)),U_9448))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9447),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9447),sK228(U_9448,U_9447)),sK229(U_9448,U_9447))),hAPP(hAPP(c_Set_Oinsert(U_9447),sK228(U_9448,U_9447)),hAPP(hAPP(c_Set_Oinsert(U_9447),sK229(U_9448,U_9447)),c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))))))
      | U_9448 = c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9447),U_9448))
      | ~ class_Orderings_Olinorder(U_9447) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_9445,sK229(U_9448,U_9447))],[f_2287_3]) ).

cnf(f_2287_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9447),c_Big__Operators_Olattice_OInf__fin(U_9447,c_Orderings_Oord__class_Omin(U_9447),U_9448)),U_9448))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9447),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9447),sK228(U_9448,U_9447)),sK229(U_9448,U_9447))),hAPP(hAPP(c_Set_Oinsert(U_9447),sK228(U_9448,U_9447)),hAPP(hAPP(c_Set_Oinsert(U_9447),sK229(U_9448,U_9447)),c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))))))
    | U_9448 = c_Orderings_Obot__class_Obot(tc_fun(U_9447,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9447),U_9448))
    | ~ class_Orderings_Olinorder(U_9447) ),
    inference(clausify,[status(thm)],[f_2287_4]) ).

fof(f_2288_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).

fof(f_2288_2,plain,
    ! [U_9452,U_9451] :
      ( hBOOL(hAPP(hAPP(c_member(U_9451),c_Big__Operators_Olinorder__class_OMax(U_9451,U_9452)),U_9452))
      | ? [U_9450,U_9449] : ~ hBOOL(hAPP(hAPP(c_member(U_9451),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9451),U_9450),U_9449)),hAPP(hAPP(c_Set_Oinsert(U_9451),U_9450),hAPP(hAPP(c_Set_Oinsert(U_9451),U_9449),c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))))))
      | U_9452 = c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9451),U_9452))
      | ~ class_Orderings_Olinorder(U_9451) ),
    inference(variable_rename,[status(thm)],[f_2288_1]) ).

fof(f_2288_3,plain,
    ! [U_9452,U_9451] :
      ( hBOOL(hAPP(hAPP(c_member(U_9451),c_Big__Operators_Olinorder__class_OMax(U_9451,U_9452)),U_9452))
      | ? [U_9449] : ~ hBOOL(hAPP(hAPP(c_member(U_9451),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9451),sK230(U_9452,U_9451)),U_9449)),hAPP(hAPP(c_Set_Oinsert(U_9451),sK230(U_9452,U_9451)),hAPP(hAPP(c_Set_Oinsert(U_9451),U_9449),c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))))))
      | U_9452 = c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9451),U_9452))
      | ~ class_Orderings_Olinorder(U_9451) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_9450,sK230(U_9452,U_9451))],[f_2288_2]) ).

fof(f_2288_4,plain,
    ! [U_9452,U_9451] :
      ( hBOOL(hAPP(hAPP(c_member(U_9451),c_Big__Operators_Olinorder__class_OMax(U_9451,U_9452)),U_9452))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9451),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9451),sK230(U_9452,U_9451)),sK231(U_9452,U_9451))),hAPP(hAPP(c_Set_Oinsert(U_9451),sK230(U_9452,U_9451)),hAPP(hAPP(c_Set_Oinsert(U_9451),sK231(U_9452,U_9451)),c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))))))
      | U_9452 = c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9451),U_9452))
      | ~ class_Orderings_Olinorder(U_9451) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_9449,sK231(U_9452,U_9451))],[f_2288_3]) ).

cnf(f_2288_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9451),c_Big__Operators_Olinorder__class_OMax(U_9451,U_9452)),U_9452))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9451),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9451),sK230(U_9452,U_9451)),sK231(U_9452,U_9451))),hAPP(hAPP(c_Set_Oinsert(U_9451),sK230(U_9452,U_9451)),hAPP(hAPP(c_Set_Oinsert(U_9451),sK231(U_9452,U_9451)),c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))))))
    | U_9452 = c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9451),U_9452))
    | ~ class_Orderings_Olinorder(U_9451) ),
    inference(clausify,[status(thm)],[f_2288_4]) ).

fof(f_2289_1,plain,
    ! [V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).

fof(f_2289_2,plain,
    ! [U_9456,U_9455] :
      ( hBOOL(hAPP(hAPP(c_member(U_9455),c_Big__Operators_Olinorder__class_OMin(U_9455,U_9456)),U_9456))
      | ? [U_9454,U_9453] : ~ hBOOL(hAPP(hAPP(c_member(U_9455),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9455),U_9454),U_9453)),hAPP(hAPP(c_Set_Oinsert(U_9455),U_9454),hAPP(hAPP(c_Set_Oinsert(U_9455),U_9453),c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))))))
      | U_9456 = c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9455),U_9456))
      | ~ class_Orderings_Olinorder(U_9455) ),
    inference(variable_rename,[status(thm)],[f_2289_1]) ).

fof(f_2289_3,plain,
    ! [U_9456,U_9455] :
      ( hBOOL(hAPP(hAPP(c_member(U_9455),c_Big__Operators_Olinorder__class_OMin(U_9455,U_9456)),U_9456))
      | ? [U_9453] : ~ hBOOL(hAPP(hAPP(c_member(U_9455),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9455),sK232(U_9456,U_9455)),U_9453)),hAPP(hAPP(c_Set_Oinsert(U_9455),sK232(U_9456,U_9455)),hAPP(hAPP(c_Set_Oinsert(U_9455),U_9453),c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))))))
      | U_9456 = c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9455),U_9456))
      | ~ class_Orderings_Olinorder(U_9455) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_9454,sK232(U_9456,U_9455))],[f_2289_2]) ).

fof(f_2289_4,plain,
    ! [U_9456,U_9455] :
      ( hBOOL(hAPP(hAPP(c_member(U_9455),c_Big__Operators_Olinorder__class_OMin(U_9455,U_9456)),U_9456))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9455),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9455),sK232(U_9456,U_9455)),sK233(U_9456,U_9455))),hAPP(hAPP(c_Set_Oinsert(U_9455),sK232(U_9456,U_9455)),hAPP(hAPP(c_Set_Oinsert(U_9455),sK233(U_9456,U_9455)),c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))))))
      | U_9456 = c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9455),U_9456))
      | ~ class_Orderings_Olinorder(U_9455) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_9453,sK233(U_9456,U_9455))],[f_2289_3]) ).

cnf(f_2289_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9455),c_Big__Operators_Olinorder__class_OMin(U_9455,U_9456)),U_9456))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9455),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9455),sK232(U_9456,U_9455)),sK233(U_9456,U_9455))),hAPP(hAPP(c_Set_Oinsert(U_9455),sK232(U_9456,U_9455)),hAPP(hAPP(c_Set_Oinsert(U_9455),sK233(U_9456,U_9455)),c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))))))
    | U_9456 = c_Orderings_Obot__class_Obot(tc_fun(U_9455,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9455),U_9456))
    | ~ class_Orderings_Olinorder(U_9455) ),
    inference(clausify,[status(thm)],[f_2289_4]) ).

fof(f_2290_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).

fof(f_2290_2,plain,
    ! [U_9462,U_9461,U_9460,U_9459,U_9458] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9460)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9461))
      | ? [U_9457] :
          ( hAPP(U_9462,U_9457) != c_Groups_Oone__class_Oone(U_9458)
          & hBOOL(hAPP(hAPP(c_member(U_9459),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9460))
      | ~ class_Groups_Ocomm__monoid__mult(U_9458) ),
    inference(variable_rename,[status(thm)],[f_2290_1]) ).

fof(f_2290_3,plain,
    ! [U_9462,U_9461,U_9460,U_9459,U_9458] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9460)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9461))
      | ( hAPP(U_9462,sK234(U_9462,U_9461,U_9460,U_9459,U_9458)) != c_Groups_Oone__class_Oone(U_9458)
        & hBOOL(hAPP(hAPP(c_member(U_9459),sK234(U_9462,U_9461,U_9460,U_9459,U_9458)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9460))
      | ~ class_Groups_Ocomm__monoid__mult(U_9458) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_9457,sK234(U_9462,U_9461,U_9460,U_9459,U_9458))],[f_2290_2]) ).

cnf(f_2290_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9459),sK234(U_9462,U_9461,U_9460,U_9459,U_9458)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9460)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9460))
    | ~ class_Groups_Ocomm__monoid__mult(U_9458) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

cnf(f_2290_5,plain,
    ( hAPP(U_9462,sK234(U_9462,U_9461,U_9460,U_9459,U_9458)) != c_Groups_Oone__class_Oone(U_9458)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9459,tc_HOL_Obool)),U_9460),U_9461)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9460)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9459,U_9458),U_9462),U_9461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9459),U_9460))
    | ~ class_Groups_Ocomm__monoid__mult(U_9458) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

fof(f_2291_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).

fof(f_2291_2,plain,
    ! [U_9468,U_9467,U_9466,U_9465,U_9464] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9467))
      | ? [U_9463] :
          ( hAPP(U_9468,U_9463) != c_Groups_Oone__class_Oone(U_9464)
          & hBOOL(hAPP(hAPP(c_member(U_9465),U_9463),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9467))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9466))
      | ~ class_Groups_Ocomm__monoid__mult(U_9464) ),
    inference(variable_rename,[status(thm)],[f_2291_1]) ).

fof(f_2291_3,plain,
    ! [U_9468,U_9467,U_9466,U_9465,U_9464] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9467))
      | ( hAPP(U_9468,sK235(U_9468,U_9467,U_9466,U_9465,U_9464)) != c_Groups_Oone__class_Oone(U_9464)
        & hBOOL(hAPP(hAPP(c_member(U_9465),sK235(U_9468,U_9467,U_9466,U_9465,U_9464)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9467))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9466))
      | ~ class_Groups_Ocomm__monoid__mult(U_9464) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_9463,sK235(U_9468,U_9467,U_9466,U_9465,U_9464))],[f_2291_2]) ).

cnf(f_2291_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9465),sK235(U_9468,U_9467,U_9466,U_9465,U_9464)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9467))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9467))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9466))
    | ~ class_Groups_Ocomm__monoid__mult(U_9464) ),
    inference(clausify,[status(thm)],[f_2291_3]) ).

cnf(f_2291_5,plain,
    ( hAPP(U_9468,sK235(U_9468,U_9467,U_9466,U_9465,U_9464)) != c_Groups_Oone__class_Oone(U_9464)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9465,tc_HOL_Obool)),U_9466),U_9467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9466)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9465,U_9464),U_9468),U_9467))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9467))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9465),U_9466))
    | ~ class_Groups_Ocomm__monoid__mult(U_9464) ),
    inference(clausify,[status(thm)],[f_2291_3]) ).

fof(f_2292_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2))
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).

fof(f_2292_2,plain,
    ! [U_9474,U_9473,U_9472,U_9471,U_9470,U_9469] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9470,U_9469),hAPP(hAPP(c_COMBC(U_9470,U_9469,U_9469),hAPP(hAPP(c_COMBS(U_9470,U_9469,tc_fun(U_9469,U_9469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9469,tc_fun(U_9469,U_9469)),U_9470),c_If(U_9469)),hAPP(hAPP(c_COMBC(U_9470,U_9470,tc_HOL_Obool),c_fequal),U_9472))),U_9473)),U_9474)),U_9471) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9469),U_9474),hAPP(c_Finite__Set_Ocard(U_9470),U_9471))
          | hBOOL(hAPP(hAPP(c_member(U_9470),U_9472),U_9471)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9470,U_9469),hAPP(hAPP(c_COMBC(U_9470,U_9469,U_9469),hAPP(hAPP(c_COMBS(U_9470,U_9469,tc_fun(U_9469,U_9469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9469,tc_fun(U_9469,U_9469)),U_9470),c_If(U_9469)),hAPP(hAPP(c_COMBC(U_9470,U_9470,tc_HOL_Obool),c_fequal),U_9472))),U_9473)),U_9474)),U_9471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9469),hAPP(U_9473,U_9472)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9469),U_9474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9470),U_9471)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9470),U_9472),U_9471)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9470),U_9471))
      | ~ class_Groups_Ocomm__monoid__mult(U_9469) ),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

cnf(f_2292_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9470,U_9469),hAPP(hAPP(c_COMBC(U_9470,U_9469,U_9469),hAPP(hAPP(c_COMBS(U_9470,U_9469,tc_fun(U_9469,U_9469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9469,tc_fun(U_9469,U_9469)),U_9470),c_If(U_9469)),hAPP(hAPP(c_COMBC(U_9470,U_9470,tc_HOL_Obool),c_fequal),U_9472))),U_9473)),U_9474)),U_9471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9469),hAPP(U_9473,U_9472)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9469),U_9474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9470),U_9471)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9470),U_9472),U_9471))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9470),U_9471))
    | ~ class_Groups_Ocomm__monoid__mult(U_9469) ),
    inference(clausify,[status(thm)],[f_2292_2]) ).

cnf(f_2292_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9470,U_9469),hAPP(hAPP(c_COMBC(U_9470,U_9469,U_9469),hAPP(hAPP(c_COMBS(U_9470,U_9469,tc_fun(U_9469,U_9469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9469,tc_fun(U_9469,U_9469)),U_9470),c_If(U_9469)),hAPP(hAPP(c_COMBC(U_9470,U_9470,tc_HOL_Obool),c_fequal),U_9472))),U_9473)),U_9474)),U_9471) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9469),U_9474),hAPP(c_Finite__Set_Ocard(U_9470),U_9471))
    | hBOOL(hAPP(hAPP(c_member(U_9470),U_9472),U_9471))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9470),U_9471))
    | ~ class_Groups_Ocomm__monoid__mult(U_9469) ),
    inference(clausify,[status(thm)],[f_2292_2]) ).

fof(f_2293_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_2293_2,plain,
    ! [U_9476,U_9475] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_9475),U_9476) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9475),hAPP(c_Int_Onat,U_9476))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9476),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_9475),U_9476) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9475),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9475),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9476))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9476),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_9475) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

cnf(f_2293_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9475),U_9476) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9475),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9475),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9476))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9476),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_9475) ),
    inference(clausify,[status(thm)],[f_2293_2]) ).

cnf(f_2293_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9475),U_9476) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9475),hAPP(c_Int_Onat,U_9476))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9476),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_9475) ),
    inference(clausify,[status(thm)],[f_2293_2]) ).

fof(f_2294_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) )
      | hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).

fof(f_2294_2,plain,
    ! [U_9481,U_9480,U_9479,U_9478,U_9477] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),U_9479),hAPP(hAPP(c_Set_Oinsert(U_9478),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9478,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),U_9479)
          | hBOOL(hAPP(hAPP(c_member(U_9478),U_9481),U_9479)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),U_9479),hAPP(hAPP(c_Set_Oinsert(U_9478),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9478,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9477),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),U_9479)),hAPP(U_9480,U_9481))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9478),U_9481),U_9479)) ) )
      | hAPP(U_9480,U_9481) = c_Groups_Ozero__class_Ozero(U_9477)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9478),U_9479))
      | ~ class_Fields_Ofield(U_9477) ),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

cnf(f_2294_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),U_9479),hAPP(hAPP(c_Set_Oinsert(U_9478),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9478,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9477),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),U_9479)),hAPP(U_9480,U_9481))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9478),U_9481),U_9479))
    | hAPP(U_9480,U_9481) = c_Groups_Ozero__class_Ozero(U_9477)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9478),U_9479))
    | ~ class_Fields_Ofield(U_9477) ),
    inference(clausify,[status(thm)],[f_2294_2]) ).

cnf(f_2294_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),U_9479),hAPP(hAPP(c_Set_Oinsert(U_9478),U_9481),c_Orderings_Obot__class_Obot(tc_fun(U_9478,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9478,U_9477),U_9480),U_9479)
    | hBOOL(hAPP(hAPP(c_member(U_9478),U_9481),U_9479))
    | hAPP(U_9480,U_9481) = c_Groups_Ozero__class_Ozero(U_9477)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9478),U_9479))
    | ~ class_Fields_Ofield(U_9477) ),
    inference(clausify,[status(thm)],[f_2294_2]) ).

fof(f_2295_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_2295_2,plain,
    ! [U_9483,U_9482] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9482),U_9483))
      | ~ c_Nat__Transfer_Ois__nat(U_9482) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

cnf(f_2295_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9482),U_9483))
    | ~ c_Nat__Transfer_Ois__nat(U_9482) ),
    inference(clausify,[status(thm)],[f_2295_2]) ).

fof(f_2296_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_2296_2,plain,
    ! [U_9484] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9484)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9484),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

cnf(f_2296_3,plain,
    hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9484)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9484),
    inference(clausify,[status(thm)],[f_2296_2]) ).

fof(f_2297_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_2297_2,plain,
    ! [U_9486,U_9485] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9485),U_9486),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_9486
      | ~ class_Rings_Ocomm__semiring__1(U_9485) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

cnf(f_2297_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9485),U_9486),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_9486
    | ~ class_Rings_Ocomm__semiring__1(U_9485) ),
    inference(clausify,[status(thm)],[f_2297_2]) ).

fof(f_2298_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_2298_2,plain,
    ! [U_9488,U_9487] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9487),U_9488),c_Groups_Oone__class_Oone(U_9487)) = U_9488
      | ~ class_Rings_Odivision__ring(U_9487) ),
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

cnf(f_2298_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9487),U_9488),c_Groups_Oone__class_Oone(U_9487)) = U_9488
    | ~ class_Rings_Odivision__ring(U_9487) ),
    inference(clausify,[status(thm)],[f_2298_2]) ).

fof(f_2299_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_2299_2,plain,
    ! [U_9490,U_9489] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9489)),U_9490) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9489),U_9490)),
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

cnf(f_2299_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9489)),U_9490) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9489),U_9490)),
    inference(clausify,[status(thm)],[f_2299_2]) ).

fof(f_2300_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_2300_2,plain,
    ! [U_9492,U_9491] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9491),U_9492)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9491)),U_9492),
    inference(variable_rename,[status(thm)],[f_2300_1]) ).

cnf(f_2300_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9491),U_9492)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9491)),U_9492),
    inference(clausify,[status(thm)],[f_2300_2]) ).

fof(f_2301_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_2301_2,plain,
    ! [U_9494,U_9493] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9493)),U_9494) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9493),U_9494)),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

cnf(f_2301_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9493)),U_9494) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9493),U_9494)),
    inference(clausify,[status(thm)],[f_2301_2]) ).

fof(f_2302_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_2302_2,plain,
    ! [U_9497,U_9496,U_9495] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9495),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9496),U_9497)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9495),hAPP(c_Int_Oring__1__class_Oof__int(U_9495),U_9496)),U_9497)
      | ~ class_Rings_Oring__1(U_9495) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

cnf(f_2302_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9495),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9496),U_9497)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9495),hAPP(c_Int_Oring__1__class_Oof__int(U_9495),U_9496)),U_9497)
    | ~ class_Rings_Oring__1(U_9495) ),
    inference(clausify,[status(thm)],[f_2302_2]) ).

fof(f_2303_1,plain,
    ! [V_z_2,V_w_2,T_a] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
          | V_w_2 != V_z_2 )
        & ( V_w_2 = V_z_2
          | hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) != hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).

fof(f_2303_2,plain,
    ! [U_9500,U_9499,U_9498] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9499) = hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9500)
          | U_9499 != U_9500 )
        & ( U_9499 = U_9500
          | hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9499) != hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9500) ) )
      | ~ class_Int_Oring__char__0(U_9498) ),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

cnf(f_2303_3,plain,
    ( U_9499 = U_9500
    | hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9499) != hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9500)
    | ~ class_Int_Oring__char__0(U_9498) ),
    inference(clausify,[status(thm)],[f_2303_2]) ).

cnf(f_2303_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9499) = hAPP(c_Int_Oring__1__class_Oof__int(U_9498),U_9500)
    | U_9499 != U_9500
    | ~ class_Int_Oring__char__0(U_9498) ),
    inference(clausify,[status(thm)],[f_2303_2]) ).

fof(f_2304_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_2304_2,plain,
    ! [U_9504,U_9503,U_9502,U_9501] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9501),U_9502),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9501),U_9503),U_9504)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9501),U_9502),U_9503)),U_9504)
      | ~ class_Rings_Odivision__ring(U_9501) ),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

cnf(f_2304_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9501),U_9502),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9501),U_9503),U_9504)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9501),U_9502),U_9503)),U_9504)
    | ~ class_Rings_Odivision__ring(U_9501) ),
    inference(clausify,[status(thm)],[f_2304_2]) ).

fof(f_2305_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_2305_2,plain,
    ! [U_9508,U_9507,U_9506,U_9505] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9505),U_9506),U_9507)),U_9508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),U_9506),U_9508)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),U_9507),U_9508))
      | ~ class_Rings_Odivision__ring(U_9505) ),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

cnf(f_2305_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9505),U_9506),U_9507)),U_9508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),U_9506),U_9508)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9505),U_9507),U_9508))
    | ~ class_Rings_Odivision__ring(U_9505) ),
    inference(clausify,[status(thm)],[f_2305_2]) ).

fof(f_2306_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_2306_2,plain,
    ! [U_9510,U_9509] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9509),c_Groups_Ozero__class_Ozero(U_9509)),U_9510) = c_Groups_Ozero__class_Ozero(U_9509)
      | ~ class_Rings_Odivision__ring(U_9509) ),
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

cnf(f_2306_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9509),c_Groups_Ozero__class_Ozero(U_9509)),U_9510) = c_Groups_Ozero__class_Ozero(U_9509)
    | ~ class_Rings_Odivision__ring(U_9509) ),
    inference(clausify,[status(thm)],[f_2306_2]) ).

fof(f_2307_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_2307_2,plain,
    ! [U_9512,U_9511] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9511),U_9512),c_Groups_Ozero__class_Ozero(U_9511)) = c_Groups_Ozero__class_Ozero(U_9511)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_9511) ),
    inference(variable_rename,[status(thm)],[f_2307_1]) ).

cnf(f_2307_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9511),U_9512),c_Groups_Ozero__class_Ozero(U_9511)) = c_Groups_Ozero__class_Ozero(U_9511)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_9511) ),
    inference(clausify,[status(thm)],[f_2307_2]) ).

fof(f_2308_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_2308_2,plain,
    ! [U_9516,U_9515,U_9514,U_9513] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9513),U_9514),U_9515)),U_9516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9513),hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),U_9514),U_9516)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),U_9515),U_9516))
      | ~ class_Rings_Ocomm__semiring__1(U_9513) ),
    inference(variable_rename,[status(thm)],[f_2308_1]) ).

cnf(f_2308_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9513),U_9514),U_9515)),U_9516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9513),hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),U_9514),U_9516)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9513),U_9515),U_9516))
    | ~ class_Rings_Ocomm__semiring__1(U_9513) ),
    inference(clausify,[status(thm)],[f_2308_2]) ).

fof(f_2309_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_2309_2,plain,
    ! [U_9520,U_9519,U_9518,U_9517] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9517),U_9518),U_9519)),U_9520) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),U_9518),U_9520)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),U_9519),U_9520))
      | ~ class_Rings_Odivision__ring(U_9517) ),
    inference(variable_rename,[status(thm)],[f_2309_1]) ).

cnf(f_2309_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9517),U_9518),U_9519)),U_9520) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),U_9518),U_9520)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9517),U_9519),U_9520))
    | ~ class_Rings_Odivision__ring(U_9517) ),
    inference(clausify,[status(thm)],[f_2309_2]) ).

fof(f_2310_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_2310_2,plain,
    ! [U_9524,U_9523,U_9522,U_9521] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),U_9522),U_9523)),U_9524) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),U_9522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9523),U_9524))
      | ~ class_Rings_Ocomm__semiring__1(U_9521) ),
    inference(variable_rename,[status(thm)],[f_2310_1]) ).

cnf(f_2310_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),U_9522),U_9523)),U_9524) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9521),U_9522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9523),U_9524))
    | ~ class_Rings_Ocomm__semiring__1(U_9521) ),
    inference(clausify,[status(thm)],[f_2310_2]) ).

fof(f_2311_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_2311_2,plain,
    ! [U_9527,U_9526,U_9525] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9525),U_9526)),U_9527) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9526),U_9527)),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

cnf(f_2311_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9525),U_9526)),U_9527) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9526),U_9527)),
    inference(clausify,[status(thm)],[f_2311_2]) ).

fof(f_2312_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_2312_2,plain,
    ! [U_9530,U_9529,U_9528] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9528),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9528),U_9529),U_9530)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9528),hAPP(c_Groups_Ouminus__class_Ouminus(U_9528),U_9529)),U_9530)
      | ~ class_Rings_Odivision__ring(U_9528) ),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

cnf(f_2312_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9528),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9528),U_9529),U_9530)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9528),hAPP(c_Groups_Ouminus__class_Ouminus(U_9528),U_9529)),U_9530)
    | ~ class_Rings_Odivision__ring(U_9528) ),
    inference(clausify,[status(thm)],[f_2312_2]) ).

fof(f_2313_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_2313_2,plain,
    ! [U_9532,U_9531] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9531),U_9532)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_9531)),U_9532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9531)) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

cnf(f_2313_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9531),U_9532)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_9531)),U_9532)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9531)) ),
    inference(clausify,[status(thm)],[f_2313_2]) ).

fof(f_2314_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_2314_2,plain,
    ! [U_9534,U_9533] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_9533)),U_9534) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9533),U_9534))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9533)) ),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

cnf(f_2314_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_9533)),U_9534) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9533),U_9534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9533)) ),
    inference(clausify,[status(thm)],[f_2314_2]) ).

fof(f_2315_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).

fof(f_2315_2,plain,
    ! [U_9539,U_9538,U_9537,U_9536,U_9535] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9535),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9536,U_9535),U_9537),U_9538)),U_9539) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9536,U_9535),hAPP(hAPP(c_COMBC(U_9536,U_9535,U_9535),hAPP(hAPP(c_COMBB(U_9535,tc_fun(U_9535,U_9535),U_9536),c_Rings_Oinverse__class_Odivide(U_9535)),U_9537)),U_9539)),U_9538)
      | ~ class_Fields_Ofield(U_9535) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

cnf(f_2315_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9535),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9536,U_9535),U_9537),U_9538)),U_9539) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9536,U_9535),hAPP(hAPP(c_COMBC(U_9536,U_9535,U_9535),hAPP(hAPP(c_COMBB(U_9535,tc_fun(U_9535,U_9535),U_9536),c_Rings_Oinverse__class_Odivide(U_9535)),U_9537)),U_9539)),U_9538)
    | ~ class_Fields_Ofield(U_9535) ),
    inference(clausify,[status(thm)],[f_2315_2]) ).

fof(f_2316_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) != V_b_2 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).

fof(f_2316_2,plain,
    ! [U_9543,U_9542,U_9541,U_9540] :
      ( ( ( U_9542 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9540),U_9543),U_9541)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9540),U_9542),U_9541) != U_9543 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9540),U_9542),U_9541) = U_9543
          | U_9542 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9540),U_9543),U_9541) ) )
      | U_9541 = c_Groups_Ozero__class_Ozero(U_9540)
      | ~ class_Rings_Odivision__ring(U_9540) ),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

cnf(f_2316_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9540),U_9542),U_9541) = U_9543
    | U_9542 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9540),U_9543),U_9541)
    | U_9541 = c_Groups_Ozero__class_Ozero(U_9540)
    | ~ class_Rings_Odivision__ring(U_9540) ),
    inference(clausify,[status(thm)],[f_2316_2]) ).

cnf(f_2316_4,plain,
    ( U_9542 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9540),U_9543),U_9541)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9540),U_9542),U_9541) != U_9543
    | U_9541 = c_Groups_Ozero__class_Ozero(U_9540)
    | ~ class_Rings_Odivision__ring(U_9540) ),
    inference(clausify,[status(thm)],[f_2316_2]) ).

fof(f_2317_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) != V_a_2 ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).

fof(f_2317_2,plain,
    ! [U_9547,U_9546,U_9545,U_9544] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9544),U_9546),U_9545) = U_9547
          | U_9546 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9544),U_9547),U_9545) )
        & ( U_9546 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9544),U_9547),U_9545)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9544),U_9546),U_9545) != U_9547 ) )
      | U_9545 = c_Groups_Ozero__class_Ozero(U_9544)
      | ~ class_Rings_Odivision__ring(U_9544) ),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

cnf(f_2317_3,plain,
    ( U_9546 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9544),U_9547),U_9545)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9544),U_9546),U_9545) != U_9547
    | U_9545 = c_Groups_Ozero__class_Ozero(U_9544)
    | ~ class_Rings_Odivision__ring(U_9544) ),
    inference(clausify,[status(thm)],[f_2317_2]) ).

cnf(f_2317_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9544),U_9546),U_9545) = U_9547
    | U_9546 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9544),U_9547),U_9545)
    | U_9545 = c_Groups_Ozero__class_Ozero(U_9544)
    | ~ class_Rings_Odivision__ring(U_9544) ),
    inference(clausify,[status(thm)],[f_2317_2]) ).

fof(f_2318_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_2318_2,plain,
    ! [U_9551,U_9550,U_9549,U_9548] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9548),U_9550),U_9549) = U_9551
      | U_9550 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9548),U_9551),U_9549)
      | U_9549 = c_Groups_Ozero__class_Ozero(U_9548)
      | ~ class_Rings_Odivision__ring(U_9548) ),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

cnf(f_2318_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9548),U_9550),U_9549) = U_9551
    | U_9550 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9548),U_9551),U_9549)
    | U_9549 = c_Groups_Ozero__class_Ozero(U_9548)
    | ~ class_Rings_Odivision__ring(U_9548) ),
    inference(clausify,[status(thm)],[f_2318_2]) ).

fof(f_2319_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_2319_2,plain,
    ! [U_9555,U_9554,U_9553,U_9552] :
      ( U_9554 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9552),U_9555),U_9553)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9552),U_9554),U_9553) != U_9555
      | U_9553 = c_Groups_Ozero__class_Ozero(U_9552)
      | ~ class_Rings_Odivision__ring(U_9552) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

cnf(f_2319_3,plain,
    ( U_9554 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9552),U_9555),U_9553)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9552),U_9554),U_9553) != U_9555
    | U_9553 = c_Groups_Ozero__class_Ozero(U_9552)
    | ~ class_Rings_Odivision__ring(U_9552) ),
    inference(clausify,[status(thm)],[f_2319_2]) ).

fof(f_2320_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_2320_2,plain,
    ! [U_9557,U_9556] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9556),U_9557),U_9557) = c_Groups_Oone__class_Oone(U_9556)
          | U_9557 = c_Groups_Ozero__class_Ozero(U_9556) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9556),U_9557),U_9557) = c_Groups_Ozero__class_Ozero(U_9556)
          | U_9557 != c_Groups_Ozero__class_Ozero(U_9556) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_9556) ),
    inference(variable_rename,[status(thm)],[f_2320_1]) ).

cnf(f_2320_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9556),U_9557),U_9557) = c_Groups_Ozero__class_Ozero(U_9556)
    | U_9557 != c_Groups_Ozero__class_Ozero(U_9556)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_9556) ),
    inference(clausify,[status(thm)],[f_2320_2]) ).

cnf(f_2320_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9556),U_9557),U_9557) = c_Groups_Oone__class_Oone(U_9556)
    | U_9557 = c_Groups_Ozero__class_Ozero(U_9556)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_9556) ),
    inference(clausify,[status(thm)],[f_2320_2]) ).

fof(f_2321_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_2321_2,plain,
    ! [U_9559,U_9558] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9558),U_9559),U_9559) = c_Groups_Oone__class_Oone(U_9558)
      | U_9559 = c_Groups_Ozero__class_Ozero(U_9558)
      | ~ class_Rings_Odivision__ring(U_9558) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

cnf(f_2321_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9558),U_9559),U_9559) = c_Groups_Oone__class_Oone(U_9558)
    | U_9559 = c_Groups_Ozero__class_Ozero(U_9558)
    | ~ class_Rings_Odivision__ring(U_9558) ),
    inference(clausify,[status(thm)],[f_2321_2]) ).

fof(f_2322_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_a) ) )
      | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).

fof(f_2322_2,plain,
    ! [U_9562,U_9561,U_9560] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9560),U_9562),U_9561) = c_Groups_Oone__class_Oone(U_9560)
          | U_9562 != U_9561 )
        & ( U_9562 = U_9561
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9560),U_9562),U_9561) != c_Groups_Oone__class_Oone(U_9560) ) )
      | U_9561 = c_Groups_Ozero__class_Ozero(U_9560)
      | ~ class_Rings_Odivision__ring(U_9560) ),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

cnf(f_2322_3,plain,
    ( U_9562 = U_9561
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9560),U_9562),U_9561) != c_Groups_Oone__class_Oone(U_9560)
    | U_9561 = c_Groups_Ozero__class_Ozero(U_9560)
    | ~ class_Rings_Odivision__ring(U_9560) ),
    inference(clausify,[status(thm)],[f_2322_2]) ).

cnf(f_2322_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9560),U_9562),U_9561) = c_Groups_Oone__class_Oone(U_9560)
    | U_9562 != U_9561
    | U_9561 = c_Groups_Ozero__class_Ozero(U_9560)
    | ~ class_Rings_Odivision__ring(U_9560) ),
    inference(clausify,[status(thm)],[f_2322_2]) ).

fof(f_2323_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_2323_2,plain,
    ! [U_9565,U_9564,U_9563] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9563),hAPP(c_Groups_Ouminus__class_Ouminus(U_9563),U_9565)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9563),U_9564)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9563),U_9565),U_9564)
      | U_9564 = c_Groups_Ozero__class_Ozero(U_9563)
      | ~ class_Rings_Odivision__ring(U_9563) ),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

cnf(f_2323_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9563),hAPP(c_Groups_Ouminus__class_Ouminus(U_9563),U_9565)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9563),U_9564)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9563),U_9565),U_9564)
    | U_9564 = c_Groups_Ozero__class_Ozero(U_9563)
    | ~ class_Rings_Odivision__ring(U_9563) ),
    inference(clausify,[status(thm)],[f_2323_2]) ).

fof(f_2324_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_2324_2,plain,
    ! [U_9568,U_9567,U_9566] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9566),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9566),U_9568),U_9567)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9566),U_9568),hAPP(c_Groups_Ouminus__class_Ouminus(U_9566),U_9567))
      | U_9567 = c_Groups_Ozero__class_Ozero(U_9566)
      | ~ class_Rings_Odivision__ring(U_9566) ),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

cnf(f_2324_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9566),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9566),U_9568),U_9567)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9566),U_9568),hAPP(c_Groups_Ouminus__class_Ouminus(U_9566),U_9567))
    | U_9567 = c_Groups_Ozero__class_Ozero(U_9566)
    | ~ class_Rings_Odivision__ring(U_9566) ),
    inference(clausify,[status(thm)],[f_2324_2]) ).

fof(f_2325_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_2325_2,plain,
    ! [U_9571,U_9570,U_9569] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9569),U_9570),hAPP(c_Nat_OSuc,U_9571)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9569),U_9570),hAPP(hAPP(c_Power_Opower__class_Opower(U_9569),U_9570),U_9571))
      | ~ class_Rings_Ocomm__semiring__1(U_9569) ),
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

cnf(f_2325_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9569),U_9570),hAPP(c_Nat_OSuc,U_9571)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9569),U_9570),hAPP(hAPP(c_Power_Opower__class_Opower(U_9569),U_9570),U_9571))
    | ~ class_Rings_Ocomm__semiring__1(U_9569) ),
    inference(clausify,[status(thm)],[f_2325_2]) ).

fof(f_2326_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_2326_2,plain,
    ! [U_9574,U_9573,U_9572] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9572),U_9573),hAPP(hAPP(c_Power_Opower__class_Opower(U_9572),U_9573),U_9574)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9572),U_9573),hAPP(c_Nat_OSuc,U_9574))
      | ~ class_Rings_Ocomm__semiring__1(U_9572) ),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

cnf(f_2326_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9572),U_9573),hAPP(hAPP(c_Power_Opower__class_Opower(U_9572),U_9573),U_9574)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9572),U_9573),hAPP(c_Nat_OSuc,U_9574))
    | ~ class_Rings_Ocomm__semiring__1(U_9572) ),
    inference(clausify,[status(thm)],[f_2326_2]) ).

fof(f_2327_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_2327_2,plain,
    ! [U_9577,U_9576,U_9575] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9575),hAPP(hAPP(c_Power_Opower__class_Opower(U_9575),U_9576),U_9577)),U_9576) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9575),U_9576),hAPP(c_Nat_OSuc,U_9577))
      | ~ class_Rings_Ocomm__semiring__1(U_9575) ),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

cnf(f_2327_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9575),hAPP(hAPP(c_Power_Opower__class_Opower(U_9575),U_9576),U_9577)),U_9576) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9575),U_9576),hAPP(c_Nat_OSuc,U_9577))
    | ~ class_Rings_Ocomm__semiring__1(U_9575) ),
    inference(clausify,[status(thm)],[f_2327_2]) ).

fof(f_2328_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_2328_2,plain,
    ! [U_9579,U_9578] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9578),U_9579),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_9578)
      | ~ class_Rings_Ocomm__semiring__1(U_9578) ),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

cnf(f_2328_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9578),U_9579),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_9578)
    | ~ class_Rings_Ocomm__semiring__1(U_9578) ),
    inference(clausify,[status(thm)],[f_2328_2]) ).

fof(f_2329_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_2329_2,plain,
    ! [U_9583,U_9582,U_9581,U_9580] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9580),hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),U_9582)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),U_9583)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9582),U_9583))
      | ~ class_Rings_Ocomm__semiring__1(U_9580) ),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

cnf(f_2329_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9580),hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),U_9582)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),U_9583)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9580),U_9581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9582),U_9583))
    | ~ class_Rings_Ocomm__semiring__1(U_9580) ),
    inference(clausify,[status(thm)],[f_2329_2]) ).

fof(f_2330_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_2330_2,plain,
    ! [U_9585,U_9584] :
      ( 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_9584),U_9585)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9584)) ),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

cnf(f_2330_3,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_9584),U_9585)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9584)) ),
    inference(clausify,[status(thm)],[f_2330_2]) ).

fof(f_2331_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_2331_2,plain,
    ! [U_9588,U_9587,U_9586] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9587),U_9588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),U_9587)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),U_9588)),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

cnf(f_2331_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9587),U_9588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),U_9587)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_9586),U_9588)),
    inference(clausify,[status(thm)],[f_2331_2]) ).

fof(f_2332_1,plain,
    ! [V_n_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).

fof(f_2332_2,plain,
    ! [U_9591,U_9590,U_9589] :
      ( hBOOL(hAPP(hAPP(c_member(U_9589),hAPP(hAPP(c_Power_Opower__class_Opower(U_9589),U_9590),U_9591)),c_Int_Oring__1__class_OInts(U_9589)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9589),U_9590),c_Int_Oring__1__class_OInts(U_9589)))
      | ~ class_Rings_Oring__1(U_9589) ),
    inference(variable_rename,[status(thm)],[f_2332_1]) ).

cnf(f_2332_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9589),hAPP(hAPP(c_Power_Opower__class_Opower(U_9589),U_9590),U_9591)),c_Int_Oring__1__class_OInts(U_9589)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9589),U_9590),c_Int_Oring__1__class_OInts(U_9589)))
    | ~ class_Rings_Oring__1(U_9589) ),
    inference(clausify,[status(thm)],[f_2332_2]) ).

fof(f_2333_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_2333_2,plain,
    ! [U_9592] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9592),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_9592)
      | ~ class_Rings_Oring__1(U_9592) ),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

cnf(f_2333_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9592),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_9592)
    | ~ class_Rings_Oring__1(U_9592) ),
    inference(clausify,[status(thm)],[f_2333_2]) ).

fof(f_2334_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a) != hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).

fof(f_2334_2,plain,
    ! [U_9594,U_9593] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_9593) = hAPP(c_Int_Oring__1__class_Oof__int(U_9593),U_9594)
          | U_9594 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_9594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_9593) != hAPP(c_Int_Oring__1__class_Oof__int(U_9593),U_9594) ) )
      | ~ class_Int_Oring__char__0(U_9593) ),
    inference(variable_rename,[status(thm)],[f_2334_1]) ).

cnf(f_2334_3,plain,
    ( U_9594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_9593) != hAPP(c_Int_Oring__1__class_Oof__int(U_9593),U_9594)
    | ~ class_Int_Oring__char__0(U_9593) ),
    inference(clausify,[status(thm)],[f_2334_2]) ).

cnf(f_2334_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_9593) = hAPP(c_Int_Oring__1__class_Oof__int(U_9593),U_9594)
    | U_9594 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_9593) ),
    inference(clausify,[status(thm)],[f_2334_2]) ).

fof(f_2335_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
          | 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_a),V_z_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).

fof(f_2335_2,plain,
    ! [U_9596,U_9595] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_9595),U_9596) = c_Groups_Ozero__class_Ozero(U_9595)
          | U_9596 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_9596 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_9595),U_9596) != c_Groups_Ozero__class_Ozero(U_9595) ) )
      | ~ class_Int_Oring__char__0(U_9595) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

cnf(f_2335_3,plain,
    ( U_9596 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_9595),U_9596) != c_Groups_Ozero__class_Ozero(U_9595)
    | ~ class_Int_Oring__char__0(U_9595) ),
    inference(clausify,[status(thm)],[f_2335_2]) ).

cnf(f_2335_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9595),U_9596) = c_Groups_Ozero__class_Ozero(U_9595)
    | U_9596 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_9595) ),
    inference(clausify,[status(thm)],[f_2335_2]) ).

fof(f_2336_1,plain,
    ! [V_z_2,V_w_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).

fof(f_2336_2,plain,
    ! [U_9599,U_9598,U_9597] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9597),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9598)),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9599)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9598),U_9599)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9598),U_9599))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9597),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9598)),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9599))) ) )
      | ~ class_Rings_Olinordered__idom(U_9597) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

cnf(f_2336_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9598),U_9599))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9597),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9598)),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9599)))
    | ~ class_Rings_Olinordered__idom(U_9597) ),
    inference(clausify,[status(thm)],[f_2336_2]) ).

cnf(f_2336_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9597),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9598)),hAPP(c_Int_Oring__1__class_Oof__int(U_9597),U_9599)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9598),U_9599))
    | ~ class_Rings_Olinordered__idom(U_9597) ),
    inference(clausify,[status(thm)],[f_2336_2]) ).

fof(f_2337_1,plain,
    ! [V_z_2,V_w_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).

fof(f_2337_2,plain,
    ! [U_9602,U_9601,U_9600] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9600),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9601)),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9602)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9601),U_9602)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9601),U_9602))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9600),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9601)),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9602))) ) )
      | ~ class_Rings_Olinordered__idom(U_9600) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

cnf(f_2337_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9601),U_9602))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9600),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9601)),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9602)))
    | ~ class_Rings_Olinordered__idom(U_9600) ),
    inference(clausify,[status(thm)],[f_2337_2]) ).

cnf(f_2337_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9600),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9601)),hAPP(c_Int_Oring__1__class_Oof__int(U_9600),U_9602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9601),U_9602))
    | ~ class_Rings_Olinordered__idom(U_9600) ),
    inference(clausify,[status(thm)],[f_2337_2]) ).

fof(f_2338_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_2338_2,plain,
    ! [U_9605,U_9604,U_9603] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9604),U_9605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9603),hAPP(c_Int_Oring__1__class_Oof__int(U_9603),U_9604)),hAPP(c_Int_Oring__1__class_Oof__int(U_9603),U_9605))
      | ~ class_Rings_Oring__1(U_9603) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

cnf(f_2338_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9604),U_9605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9603),hAPP(c_Int_Oring__1__class_Oof__int(U_9603),U_9604)),hAPP(c_Int_Oring__1__class_Oof__int(U_9603),U_9605))
    | ~ class_Rings_Oring__1(U_9603) ),
    inference(clausify,[status(thm)],[f_2338_2]) ).

fof(f_2339_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_2339_2,plain,
    ! [U_9608,U_9607,U_9606] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9607),U_9608)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9606),hAPP(c_Int_Oring__1__class_Oof__int(U_9606),U_9607)),hAPP(c_Int_Oring__1__class_Oof__int(U_9606),U_9608))
      | ~ class_Rings_Oring__1(U_9606) ),
    inference(variable_rename,[status(thm)],[f_2339_1]) ).

cnf(f_2339_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9607),U_9608)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9606),hAPP(c_Int_Oring__1__class_Oof__int(U_9606),U_9607)),hAPP(c_Int_Oring__1__class_Oof__int(U_9606),U_9608))
    | ~ class_Rings_Oring__1(U_9606) ),
    inference(clausify,[status(thm)],[f_2339_2]) ).

fof(f_2340_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).

fof(f_2340_2,plain,
    ! [U_9613,U_9612,U_9611,U_9610,U_9609] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),hAPP(hAPP(c_COMBS(U_9610,U_9609,U_9609),hAPP(hAPP(c_COMBB(U_9609,tc_fun(U_9609,U_9609),U_9610),c_Rings_Oinverse__class_Odivide(U_9609)),U_9612)),U_9613)),U_9611) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),U_9612),U_9611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),U_9613),U_9611))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9610),U_9611))
      | ~ class_Fields_Ofield__inverse__zero(U_9609) ),
    inference(variable_rename,[status(thm)],[f_2340_1]) ).

cnf(f_2340_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),hAPP(hAPP(c_COMBS(U_9610,U_9609,U_9609),hAPP(hAPP(c_COMBB(U_9609,tc_fun(U_9609,U_9609),U_9610),c_Rings_Oinverse__class_Odivide(U_9609)),U_9612)),U_9613)),U_9611) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),U_9612),U_9611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9610,U_9609),U_9613),U_9611))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9610),U_9611))
    | ~ class_Fields_Ofield__inverse__zero(U_9609) ),
    inference(clausify,[status(thm)],[f_2340_2]) ).

fof(f_2341_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_2341_2,plain,
    ! [U_9614] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9614),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_9614)
      | ~ class_Rings_Oring__1(U_9614) ),
    inference(variable_rename,[status(thm)],[f_2341_1]) ).

cnf(f_2341_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9614),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_9614)
    | ~ class_Rings_Oring__1(U_9614) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

fof(f_2342_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_2342_2,plain,
    ! [U_9617,U_9616,U_9615] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9616),U_9617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9615),hAPP(c_Int_Oring__1__class_Oof__int(U_9615),U_9616)),hAPP(c_Int_Oring__1__class_Oof__int(U_9615),U_9617))
      | ~ class_Rings_Oring__1(U_9615) ),
    inference(variable_rename,[status(thm)],[f_2342_1]) ).

cnf(f_2342_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9616),U_9617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9615),hAPP(c_Int_Oring__1__class_Oof__int(U_9615),U_9616)),hAPP(c_Int_Oring__1__class_Oof__int(U_9615),U_9617))
    | ~ class_Rings_Oring__1(U_9615) ),
    inference(clausify,[status(thm)],[f_2342_2]) ).

fof(f_2343_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_2343_2,plain,
    ! [U_9619,U_9618] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9618),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9619)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9618),U_9619)
      | ~ class_Rings_Oring__1(U_9618) ),
    inference(variable_rename,[status(thm)],[f_2343_1]) ).

cnf(f_2343_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9618),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9619)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9618),U_9619)
    | ~ class_Rings_Oring__1(U_9618) ),
    inference(clausify,[status(thm)],[f_2343_2]) ).

fof(f_2344_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_2344_2,plain,
    ! [U_9621,U_9620] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9621)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9620),hAPP(c_Int_Oring__1__class_Oof__int(U_9620),U_9621))
      | ~ class_Rings_Oring__1(U_9620) ),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

cnf(f_2344_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9621)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9620),hAPP(c_Int_Oring__1__class_Oof__int(U_9620),U_9621))
    | ~ class_Rings_Oring__1(U_9620) ),
    inference(clausify,[status(thm)],[f_2344_2]) ).

fof(f_2345_1,plain,
    ! [V_z_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).

fof(f_2345_2,plain,
    ! [U_9623,U_9622] :
      ( hBOOL(hAPP(hAPP(c_member(U_9622),hAPP(c_Int_Oring__1__class_Oof__int(U_9622),U_9623)),c_Int_Oring__1__class_OInts(U_9622)))
      | ~ class_Rings_Oring__1(U_9622) ),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

cnf(f_2345_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9622),hAPP(c_Int_Oring__1__class_Oof__int(U_9622),U_9623)),c_Int_Oring__1__class_OInts(U_9622)))
    | ~ class_Rings_Oring__1(U_9622) ),
    inference(clausify,[status(thm)],[f_2345_2]) ).

fof(f_2346_1,plain,
    ! [V_n_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a)))
      | V_x_2 = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).

fof(f_2346_2,plain,
    ! [U_9626,U_9625,U_9624] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9624),hAPP(c_Power_Opower__class_Opower(U_9624),U_9625)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9626)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9624),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9624),hAPP(hAPP(c_Power_Opower__class_Opower(U_9624),U_9625),U_9626)),c_Groups_Oone__class_Oone(U_9624))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9624),U_9625),c_Groups_Oone__class_Oone(U_9624)))
      | U_9625 = c_Groups_Oone__class_Oone(U_9624)
      | ~ class_Fields_Ofield(U_9624) ),
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

cnf(f_2346_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9624),hAPP(c_Power_Opower__class_Opower(U_9624),U_9625)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9626)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9624),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9624),hAPP(hAPP(c_Power_Opower__class_Opower(U_9624),U_9625),U_9626)),c_Groups_Oone__class_Oone(U_9624))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9624),U_9625),c_Groups_Oone__class_Oone(U_9624)))
    | U_9625 = c_Groups_Oone__class_Oone(U_9624)
    | ~ class_Fields_Ofield(U_9624) ),
    inference(clausify,[status(thm)],[f_2346_2]) ).

fof(f_2347_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_2347_2,plain,
    ! [U_9628,U_9627] : 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_9627)),U_9628))),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

cnf(f_2347_3,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_9627)),U_9628))),
    inference(clausify,[status(thm)],[f_2347_2]) ).

fof(f_2348_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).

fof(f_2348_2,plain,
    ! [U_9632,U_9631,U_9630,U_9629] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9629),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9630,tc_Int_Oint),U_9631),U_9632)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9630,U_9629),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9629,U_9630),c_Int_Oring__1__class_Oof__int(U_9629)),U_9631)),U_9632)
      | ~ class_Rings_Oring__1(U_9629) ),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

cnf(f_2348_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9629),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9630,tc_Int_Oint),U_9631),U_9632)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9630,U_9629),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9629,U_9630),c_Int_Oring__1__class_Oof__int(U_9629)),U_9631)),U_9632)
    | ~ class_Rings_Oring__1(U_9629) ),
    inference(clausify,[status(thm)],[f_2348_2]) ).

fof(f_2349_1,plain,
    ! [V_y_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).

fof(f_2349_2,plain,
    ! [U_9636,U_9635,U_9634,U_9633] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9634,U_9633),hAPP(c_COMBK(U_9633,U_9634),U_9636)),U_9635) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9633),U_9636),hAPP(c_Finite__Set_Ocard(U_9634),U_9635))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9634),U_9635))
      | ~ class_Groups_Ocomm__monoid__mult(U_9633) ),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

cnf(f_2349_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9634,U_9633),hAPP(c_COMBK(U_9633,U_9634),U_9636)),U_9635) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9633),U_9636),hAPP(c_Finite__Set_Ocard(U_9634),U_9635))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9634),U_9635))
    | ~ class_Groups_Ocomm__monoid__mult(U_9633) ),
    inference(clausify,[status(thm)],[f_2349_2]) ).

fof(f_2350_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_a)
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).

fof(f_2350_2,plain,
    ! [U_9640,U_9639,U_9638,U_9637] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9637),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9638,tc_Int_Oint),U_9639),U_9640)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9638,U_9637),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9637,U_9638),c_Int_Oring__1__class_Oof__int(U_9637)),U_9639)),U_9640)
      | ~ class_Rings_Oring__1(U_9637)
      | ~ class_Groups_Ocomm__monoid__mult(U_9637) ),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

cnf(f_2350_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9637),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9638,tc_Int_Oint),U_9639),U_9640)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9638,U_9637),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9637,U_9638),c_Int_Oring__1__class_Oof__int(U_9637)),U_9639)),U_9640)
    | ~ class_Rings_Oring__1(U_9637)
    | ~ class_Groups_Ocomm__monoid__mult(U_9637) ),
    inference(clausify,[status(thm)],[f_2350_2]) ).

fof(f_2351_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_2351_2,plain,
    ! [U_9642,U_9641] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9642),U_9641) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9642),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9641),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_9641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9642),U_9641) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_9641 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

fof(f_2351_3,plain,
    ( ! [U_9646,U_9644] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9646),U_9644) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9646),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9644),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_9644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_9645,U_9643] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9645),U_9643) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_9643 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2351_2]) ).

cnf(f_2351_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9645),U_9643) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_9643 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2351_3]) ).

cnf(f_2351_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9646),U_9644) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9646),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9644),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_9644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2351_3]) ).

fof(f_2352_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_2352_2,plain,
    ! [U_9648,U_9647] :
      ( ( 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_9647)),U_9648)))
        | ( U_9648 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_9648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9647 != 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_9647)),U_9648))) ) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

fof(f_2352_3,plain,
    ( ! [U_9652,U_9650] :
        ( 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_9650)),U_9652)))
        | ( U_9652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_9650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_9651,U_9649] :
        ( U_9651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_9649 != 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_9649)),U_9651))) ) ),
    inference(miniscope,[status(thm)],[f_2352_2]) ).

cnf(f_2352_4,plain,
    ( U_9651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_9649 != 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_9649)),U_9651))) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

cnf(f_2352_5,plain,
    ( U_9650 = 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_9650)),U_9652))) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

cnf(f_2352_6,plain,
    ( U_9652 != 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9650)),U_9652))) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

fof(f_2353_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).

fof(f_2353_2,plain,
    ! [U_9654,U_9653] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9653),c_Groups_Ozero__class_Ozero(U_9653)),hAPP(c_Int_Oring__1__class_Oof__int(U_9653),U_9654)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9654)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9654))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9653),c_Groups_Ozero__class_Ozero(U_9653)),hAPP(c_Int_Oring__1__class_Oof__int(U_9653),U_9654))) ) )
      | ~ class_Rings_Olinordered__idom(U_9653) ),
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

cnf(f_2353_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9653),c_Groups_Ozero__class_Ozero(U_9653)),hAPP(c_Int_Oring__1__class_Oof__int(U_9653),U_9654)))
    | ~ class_Rings_Olinordered__idom(U_9653) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

cnf(f_2353_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9653),c_Groups_Ozero__class_Ozero(U_9653)),hAPP(c_Int_Oring__1__class_Oof__int(U_9653),U_9654)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9654))
    | ~ class_Rings_Olinordered__idom(U_9653) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

fof(f_2354_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ 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_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).

fof(f_2354_2,plain,
    ! [U_9656,U_9655] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9655),hAPP(c_Int_Oring__1__class_Oof__int(U_9655),U_9656)),c_Groups_Ozero__class_Ozero(U_9655)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9656),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9656),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9655),hAPP(c_Int_Oring__1__class_Oof__int(U_9655),U_9656)),c_Groups_Ozero__class_Ozero(U_9655))) ) )
      | ~ class_Rings_Olinordered__idom(U_9655) ),
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

cnf(f_2354_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9656),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9655),hAPP(c_Int_Oring__1__class_Oof__int(U_9655),U_9656)),c_Groups_Ozero__class_Ozero(U_9655)))
    | ~ class_Rings_Olinordered__idom(U_9655) ),
    inference(clausify,[status(thm)],[f_2354_2]) ).

cnf(f_2354_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9655),hAPP(c_Int_Oring__1__class_Oof__int(U_9655),U_9656)),c_Groups_Ozero__class_Ozero(U_9655)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9656),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_9655) ),
    inference(clausify,[status(thm)],[f_2354_2]) ).

fof(f_2355_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).

fof(f_2355_2,plain,
    ! [U_9658,U_9657] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9657),c_Groups_Ozero__class_Ozero(U_9657)),hAPP(c_Int_Oring__1__class_Oof__int(U_9657),U_9658)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9658)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9658))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9657),c_Groups_Ozero__class_Ozero(U_9657)),hAPP(c_Int_Oring__1__class_Oof__int(U_9657),U_9658))) ) )
      | ~ class_Rings_Olinordered__idom(U_9657) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

cnf(f_2355_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9657),c_Groups_Ozero__class_Ozero(U_9657)),hAPP(c_Int_Oring__1__class_Oof__int(U_9657),U_9658)))
    | ~ class_Rings_Olinordered__idom(U_9657) ),
    inference(clausify,[status(thm)],[f_2355_2]) ).

cnf(f_2355_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9657),c_Groups_Ozero__class_Ozero(U_9657)),hAPP(c_Int_Oring__1__class_Oof__int(U_9657),U_9658)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9658))
    | ~ class_Rings_Olinordered__idom(U_9657) ),
    inference(clausify,[status(thm)],[f_2355_2]) ).

fof(f_2356_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ 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_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).

fof(f_2356_2,plain,
    ! [U_9660,U_9659] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9659),hAPP(c_Int_Oring__1__class_Oof__int(U_9659),U_9660)),c_Groups_Ozero__class_Ozero(U_9659)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9660),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9660),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9659),hAPP(c_Int_Oring__1__class_Oof__int(U_9659),U_9660)),c_Groups_Ozero__class_Ozero(U_9659))) ) )
      | ~ class_Rings_Olinordered__idom(U_9659) ),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

cnf(f_2356_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9660),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9659),hAPP(c_Int_Oring__1__class_Oof__int(U_9659),U_9660)),c_Groups_Ozero__class_Ozero(U_9659)))
    | ~ class_Rings_Olinordered__idom(U_9659) ),
    inference(clausify,[status(thm)],[f_2356_2]) ).

cnf(f_2356_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9659),hAPP(c_Int_Oring__1__class_Oof__int(U_9659),U_9660)),c_Groups_Ozero__class_Ozero(U_9659)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9660),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_9659) ),
    inference(clausify,[status(thm)],[f_2356_2]) ).

fof(f_2357_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_2357_2,plain,
    ! [U_9662,U_9661] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9661),hAPP(c_Int_Onat,U_9662)) = hAPP(c_Int_Oring__1__class_Oof__int(U_9661),U_9662)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9662))
      | ~ class_Rings_Oring__1(U_9661) ),
    inference(variable_rename,[status(thm)],[f_2357_1]) ).

cnf(f_2357_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9661),hAPP(c_Int_Onat,U_9662)) = hAPP(c_Int_Oring__1__class_Oof__int(U_9661),U_9662)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9662))
    | ~ class_Rings_Oring__1(U_9661) ),
    inference(clausify,[status(thm)],[f_2357_2]) ).

fof(f_2358_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_2358_2,plain,
    ! [U_9666,U_9665,U_9664,U_9663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9663),hAPP(hAPP(c_Power_Opower__class_Opower(U_9663),U_9664),U_9666)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9663),U_9665),U_9666)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9663),c_Groups_Ozero__class_Ozero(U_9663)),U_9664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9663),U_9664),U_9665))
      | ~ class_Rings_Olinordered__semidom(U_9663) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

cnf(f_2358_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9663),hAPP(hAPP(c_Power_Opower__class_Opower(U_9663),U_9664),U_9666)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9663),U_9665),U_9666)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9663),c_Groups_Ozero__class_Ozero(U_9663)),U_9664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9663),U_9664),U_9665))
    | ~ class_Rings_Olinordered__semidom(U_9663) ),
    inference(clausify,[status(thm)],[f_2358_2]) ).

fof(f_2359_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_2359_2,plain,
    ! [U_9670,U_9669,U_9668,U_9667] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9670),U_9669)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9667),hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),U_9670)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),U_9669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9669),U_9670))
      | U_9668 = c_Groups_Ozero__class_Ozero(U_9667)
      | ~ class_Fields_Ofield(U_9667) ),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

cnf(f_2359_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9670),U_9669)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9667),hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),U_9670)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9667),U_9668),U_9669))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9669),U_9670))
    | U_9668 = c_Groups_Ozero__class_Ozero(U_9667)
    | ~ class_Fields_Ofield(U_9667) ),
    inference(clausify,[status(thm)],[f_2359_2]) ).

fof(f_2360_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_2360_2,plain,
    ! [U_9673,U_9672,U_9671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9671),c_Groups_Oone__class_Oone(U_9671)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9671),U_9672),U_9673)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9673))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9671),c_Groups_Oone__class_Oone(U_9671)),U_9672))
      | ~ class_Rings_Olinordered__semidom(U_9671) ),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

cnf(f_2360_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9671),c_Groups_Oone__class_Oone(U_9671)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9671),U_9672),U_9673)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9673))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9671),c_Groups_Oone__class_Oone(U_9671)),U_9672))
    | ~ class_Rings_Olinordered__semidom(U_9671) ),
    inference(clausify,[status(thm)],[f_2360_2]) ).

fof(f_2361_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).

fof(f_2361_2,plain,
    ! [U_9677,U_9676,U_9675,U_9674] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9674),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9676)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9677)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9676),U_9677)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9676),U_9677))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9674),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9676)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9677))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9674),c_Groups_Oone__class_Oone(U_9674)),U_9675))
      | ~ class_Rings_Olinordered__semidom(U_9674) ),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

cnf(f_2361_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9676),U_9677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9674),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9676)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9677)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9674),c_Groups_Oone__class_Oone(U_9674)),U_9675))
    | ~ class_Rings_Olinordered__semidom(U_9674) ),
    inference(clausify,[status(thm)],[f_2361_2]) ).

cnf(f_2361_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9674),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9676)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9674),U_9675),U_9677)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9676),U_9677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9674),c_Groups_Oone__class_Oone(U_9674)),U_9675))
    | ~ class_Rings_Olinordered__semidom(U_9674) ),
    inference(clausify,[status(thm)],[f_2361_2]) ).

fof(f_2362_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_2362_2,plain,
    ! [U_9680,U_9679,U_9678] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9678),U_9679),U_9680) != c_Groups_Ozero__class_Ozero(U_9678)
      | U_9679 = c_Groups_Ozero__class_Ozero(U_9678)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_9678) ),
    inference(variable_rename,[status(thm)],[f_2362_1]) ).

cnf(f_2362_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9678),U_9679),U_9680) != c_Groups_Ozero__class_Ozero(U_9678)
    | U_9679 = c_Groups_Ozero__class_Ozero(U_9678)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_9678) ),
    inference(clausify,[status(thm)],[f_2362_2]) ).

fof(f_2363_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_2363_2,plain,
    ! [U_9682,U_9681] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9681),U_9682) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_9681 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_9682 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_9681 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_9682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9681),U_9682) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

fof(f_2363_3,plain,
    ( ! [U_9686,U_9684] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9684),U_9686) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_9684 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_9686 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_9685,U_9683] :
        ( U_9683 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_9685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9683),U_9685) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_2363_2]) ).

cnf(f_2363_4,plain,
    ( U_9683 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_9685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9683),U_9685) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_5,plain,
    ( U_9686 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9684),U_9686) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_6,plain,
    ( U_9684 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9684),U_9686) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

fof(f_2364_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_2364_2,plain,
    ! [U_9687] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9687) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

cnf(f_2364_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9687) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2364_2]) ).

fof(f_2365_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_2365_2,plain,
    ! [U_9690,U_9689,U_9688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9689),U_9690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9688),U_9689)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9688),U_9690)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9688)) ),
    inference(variable_rename,[status(thm)],[f_2365_1]) ).

cnf(f_2365_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9689),U_9690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9688),U_9689)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9688),U_9690)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9688)) ),
    inference(clausify,[status(thm)],[f_2365_2]) ).

fof(f_2366_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_2366_2,plain,
    ! [U_9692,U_9691] :
      ( ( 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_9691),U_9692)))
        | ( U_9692 != 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_9691)) ) )
      & ( U_9692 = 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_9691))
        | ~ 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_9691),U_9692))) ) ),
    inference(variable_rename,[status(thm)],[f_2366_1]) ).

fof(f_2366_3,plain,
    ( ! [U_9696,U_9694] :
        ( 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_9694),U_9696)))
        | ( U_9696 != 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_9694)) ) )
    & ! [U_9695,U_9693] :
        ( U_9695 = 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_9693))
        | ~ 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_9693),U_9695))) ) ),
    inference(miniscope,[status(thm)],[f_2366_2]) ).

cnf(f_2366_4,plain,
    ( U_9695 = 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_9693))
    | ~ 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_9693),U_9695))) ),
    inference(clausify,[status(thm)],[f_2366_3]) ).

cnf(f_2366_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9694))
    | 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_9694),U_9696))) ),
    inference(clausify,[status(thm)],[f_2366_3]) ).

cnf(f_2366_6,plain,
    ( U_9696 != 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9694),U_9696))) ),
    inference(clausify,[status(thm)],[f_2366_3]) ).

fof(f_2367_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_2367_2,plain,
    ! [U_9700,U_9699,U_9698,U_9697] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698),U_9699)),U_9700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),U_9698),U_9700)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),U_9699),U_9700))
      | ~ class_Groups_Ocomm__monoid__mult(U_9697) ),
    inference(variable_rename,[status(thm)],[f_2367_1]) ).

cnf(f_2367_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),U_9698),U_9699)),U_9700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9697),hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),U_9698),U_9700)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9697),U_9699),U_9700))
    | ~ class_Groups_Ocomm__monoid__mult(U_9697) ),
    inference(clausify,[status(thm)],[f_2367_2]) ).

fof(f_2368_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_2368_2,plain,
    ! [U_9703,U_9702,U_9701] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9702),U_9703)),U_9702) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),U_9702),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9702),U_9703))
      | ~ class_Groups_Omonoid__mult(U_9701) ),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

cnf(f_2368_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9702),U_9703)),U_9702) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),U_9702),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9702),U_9703))
    | ~ class_Groups_Omonoid__mult(U_9701) ),
    inference(clausify,[status(thm)],[f_2368_2]) ).

fof(f_2369_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_2369_2,plain,
    ! [U_9705,U_9704] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9704),c_Groups_Oone__class_Oone(U_9704)),U_9705) = c_Groups_Oone__class_Oone(U_9704)
      | ~ class_Groups_Omonoid__mult(U_9704) ),
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

cnf(f_2369_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9704),c_Groups_Oone__class_Oone(U_9704)),U_9705) = c_Groups_Oone__class_Oone(U_9704)
    | ~ class_Groups_Omonoid__mult(U_9704) ),
    inference(clausify,[status(thm)],[f_2369_2]) ).

fof(f_2370_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_2370_2,plain,
    ! [U_9708,U_9707,U_9706] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9706),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9707),U_9708)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9706),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9706),U_9707)),U_9708)
      | ~ class_Rings_Osemiring__1(U_9706) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

cnf(f_2370_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9706),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_9707),U_9708)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9706),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9706),U_9707)),U_9708)
    | ~ class_Rings_Osemiring__1(U_9706) ),
    inference(clausify,[status(thm)],[f_2370_2]) ).

fof(f_2371_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_2371_2,plain,
    ! [U_9712,U_9711,U_9710,U_9709] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),U_9710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9711),U_9712)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),U_9710),U_9711)),U_9712)
      | ~ class_Groups_Omonoid__mult(U_9709) ),
    inference(variable_rename,[status(thm)],[f_2371_1]) ).

cnf(f_2371_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),U_9710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9711),U_9712)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),hAPP(hAPP(c_Power_Opower__class_Opower(U_9709),U_9710),U_9711)),U_9712)
    | ~ class_Groups_Omonoid__mult(U_9709) ),
    inference(clausify,[status(thm)],[f_2371_2]) ).

fof(f_2372_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_2372_2,plain,
    ! [U_9716,U_9715,U_9714,U_9713] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9713),U_9714),U_9715)),U_9716) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9713),hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),U_9714),U_9716)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),U_9715),U_9716))
      | ~ class_Fields_Ofield__inverse__zero(U_9713) ),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

cnf(f_2372_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9713),U_9714),U_9715)),U_9716) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9713),hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),U_9714),U_9716)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9713),U_9715),U_9716))
    | ~ class_Fields_Ofield__inverse__zero(U_9713) ),
    inference(clausify,[status(thm)],[f_2372_2]) ).

fof(f_2373_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_2373_2,plain,
    ! [U_9719,U_9718,U_9717] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9717),hAPP(hAPP(c_Power_Opower__class_Opower(U_9717),U_9718),U_9719)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9717),hAPP(c_Groups_Oabs__class_Oabs(U_9717),U_9718)),U_9719)
      | ~ class_Rings_Olinordered__idom(U_9717) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

cnf(f_2373_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9717),hAPP(hAPP(c_Power_Opower__class_Opower(U_9717),U_9718),U_9719)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9717),hAPP(c_Groups_Oabs__class_Oabs(U_9717),U_9718)),U_9719)
    | ~ class_Rings_Olinordered__idom(U_9717) ),
    inference(clausify,[status(thm)],[f_2373_2]) ).

fof(f_2374_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_2374_2,plain,
    ! [U_9721,U_9720] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9720),U_9721),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_9721
      | ~ class_Groups_Omonoid__mult(U_9720) ),
    inference(variable_rename,[status(thm)],[f_2374_1]) ).

cnf(f_2374_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9720),U_9721),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_9721
    | ~ class_Groups_Omonoid__mult(U_9720) ),
    inference(clausify,[status(thm)],[f_2374_2]) ).

fof(f_2375_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_2375_2,plain,
    ! [U_9725,U_9724,U_9723,U_9722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),hAPP(hAPP(c_Power_Opower__class_Opower(U_9722),U_9723),U_9725)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9722),U_9724),U_9725)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),c_Groups_Ozero__class_Ozero(U_9722)),U_9723))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),U_9723),U_9724))
      | ~ class_Rings_Olinordered__semidom(U_9722) ),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

cnf(f_2375_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),hAPP(hAPP(c_Power_Opower__class_Opower(U_9722),U_9723),U_9725)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9722),U_9724),U_9725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),c_Groups_Ozero__class_Ozero(U_9722)),U_9723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),U_9723),U_9724))
    | ~ class_Rings_Olinordered__semidom(U_9722) ),
    inference(clausify,[status(thm)],[f_2375_2]) ).

fof(f_2376_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_2376_2,plain,
    ! [U_9728,U_9727,U_9726] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9726),c_Groups_Ozero__class_Ozero(U_9726)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9726),U_9727),U_9728)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9726),c_Groups_Ozero__class_Ozero(U_9726)),U_9727))
      | ~ class_Rings_Olinordered__semidom(U_9726) ),
    inference(variable_rename,[status(thm)],[f_2376_1]) ).

cnf(f_2376_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9726),c_Groups_Ozero__class_Ozero(U_9726)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9726),U_9727),U_9728)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9726),c_Groups_Ozero__class_Ozero(U_9726)),U_9727))
    | ~ class_Rings_Olinordered__semidom(U_9726) ),
    inference(clausify,[status(thm)],[f_2376_2]) ).

fof(f_2377_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_2377_2,plain,
    ! [U_9731,U_9730,U_9729] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9729),c_Groups_Ozero__class_Ozero(U_9729)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9729),U_9730),U_9731)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9729),c_Groups_Ozero__class_Ozero(U_9729)),U_9730))
      | ~ class_Rings_Olinordered__semidom(U_9729) ),
    inference(variable_rename,[status(thm)],[f_2377_1]) ).

cnf(f_2377_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9729),c_Groups_Ozero__class_Ozero(U_9729)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9729),U_9730),U_9731)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9729),c_Groups_Ozero__class_Ozero(U_9729)),U_9730))
    | ~ class_Rings_Olinordered__semidom(U_9729) ),
    inference(clausify,[status(thm)],[f_2377_2]) ).

fof(f_2378_1,plain,
    ! [V_n_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Ozero__neq__one(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a)
      | ~ class_Rings_Omult__zero(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).

fof(f_2378_2,plain,
    ! [U_9734,U_9733,U_9732] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9732),U_9733),U_9734) = c_Groups_Ozero__class_Ozero(U_9732)
          | U_9734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_9733 != c_Groups_Ozero__class_Ozero(U_9732) )
        & ( ( U_9734 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_9733 = c_Groups_Ozero__class_Ozero(U_9732) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_9732),U_9733),U_9734) != c_Groups_Ozero__class_Ozero(U_9732) ) )
      | ~ class_Rings_Ozero__neq__one(U_9732)
      | ~ class_Rings_Ono__zero__divisors(U_9732)
      | ~ class_Rings_Omult__zero(U_9732)
      | ~ class_Power_Opower(U_9732) ),
    inference(variable_rename,[status(thm)],[f_2378_1]) ).

cnf(f_2378_3,plain,
    ( U_9733 = c_Groups_Ozero__class_Ozero(U_9732)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_9732),U_9733),U_9734) != c_Groups_Ozero__class_Ozero(U_9732)
    | ~ class_Rings_Ozero__neq__one(U_9732)
    | ~ class_Rings_Ono__zero__divisors(U_9732)
    | ~ class_Rings_Omult__zero(U_9732)
    | ~ class_Power_Opower(U_9732) ),
    inference(clausify,[status(thm)],[f_2378_2]) ).

cnf(f_2378_4,plain,
    ( U_9734 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_9732),U_9733),U_9734) != c_Groups_Ozero__class_Ozero(U_9732)
    | ~ class_Rings_Ozero__neq__one(U_9732)
    | ~ class_Rings_Ono__zero__divisors(U_9732)
    | ~ class_Rings_Omult__zero(U_9732)
    | ~ class_Power_Opower(U_9732) ),
    inference(clausify,[status(thm)],[f_2378_2]) ).

cnf(f_2378_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9732),U_9733),U_9734) = c_Groups_Ozero__class_Ozero(U_9732)
    | U_9734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_9733 != c_Groups_Ozero__class_Ozero(U_9732)
    | ~ class_Rings_Ozero__neq__one(U_9732)
    | ~ class_Rings_Ono__zero__divisors(U_9732)
    | ~ class_Rings_Omult__zero(U_9732)
    | ~ class_Power_Opower(U_9732) ),
    inference(clausify,[status(thm)],[f_2378_2]) ).

fof(f_2379_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_2379_2,plain,
    ! [U_9737,U_9736,U_9735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9735),c_Groups_Oone__class_Oone(U_9735)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9735),U_9736),U_9737)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9735),c_Groups_Oone__class_Oone(U_9735)),U_9736))
      | ~ class_Rings_Olinordered__semidom(U_9735) ),
    inference(variable_rename,[status(thm)],[f_2379_1]) ).

cnf(f_2379_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9735),c_Groups_Oone__class_Oone(U_9735)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9735),U_9736),U_9737)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9735),c_Groups_Oone__class_Oone(U_9735)),U_9736))
    | ~ class_Rings_Olinordered__semidom(U_9735) ),
    inference(clausify,[status(thm)],[f_2379_2]) ).

fof(f_2380_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_2380_2,plain,
    ! [U_9739,U_9738] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9738),c_Groups_Ozero__class_Ozero(U_9738)),hAPP(c_Nat_OSuc,U_9739)) = c_Groups_Ozero__class_Ozero(U_9738)
      | ~ class_Rings_Osemiring__0(U_9738)
      | ~ class_Power_Opower(U_9738) ),
    inference(variable_rename,[status(thm)],[f_2380_1]) ).

cnf(f_2380_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9738),c_Groups_Ozero__class_Ozero(U_9738)),hAPP(c_Nat_OSuc,U_9739)) = c_Groups_Ozero__class_Ozero(U_9738)
    | ~ class_Rings_Osemiring__0(U_9738)
    | ~ class_Power_Opower(U_9738) ),
    inference(clausify,[status(thm)],[f_2380_2]) ).

fof(f_2381_1,plain,
    ! [V_n_2,V_m_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).

fof(f_2381_2,plain,
    ! [U_9743,U_9742,U_9741,U_9740] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9742) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9743)
          | U_9742 != U_9743 )
        & ( U_9742 = U_9743
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9742) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9743) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9740),c_Groups_Oone__class_Oone(U_9740)),U_9741))
      | ~ class_Rings_Olinordered__semidom(U_9740) ),
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

cnf(f_2381_3,plain,
    ( U_9742 = U_9743
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9742) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9743)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9740),c_Groups_Oone__class_Oone(U_9740)),U_9741))
    | ~ class_Rings_Olinordered__semidom(U_9740) ),
    inference(clausify,[status(thm)],[f_2381_2]) ).

cnf(f_2381_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9742) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9740),U_9741),U_9743)
    | U_9742 != U_9743
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9740),c_Groups_Oone__class_Oone(U_9740)),U_9741))
    | ~ class_Rings_Olinordered__semidom(U_9740) ),
    inference(clausify,[status(thm)],[f_2381_2]) ).

fof(f_2382_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_2382_2,plain,
    ! [U_9746,U_9745,U_9744] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9744),U_9745),hAPP(c_Nat_OSuc,U_9746)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9744),hAPP(hAPP(c_Power_Opower__class_Opower(U_9744),U_9745),U_9746)),U_9745)
      | ~ class_Groups_Omonoid__mult(U_9744) ),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

cnf(f_2382_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9744),U_9745),hAPP(c_Nat_OSuc,U_9746)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9744),hAPP(hAPP(c_Power_Opower__class_Opower(U_9744),U_9745),U_9746)),U_9745)
    | ~ class_Groups_Omonoid__mult(U_9744) ),
    inference(clausify,[status(thm)],[f_2382_2]) ).

fof(f_2383_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_2383_2,plain,
    ! [U_9749,U_9748,U_9747] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9747),U_9748),hAPP(c_Nat_OSuc,U_9749)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9747),U_9748),hAPP(hAPP(c_Power_Opower__class_Opower(U_9747),U_9748),U_9749))
      | ~ class_Power_Opower(U_9747) ),
    inference(variable_rename,[status(thm)],[f_2383_1]) ).

cnf(f_2383_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9747),U_9748),hAPP(c_Nat_OSuc,U_9749)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9747),U_9748),hAPP(hAPP(c_Power_Opower__class_Opower(U_9747),U_9748),U_9749))
    | ~ class_Power_Opower(U_9747) ),
    inference(clausify,[status(thm)],[f_2383_2]) ).

fof(f_2384_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_2384_2,plain,
    ! [U_9751,U_9750] :
      ( 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_9750),U_9751)))
      | ~ 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_9750)) ),
    inference(variable_rename,[status(thm)],[f_2384_1]) ).

cnf(f_2384_3,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_9750),U_9751)))
    | ~ 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_9750)) ),
    inference(clausify,[status(thm)],[f_2384_2]) ).

fof(f_2385_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_2385_2,plain,
    ! [U_9753,U_9752] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9752),U_9753),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_9752)
      | ~ class_Power_Opower(U_9752) ),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

cnf(f_2385_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9752),U_9753),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_9752)
    | ~ class_Power_Opower(U_9752) ),
    inference(clausify,[status(thm)],[f_2385_2]) ).

fof(f_2386_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_2386_2,plain,
    ! [U_9757,U_9756,U_9755,U_9754] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9756),U_9757)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9754),hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),U_9756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),U_9757))
      | ~ class_Groups_Omonoid__mult(U_9754) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

cnf(f_2386_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9756),U_9757)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9754),hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),U_9756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9754),U_9755),U_9757))
    | ~ class_Groups_Omonoid__mult(U_9754) ),
    inference(clausify,[status(thm)],[f_2386_2]) ).

fof(f_2387_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_2387_2,plain,
    ! [U_9761,U_9760,U_9759,U_9758] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9758),U_9760),U_9759)),U_9761) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9758),hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),U_9760),U_9761)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),U_9759),U_9761))
      | U_9759 = c_Groups_Ozero__class_Ozero(U_9758)
      | ~ class_Fields_Ofield(U_9758) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

cnf(f_2387_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9758),U_9760),U_9759)),U_9761) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9758),hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),U_9760),U_9761)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9758),U_9759),U_9761))
    | U_9759 = c_Groups_Ozero__class_Ozero(U_9758)
    | ~ class_Fields_Ofield(U_9758) ),
    inference(clausify,[status(thm)],[f_2387_2]) ).

fof(f_2388_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_2388_2,plain,
    ! [U_9764,U_9763,U_9762] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9762),c_Groups_Oone__class_Oone(U_9762)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9762),U_9763),U_9764)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9762),c_Groups_Oone__class_Oone(U_9762)),U_9763)),U_9764)
      | ~ class_Fields_Ofield__inverse__zero(U_9762) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

cnf(f_2388_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9762),c_Groups_Oone__class_Oone(U_9762)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9762),U_9763),U_9764)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9762),c_Groups_Oone__class_Oone(U_9762)),U_9763)),U_9764)
    | ~ class_Fields_Ofield__inverse__zero(U_9762) ),
    inference(clausify,[status(thm)],[f_2388_2]) ).

fof(f_2389_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_2389_2,plain,
    ! [U_9767,U_9766,U_9765] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9765),hAPP(hAPP(c_Power_Opower__class_Opower(U_9765),hAPP(c_Groups_Ouminus__class_Ouminus(U_9765),U_9766)),U_9767)) = hAPP(c_Groups_Oabs__class_Oabs(U_9765),hAPP(hAPP(c_Power_Opower__class_Opower(U_9765),U_9766),U_9767))
      | ~ class_Rings_Olinordered__idom(U_9765) ),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

cnf(f_2389_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9765),hAPP(hAPP(c_Power_Opower__class_Opower(U_9765),hAPP(c_Groups_Ouminus__class_Ouminus(U_9765),U_9766)),U_9767)) = hAPP(c_Groups_Oabs__class_Oabs(U_9765),hAPP(hAPP(c_Power_Opower__class_Opower(U_9765),U_9766),U_9767))
    | ~ class_Rings_Olinordered__idom(U_9765) ),
    inference(clausify,[status(thm)],[f_2389_2]) ).

fof(f_2390_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_2390_2,plain,
    ! [U_9771,U_9770,U_9769,U_9768] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9768),U_9769),U_9771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9768),c_Groups_Ozero__class_Ozero(U_9768)),U_9771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9768),hAPP(hAPP(c_Power_Opower__class_Opower(U_9768),U_9769),U_9770)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9768),U_9771),U_9770)))
      | ~ class_Rings_Olinordered__semidom(U_9768) ),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

cnf(f_2390_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9768),U_9769),U_9771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9768),c_Groups_Ozero__class_Ozero(U_9768)),U_9771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9768),hAPP(hAPP(c_Power_Opower__class_Opower(U_9768),U_9769),U_9770)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9768),U_9771),U_9770)))
    | ~ class_Rings_Olinordered__semidom(U_9768) ),
    inference(clausify,[status(thm)],[f_2390_2]) ).

fof(f_2391_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_2391_2,plain,
    ! [U_9775,U_9774,U_9773,U_9772] :
      ( U_9773 = U_9775
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),c_Groups_Ozero__class_Ozero(U_9772)),U_9775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),c_Groups_Ozero__class_Ozero(U_9772)),U_9773))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_9772),U_9773),hAPP(c_Nat_OSuc,U_9774)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9772),U_9775),hAPP(c_Nat_OSuc,U_9774))
      | ~ class_Rings_Olinordered__semidom(U_9772) ),
    inference(variable_rename,[status(thm)],[f_2391_1]) ).

cnf(f_2391_3,plain,
    ( U_9773 = U_9775
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),c_Groups_Ozero__class_Ozero(U_9772)),U_9775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),c_Groups_Ozero__class_Ozero(U_9772)),U_9773))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_9772),U_9773),hAPP(c_Nat_OSuc,U_9774)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9772),U_9775),hAPP(c_Nat_OSuc,U_9774))
    | ~ class_Rings_Olinordered__semidom(U_9772) ),
    inference(clausify,[status(thm)],[f_2391_2]) ).

fof(f_2392_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_2392_2,plain,
    ! [U_9779,U_9778,U_9777,U_9776] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),U_9777),U_9779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),c_Groups_Ozero__class_Ozero(U_9776)),U_9779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),hAPP(hAPP(c_Power_Opower__class_Opower(U_9776),U_9777),hAPP(c_Nat_OSuc,U_9778))),hAPP(hAPP(c_Power_Opower__class_Opower(U_9776),U_9779),hAPP(c_Nat_OSuc,U_9778))))
      | ~ class_Rings_Olinordered__semidom(U_9776) ),
    inference(variable_rename,[status(thm)],[f_2392_1]) ).

cnf(f_2392_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),U_9777),U_9779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),c_Groups_Ozero__class_Ozero(U_9776)),U_9779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9776),hAPP(hAPP(c_Power_Opower__class_Opower(U_9776),U_9777),hAPP(c_Nat_OSuc,U_9778))),hAPP(hAPP(c_Power_Opower__class_Opower(U_9776),U_9779),hAPP(c_Nat_OSuc,U_9778))))
    | ~ class_Rings_Olinordered__semidom(U_9776) ),
    inference(clausify,[status(thm)],[f_2392_2]) ).

fof(f_2393_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_2393_2,plain,
    ! [U_9782,U_9781,U_9780] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9780),c_Groups_Oone__class_Oone(U_9780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9780),U_9781),hAPP(hAPP(c_Power_Opower__class_Opower(U_9780),U_9781),U_9782))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9780),c_Groups_Oone__class_Oone(U_9780)),U_9781))
      | ~ class_Rings_Olinordered__semidom(U_9780) ),
    inference(variable_rename,[status(thm)],[f_2393_1]) ).

cnf(f_2393_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9780),c_Groups_Oone__class_Oone(U_9780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9780),U_9781),hAPP(hAPP(c_Power_Opower__class_Opower(U_9780),U_9781),U_9782))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9780),c_Groups_Oone__class_Oone(U_9780)),U_9781))
    | ~ class_Rings_Olinordered__semidom(U_9780) ),
    inference(clausify,[status(thm)],[f_2393_2]) ).

fof(f_2394_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_2394_2,plain,
    ! [U_9785,U_9784,U_9783] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9783),hAPP(hAPP(c_Power_Opower__class_Opower(U_9783),U_9784),U_9785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9783),U_9784),hAPP(hAPP(c_Power_Opower__class_Opower(U_9783),U_9784),U_9785))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9783),c_Groups_Oone__class_Oone(U_9783)),U_9784))
      | ~ class_Rings_Olinordered__semidom(U_9783) ),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

cnf(f_2394_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9783),hAPP(hAPP(c_Power_Opower__class_Opower(U_9783),U_9784),U_9785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9783),U_9784),hAPP(hAPP(c_Power_Opower__class_Opower(U_9783),U_9784),U_9785))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9783),c_Groups_Oone__class_Oone(U_9783)),U_9784))
    | ~ class_Rings_Olinordered__semidom(U_9783) ),
    inference(clausify,[status(thm)],[f_2394_2]) ).

fof(f_2395_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_2395_2,plain,
    ! [U_9787,U_9786] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9786),c_Groups_Ozero__class_Ozero(U_9786)),U_9787) = c_Groups_Ozero__class_Ozero(U_9786)
          | U_9787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9786),c_Groups_Ozero__class_Ozero(U_9786)),U_9787) = c_Groups_Oone__class_Oone(U_9786)
          | U_9787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_9786)
      | ~ class_Power_Opower(U_9786) ),
    inference(variable_rename,[status(thm)],[f_2395_1]) ).

cnf(f_2395_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9786),c_Groups_Ozero__class_Ozero(U_9786)),U_9787) = c_Groups_Oone__class_Oone(U_9786)
    | U_9787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_9786)
    | ~ class_Power_Opower(U_9786) ),
    inference(clausify,[status(thm)],[f_2395_2]) ).

cnf(f_2395_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9786),c_Groups_Ozero__class_Ozero(U_9786)),U_9787) = c_Groups_Ozero__class_Ozero(U_9786)
    | U_9787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_9786)
    | ~ class_Power_Opower(U_9786) ),
    inference(clausify,[status(thm)],[f_2395_2]) ).

fof(f_2396_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_2396_2,plain,
    ! [U_9790,U_9789,U_9788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9788),c_Groups_Oone__class_Oone(U_9788)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9788),U_9789),hAPP(c_Nat_OSuc,U_9790))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9788),c_Groups_Oone__class_Oone(U_9788)),U_9789))
      | ~ class_Rings_Olinordered__semidom(U_9788) ),
    inference(variable_rename,[status(thm)],[f_2396_1]) ).

cnf(f_2396_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9788),c_Groups_Oone__class_Oone(U_9788)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9788),U_9789),hAPP(c_Nat_OSuc,U_9790))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9788),c_Groups_Oone__class_Oone(U_9788)),U_9789))
    | ~ class_Rings_Olinordered__semidom(U_9788) ),
    inference(clausify,[status(thm)],[f_2396_2]) ).

fof(f_2397_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).

fof(f_2397_2,plain,
    ! [U_9794,U_9793,U_9792,U_9791] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9793)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9794)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9793),U_9794)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9793),U_9794))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9793)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9794))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),c_Groups_Oone__class_Oone(U_9791)),U_9792))
      | ~ class_Rings_Olinordered__semidom(U_9791) ),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

cnf(f_2397_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9793),U_9794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9793)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),c_Groups_Oone__class_Oone(U_9791)),U_9792))
    | ~ class_Rings_Olinordered__semidom(U_9791) ),
    inference(clausify,[status(thm)],[f_2397_2]) ).

cnf(f_2397_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9793)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9791),U_9792),U_9794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9793),U_9794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9791),c_Groups_Oone__class_Oone(U_9791)),U_9792))
    | ~ class_Rings_Olinordered__semidom(U_9791) ),
    inference(clausify,[status(thm)],[f_2397_2]) ).

fof(f_2398_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_2398_2,plain,
    ! [U_9798,U_9797,U_9796,U_9795] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9797),U_9798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),hAPP(hAPP(c_Power_Opower__class_Opower(U_9795),U_9796),U_9797)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9795),U_9796),U_9798)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),c_Groups_Oone__class_Oone(U_9795)),U_9796))
      | ~ class_Rings_Olinordered__semidom(U_9795) ),
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

cnf(f_2398_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9797),U_9798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),hAPP(hAPP(c_Power_Opower__class_Opower(U_9795),U_9796),U_9797)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9795),U_9796),U_9798)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),c_Groups_Oone__class_Oone(U_9795)),U_9796))
    | ~ class_Rings_Olinordered__semidom(U_9795) ),
    inference(clausify,[status(thm)],[f_2398_2]) ).

fof(f_2399_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_2399_2,plain,
    ! [U_9802,U_9801,U_9800,U_9799] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9799),hAPP(hAPP(c_Power_Opower__class_Opower(U_9799),U_9802),U_9800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9799),U_9802),U_9801)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9799),c_Groups_Oone__class_Oone(U_9799)),U_9802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9800),U_9801))
      | ~ class_Rings_Olinordered__semidom(U_9799) ),
    inference(variable_rename,[status(thm)],[f_2399_1]) ).

cnf(f_2399_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9799),hAPP(hAPP(c_Power_Opower__class_Opower(U_9799),U_9802),U_9800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9799),U_9802),U_9801)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9799),c_Groups_Oone__class_Oone(U_9799)),U_9802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9800),U_9801))
    | ~ class_Rings_Olinordered__semidom(U_9799) ),
    inference(clausify,[status(thm)],[f_2399_2]) ).

fof(f_2400_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_2400_2,plain,
    ! [U_9805,U_9804,U_9803] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9803),c_Groups_Ozero__class_Ozero(U_9803)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9803),hAPP(c_Groups_Oabs__class_Oabs(U_9803),U_9804)),U_9805)))
      | ~ class_Rings_Olinordered__idom(U_9803) ),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

cnf(f_2400_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9803),c_Groups_Ozero__class_Ozero(U_9803)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9803),hAPP(c_Groups_Oabs__class_Oabs(U_9803),U_9804)),U_9805)))
    | ~ class_Rings_Olinordered__idom(U_9803) ),
    inference(clausify,[status(thm)],[f_2400_2]) ).

fof(f_2401_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_2401_2,plain,
    ! [U_9809,U_9808,U_9807,U_9806] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9806),hAPP(hAPP(c_Power_Opower__class_Opower(U_9806),U_9809),U_9807)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9806),U_9809),U_9808)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9806),c_Groups_Oone__class_Oone(U_9806)),U_9809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9807),U_9808))
      | ~ class_Rings_Olinordered__semidom(U_9806) ),
    inference(variable_rename,[status(thm)],[f_2401_1]) ).

cnf(f_2401_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9806),hAPP(hAPP(c_Power_Opower__class_Opower(U_9806),U_9809),U_9807)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9806),U_9809),U_9808)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9806),c_Groups_Oone__class_Oone(U_9806)),U_9809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9807),U_9808))
    | ~ class_Rings_Olinordered__semidom(U_9806) ),
    inference(clausify,[status(thm)],[f_2401_2]) ).

fof(f_2402_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_2402_2,plain,
    ! [U_9812,U_9811,U_9810] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),hAPP(c_Groups_Ouminus__class_Ouminus(U_9810),U_9811)),U_9812) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9810),hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),hAPP(c_Groups_Ouminus__class_Ouminus(U_9810),c_Groups_Oone__class_Oone(U_9810))),U_9812)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),U_9811),U_9812))
      | ~ class_Rings_Oring__1(U_9810) ),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

cnf(f_2402_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),hAPP(c_Groups_Ouminus__class_Ouminus(U_9810),U_9811)),U_9812) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9810),hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),hAPP(c_Groups_Ouminus__class_Ouminus(U_9810),c_Groups_Oone__class_Oone(U_9810))),U_9812)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9810),U_9811),U_9812))
    | ~ class_Rings_Oring__1(U_9810) ),
    inference(clausify,[status(thm)],[f_2402_2]) ).

fof(f_2403_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_2403_2,plain,
    ! [U_9815,U_9814,U_9813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9813),U_9814),hAPP(hAPP(c_Power_Opower__class_Opower(U_9813),U_9814),U_9815))),hAPP(hAPP(c_Power_Opower__class_Opower(U_9813),U_9814),U_9815)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),U_9814),c_Groups_Oone__class_Oone(U_9813)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),c_Groups_Ozero__class_Ozero(U_9813)),U_9814))
      | ~ class_Rings_Olinordered__semidom(U_9813) ),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

cnf(f_2403_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9813),U_9814),hAPP(hAPP(c_Power_Opower__class_Opower(U_9813),U_9814),U_9815))),hAPP(hAPP(c_Power_Opower__class_Opower(U_9813),U_9814),U_9815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),U_9814),c_Groups_Oone__class_Oone(U_9813)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9813),c_Groups_Ozero__class_Ozero(U_9813)),U_9814))
    | ~ class_Rings_Olinordered__semidom(U_9813) ),
    inference(clausify,[status(thm)],[f_2403_2]) ).

fof(f_2404_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_2404_2,plain,
    ! [U_9819,U_9818,U_9817,U_9816] :
      ( U_9817 = U_9819
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9816),c_Groups_Ozero__class_Ozero(U_9816)),U_9819))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9816),c_Groups_Ozero__class_Ozero(U_9816)),U_9817))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_9816),U_9817),U_9818) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9816),U_9819),U_9818)
      | ~ class_Rings_Olinordered__semidom(U_9816) ),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

cnf(f_2404_3,plain,
    ( U_9817 = U_9819
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9816),c_Groups_Ozero__class_Ozero(U_9816)),U_9819))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9816),c_Groups_Ozero__class_Ozero(U_9816)),U_9817))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_9816),U_9817),U_9818) != hAPP(hAPP(c_Power_Opower__class_Opower(U_9816),U_9819),U_9818)
    | ~ class_Rings_Olinordered__semidom(U_9816) ),
    inference(clausify,[status(thm)],[f_2404_2]) ).

fof(f_2405_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_2405_2,plain,
    ! [U_9822,U_9821,U_9820] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),hAPP(hAPP(c_Power_Opower__class_Opower(U_9820),U_9821),hAPP(c_Nat_OSuc,U_9822))),c_Groups_Oone__class_Oone(U_9820)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),U_9821),c_Groups_Oone__class_Oone(U_9820)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),c_Groups_Ozero__class_Ozero(U_9820)),U_9821))
      | ~ class_Rings_Olinordered__semidom(U_9820) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

cnf(f_2405_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),hAPP(hAPP(c_Power_Opower__class_Opower(U_9820),U_9821),hAPP(c_Nat_OSuc,U_9822))),c_Groups_Oone__class_Oone(U_9820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),U_9821),c_Groups_Oone__class_Oone(U_9820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9820),c_Groups_Ozero__class_Ozero(U_9820)),U_9821))
    | ~ class_Rings_Olinordered__semidom(U_9820) ),
    inference(clausify,[status(thm)],[f_2405_2]) ).

fof(f_2406_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_2406_2,plain,
    ! [U_9826,U_9825,U_9824,U_9823] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),hAPP(hAPP(c_Power_Opower__class_Opower(U_9823),U_9826),U_9825)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9823),U_9826),U_9824)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),U_9826),c_Groups_Oone__class_Oone(U_9823)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),c_Groups_Ozero__class_Ozero(U_9823)),U_9826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9824),U_9825))
      | ~ class_Rings_Olinordered__semidom(U_9823) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

cnf(f_2406_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),hAPP(hAPP(c_Power_Opower__class_Opower(U_9823),U_9826),U_9825)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9823),U_9826),U_9824)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),U_9826),c_Groups_Oone__class_Oone(U_9823)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9823),c_Groups_Ozero__class_Ozero(U_9823)),U_9826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9824),U_9825))
    | ~ class_Rings_Olinordered__semidom(U_9823) ),
    inference(clausify,[status(thm)],[f_2406_2]) ).

fof(f_2407_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_2407_2,plain,
    ! [U_9830,U_9829,U_9828,U_9827] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),hAPP(hAPP(c_Power_Opower__class_Opower(U_9827),U_9830),U_9829)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9827),U_9830),U_9828)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),U_9830),c_Groups_Oone__class_Oone(U_9827)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),c_Groups_Ozero__class_Ozero(U_9827)),U_9830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9828),U_9829))
      | ~ class_Rings_Olinordered__semidom(U_9827) ),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

cnf(f_2407_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),hAPP(hAPP(c_Power_Opower__class_Opower(U_9827),U_9830),U_9829)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9827),U_9830),U_9828)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),U_9830),c_Groups_Oone__class_Oone(U_9827)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9827),c_Groups_Ozero__class_Ozero(U_9827)),U_9830))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9828),U_9829))
    | ~ class_Rings_Olinordered__semidom(U_9827) ),
    inference(clausify,[status(thm)],[f_2407_2]) ).

fof(f_2408_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_2408_2,plain,
    ! [U_9834,U_9833,U_9832,U_9831] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9833),U_9834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9831),hAPP(hAPP(c_Power_Opower__class_Opower(U_9831),U_9832),U_9833)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9831),U_9832),U_9834)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9831),c_Groups_Oone__class_Oone(U_9831)),U_9832))
      | ~ class_Rings_Olinordered__semidom(U_9831) ),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

cnf(f_2408_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9833),U_9834))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9831),hAPP(hAPP(c_Power_Opower__class_Opower(U_9831),U_9832),U_9833)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9831),U_9832),U_9834)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9831),c_Groups_Oone__class_Oone(U_9831)),U_9832))
    | ~ class_Rings_Olinordered__semidom(U_9831) ),
    inference(clausify,[status(thm)],[f_2408_2]) ).

fof(f_2409_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).

fof(f_2409_2,plain,
    ! [U_9838,U_9837,U_9836,U_9835] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

cnf(f_2409_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),c_Groups_Ozero__class_Ozero(U_9835)),U_9838))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9835),U_9838),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

cnf(f_2409_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),c_Groups_Ozero__class_Ozero(U_9835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9835),U_9836),U_9838)),U_9837))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9835),U_9836),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9835),U_9837),U_9838)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9835) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

fof(f_2410_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).

fof(f_2410_2,plain,
    ! [U_9842,U_9841,U_9840,U_9839] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

cnf(f_2410_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9839),U_9841),c_Groups_Ozero__class_Ozero(U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

cnf(f_2410_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),c_Groups_Ozero__class_Ozero(U_9839)),U_9842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)),U_9840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),U_9840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9839),U_9842),U_9841)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9839),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9839),U_9840),U_9841)),U_9842))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9839) ),
    inference(clausify,[status(thm)],[f_2410_2]) ).

fof(f_2411_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).

fof(f_2411_2,plain,
    ! [U_9846,U_9845,U_9844,U_9843] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),U_9845),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9843),U_9846),U_9844)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9843),U_9845),U_9844)),U_9846)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9843),U_9845),U_9844)),U_9846))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),U_9845),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9843),U_9846),U_9844))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9843),c_Groups_Ozero__class_Ozero(U_9843)),U_9844))
      | ~ class_Fields_Olinordered__field(U_9843) ),
    inference(variable_rename,[status(thm)],[f_2411_1]) ).

cnf(f_2411_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9843),U_9845),U_9844)),U_9846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),U_9845),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9843),U_9846),U_9844)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9843),c_Groups_Ozero__class_Ozero(U_9843)),U_9844))
    | ~ class_Fields_Olinordered__field(U_9843) ),
    inference(clausify,[status(thm)],[f_2411_2]) ).

cnf(f_2411_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),U_9845),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9843),U_9846),U_9844)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9843),U_9845),U_9844)),U_9846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9843),c_Groups_Ozero__class_Ozero(U_9843)),U_9844))
    | ~ class_Fields_Olinordered__field(U_9843) ),
    inference(clausify,[status(thm)],[f_2411_2]) ).

fof(f_2412_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).

fof(f_2412_2,plain,
    ! [U_9850,U_9849,U_9848,U_9847] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9847),U_9849),U_9848)),U_9850))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),U_9849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9847),U_9850),U_9848))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),U_9849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9847),U_9850),U_9848)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9847),U_9849),U_9848)),U_9850)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9847),c_Groups_Ozero__class_Ozero(U_9847)),U_9848))
      | ~ class_Fields_Olinordered__field(U_9847) ),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

cnf(f_2412_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),U_9849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9847),U_9850),U_9848)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9847),U_9849),U_9848)),U_9850))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9847),c_Groups_Ozero__class_Ozero(U_9847)),U_9848))
    | ~ class_Fields_Olinordered__field(U_9847) ),
    inference(clausify,[status(thm)],[f_2412_2]) ).

cnf(f_2412_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9847),U_9849),U_9848)),U_9850))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9847),U_9849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9847),U_9850),U_9848)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9847),c_Groups_Ozero__class_Ozero(U_9847)),U_9848))
    | ~ class_Fields_Olinordered__field(U_9847) ),
    inference(clausify,[status(thm)],[f_2412_2]) ).

fof(f_2413_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_2413_2,plain,
    ! [U_9855,U_9854,U_9853,U_9852,U_9851] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),U_9852),U_9853)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),U_9854),U_9855)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),U_9852),U_9854)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),U_9853),U_9855))
      | ~ class_Fields_Ofield__inverse__zero(U_9851) ),
    inference(variable_rename,[status(thm)],[f_2413_1]) ).

cnf(f_2413_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),U_9852),U_9853)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),U_9854),U_9855)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9851),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),U_9852),U_9854)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9851),U_9853),U_9855))
    | ~ class_Fields_Ofield__inverse__zero(U_9851) ),
    inference(clausify,[status(thm)],[f_2413_2]) ).

fof(f_2414_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_2414_2,plain,
    ! [U_9858,U_9857,U_9856] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9856),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9856),U_9857),U_9858)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9856),U_9857),hAPP(c_Groups_Ouminus__class_Ouminus(U_9856),U_9858))
      | ~ class_Fields_Ofield__inverse__zero(U_9856) ),
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

cnf(f_2414_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9856),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9856),U_9857),U_9858)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9856),U_9857),hAPP(c_Groups_Ouminus__class_Ouminus(U_9856),U_9858))
    | ~ class_Fields_Ofield__inverse__zero(U_9856) ),
    inference(clausify,[status(thm)],[f_2414_2]) ).

fof(f_2415_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_2415_2,plain,
    ! [U_9861,U_9860,U_9859] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9859),hAPP(c_Groups_Ouminus__class_Ouminus(U_9859),U_9860)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9859),U_9861)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9859),U_9860),U_9861)
      | ~ class_Fields_Ofield__inverse__zero(U_9859) ),
    inference(variable_rename,[status(thm)],[f_2415_1]) ).

cnf(f_2415_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9859),hAPP(c_Groups_Ouminus__class_Ouminus(U_9859),U_9860)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9859),U_9861)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9859),U_9860),U_9861)
    | ~ class_Fields_Ofield__inverse__zero(U_9859) ),
    inference(clausify,[status(thm)],[f_2415_2]) ).

fof(f_2416_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_2416_2,plain,
    ! [U_9864,U_9863,U_9862] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9862),U_9863),U_9864)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9862),hAPP(c_Groups_Oabs__class_Oabs(U_9862),U_9863)),hAPP(c_Groups_Oabs__class_Oabs(U_9862),U_9864))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9862) ),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

cnf(f_2416_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9862),U_9863),U_9864)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9862),hAPP(c_Groups_Oabs__class_Oabs(U_9862),U_9863)),hAPP(c_Groups_Oabs__class_Oabs(U_9862),U_9864))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9862) ),
    inference(clausify,[status(thm)],[f_2416_2]) ).

fof(f_2417_1,plain,
    ! [V_b_2,V_a_2,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_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
          | ~ 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_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).

fof(f_2417_2,plain,
    ! [U_9867,U_9866,U_9865] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9867),c_Groups_Ozero__class_Ozero(U_9865)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9866),c_Groups_Ozero__class_Ozero(U_9865))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9867))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9866)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9867),c_Groups_Ozero__class_Ozero(U_9865)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9866),c_Groups_Ozero__class_Ozero(U_9865))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9867))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9866)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

cnf(f_2417_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9866),c_Groups_Ozero__class_Ozero(U_9865)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9866))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

cnf(f_2417_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9867),c_Groups_Ozero__class_Ozero(U_9865)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9866))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

cnf(f_2417_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9866),c_Groups_Ozero__class_Ozero(U_9865)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9867))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

cnf(f_2417_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9867),c_Groups_Ozero__class_Ozero(U_9865)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9867))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

cnf(f_2417_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9867))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),U_9866))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

cnf(f_2417_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9867),c_Groups_Ozero__class_Ozero(U_9865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),U_9866),c_Groups_Ozero__class_Ozero(U_9865)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9865),c_Groups_Ozero__class_Ozero(U_9865)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9865),U_9866),U_9867)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9865) ),
    inference(clausify,[status(thm)],[f_2417_2]) ).

fof(f_2418_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),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_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).

fof(f_2418_2,plain,
    ! [U_9870,U_9869,U_9868] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9870))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9869),c_Groups_Ozero__class_Ozero(U_9868))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9870),c_Groups_Ozero__class_Ozero(U_9868)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9869)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9870))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9869),c_Groups_Ozero__class_Ozero(U_9868))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9870),c_Groups_Ozero__class_Ozero(U_9868)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9869)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(variable_rename,[status(thm)],[f_2418_1]) ).

cnf(f_2418_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9869),c_Groups_Ozero__class_Ozero(U_9868)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

cnf(f_2418_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9870))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

cnf(f_2418_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9869),c_Groups_Ozero__class_Ozero(U_9868)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9870),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

cnf(f_2418_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9870))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9870),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

cnf(f_2418_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9870),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9869))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

cnf(f_2418_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),c_Groups_Ozero__class_Ozero(U_9868)),U_9870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),U_9869),c_Groups_Ozero__class_Ozero(U_9868)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9868),U_9869),U_9870)),c_Groups_Ozero__class_Ozero(U_9868)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9868) ),
    inference(clausify,[status(thm)],[f_2418_2]) ).

fof(f_2419_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_2419_2,plain,
    ! [U_9874,U_9873,U_9872,U_9871] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9871),U_9872),U_9874)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9871),U_9873),U_9874)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),c_Groups_Ozero__class_Ozero(U_9871)),U_9874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),U_9872),U_9873))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9871) ),
    inference(variable_rename,[status(thm)],[f_2419_1]) ).

cnf(f_2419_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9871),U_9872),U_9874)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9871),U_9873),U_9874)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),c_Groups_Ozero__class_Ozero(U_9871)),U_9874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9871),U_9872),U_9873))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9871) ),
    inference(clausify,[status(thm)],[f_2419_2]) ).

fof(f_2420_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_2420_2,plain,
    ! [U_9878,U_9877,U_9876,U_9875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9875),U_9877),U_9878)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9875),U_9876),U_9878)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),U_9878),c_Groups_Ozero__class_Ozero(U_9875)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),U_9876),U_9877))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9875) ),
    inference(variable_rename,[status(thm)],[f_2420_1]) ).

cnf(f_2420_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9875),U_9877),U_9878)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9875),U_9876),U_9878)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),U_9878),c_Groups_Ozero__class_Ozero(U_9875)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9875),U_9876),U_9877))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9875) ),
    inference(clausify,[status(thm)],[f_2420_2]) ).

fof(f_2421_1,plain,
    ! [V_b_2,V_a_2,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_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),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_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
          | ~ 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_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).

fof(f_2421_2,plain,
    ! [U_9881,U_9880,U_9879] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9881),c_Groups_Ozero__class_Ozero(U_9879)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9880),c_Groups_Ozero__class_Ozero(U_9879))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9881))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9880)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9881),c_Groups_Ozero__class_Ozero(U_9879)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9880),c_Groups_Ozero__class_Ozero(U_9879))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9881))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9880)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(variable_rename,[status(thm)],[f_2421_1]) ).

cnf(f_2421_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9880),c_Groups_Ozero__class_Ozero(U_9879)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9880))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

cnf(f_2421_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9881),c_Groups_Ozero__class_Ozero(U_9879)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9880))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

cnf(f_2421_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9880),c_Groups_Ozero__class_Ozero(U_9879)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

cnf(f_2421_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9881),c_Groups_Ozero__class_Ozero(U_9879)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

cnf(f_2421_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),U_9880))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

cnf(f_2421_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9881),c_Groups_Ozero__class_Ozero(U_9879)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),U_9880),c_Groups_Ozero__class_Ozero(U_9879)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9879),c_Groups_Ozero__class_Ozero(U_9879)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9879),U_9880),U_9881)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9879) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

fof(f_2422_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),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_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),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_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),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_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).

fof(f_2422_2,plain,
    ! [U_9884,U_9883,U_9882] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9884))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9883),c_Groups_Ozero__class_Ozero(U_9882))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9884),c_Groups_Ozero__class_Ozero(U_9882)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9883)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9884))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9883),c_Groups_Ozero__class_Ozero(U_9882))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9884),c_Groups_Ozero__class_Ozero(U_9882)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9883)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

cnf(f_2422_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9883),c_Groups_Ozero__class_Ozero(U_9882)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9883))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

cnf(f_2422_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9884))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9883))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

cnf(f_2422_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9883),c_Groups_Ozero__class_Ozero(U_9882)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9884),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

cnf(f_2422_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9884))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9884),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

cnf(f_2422_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9884),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9883))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

cnf(f_2422_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),c_Groups_Ozero__class_Ozero(U_9882)),U_9884))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),U_9883),c_Groups_Ozero__class_Ozero(U_9882)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9882),U_9883),U_9884)),c_Groups_Ozero__class_Ozero(U_9882)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9882) ),
    inference(clausify,[status(thm)],[f_2422_2]) ).

fof(f_2423_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_2423_2,plain,
    ! [U_9887,U_9886,U_9885] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9885),U_9886),U_9887)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),U_9887))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),U_9886))
      | ~ class_Fields_Olinordered__field(U_9885) ),
    inference(variable_rename,[status(thm)],[f_2423_1]) ).

cnf(f_2423_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9885),U_9886),U_9887)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),U_9887))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9885),c_Groups_Ozero__class_Ozero(U_9885)),U_9886))
    | ~ class_Fields_Olinordered__field(U_9885) ),
    inference(clausify,[status(thm)],[f_2423_2]) ).

fof(f_2424_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_2424_2,plain,
    ! [U_9890,U_9889,U_9888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9888),U_9889),U_9890)),c_Groups_Ozero__class_Ozero(U_9888)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),U_9890),c_Groups_Ozero__class_Ozero(U_9888)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),c_Groups_Ozero__class_Ozero(U_9888)),U_9889))
      | ~ class_Fields_Olinordered__field(U_9888) ),
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

cnf(f_2424_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9888),U_9889),U_9890)),c_Groups_Ozero__class_Ozero(U_9888)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),U_9890),c_Groups_Ozero__class_Ozero(U_9888)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9888),c_Groups_Ozero__class_Ozero(U_9888)),U_9889))
    | ~ class_Fields_Olinordered__field(U_9888) ),
    inference(clausify,[status(thm)],[f_2424_2]) ).

fof(f_2425_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_2425_2,plain,
    ! [U_9893,U_9892,U_9891] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9891),U_9892),U_9893)),c_Groups_Ozero__class_Ozero(U_9891)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),c_Groups_Ozero__class_Ozero(U_9891)),U_9893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),U_9892),c_Groups_Ozero__class_Ozero(U_9891)))
      | ~ class_Fields_Olinordered__field(U_9891) ),
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

cnf(f_2425_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9891),U_9892),U_9893)),c_Groups_Ozero__class_Ozero(U_9891)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),c_Groups_Ozero__class_Ozero(U_9891)),U_9893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9891),U_9892),c_Groups_Ozero__class_Ozero(U_9891)))
    | ~ class_Fields_Olinordered__field(U_9891) ),
    inference(clausify,[status(thm)],[f_2425_2]) ).

fof(f_2426_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_2426_2,plain,
    ! [U_9896,U_9895,U_9894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),c_Groups_Ozero__class_Ozero(U_9894)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9894),U_9895),U_9896)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),U_9896),c_Groups_Ozero__class_Ozero(U_9894)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),U_9895),c_Groups_Ozero__class_Ozero(U_9894)))
      | ~ class_Fields_Olinordered__field(U_9894) ),
    inference(variable_rename,[status(thm)],[f_2426_1]) ).

cnf(f_2426_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),c_Groups_Ozero__class_Ozero(U_9894)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9894),U_9895),U_9896)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),U_9896),c_Groups_Ozero__class_Ozero(U_9894)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9894),U_9895),c_Groups_Ozero__class_Ozero(U_9894)))
    | ~ class_Fields_Olinordered__field(U_9894) ),
    inference(clausify,[status(thm)],[f_2426_2]) ).

fof(f_2427_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_2427_2,plain,
    ! [U_9900,U_9899,U_9898,U_9897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9897),U_9898),U_9900)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9897),U_9899),U_9900)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),c_Groups_Ozero__class_Ozero(U_9897)),U_9900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),U_9898),U_9899))
      | ~ class_Fields_Olinordered__field(U_9897) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

cnf(f_2427_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9897),U_9898),U_9900)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9897),U_9899),U_9900)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),c_Groups_Ozero__class_Ozero(U_9897)),U_9900))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9897),U_9898),U_9899))
    | ~ class_Fields_Olinordered__field(U_9897) ),
    inference(clausify,[status(thm)],[f_2427_2]) ).

fof(f_2428_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_2428_2,plain,
    ! [U_9904,U_9903,U_9902,U_9901] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9901),U_9903),U_9904)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9901),U_9902),U_9904)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),U_9904),c_Groups_Ozero__class_Ozero(U_9901)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),U_9902),U_9903))
      | ~ class_Fields_Olinordered__field(U_9901) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

cnf(f_2428_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9901),U_9903),U_9904)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9901),U_9902),U_9904)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),U_9904),c_Groups_Ozero__class_Ozero(U_9901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9901),U_9902),U_9903))
    | ~ class_Fields_Olinordered__field(U_9901) ),
    inference(clausify,[status(thm)],[f_2428_2]) ).

fof(f_2429_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) ) )
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).

fof(f_2429_2,plain,
    ! [U_9908,U_9907,U_9906,U_9905] :
      ( ( ( U_9906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
          | ( U_9906 != c_Groups_Ozero__class_Ozero(U_9905)
            & U_9908 = c_Groups_Ozero__class_Ozero(U_9905) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9905),U_9906),U_9908) != U_9907
            & U_9908 != c_Groups_Ozero__class_Ozero(U_9905) ) )
        & ( ( ( U_9906 = c_Groups_Ozero__class_Ozero(U_9905)
              | U_9908 != c_Groups_Ozero__class_Ozero(U_9905) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9905),U_9906),U_9908) = U_9907
              | U_9908 = c_Groups_Ozero__class_Ozero(U_9905) ) )
          | U_9906 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

cnf(f_2429_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9905),U_9906),U_9908) = U_9907
    | U_9908 = c_Groups_Ozero__class_Ozero(U_9905)
    | U_9906 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

cnf(f_2429_4,plain,
    ( U_9906 = c_Groups_Ozero__class_Ozero(U_9905)
    | U_9908 != c_Groups_Ozero__class_Ozero(U_9905)
    | U_9906 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

cnf(f_2429_5,plain,
    ( U_9908 = c_Groups_Ozero__class_Ozero(U_9905)
    | U_9908 != c_Groups_Ozero__class_Ozero(U_9905)
    | U_9906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

cnf(f_2429_6,plain,
    ( U_9906 != c_Groups_Ozero__class_Ozero(U_9905)
    | U_9908 != c_Groups_Ozero__class_Ozero(U_9905)
    | U_9906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

cnf(f_2429_7,plain,
    ( U_9908 = c_Groups_Ozero__class_Ozero(U_9905)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9905),U_9906),U_9908) != U_9907
    | U_9906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

cnf(f_2429_8,plain,
    ( U_9906 != c_Groups_Ozero__class_Ozero(U_9905)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9905),U_9906),U_9908) != U_9907
    | U_9906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9905),U_9907),U_9908)
    | ~ class_Fields_Ofield__inverse__zero(U_9905) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

fof(f_2430_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) != V_a_2 ) )
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).

fof(f_2430_2,plain,
    ! [U_9912,U_9911,U_9910,U_9909] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) = U_9912
          | ( U_9912 != c_Groups_Ozero__class_Ozero(U_9909)
            & U_9911 = c_Groups_Ozero__class_Ozero(U_9909) )
          | ( U_9910 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9909),U_9912),U_9911)
            & U_9911 != c_Groups_Ozero__class_Ozero(U_9909) ) )
        & ( ( ( U_9912 = c_Groups_Ozero__class_Ozero(U_9909)
              | U_9911 != c_Groups_Ozero__class_Ozero(U_9909) )
            & ( U_9910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9909),U_9912),U_9911)
              | U_9911 = c_Groups_Ozero__class_Ozero(U_9909) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) != U_9912 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

cnf(f_2430_3,plain,
    ( U_9910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9909),U_9912),U_9911)
    | U_9911 = c_Groups_Ozero__class_Ozero(U_9909)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) != U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

cnf(f_2430_4,plain,
    ( U_9912 = c_Groups_Ozero__class_Ozero(U_9909)
    | U_9911 != c_Groups_Ozero__class_Ozero(U_9909)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) != U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

cnf(f_2430_5,plain,
    ( U_9911 = c_Groups_Ozero__class_Ozero(U_9909)
    | U_9911 != c_Groups_Ozero__class_Ozero(U_9909)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) = U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

cnf(f_2430_6,plain,
    ( U_9912 != c_Groups_Ozero__class_Ozero(U_9909)
    | U_9911 != c_Groups_Ozero__class_Ozero(U_9909)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) = U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

cnf(f_2430_7,plain,
    ( U_9911 = c_Groups_Ozero__class_Ozero(U_9909)
    | U_9910 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9909),U_9912),U_9911)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) = U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

cnf(f_2430_8,plain,
    ( U_9912 != c_Groups_Ozero__class_Ozero(U_9909)
    | U_9910 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9909),U_9912),U_9911)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9909),U_9910),U_9911) = U_9912
    | ~ class_Fields_Ofield__inverse__zero(U_9909) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

fof(f_2431_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_2431_2,plain,
    ! [U_9916,U_9915,U_9914,U_9913] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9913),U_9915),U_9914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9913),U_9916),U_9914)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9913),U_9915),U_9916)
      | U_9914 = c_Groups_Ozero__class_Ozero(U_9913)
      | ~ class_Fields_Ofield__inverse__zero(U_9913) ),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

cnf(f_2431_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9913),U_9915),U_9914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9913),U_9916),U_9914)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9913),U_9915),U_9916)
    | U_9914 = c_Groups_Ozero__class_Ozero(U_9913)
    | ~ class_Fields_Ofield__inverse__zero(U_9913) ),
    inference(clausify,[status(thm)],[f_2431_2]) ).

fof(f_2432_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_2432_2,plain,
    ! [U_9920,U_9919,U_9918,U_9917] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),U_9918),U_9919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),U_9918),U_9920)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9917),U_9919),U_9920)
      | U_9918 = c_Groups_Ozero__class_Ozero(U_9917)
      | ~ class_Fields_Ofield__inverse__zero(U_9917) ),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

cnf(f_2432_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),U_9918),U_9919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),U_9918),U_9920)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9917),U_9919),U_9920)
    | U_9918 = c_Groups_Ozero__class_Ozero(U_9917)
    | ~ class_Fields_Ofield__inverse__zero(U_9917) ),
    inference(clausify,[status(thm)],[f_2432_2]) ).

fof(f_2433_1,plain,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) ) )
      | V_z_2 = c_Groups_Ozero__class_Ozero(T_a)
      | V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).

fof(f_2433_2,plain,
    ! [U_9925,U_9924,U_9923,U_9922,U_9921] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9924),U_9922) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9925),U_9923)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9924),U_9923) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9925),U_9922) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9924),U_9923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9925),U_9922)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9924),U_9922) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9925),U_9923) ) )
      | U_9923 = c_Groups_Ozero__class_Ozero(U_9921)
      | U_9922 = c_Groups_Ozero__class_Ozero(U_9921)
      | ~ class_Fields_Ofield(U_9921) ),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

cnf(f_2433_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9924),U_9923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9925),U_9922)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9924),U_9922) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9925),U_9923)
    | U_9923 = c_Groups_Ozero__class_Ozero(U_9921)
    | U_9922 = c_Groups_Ozero__class_Ozero(U_9921)
    | ~ class_Fields_Ofield(U_9921) ),
    inference(clausify,[status(thm)],[f_2433_2]) ).

cnf(f_2433_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9924),U_9922) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9921),U_9925),U_9923)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9924),U_9923) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9921),U_9925),U_9922)
    | U_9923 = c_Groups_Ozero__class_Ozero(U_9921)
    | U_9922 = c_Groups_Ozero__class_Ozero(U_9921)
    | ~ class_Fields_Ofield(U_9921) ),
    inference(clausify,[status(thm)],[f_2433_2]) ).

fof(f_2434_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_2434_2,plain,
    ! [U_9928,U_9927,U_9926] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_9926),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9926),U_9928),U_9927)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9926),hAPP(c_Groups_Oabs__class_Oabs(U_9926),U_9928)),hAPP(c_Groups_Oabs__class_Oabs(U_9926),U_9927))
      | U_9927 = c_Groups_Ozero__class_Ozero(U_9926)
      | ~ class_Fields_Olinordered__field(U_9926) ),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

cnf(f_2434_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_9926),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9926),U_9928),U_9927)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9926),hAPP(c_Groups_Oabs__class_Oabs(U_9926),U_9928)),hAPP(c_Groups_Oabs__class_Oabs(U_9926),U_9927))
    | U_9927 = c_Groups_Ozero__class_Ozero(U_9926)
    | ~ class_Fields_Olinordered__field(U_9926) ),
    inference(clausify,[status(thm)],[f_2434_2]) ).

fof(f_2435_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_2435_2,plain,
    ! [U_9931,U_9930,U_9929] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9929),U_9930),U_9931)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),U_9931))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),U_9930))
      | ~ class_Fields_Olinordered__field(U_9929) ),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

cnf(f_2435_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9929),U_9930),U_9931)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),U_9931))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9929),c_Groups_Ozero__class_Ozero(U_9929)),U_9930))
    | ~ class_Fields_Olinordered__field(U_9929) ),
    inference(clausify,[status(thm)],[f_2435_2]) ).

fof(f_2436_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_2436_2,plain,
    ! [U_9934,U_9933,U_9932] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9932),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9932),U_9933),U_9934)),c_Groups_Ozero__class_Ozero(U_9932)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9932),U_9934),c_Groups_Ozero__class_Ozero(U_9932)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9932),c_Groups_Ozero__class_Ozero(U_9932)),U_9933))
      | ~ class_Fields_Olinordered__field(U_9932) ),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

cnf(f_2436_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9932),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9932),U_9933),U_9934)),c_Groups_Ozero__class_Ozero(U_9932)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9932),U_9934),c_Groups_Ozero__class_Ozero(U_9932)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9932),c_Groups_Ozero__class_Ozero(U_9932)),U_9933))
    | ~ class_Fields_Olinordered__field(U_9932) ),
    inference(clausify,[status(thm)],[f_2436_2]) ).

fof(f_2437_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_2437_2,plain,
    ! [U_9939,U_9938,U_9937,U_9936,U_9935] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9935),U_9936),U_9939)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9935),U_9937),U_9938)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),U_9938),U_9939))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),c_Groups_Ozero__class_Ozero(U_9935)),U_9938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9935),U_9936),U_9937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),c_Groups_Ozero__class_Ozero(U_9935)),U_9936))
      | ~ class_Fields_Olinordered__field(U_9935) ),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

cnf(f_2437_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9935),U_9936),U_9939)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9935),U_9937),U_9938)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),U_9938),U_9939))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),c_Groups_Ozero__class_Ozero(U_9935)),U_9938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9935),U_9936),U_9937))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9935),c_Groups_Ozero__class_Ozero(U_9935)),U_9936))
    | ~ class_Fields_Olinordered__field(U_9935) ),
    inference(clausify,[status(thm)],[f_2437_2]) ).

fof(f_2438_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_2438_2,plain,
    ! [U_9944,U_9943,U_9942,U_9941,U_9940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9940),U_9941),U_9944)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9940),U_9942),U_9943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9940),U_9943),U_9944))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),c_Groups_Ozero__class_Ozero(U_9940)),U_9943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),U_9941),U_9942))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9940),c_Groups_Ozero__class_Ozero(U_9940)),U_9941))
      | ~ class_Fields_Olinordered__field(U_9940) ),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

cnf(f_2438_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9940),U_9941),U_9944)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9940),U_9942),U_9943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9940),U_9943),U_9944))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),c_Groups_Ozero__class_Ozero(U_9940)),U_9943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9940),U_9941),U_9942))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9940),c_Groups_Ozero__class_Ozero(U_9940)),U_9941))
    | ~ class_Fields_Olinordered__field(U_9940) ),
    inference(clausify,[status(thm)],[f_2438_2]) ).

fof(f_2439_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_2439_2,plain,
    ! [U_9949,U_9948,U_9947,U_9946,U_9945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9945),U_9946),U_9949)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9945),U_9947),U_9948)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),U_9948),U_9949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9945),c_Groups_Ozero__class_Ozero(U_9945)),U_9948))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),U_9946),U_9947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),c_Groups_Ozero__class_Ozero(U_9945)),U_9946))
      | ~ class_Fields_Olinordered__field(U_9945) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

cnf(f_2439_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9945),U_9946),U_9949)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9945),U_9947),U_9948)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),U_9948),U_9949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9945),c_Groups_Ozero__class_Ozero(U_9945)),U_9948))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),U_9946),U_9947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9945),c_Groups_Ozero__class_Ozero(U_9945)),U_9946))
    | ~ class_Fields_Olinordered__field(U_9945) ),
    inference(clausify,[status(thm)],[f_2439_2]) ).

fof(f_2440_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_2440_2,plain,
    ! [U_9952,U_9951,U_9950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9950),U_9951),U_9952)),c_Groups_Ozero__class_Ozero(U_9950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9950),c_Groups_Ozero__class_Ozero(U_9950)),U_9952))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9950),U_9951),c_Groups_Ozero__class_Ozero(U_9950)))
      | ~ class_Fields_Olinordered__field(U_9950) ),
    inference(variable_rename,[status(thm)],[f_2440_1]) ).

cnf(f_2440_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9950),U_9951),U_9952)),c_Groups_Ozero__class_Ozero(U_9950)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9950),c_Groups_Ozero__class_Ozero(U_9950)),U_9952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9950),U_9951),c_Groups_Ozero__class_Ozero(U_9950)))
    | ~ class_Fields_Olinordered__field(U_9950) ),
    inference(clausify,[status(thm)],[f_2440_2]) ).

fof(f_2441_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_2441_2,plain,
    ! [U_9955,U_9954,U_9953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9953),c_Groups_Ozero__class_Ozero(U_9953)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9953),U_9954),U_9955)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9953),U_9955),c_Groups_Ozero__class_Ozero(U_9953)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9953),U_9954),c_Groups_Ozero__class_Ozero(U_9953)))
      | ~ class_Fields_Olinordered__field(U_9953) ),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

cnf(f_2441_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9953),c_Groups_Ozero__class_Ozero(U_9953)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9953),U_9954),U_9955)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9953),U_9955),c_Groups_Ozero__class_Ozero(U_9953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9953),U_9954),c_Groups_Ozero__class_Ozero(U_9953)))
    | ~ class_Fields_Olinordered__field(U_9953) ),
    inference(clausify,[status(thm)],[f_2441_2]) ).

fof(f_2442_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_2442_2,plain,
    ! [U_9959,U_9958,U_9957,U_9956] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9956),U_9959),U_9957)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9956),U_9959),U_9958)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),c_Groups_Ozero__class_Ozero(U_9956)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9956),U_9957),U_9958)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),U_9959),c_Groups_Ozero__class_Ozero(U_9956)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),U_9957),U_9958))
      | ~ class_Fields_Olinordered__field(U_9956) ),
    inference(variable_rename,[status(thm)],[f_2442_1]) ).

cnf(f_2442_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9956),U_9959),U_9957)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9956),U_9959),U_9958)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),c_Groups_Ozero__class_Ozero(U_9956)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9956),U_9957),U_9958)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),U_9959),c_Groups_Ozero__class_Ozero(U_9956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9956),U_9957),U_9958))
    | ~ class_Fields_Olinordered__field(U_9956) ),
    inference(clausify,[status(thm)],[f_2442_2]) ).

fof(f_2443_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_2443_2,plain,
    ! [U_9963,U_9962,U_9961,U_9960] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),U_9963),U_9962)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),U_9963),U_9961)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),c_Groups_Ozero__class_Ozero(U_9960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9960),U_9962),U_9961)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),c_Groups_Ozero__class_Ozero(U_9960)),U_9963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),U_9961),U_9962))
      | ~ class_Fields_Olinordered__field(U_9960) ),
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

cnf(f_2443_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),U_9963),U_9962)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),U_9963),U_9961)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),c_Groups_Ozero__class_Ozero(U_9960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9960),U_9962),U_9961)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),c_Groups_Ozero__class_Ozero(U_9960)),U_9963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9960),U_9961),U_9962))
    | ~ class_Fields_Olinordered__field(U_9960) ),
    inference(clausify,[status(thm)],[f_2443_2]) ).

fof(f_2444_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).

fof(f_2444_2,plain,
    ! [U_9967,U_9966,U_9965,U_9964] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9964),U_9966),U_9965)),U_9967))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9964),U_9967),U_9965)),U_9966)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9964),U_9967),U_9965)),U_9966))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9964),U_9966),U_9965)),U_9967)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),U_9965),c_Groups_Ozero__class_Ozero(U_9964)))
      | ~ class_Fields_Olinordered__field(U_9964) ),
    inference(variable_rename,[status(thm)],[f_2444_1]) ).

cnf(f_2444_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9964),U_9967),U_9965)),U_9966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9964),U_9966),U_9965)),U_9967))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),U_9965),c_Groups_Ozero__class_Ozero(U_9964)))
    | ~ class_Fields_Olinordered__field(U_9964) ),
    inference(clausify,[status(thm)],[f_2444_2]) ).

cnf(f_2444_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9964),U_9966),U_9965)),U_9967))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9964),U_9967),U_9965)),U_9966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9964),U_9965),c_Groups_Ozero__class_Ozero(U_9964)))
    | ~ class_Fields_Olinordered__field(U_9964) ),
    inference(clausify,[status(thm)],[f_2444_2]) ).

fof(f_2445_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).

fof(f_2445_2,plain,
    ! [U_9971,U_9970,U_9969,U_9968] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9968),U_9971),U_9969)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9968),U_9970),U_9969))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9968),U_9970),U_9969)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9968),U_9971),U_9969))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9969),c_Groups_Ozero__class_Ozero(U_9968)))
      | ~ class_Fields_Olinordered__field(U_9968) ),
    inference(variable_rename,[status(thm)],[f_2445_1]) ).

cnf(f_2445_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9968),U_9970),U_9969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9968),U_9971),U_9969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9969),c_Groups_Ozero__class_Ozero(U_9968)))
    | ~ class_Fields_Olinordered__field(U_9968) ),
    inference(clausify,[status(thm)],[f_2445_2]) ).

cnf(f_2445_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9968),U_9971),U_9969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9968),U_9970),U_9969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9968),U_9969),c_Groups_Ozero__class_Ozero(U_9968)))
    | ~ class_Fields_Olinordered__field(U_9968) ),
    inference(clausify,[status(thm)],[f_2445_2]) ).

fof(f_2446_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_2446_2,plain,
    ! [U_9975,U_9974,U_9973,U_9972] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),U_9974),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9972),U_9975),U_9973)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9972),U_9974),U_9973)),U_9975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),c_Groups_Ozero__class_Ozero(U_9972)),U_9973))
      | ~ class_Fields_Olinordered__field(U_9972) ),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

cnf(f_2446_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),U_9974),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9972),U_9975),U_9973)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9972),U_9974),U_9973)),U_9975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9972),c_Groups_Ozero__class_Ozero(U_9972)),U_9973))
    | ~ class_Fields_Olinordered__field(U_9972) ),
    inference(clausify,[status(thm)],[f_2446_2]) ).

fof(f_2447_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_2447_2,plain,
    ! [U_9979,U_9978,U_9977,U_9976] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9976),U_9978),U_9977)),U_9979))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),U_9978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9976),U_9979),U_9977)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),c_Groups_Ozero__class_Ozero(U_9976)),U_9977))
      | ~ class_Fields_Olinordered__field(U_9976) ),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

cnf(f_2447_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9976),U_9978),U_9977)),U_9979))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),U_9978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9976),U_9979),U_9977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9976),c_Groups_Ozero__class_Ozero(U_9976)),U_9977))
    | ~ class_Fields_Olinordered__field(U_9976) ),
    inference(clausify,[status(thm)],[f_2447_2]) ).

fof(f_2448_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).

fof(f_2448_2,plain,
    ! [U_9983,U_9982,U_9981,U_9980] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9980),U_9982),U_9981)),U_9983))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),U_9982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9980),U_9983),U_9981))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),U_9982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9980),U_9983),U_9981)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9980),U_9982),U_9981)),U_9983)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),c_Groups_Ozero__class_Ozero(U_9980)),U_9981))
      | ~ class_Fields_Olinordered__field(U_9980) ),
    inference(variable_rename,[status(thm)],[f_2448_1]) ).

cnf(f_2448_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),U_9982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9980),U_9983),U_9981)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9980),U_9982),U_9981)),U_9983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),c_Groups_Ozero__class_Ozero(U_9980)),U_9981))
    | ~ class_Fields_Olinordered__field(U_9980) ),
    inference(clausify,[status(thm)],[f_2448_2]) ).

cnf(f_2448_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9980),U_9982),U_9981)),U_9983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),U_9982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9980),U_9983),U_9981)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9980),c_Groups_Ozero__class_Ozero(U_9980)),U_9981))
    | ~ class_Fields_Olinordered__field(U_9980) ),
    inference(clausify,[status(thm)],[f_2448_2]) ).

fof(f_2449_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).

fof(f_2449_2,plain,
    ! [U_9987,U_9986,U_9985,U_9984] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),U_9986),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9984),U_9987),U_9985)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9984),U_9986),U_9985)),U_9987)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9984),U_9986),U_9985)),U_9987))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),U_9986),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9984),U_9987),U_9985))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),c_Groups_Ozero__class_Ozero(U_9984)),U_9985))
      | ~ class_Fields_Olinordered__field(U_9984) ),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

cnf(f_2449_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9984),U_9986),U_9985)),U_9987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),U_9986),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9984),U_9987),U_9985)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),c_Groups_Ozero__class_Ozero(U_9984)),U_9985))
    | ~ class_Fields_Olinordered__field(U_9984) ),
    inference(clausify,[status(thm)],[f_2449_2]) ).

cnf(f_2449_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),U_9986),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9984),U_9987),U_9985)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9984),U_9986),U_9985)),U_9987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9984),c_Groups_Ozero__class_Ozero(U_9984)),U_9985))
    | ~ class_Fields_Olinordered__field(U_9984) ),
    inference(clausify,[status(thm)],[f_2449_2]) ).

fof(f_2450_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).

fof(f_2450_2,plain,
    ! [U_9991,U_9990,U_9989,U_9988] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

cnf(f_2450_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9990),c_Groups_Ozero__class_Ozero(U_9988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

cnf(f_2450_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),c_Groups_Ozero__class_Ozero(U_9988)),U_9991))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)),U_9989))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),U_9989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9988),U_9991),U_9990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9988),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9988),U_9989),U_9990)),U_9991))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9988) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

fof(f_2451_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).

fof(f_2451_2,plain,
    ! [U_9995,U_9994,U_9993,U_9992] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

cnf(f_2451_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),c_Groups_Ozero__class_Ozero(U_9992)),U_9995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9995),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

cnf(f_2451_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),c_Groups_Ozero__class_Ozero(U_9992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9992),U_9993),U_9995)),U_9994))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9992),U_9993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9992),U_9994),U_9995)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_9992) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

fof(f_2452_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_2452_2,plain,
    ! [U_10000,U_9999,U_9998,U_9997,U_9996] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9996),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),U_9999),U_9997)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),U_10000),U_9998)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_9999),U_9998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_10000),U_9997))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_9997),U_9998))
      | U_9998 = c_Groups_Ozero__class_Ozero(U_9996)
      | U_9997 = c_Groups_Ozero__class_Ozero(U_9996)
      | ~ class_Fields_Ofield(U_9996) ),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

cnf(f_2452_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9996),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),U_9999),U_9997)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),U_10000),U_9998)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_9999),U_9998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_10000),U_9997))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9996),U_9997),U_9998))
    | U_9998 = c_Groups_Ozero__class_Ozero(U_9996)
    | U_9997 = c_Groups_Ozero__class_Ozero(U_9996)
    | ~ class_Fields_Ofield(U_9996) ),
    inference(clausify,[status(thm)],[f_2452_2]) ).

fof(f_2453_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_2453_2,plain,
    ! [U_10004,U_10003,U_10002,U_10001] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10001),U_10003),U_10002)),U_10004) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10001),U_10003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10001),U_10002),U_10004))),U_10002)
      | U_10002 = c_Groups_Ozero__class_Ozero(U_10001)
      | ~ class_Fields_Ofield(U_10001) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

cnf(f_2453_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10001),U_10003),U_10002)),U_10004) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10001),U_10003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10001),U_10002),U_10004))),U_10002)
    | U_10002 = c_Groups_Ozero__class_Ozero(U_10001)
    | ~ class_Fields_Ofield(U_10001) ),
    inference(clausify,[status(thm)],[f_2453_2]) ).

fof(f_2454_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_2454_2,plain,
    ! [U_10008,U_10007,U_10006,U_10005] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10005),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10005),U_10007),U_10006)),U_10008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10005),U_10007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10005),U_10008),U_10006))),U_10006)
      | U_10006 = c_Groups_Ozero__class_Ozero(U_10005)
      | ~ class_Fields_Ofield__inverse__zero(U_10005) ),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

cnf(f_2454_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10005),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10005),U_10007),U_10006)),U_10008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10005),U_10007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10005),U_10008),U_10006))),U_10006)
    | U_10006 = c_Groups_Ozero__class_Ozero(U_10005)
    | ~ class_Fields_Ofield__inverse__zero(U_10005) ),
    inference(clausify,[status(thm)],[f_2454_2]) ).

fof(f_2455_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_2455_2,plain,
    ! [U_10012,U_10011,U_10010,U_10009] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10009),U_10011),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10009),U_10012),U_10010)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10009),U_10010),U_10011)),U_10012)),U_10010)
      | U_10010 = c_Groups_Ozero__class_Ozero(U_10009)
      | ~ class_Fields_Ofield(U_10009) ),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

cnf(f_2455_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10009),U_10011),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10009),U_10012),U_10010)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10009),U_10010),U_10011)),U_10012)),U_10010)
    | U_10010 = c_Groups_Ozero__class_Ozero(U_10009)
    | ~ class_Fields_Ofield(U_10009) ),
    inference(clausify,[status(thm)],[f_2455_2]) ).

fof(f_2456_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_2456_2,plain,
    ! [U_10016,U_10015,U_10014,U_10013] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10013),U_10015),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10013),U_10016),U_10014)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10013),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10013),U_10016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10013),U_10015),U_10014))),U_10014)
      | U_10014 = c_Groups_Ozero__class_Ozero(U_10013)
      | ~ class_Fields_Ofield__inverse__zero(U_10013) ),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

cnf(f_2456_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10013),U_10015),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10013),U_10016),U_10014)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10013),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10013),U_10016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10013),U_10015),U_10014))),U_10014)
    | U_10014 = c_Groups_Ozero__class_Ozero(U_10013)
    | ~ class_Fields_Ofield__inverse__zero(U_10013) ),
    inference(clausify,[status(thm)],[f_2456_2]) ).

fof(f_2457_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_2457_2,plain,
    ! [U_10020,U_10019,U_10018,U_10017] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10017),U_10019),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10017),U_10020),U_10018)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10017),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10017),U_10018),U_10019)),U_10020)),U_10018)
      | U_10018 = c_Groups_Ozero__class_Ozero(U_10017)
      | ~ class_Fields_Ofield(U_10017) ),
    inference(variable_rename,[status(thm)],[f_2457_1]) ).

cnf(f_2457_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10017),U_10019),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10017),U_10020),U_10018)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10017),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10017),U_10018),U_10019)),U_10020)),U_10018)
    | U_10018 = c_Groups_Ozero__class_Ozero(U_10017)
    | ~ class_Fields_Ofield(U_10017) ),
    inference(clausify,[status(thm)],[f_2457_2]) ).

fof(f_2458_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_2458_2,plain,
    ! [U_10024,U_10023,U_10022,U_10021] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10021),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10021),U_10023),U_10022)),U_10024) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10021),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10021),U_10023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10021),U_10022),U_10024))),U_10022)
      | U_10022 = c_Groups_Ozero__class_Ozero(U_10021)
      | ~ class_Fields_Ofield(U_10021) ),
    inference(variable_rename,[status(thm)],[f_2458_1]) ).

cnf(f_2458_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10021),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10021),U_10023),U_10022)),U_10024) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10021),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10021),U_10023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10021),U_10022),U_10024))),U_10022)
    | U_10022 = c_Groups_Ozero__class_Ozero(U_10021)
    | ~ class_Fields_Ofield(U_10021) ),
    inference(clausify,[status(thm)],[f_2458_2]) ).

fof(f_2459_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_2459_2,plain,
    ! [U_10029,U_10028,U_10027,U_10026,U_10025] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10025),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),U_10028),U_10026)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),U_10029),U_10027)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10028),U_10027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10029),U_10026))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10026),U_10027))
      | U_10027 = c_Groups_Ozero__class_Ozero(U_10025)
      | U_10026 = c_Groups_Ozero__class_Ozero(U_10025)
      | ~ class_Fields_Ofield(U_10025) ),
    inference(variable_rename,[status(thm)],[f_2459_1]) ).

cnf(f_2459_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10025),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),U_10028),U_10026)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),U_10029),U_10027)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10028),U_10027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10029),U_10026))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10025),U_10026),U_10027))
    | U_10027 = c_Groups_Ozero__class_Ozero(U_10025)
    | U_10026 = c_Groups_Ozero__class_Ozero(U_10025)
    | ~ class_Fields_Ofield(U_10025) ),
    inference(clausify,[status(thm)],[f_2459_2]) ).

fof(f_2460_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_2460_2,plain,
    ! [U_10032,U_10031,U_10030] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10030),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10030),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10030),U_10031),U_10032)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10030),c_Groups_Oone__class_Oone(U_10030)),c_Groups_Oone__class_Oone(U_10030)))),U_10032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10030),U_10031),U_10032))
      | ~ class_Fields_Olinordered__field(U_10030) ),
    inference(variable_rename,[status(thm)],[f_2460_1]) ).

cnf(f_2460_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10030),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10030),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10030),U_10031),U_10032)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10030),c_Groups_Oone__class_Oone(U_10030)),c_Groups_Oone__class_Oone(U_10030)))),U_10032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10030),U_10031),U_10032))
    | ~ class_Fields_Olinordered__field(U_10030) ),
    inference(clausify,[status(thm)],[f_2460_2]) ).

fof(f_2461_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_2461_2,plain,
    ! [U_10035,U_10034,U_10033] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10033),U_10034),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10033),U_10034),U_10035)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10033),c_Groups_Oone__class_Oone(U_10033)),c_Groups_Oone__class_Oone(U_10033)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10033),U_10034),U_10035))
      | ~ class_Fields_Olinordered__field(U_10033) ),
    inference(variable_rename,[status(thm)],[f_2461_1]) ).

cnf(f_2461_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10033),U_10034),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10033),U_10034),U_10035)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10033),c_Groups_Oone__class_Oone(U_10033)),c_Groups_Oone__class_Oone(U_10033)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10033),U_10034),U_10035))
    | ~ class_Fields_Olinordered__field(U_10033) ),
    inference(clausify,[status(thm)],[f_2461_2]) ).

fof(f_2462_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_2462_2,plain,
    ! [U_10038,U_10037,U_10036] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10036),hAPP(c_Groups_Oabs__class_Oabs(U_10036),U_10038)),U_10037) = hAPP(c_Groups_Oabs__class_Oabs(U_10036),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10036),U_10038),U_10037))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10036),c_Groups_Ozero__class_Ozero(U_10036)),U_10037))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_10036) ),
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

cnf(f_2462_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10036),hAPP(c_Groups_Oabs__class_Oabs(U_10036),U_10038)),U_10037) = hAPP(c_Groups_Oabs__class_Oabs(U_10036),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10036),U_10038),U_10037))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10036),c_Groups_Ozero__class_Ozero(U_10036)),U_10037))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_10036) ),
    inference(clausify,[status(thm)],[f_2462_2]) ).

fof(f_2463_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_2463_2,plain,
    ! [U_10042,U_10041,U_10040,U_10039] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10039),U_10042),U_10040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10039),U_10042),U_10041)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10039),c_Groups_Ozero__class_Ozero(U_10039)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10039),U_10040),U_10041)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),U_10042),c_Groups_Ozero__class_Ozero(U_10039)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),U_10040),U_10041))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_10039) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

cnf(f_2463_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10039),U_10042),U_10040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10039),U_10042),U_10041)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10039),c_Groups_Ozero__class_Ozero(U_10039)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10039),U_10040),U_10041)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),U_10042),c_Groups_Ozero__class_Ozero(U_10039)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10039),U_10040),U_10041))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_10039) ),
    inference(clausify,[status(thm)],[f_2463_2]) ).

fof(f_2464_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_2464_2,plain,
    ! [U_10046,U_10045,U_10044,U_10043] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10043),U_10046),U_10045)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10043),U_10046),U_10044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10043),c_Groups_Ozero__class_Ozero(U_10043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10043),U_10045),U_10044)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),c_Groups_Ozero__class_Ozero(U_10043)),U_10046))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),U_10044),U_10045))
      | ~ class_Fields_Olinordered__field(U_10043) ),
    inference(variable_rename,[status(thm)],[f_2464_1]) ).

cnf(f_2464_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10043),U_10046),U_10045)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10043),U_10046),U_10044)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10043),c_Groups_Ozero__class_Ozero(U_10043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10043),U_10045),U_10044)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),c_Groups_Ozero__class_Ozero(U_10043)),U_10046))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10043),U_10044),U_10045))
    | ~ class_Fields_Olinordered__field(U_10043) ),
    inference(clausify,[status(thm)],[f_2464_2]) ).

fof(f_2465_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).

fof(f_2465_2,plain,
    ! [U_10050,U_10049,U_10048,U_10047] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10047),U_10049),U_10048)),U_10050))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10047),U_10050),U_10048)),U_10049)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10047),U_10050),U_10048)),U_10049))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10047),U_10049),U_10048)),U_10050)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10047),U_10048),c_Groups_Ozero__class_Ozero(U_10047)))
      | ~ class_Fields_Olinordered__field(U_10047) ),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

cnf(f_2465_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10047),U_10050),U_10048)),U_10049))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10047),U_10049),U_10048)),U_10050))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10047),U_10048),c_Groups_Ozero__class_Ozero(U_10047)))
    | ~ class_Fields_Olinordered__field(U_10047) ),
    inference(clausify,[status(thm)],[f_2465_2]) ).

cnf(f_2465_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10047),U_10049),U_10048)),U_10050))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10047),U_10050),U_10048)),U_10049))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10047),U_10048),c_Groups_Ozero__class_Ozero(U_10047)))
    | ~ class_Fields_Olinordered__field(U_10047) ),
    inference(clausify,[status(thm)],[f_2465_2]) ).

fof(f_2466_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).

fof(f_2466_2,plain,
    ! [U_10054,U_10053,U_10052,U_10051] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10053),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10051),U_10054),U_10052)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10051),U_10053),U_10052))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10051),U_10053),U_10052)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10053),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10051),U_10054),U_10052))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10051),U_10052),c_Groups_Ozero__class_Ozero(U_10051)))
      | ~ class_Fields_Olinordered__field(U_10051) ),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

cnf(f_2466_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10051),U_10053),U_10052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10053),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10051),U_10054),U_10052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10051),U_10052),c_Groups_Ozero__class_Ozero(U_10051)))
    | ~ class_Fields_Olinordered__field(U_10051) ),
    inference(clausify,[status(thm)],[f_2466_2]) ).

cnf(f_2466_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10053),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10051),U_10054),U_10052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10051),U_10054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10051),U_10053),U_10052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10051),U_10052),c_Groups_Ozero__class_Ozero(U_10051)))
    | ~ class_Fields_Olinordered__field(U_10051) ),
    inference(clausify,[status(thm)],[f_2466_2]) ).

fof(f_2467_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_2467_2,plain,
    ! [U_10058,U_10057,U_10056,U_10055] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10055),U_10057),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10055),U_10058),U_10056)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10055),U_10057),U_10056)),U_10058))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10055),c_Groups_Ozero__class_Ozero(U_10055)),U_10056))
      | ~ class_Fields_Olinordered__field(U_10055) ),
    inference(variable_rename,[status(thm)],[f_2467_1]) ).

cnf(f_2467_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10055),U_10057),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10055),U_10058),U_10056)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10055),U_10057),U_10056)),U_10058))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10055),c_Groups_Ozero__class_Ozero(U_10055)),U_10056))
    | ~ class_Fields_Olinordered__field(U_10055) ),
    inference(clausify,[status(thm)],[f_2467_2]) ).

fof(f_2468_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_2468_2,plain,
    ! [U_10062,U_10061,U_10060,U_10059] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10059),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10059),U_10061),U_10060)),U_10062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10059),U_10061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10059),U_10062),U_10060)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10059),c_Groups_Ozero__class_Ozero(U_10059)),U_10060))
      | ~ class_Fields_Olinordered__field(U_10059) ),
    inference(variable_rename,[status(thm)],[f_2468_1]) ).

cnf(f_2468_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10059),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10059),U_10061),U_10060)),U_10062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10059),U_10061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10059),U_10062),U_10060)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10059),c_Groups_Ozero__class_Ozero(U_10059)),U_10060))
    | ~ class_Fields_Olinordered__field(U_10059) ),
    inference(clausify,[status(thm)],[f_2468_2]) ).

fof(f_2469_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).

fof(f_2469_2,plain,
    ! [U_10068,U_10067,U_10066,U_10065,U_10064] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10066)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)))
      | ? [U_10063] :
          ( hAPP(U_10068,U_10063) = c_Groups_Ozero__class_Ozero(U_10064)
          & hBOOL(hAPP(hAPP(c_member(U_10065),U_10063),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10067))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066))
      | ~ class_Fields_Ofield(U_10064) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

fof(f_2469_3,plain,
    ! [U_10068,U_10067,U_10066,U_10065,U_10064] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10066)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)))
      | ( hAPP(U_10068,sK236(U_10068,U_10067,U_10066,U_10065,U_10064)) = c_Groups_Ozero__class_Ozero(U_10064)
        & hBOOL(hAPP(hAPP(c_member(U_10065),sK236(U_10068,U_10067,U_10066,U_10065,U_10064)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10067))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066))
      | ~ class_Fields_Ofield(U_10064) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_10063,sK236(U_10068,U_10067,U_10066,U_10065,U_10064))],[f_2469_2]) ).

cnf(f_2469_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10065),sK236(U_10068,U_10067,U_10066,U_10065,U_10064)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10066)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10067))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066))
    | ~ class_Fields_Ofield(U_10064) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

cnf(f_2469_5,plain,
    ( hAPP(U_10068,sK236(U_10068,U_10067,U_10066,U_10065,U_10064)) = c_Groups_Ozero__class_Ozero(U_10064)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10066)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),U_10067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10065,U_10064),U_10068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10065,tc_HOL_Obool)),U_10066),U_10067)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10067))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10065),U_10066))
    | ~ class_Fields_Ofield(U_10064) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

fof(f_2470_1,plain,
    ! [V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),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_a),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).

fof(f_2470_2,plain,
    ! [U_10070,U_10069] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_10069,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10069),U_10070)) = 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_10069),U_10070))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10069),U_10070)) ),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

cnf(f_2470_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_10069,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10069),U_10070)) = 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_10069),U_10070))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10069),U_10070)) ),
    inference(clausify,[status(thm)],[f_2470_2]) ).

fof(f_2471_1,plain,
    ! [T_a] :
      ( c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).

fof(f_2471_2,plain,
    ! [U_10071] :
      ( c_Power_Opower__class_Opower(U_10071) = c_Power_Opower_Opower(U_10071,c_Groups_Oone__class_Oone(U_10071),c_Groups_Otimes__class_Otimes(U_10071))
      | ~ class_Power_Opower(U_10071) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

cnf(f_2471_3,plain,
    ( c_Power_Opower__class_Opower(U_10071) = c_Power_Opower_Opower(U_10071,c_Groups_Oone__class_Oone(U_10071),c_Groups_Otimes__class_Otimes(U_10071))
    | ~ class_Power_Opower(U_10071) ),
    inference(clausify,[status(thm)],[f_2471_2]) ).

fof(f_2472_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_2472_2,plain,
    ! [U_10073,U_10072] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10073),U_10072)),U_10073) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10072),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_10073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10072)) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

cnf(f_2472_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10073),U_10072)),U_10073) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10072),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_10073))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10072)) ),
    inference(clausify,[status(thm)],[f_2472_2]) ).

fof(f_2473_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_PowI]) ).

fof(f_2473_2,plain,
    ! [U_10076,U_10075,U_10074] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(c_Set_OPow(U_10074),U_10076)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),U_10076)) ),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

cnf(f_2473_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(c_Set_OPow(U_10074),U_10076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),U_10076)) ),
    inference(clausify,[status(thm)],[f_2473_2]) ).

fof(f_2474_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_2474_2,plain,
    ! [U_10078,U_10077] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10078)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10077)),U_10078),
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

cnf(f_2474_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10078)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10077)),U_10078),
    inference(clausify,[status(thm)],[f_2474_2]) ).

fof(f_2475_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_2475_2,plain,
    ! [U_10080,U_10079] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10079)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10080)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10079),U_10080),
    inference(variable_rename,[status(thm)],[f_2475_1]) ).

cnf(f_2475_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10079)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10080)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10079),U_10080),
    inference(clausify,[status(thm)],[f_2475_2]) ).

fof(f_2476_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_2476_2,plain,
    ! [U_10081] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10081) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

cnf(f_2476_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10081) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2476_2]) ).

fof(f_2477_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_2477_2,plain,
    ! [U_10083,U_10082] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10082),U_10083))
      | ~ c_Nat__Transfer_Ois__nat(U_10083)
      | ~ c_Nat__Transfer_Ois__nat(U_10082) ),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

cnf(f_2477_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10082),U_10083))
    | ~ c_Nat__Transfer_Ois__nat(U_10083)
    | ~ c_Nat__Transfer_Ois__nat(U_10082) ),
    inference(clausify,[status(thm)],[f_2477_2]) ).

fof(f_2478_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_2478_2,plain,
    ! [U_10085,U_10084] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10084),U_10085),c_Groups_Oone__class_Oone(U_10084)) = U_10085
      | ~ class_Divides_Osemiring__div(U_10084) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

cnf(f_2478_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10084),U_10085),c_Groups_Oone__class_Oone(U_10084)) = U_10085
    | ~ class_Divides_Osemiring__div(U_10084) ),
    inference(clausify,[status(thm)],[f_2478_2]) ).

fof(f_2479_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_2479_2,plain,
    ! [U_10087,U_10086] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10086),U_10087),c_Groups_Ozero__class_Ozero(U_10086)) = c_Groups_Ozero__class_Ozero(U_10086)
      | ~ class_Divides_Osemiring__div(U_10086) ),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

cnf(f_2479_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10086),U_10087),c_Groups_Ozero__class_Ozero(U_10086)) = c_Groups_Ozero__class_Ozero(U_10086)
    | ~ class_Divides_Osemiring__div(U_10086) ),
    inference(clausify,[status(thm)],[f_2479_2]) ).

fof(f_2480_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_2480_2,plain,
    ! [U_10089,U_10088] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10088),c_Groups_Ozero__class_Ozero(U_10088)),U_10089) = c_Groups_Ozero__class_Ozero(U_10088)
      | ~ class_Divides_Osemiring__div(U_10088) ),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

cnf(f_2480_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10088),c_Groups_Ozero__class_Ozero(U_10088)),U_10089) = c_Groups_Ozero__class_Ozero(U_10088)
    | ~ class_Divides_Osemiring__div(U_10088) ),
    inference(clausify,[status(thm)],[f_2480_2]) ).

fof(f_2481_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).

fof(f_2481_2,plain,
    ! [U_10091,U_10090] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_10090,tc_HOL_Obool)),U_10091),hAPP(c_Set_OPow(U_10090),U_10091))),
    inference(variable_rename,[status(thm)],[f_2481_1]) ).

cnf(f_2481_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_10090,tc_HOL_Obool)),U_10091),hAPP(c_Set_OPow(U_10090),U_10091))),
    inference(clausify,[status(thm)],[f_2481_2]) ).

fof(f_2482_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2)
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).

fof(f_2482_2,plain,
    ! [U_10096,U_10095,U_10094,U_10093,U_10092] :
      ( hAPP(c_Set_Oimage(tc_fun(U_10092,tc_HOL_Obool),tc_fun(U_10093,tc_HOL_Obool),c_Set_Oimage(U_10092,U_10093,U_10094)),hAPP(c_Set_OPow(U_10092),U_10095)) = hAPP(c_Set_OPow(U_10093),U_10096)
      | hAPP(c_Set_Oimage(U_10092,U_10093,U_10094),U_10095) != U_10096 ),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

cnf(f_2482_3,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_10092,tc_HOL_Obool),tc_fun(U_10093,tc_HOL_Obool),c_Set_Oimage(U_10092,U_10093,U_10094)),hAPP(c_Set_OPow(U_10092),U_10095)) = hAPP(c_Set_OPow(U_10093),U_10096)
    | hAPP(c_Set_Oimage(U_10092,U_10093,U_10094),U_10095) != U_10096 ),
    inference(clausify,[status(thm)],[f_2482_2]) ).

fof(f_2483_1,plain,
    ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).

fof(f_2483_2,plain,
    ! [U_10098,U_10097] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10097,tc_HOL_Obool),hAPP(c_Set_OPow(U_10097),U_10098)) = U_10098,
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

cnf(f_2483_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10097,tc_HOL_Obool),hAPP(c_Set_OPow(U_10097),U_10098)) = U_10098,
    inference(clausify,[status(thm)],[f_2483_2]) ).

fof(f_2484_1,plain,
    ! [V_A_2,T_a,B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) != hAPP(c_Set_OPow(T_a),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).

fof(f_2484_2,plain,
    ! [U_10101,U_10100,U_10099] : hAPP(c_Set_Oimage(U_10100,tc_fun(U_10100,tc_HOL_Obool),U_10099),U_10101) != hAPP(c_Set_OPow(U_10100),U_10101),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

cnf(f_2484_3,plain,
    hAPP(c_Set_Oimage(U_10100,tc_fun(U_10100,tc_HOL_Obool),U_10099),U_10101) != hAPP(c_Set_OPow(U_10100),U_10101),
    inference(clausify,[status(thm)],[f_2484_2]) ).

fof(f_2485_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).

fof(f_2485_2,plain,
    ! [U_10103,U_10102] : hAPP(c_Set_OPow(U_10102),U_10103) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10102,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2485_1]) ).

cnf(f_2485_3,plain,
    hAPP(c_Set_OPow(U_10102),U_10103) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10102,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2485_2]) ).

fof(f_2486_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).

fof(f_2486_2,plain,
    ! [U_10107,U_10106,U_10105,U_10104] : hAPP(c_Set_OPow(U_10104),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10105,tc_fun(U_10104,tc_HOL_Obool)),U_10106),U_10107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10105,tc_fun(tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool)),U_10106),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool),U_10105),c_Set_OPow(U_10104)),U_10107)),
    inference(variable_rename,[status(thm)],[f_2486_1]) ).

cnf(f_2486_3,plain,
    hAPP(c_Set_OPow(U_10104),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10105,tc_fun(U_10104,tc_HOL_Obool)),U_10106),U_10107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10105,tc_fun(tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool)),U_10106),hAPP(hAPP(c_COMBB(tc_fun(U_10104,tc_HOL_Obool),tc_fun(tc_fun(U_10104,tc_HOL_Obool),tc_HOL_Obool),U_10105),c_Set_OPow(U_10104)),U_10107)),
    inference(clausify,[status(thm)],[f_2486_2]) ).

fof(f_2487_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_2487_2,plain,
    ! [U_10109,U_10108] :
      ( 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_10108),U_10109)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10109))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10108)) ),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

cnf(f_2487_3,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_10108),U_10109)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10108)) ),
    inference(clausify,[status(thm)],[f_2487_2]) ).

fof(f_2488_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_2488_2,plain,
    ! [U_10111,U_10110] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10111),U_10110)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10111),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10111),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_10111),U_10110)),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_10110)) ),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

cnf(f_2488_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10111),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_10111),U_10110)),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_10110)) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

cnf(f_2488_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10111),U_10110)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10111),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_10110)) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

fof(f_2489_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_2489_2,plain,
    ! [U_10113,U_10112] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10113),U_10112)),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_10113)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10113))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10113),U_10112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

cnf(f_2489_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10113))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10113),U_10112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2489_2]) ).

cnf(f_2489_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10113),U_10112)),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_10113))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2489_2]) ).

fof(f_2490_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_2490_2,plain,
    ! [U_10115,U_10114] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10114),U_10115)),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_10115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10114),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2490_1]) ).

cnf(f_2490_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10114),U_10115)),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_10115))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10114),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2490_2]) ).

fof(f_2491_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_2491_2,plain,
    ! [U_10116] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10116),U_10116) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_10116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

cnf(f_2491_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10116),U_10116) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_10116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2491_2]) ).

fof(f_2492_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_2492_2,plain,
    ! [U_10120,U_10119,U_10118,U_10117] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10120)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),U_10119),U_10120)
          | U_10118 = c_Groups_Ozero__class_Ozero(U_10117) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10120)) = c_Groups_Ozero__class_Ozero(U_10117)
          | U_10118 != c_Groups_Ozero__class_Ozero(U_10117) ) )
      | ~ class_Divides_Osemiring__div(U_10117) ),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

cnf(f_2492_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10120)) = c_Groups_Ozero__class_Ozero(U_10117)
    | U_10118 != c_Groups_Ozero__class_Ozero(U_10117)
    | ~ class_Divides_Osemiring__div(U_10117) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

cnf(f_2492_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10117),U_10118),U_10120)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10117),U_10119),U_10120)
    | U_10118 = c_Groups_Ozero__class_Ozero(U_10117)
    | ~ class_Divides_Osemiring__div(U_10117) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

fof(f_2493_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_2493_2,plain,
    ! [U_10123,U_10122,U_10121] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10121),U_10123),U_10122)),U_10122) = U_10123
      | U_10122 = c_Groups_Ozero__class_Ozero(U_10121)
      | ~ class_Divides_Osemiring__div(U_10121) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

cnf(f_2493_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10121),U_10123),U_10122)),U_10122) = U_10123
    | U_10122 = c_Groups_Ozero__class_Ozero(U_10121)
    | ~ class_Divides_Osemiring__div(U_10121) ),
    inference(clausify,[status(thm)],[f_2493_2]) ).

fof(f_2494_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_2494_2,plain,
    ! [U_10126,U_10125,U_10124] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10124),U_10125),U_10126)),U_10125) = U_10126
      | U_10125 = c_Groups_Ozero__class_Ozero(U_10124)
      | ~ class_Divides_Osemiring__div(U_10124) ),
    inference(variable_rename,[status(thm)],[f_2494_1]) ).

cnf(f_2494_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10124),U_10125),U_10126)),U_10125) = U_10126
    | U_10125 = c_Groups_Ozero__class_Ozero(U_10124)
    | ~ class_Divides_Osemiring__div(U_10124) ),
    inference(clausify,[status(thm)],[f_2494_2]) ).

fof(f_2495_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_2495_2,plain,
    ! [U_10130,U_10129,U_10128,U_10127] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10127),U_10129),U_10128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10127),U_10130),U_10128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10127),U_10129),U_10130)
      | U_10128 = c_Groups_Ozero__class_Ozero(U_10127)
      | ~ class_Divides_Osemiring__div(U_10127) ),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

cnf(f_2495_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10127),U_10129),U_10128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10127),U_10130),U_10128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10127),U_10129),U_10130)
    | U_10128 = c_Groups_Ozero__class_Ozero(U_10127)
    | ~ class_Divides_Osemiring__div(U_10127) ),
    inference(clausify,[status(thm)],[f_2495_2]) ).

fof(f_2496_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_2496_2,plain,
    ! [U_10134,U_10133,U_10132,U_10131] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10131),U_10132),U_10133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10131),U_10132),U_10134)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10131),U_10133),U_10134)
      | U_10132 = c_Groups_Ozero__class_Ozero(U_10131)
      | ~ class_Divides_Osemiring__div(U_10131) ),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

cnf(f_2496_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10131),U_10132),U_10133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10131),U_10132),U_10134)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10131),U_10133),U_10134)
    | U_10132 = c_Groups_Ozero__class_Ozero(U_10131)
    | ~ class_Divides_Osemiring__div(U_10131) ),
    inference(clausify,[status(thm)],[f_2496_2]) ).

fof(f_2497_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_2497_2,plain,
    ! [U_10136,U_10135] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10135),U_10136),U_10136) = c_Groups_Oone__class_Oone(U_10135)
      | U_10136 = c_Groups_Ozero__class_Ozero(U_10135)
      | ~ class_Divides_Osemiring__div(U_10135) ),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

cnf(f_2497_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10135),U_10136),U_10136) = c_Groups_Oone__class_Oone(U_10135)
    | U_10136 = c_Groups_Ozero__class_Ozero(U_10135)
    | ~ class_Divides_Osemiring__div(U_10135) ),
    inference(clausify,[status(thm)],[f_2497_2]) ).

fof(f_2498_1,plain,
    ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).

fof(f_2498_2,plain,
    ! [U_10138,U_10137] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_10137,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10137,tc_HOL_Obool))),hAPP(c_Set_OPow(U_10137),U_10138))),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

cnf(f_2498_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_10137,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10137,tc_HOL_Obool))),hAPP(c_Set_OPow(U_10137),U_10138))),
    inference(clausify,[status(thm)],[f_2498_2]) ).

fof(f_2499_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_PowD]) ).

fof(f_2499_2,plain,
    ! [U_10141,U_10140,U_10139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10139,tc_HOL_Obool)),U_10140),U_10141))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10139,tc_HOL_Obool)),U_10140),hAPP(c_Set_OPow(U_10139),U_10141))) ),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

cnf(f_2499_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10139,tc_HOL_Obool)),U_10140),U_10141))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10139,tc_HOL_Obool)),U_10140),hAPP(c_Set_OPow(U_10139),U_10141))) ),
    inference(clausify,[status(thm)],[f_2499_2]) ).

fof(f_2500_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).

fof(f_2500_2,plain,
    ! [U_10144,U_10143,U_10142] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10142,tc_HOL_Obool)),U_10143),hAPP(c_Set_OPow(U_10142),U_10144)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10142,tc_HOL_Obool)),U_10143),U_10144)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10142,tc_HOL_Obool)),U_10143),U_10144))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10142,tc_HOL_Obool)),U_10143),hAPP(c_Set_OPow(U_10142),U_10144))) ) ),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

fof(f_2500_3,plain,
    ( ! [U_10150,U_10148,U_10146] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10146,tc_HOL_Obool)),U_10148),hAPP(c_Set_OPow(U_10146),U_10150)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10146,tc_HOL_Obool)),U_10148),U_10150)) )
    & ! [U_10149,U_10147,U_10145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10145,tc_HOL_Obool)),U_10147),U_10149))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10145,tc_HOL_Obool)),U_10147),hAPP(c_Set_OPow(U_10145),U_10149))) ) ),
    inference(miniscope,[status(thm)],[f_2500_2]) ).

cnf(f_2500_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10145,tc_HOL_Obool)),U_10147),U_10149))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10145,tc_HOL_Obool)),U_10147),hAPP(c_Set_OPow(U_10145),U_10149))) ),
    inference(clausify,[status(thm)],[f_2500_3]) ).

cnf(f_2500_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10146,tc_HOL_Obool)),U_10148),hAPP(c_Set_OPow(U_10146),U_10150)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10146,tc_HOL_Obool)),U_10148),U_10150)) ),
    inference(clausify,[status(thm)],[f_2500_3]) ).

fof(f_2501_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).

fof(f_2501_2,plain,
    ! [U_10153,U_10152,U_10151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10151,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10151),U_10152)),hAPP(c_Set_OPow(U_10151),U_10153)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10151,tc_HOL_Obool)),U_10152),U_10153)) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

cnf(f_2501_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10151,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10151),U_10152)),hAPP(c_Set_OPow(U_10151),U_10153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10151,tc_HOL_Obool)),U_10152),U_10153)) ),
    inference(clausify,[status(thm)],[f_2501_2]) ).

fof(f_2502_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_2502_2,plain,
    ! [U_10156,U_10155,U_10154] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10155),U_10156)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10154),U_10156)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10156),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10154),U_10155)) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

cnf(f_2502_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10155),U_10156)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10154),U_10156)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10156),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10154),U_10155)) ),
    inference(clausify,[status(thm)],[f_2502_2]) ).

fof(f_2503_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_2503_2,plain,
    ! [U_10159,U_10158,U_10157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10157),U_10159)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10158),U_10159)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10159))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10157),U_10158)) ),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

cnf(f_2503_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10157),U_10159)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10158),U_10159)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10159))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10157),U_10158)) ),
    inference(clausify,[status(thm)],[f_2503_2]) ).

fof(f_2504_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_2504_2,plain,
    ! [U_10161,U_10160] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10160),U_10161) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10161),U_10160))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10160),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

cnf(f_2504_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10160),U_10161) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10161),U_10160))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10160),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2504_2]) ).

fof(f_2505_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_2505_2,plain,
    ! [U_10164,U_10163,U_10162] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10162),U_10163)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10162),U_10164)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10163),U_10164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10163))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10162),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

cnf(f_2505_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10162),U_10163)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10162),U_10164)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10163),U_10164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10162),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2505_2]) ).

fof(f_2506_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_2506_2,plain,
    ! [U_10166,U_10165] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10165),U_10166)),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_10166))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

cnf(f_2506_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10165),U_10166)),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_10166))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2506_2]) ).

fof(f_2507_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_2507_2,plain,
    ! [U_10168,U_10167] :
      ( ( ( 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_10168),U_10167)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10168),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10168),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_10168),U_10167))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10167),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

cnf(f_2507_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10168),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_10168),U_10167)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10167),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2507_2]) ).

cnf(f_2507_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_10168),U_10167)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10168),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10167),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2507_2]) ).

fof(f_2508_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_2508_2,plain,
    ! [U_10170,U_10169] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10169),U_10170) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10169),U_10170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10169)) ),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

cnf(f_2508_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10169),U_10170) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10169),U_10170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10169)) ),
    inference(clausify,[status(thm)],[f_2508_2]) ).

fof(f_2509_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_2509_2,plain,
    ! [U_10172,U_10171] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10171),U_10172)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10172),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_10171)) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

cnf(f_2509_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10171),U_10172)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10172),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_10171)) ),
    inference(clausify,[status(thm)],[f_2509_2]) ).

fof(f_2510_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_2510_2,plain,
    ! [U_10175,U_10174,U_10173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10173),U_10175)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10173),U_10174)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10174),U_10175))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10174))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10173)) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

cnf(f_2510_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10173),U_10175)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10173),U_10174)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10174),U_10175))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10173)) ),
    inference(clausify,[status(thm)],[f_2510_2]) ).

fof(f_2511_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_2511_2,plain,
    ! [U_10177,U_10176] :
      ( ( ( 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_10176),U_10177)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10177))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10177),U_10176)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10177))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10177),U_10176)) )
          | ~ 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_10176),U_10177))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10176)) ),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

cnf(f_2511_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10177),U_10176))
    | ~ 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_10176),U_10177)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10176)) ),
    inference(clausify,[status(thm)],[f_2511_2]) ).

cnf(f_2511_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10177))
    | ~ 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_10176),U_10177)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10176)) ),
    inference(clausify,[status(thm)],[f_2511_2]) ).

cnf(f_2511_5,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_10176),U_10177)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10177),U_10176))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10176)) ),
    inference(clausify,[status(thm)],[f_2511_2]) ).

fof(f_2512_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_2512_2,plain,
    ! [U_10179,U_10178] :
      ( ( ( 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_10179),U_10178)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10178),U_10179)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10178),U_10179))
          | ~ 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_10179),U_10178))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10178)) ),
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

cnf(f_2512_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10178),U_10179))
    | ~ 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_10179),U_10178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10178)) ),
    inference(clausify,[status(thm)],[f_2512_2]) ).

cnf(f_2512_4,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_10179),U_10178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10178),U_10179))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10178)) ),
    inference(clausify,[status(thm)],[f_2512_2]) ).

fof(f_2513_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_2513_2,plain,
    ! [U_10181,U_10180] :
      ( ( ( 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_10181),U_10180)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10181)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10181))
          | ~ 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_10181),U_10180))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10180)) ),
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

cnf(f_2513_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10181))
    | ~ 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_10181),U_10180)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10180)) ),
    inference(clausify,[status(thm)],[f_2513_2]) ).

cnf(f_2513_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_10181),U_10180)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10181))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10180)) ),
    inference(clausify,[status(thm)],[f_2513_2]) ).

fof(f_2514_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_2514_2,plain,
    ! [U_10183,U_10182] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10182),U_10183) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10183),U_10182))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10182),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10182),U_10183))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10182)) )
          & U_10183 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10183),U_10182))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10182),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10182),U_10183))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10182)) )
        | U_10183 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10182),U_10183) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

fof(f_2514_3,plain,
    ( ! [U_10187,U_10185] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10185),U_10187) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10187),U_10185))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10185),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10185),U_10187))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10185)) )
          & U_10187 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10186,U_10184] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10186),U_10184))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10184),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10184),U_10186))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10184)) )
        | U_10186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10184),U_10186) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2514_2]) ).

cnf(f_2514_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10184),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_10184))
    | U_10186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10184),U_10186) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10186),U_10184))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10184))
    | U_10186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10184),U_10186) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10184),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10184),U_10186))
    | U_10186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10184),U_10186) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10186),U_10184))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10184),U_10186))
    | U_10186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10184),U_10186) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_8,plain,
    ( U_10187 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10185),U_10187) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10185),U_10187))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10185))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10185),U_10187) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

cnf(f_2514_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10187),U_10185))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10185),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10185),U_10187) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

fof(f_2515_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_2515_2,plain,
    ! [U_10189,U_10188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10188),U_10189)),U_10188))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_10189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10188)) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

cnf(f_2515_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10188),U_10189)),U_10188))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_10189))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10188)) ),
    inference(clausify,[status(thm)],[f_2515_2]) ).

fof(f_2516_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_2516_2,plain,
    ! [U_10192,U_10191,U_10190] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10192),U_10190)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10191),U_10192)),U_10190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10190)) ),
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

cnf(f_2516_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10192),U_10190)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10191),U_10192)),U_10190)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10190)) ),
    inference(clausify,[status(thm)],[f_2516_2]) ).

fof(f_2517_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).

fof(f_2517_2,plain,
    ! [U_10194,U_10193] : hAPP(c_Set_OPow(U_10193),U_10194) = hAPP(c_Set_OCollect(tc_fun(U_10193,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_10193,tc_HOL_Obool),tc_fun(U_10193,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_10193,tc_HOL_Obool))),U_10194)),
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

cnf(f_2517_3,plain,
    hAPP(c_Set_OPow(U_10193),U_10194) = hAPP(c_Set_OCollect(tc_fun(U_10193,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_10193,tc_HOL_Obool),tc_fun(U_10193,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_10193,tc_HOL_Obool))),U_10194)),
    inference(clausify,[status(thm)],[f_2517_2]) ).

fof(f_2518_1,plain,
    ! [V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).

fof(f_2518_2,plain,
    ! [U_10196,U_10195] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10195,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10195),U_10196)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10195),U_10196)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10195),U_10196))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10195,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10195),U_10196))) ) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

fof(f_2518_3,plain,
    ( ! [U_10200,U_10198] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10198,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10198),U_10200)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10198),U_10200)) )
    & ! [U_10199,U_10197] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10197),U_10199))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10197,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10197),U_10199))) ) ),
    inference(miniscope,[status(thm)],[f_2518_2]) ).

cnf(f_2518_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10197),U_10199))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10197,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10197),U_10199))) ),
    inference(clausify,[status(thm)],[f_2518_3]) ).

cnf(f_2518_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10198,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10198),U_10200)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10198),U_10200)) ),
    inference(clausify,[status(thm)],[f_2518_3]) ).

fof(f_2519_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).

fof(f_2519_2,plain,
    ! [U_10202,U_10201] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10201,tc_HOL_Obool),tc_HOL_Obool)),U_10202),hAPP(c_Set_OPow(U_10201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10201,tc_HOL_Obool),U_10202)))),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

cnf(f_2519_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10201,tc_HOL_Obool),tc_HOL_Obool)),U_10202),hAPP(c_Set_OPow(U_10201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10201,tc_HOL_Obool),U_10202)))),
    inference(clausify,[status(thm)],[f_2519_2]) ).

fof(f_2520_1,plain,
    ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_2520_2,plain,
    ! [U_10206,U_10205,U_10204,U_10203] : hAPP(hAPP(c_Power_Opower_Opower(U_10203,U_10204,U_10205),U_10206),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10204,
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

cnf(f_2520_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_10203,U_10204,U_10205),U_10206),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10204,
    inference(clausify,[status(thm)],[f_2520_2]) ).

fof(f_2521_1,plain,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_a,V_one_2,V_times_2),V_a_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(f_2521_2,plain,
    ! [U_10211,U_10210,U_10209,U_10208,U_10207] : hAPP(hAPP(c_Power_Opower_Opower(U_10207,U_10208,U_10209),U_10210),hAPP(c_Nat_OSuc,U_10211)) = hAPP(hAPP(U_10209,U_10210),hAPP(hAPP(c_Power_Opower_Opower(U_10207,U_10208,U_10209),U_10210),U_10211)),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

cnf(f_2521_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_10207,U_10208,U_10209),U_10210),hAPP(c_Nat_OSuc,U_10211)) = hAPP(hAPP(U_10209,U_10210),hAPP(hAPP(c_Power_Opower_Opower(U_10207,U_10208,U_10209),U_10210),U_10211)),
    inference(clausify,[status(thm)],[f_2521_2]) ).

fof(f_2522_1,plain,
    ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).

fof(f_2522_2,plain,
    ! [U_10214,U_10213,U_10212] : hAPP(c_Set_OPow(U_10212),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10213),U_10214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10212),U_10214)),hAPP(c_Set_Oimage(tc_fun(U_10212,tc_HOL_Obool),tc_fun(U_10212,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10212),U_10213)),hAPP(c_Set_OPow(U_10212),U_10214))),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

cnf(f_2522_3,plain,
    hAPP(c_Set_OPow(U_10212),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10213),U_10214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10212),U_10214)),hAPP(c_Set_Oimage(tc_fun(U_10212,tc_HOL_Obool),tc_fun(U_10212,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10212),U_10213)),hAPP(c_Set_OPow(U_10212),U_10214))),
    inference(clausify,[status(thm)],[f_2522_2]) ).

fof(f_2523_1,plain,
    ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).

fof(f_2523_2,plain,
    ! [U_10215] : hAPP(c_Set_OPow(U_10215),c_Orderings_Otop__class_Otop(tc_fun(U_10215,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_10215,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

cnf(f_2523_3,plain,
    hAPP(c_Set_OPow(U_10215),c_Orderings_Otop__class_Otop(tc_fun(U_10215,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_10215,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2523_2]) ).

fof(f_2524_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_2524_2,plain,
    ! [U_10219,U_10218,U_10217,U_10216] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10216),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10216),U_10218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10216),U_10217),U_10219))),U_10217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10216),U_10219),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10216),U_10218),U_10217))
      | U_10217 = c_Groups_Ozero__class_Ozero(U_10216)
      | ~ class_Divides_Osemiring__div(U_10216) ),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

cnf(f_2524_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10216),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10216),U_10218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10216),U_10217),U_10219))),U_10217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10216),U_10219),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10216),U_10218),U_10217))
    | U_10217 = c_Groups_Ozero__class_Ozero(U_10216)
    | ~ class_Divides_Osemiring__div(U_10216) ),
    inference(clausify,[status(thm)],[f_2524_2]) ).

fof(f_2525_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_2525_2,plain,
    ! [U_10223,U_10222,U_10221,U_10220] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10220),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10220),U_10222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10220),U_10223),U_10221))),U_10221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10220),U_10223),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10220),U_10222),U_10221))
      | U_10221 = c_Groups_Ozero__class_Ozero(U_10220)
      | ~ class_Divides_Osemiring__div(U_10220) ),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

cnf(f_2525_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10220),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10220),U_10222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10220),U_10223),U_10221))),U_10221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10220),U_10223),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10220),U_10222),U_10221))
    | U_10221 = c_Groups_Ozero__class_Ozero(U_10220)
    | ~ class_Divides_Osemiring__div(U_10220) ),
    inference(clausify,[status(thm)],[f_2525_2]) ).

fof(f_2526_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_2526_2,plain,
    ! [U_10226,U_10225,U_10224] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10224),U_10226),U_10225)),U_10225) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10224),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10224),U_10226),U_10225)),c_Groups_Oone__class_Oone(U_10224))
      | U_10225 = c_Groups_Ozero__class_Ozero(U_10224)
      | ~ class_Divides_Osemiring__div(U_10224) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

cnf(f_2526_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10224),U_10226),U_10225)),U_10225) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10224),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10224),U_10226),U_10225)),c_Groups_Oone__class_Oone(U_10224))
    | U_10225 = c_Groups_Ozero__class_Ozero(U_10224)
    | ~ class_Divides_Osemiring__div(U_10224) ),
    inference(clausify,[status(thm)],[f_2526_2]) ).

fof(f_2527_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_2527_2,plain,
    ! [U_10229,U_10228,U_10227] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10227),U_10228),U_10229)),U_10228) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10227),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10227),U_10229),U_10228)),c_Groups_Oone__class_Oone(U_10227))
      | U_10228 = c_Groups_Ozero__class_Ozero(U_10227)
      | ~ class_Divides_Osemiring__div(U_10227) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

cnf(f_2527_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10227),U_10228),U_10229)),U_10228) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10227),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10227),U_10229),U_10228)),c_Groups_Oone__class_Oone(U_10227))
    | U_10228 = c_Groups_Ozero__class_Ozero(U_10227)
    | ~ class_Divides_Osemiring__div(U_10227) ),
    inference(clausify,[status(thm)],[f_2527_2]) ).

fof(f_2528_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).

fof(f_2528_2,plain,
    ! [U_10233,U_10232,U_10231,U_10230] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool)),U_10232),hAPP(hAPP(c_COMBB(tc_fun(U_10230,tc_HOL_Obool),tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool),U_10231),c_Set_OPow(U_10230)),U_10233))),hAPP(c_Set_OPow(U_10230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,tc_fun(U_10230,tc_HOL_Obool)),U_10232),U_10233)))),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

cnf(f_2528_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool)),U_10232),hAPP(hAPP(c_COMBB(tc_fun(U_10230,tc_HOL_Obool),tc_fun(tc_fun(U_10230,tc_HOL_Obool),tc_HOL_Obool),U_10231),c_Set_OPow(U_10230)),U_10233))),hAPP(c_Set_OPow(U_10230),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,tc_fun(U_10230,tc_HOL_Obool)),U_10232),U_10233)))),
    inference(clausify,[status(thm)],[f_2528_2]) ).

fof(f_2529_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).

fof(f_2529_2,plain,
    ! [U_10236,U_10235,U_10234] : hAPP(c_Set_OPow(U_10234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool)),U_10235),U_10236)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_10234,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10234),U_10235)),hAPP(c_Set_OPow(U_10234),U_10236)),
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

cnf(f_2529_3,plain,
    hAPP(c_Set_OPow(U_10234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool)),U_10235),U_10236)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_10234,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10234),U_10235)),hAPP(c_Set_OPow(U_10234),U_10236)),
    inference(clausify,[status(thm)],[f_2529_2]) ).

fof(f_2530_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).

fof(f_2530_2,plain,
    ! [U_10241,U_10240,U_10239,U_10238,U_10237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10237,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10237,tc_HOL_Obool),c_Set_Oimage(U_10238,U_10237,U_10239)),hAPP(c_Set_OPow(U_10238),U_10240))),hAPP(c_Set_OPow(U_10237),U_10241)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10237,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10238,U_10237,U_10239),U_10240)),U_10241)) ),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

cnf(f_2530_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10237,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10238,tc_HOL_Obool),tc_fun(U_10237,tc_HOL_Obool),c_Set_Oimage(U_10238,U_10237,U_10239)),hAPP(c_Set_OPow(U_10238),U_10240))),hAPP(c_Set_OPow(U_10237),U_10241)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10237,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10238,U_10237,U_10239),U_10240)),U_10241)) ),
    inference(clausify,[status(thm)],[f_2530_2]) ).

fof(f_2531_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))),
    inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).

fof(f_2531_2,plain,
    ! [U_10243,U_10242] : hAPP(c_Set_OPow(U_10242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10242,tc_HOL_Obool)),U_10243)) = hAPP(c_Set_OCollect(tc_fun(U_10242,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_10242,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),c_COMBS(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),c_COMBB(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10242,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_10242,tc_HOL_Obool)),U_10243)),c_Set_OPow(U_10242))))),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

cnf(f_2531_3,plain,
    hAPP(c_Set_OPow(U_10242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10242,tc_HOL_Obool)),U_10243)) = hAPP(c_Set_OCollect(tc_fun(U_10242,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_10242,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),c_COMBS(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_10242,tc_HOL_Obool),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_fun(U_10242,tc_HOL_Obool)),tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_10242,tc_HOL_Obool)),c_COMBB(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10242,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10242,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_10242,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_10242,tc_HOL_Obool)),U_10243)),c_Set_OPow(U_10242))))),
    inference(clausify,[status(thm)],[f_2531_2]) ).

fof(f_2532_1,plain,
    ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).

fof(f_2532_2,plain,
    ! [U_10244] : hAPP(c_Set_OPow(U_10244),c_Orderings_Obot__class_Obot(tc_fun(U_10244,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10244,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10244,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10244,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

cnf(f_2532_3,plain,
    hAPP(c_Set_OPow(U_10244),c_Orderings_Obot__class_Obot(tc_fun(U_10244,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10244,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10244,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10244,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2532_2]) ).

fof(f_2533_1,plain,
    ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).

fof(f_2533_2,plain,
    ! [U_10247,U_10246,U_10245] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10245,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10245,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10245),U_10246)),hAPP(c_Set_OPow(U_10245),U_10247))),hAPP(c_Set_OPow(U_10245),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10245,tc_HOL_Obool)),U_10246),U_10247)))),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

cnf(f_2533_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10245,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10245,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10245),U_10246)),hAPP(c_Set_OPow(U_10245),U_10247))),hAPP(c_Set_OPow(U_10245),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10245,tc_HOL_Obool)),U_10246),U_10247)))),
    inference(clausify,[status(thm)],[f_2533_2]) ).

fof(f_2534_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).

fof(f_2534_2,plain,
    ! [U_10250,U_10249,U_10248] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_10248,hAPP(hAPP(c_COMBC(U_10248,tc_fun(U_10248,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10248)),U_10249)),U_10250))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10248,tc_HOL_Obool)),U_10250),hAPP(c_Set_OPow(U_10248),U_10249))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10248,tc_HOL_Obool)),U_10250),hAPP(c_Set_OPow(U_10248),U_10249)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10248,hAPP(hAPP(c_COMBC(U_10248,tc_fun(U_10248,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10248)),U_10249)),U_10250)) ) ),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

fof(f_2534_3,plain,
    ( ! [U_10256,U_10254,U_10252] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_10252,hAPP(hAPP(c_COMBC(U_10252,tc_fun(U_10252,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10252)),U_10254)),U_10256))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10252,tc_HOL_Obool)),U_10256),hAPP(c_Set_OPow(U_10252),U_10254))) )
    & ! [U_10255,U_10253,U_10251] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10251,tc_HOL_Obool)),U_10255),hAPP(c_Set_OPow(U_10251),U_10253)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10251,hAPP(hAPP(c_COMBC(U_10251,tc_fun(U_10251,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10251)),U_10253)),U_10255)) ) ),
    inference(miniscope,[status(thm)],[f_2534_2]) ).

cnf(f_2534_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10251,tc_HOL_Obool)),U_10255),hAPP(c_Set_OPow(U_10251),U_10253)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10251,hAPP(hAPP(c_COMBC(U_10251,tc_fun(U_10251,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10251)),U_10253)),U_10255)) ),
    inference(clausify,[status(thm)],[f_2534_3]) ).

cnf(f_2534_5,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_10252,hAPP(hAPP(c_COMBC(U_10252,tc_fun(U_10252,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10252)),U_10254)),U_10256))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10252,tc_HOL_Obool)),U_10256),hAPP(c_Set_OPow(U_10252),U_10254))) ),
    inference(clausify,[status(thm)],[f_2534_3]) ).

fof(f_2535_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_2535_2,plain,
    ! [U_10260,U_10259,U_10258,U_10257] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10257),U_10258) = U_10259
      | U_10258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10260),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10258),U_10260)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10260),U_10258))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10260)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258)) )
      | U_10257 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10258),U_10259)),U_10260) ),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

cnf(f_2535_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10257),U_10258) = U_10259
    | U_10258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10257 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10258),U_10259)),U_10260) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

cnf(f_2535_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10260),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10258),U_10260))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10257),U_10258) = U_10259
    | U_10258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10257 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10258),U_10259)),U_10260) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

cnf(f_2535_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10260),U_10258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10260))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10257),U_10258) = U_10259
    | U_10258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10257 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10258),U_10259)),U_10260) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

cnf(f_2535_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10260),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10258),U_10260))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10260),U_10258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10260))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10257),U_10258) = U_10259
    | U_10258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10257 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10258),U_10259)),U_10260) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

fof(f_2536_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).

fof(f_2536_2,plain,
    ! [U_10271,U_10270,U_10269] :
      ( ( hBOOL(hAPP(U_10269,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10270),U_10271)))
        | ( ? [U_10268] :
              ( ~ hBOOL(hAPP(U_10269,U_10268))
              & ? [U_10267] :
                  ( U_10270 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10271),U_10268)),U_10267)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10271),U_10267)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10271),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_10266] :
              ( ~ hBOOL(hAPP(U_10269,U_10266))
              & ? [U_10265] :
                  ( U_10270 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10271),U_10266)),U_10265)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10265),U_10271))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10265)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10271)) )
        | ( ~ hBOOL(hAPP(U_10269,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10271 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10269,U_10264))
                | ! [U_10263] :
                    ( U_10270 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10271),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10271),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10271),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10269,U_10262))
                | ! [U_10261] :
                    ( U_10270 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10271),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10271))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10271)) )
          & ( hBOOL(hAPP(U_10269,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10271 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10269,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10270),U_10271))) ) ),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

fof(f_2536_3,plain,
    ( ! [U_10277,U_10275,U_10273] :
        ( hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277)))
        | ( ? [U_10268] :
              ( ~ hBOOL(hAPP(U_10273,U_10268))
              & ? [U_10267] :
                  ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),U_10268)),U_10267)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),U_10267)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_10266] :
              ( ~ hBOOL(hAPP(U_10273,U_10266))
              & ? [U_10265] :
                  ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),U_10266)),U_10265)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10265),U_10277))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10265)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277)) )
        | ( ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10276,U_10274,U_10272] :
        ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10272,U_10264))
                | ! [U_10263] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10272,U_10262))
                | ! [U_10261] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276)) )
          & ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ) ),
    inference(miniscope,[status(thm)],[f_2536_2]) ).

fof(f_2536_4,plain,
    ( ! [U_10277,U_10275,U_10273] :
        ( hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277)))
        | ( ? [U_10268] :
              ( ~ hBOOL(hAPP(U_10273,U_10268))
              & ? [U_10267] :
                  ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),U_10268)),U_10267)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),U_10267)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
          & ? [U_10265] :
              ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),U_10265)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10265),U_10277))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10265)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277)) )
        | ( ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10276,U_10274,U_10272] :
        ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10272,U_10264))
                | ! [U_10263] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10272,U_10262))
                | ! [U_10261] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276)) )
          & ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_10266,sK237(U_10277,U_10275,U_10273))],[f_2536_3]) ).

fof(f_2536_5,plain,
    ( ! [U_10277,U_10275,U_10273] :
        ( hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277)))
        | ( ? [U_10268] :
              ( ~ hBOOL(hAPP(U_10273,U_10268))
              & ? [U_10267] :
                  ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),U_10268)),U_10267)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),U_10267)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
          & U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277)) )
        | ( ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10276,U_10274,U_10272] :
        ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10272,U_10264))
                | ! [U_10263] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10272,U_10262))
                | ! [U_10261] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276)) )
          & ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_10265,sK238(U_10277,U_10275,U_10273))],[f_2536_4]) ).

fof(f_2536_6,plain,
    ( ! [U_10277,U_10275,U_10273] :
        ( hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277)))
        | ( ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
          & ? [U_10267] :
              ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),U_10267)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),U_10267)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
          & U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277)) )
        | ( ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10276,U_10274,U_10272] :
        ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10272,U_10264))
                | ! [U_10263] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10272,U_10262))
                | ! [U_10261] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276)) )
          & ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_10268,sK239(U_10277,U_10275,U_10273))],[f_2536_5]) ).

fof(f_2536_7,plain,
    ( ! [U_10277,U_10275,U_10273] :
        ( hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277)))
        | ( ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
          & U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
          & U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277)) )
        | ( ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10276,U_10274,U_10272] :
        ( ( ( ! [U_10264] :
                ( hBOOL(hAPP(U_10272,U_10264))
                | ! [U_10263] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10262] :
                ( hBOOL(hAPP(U_10272,U_10262))
                | ! [U_10261] :
                    ( U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276)) )
          & ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_10267,sK240(U_10277,U_10275,U_10273))],[f_2536_6]) ).

cnf(f_2536_8,plain,
    ( hBOOL(hAPP(U_10272,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10276 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_9,plain,
    ( hBOOL(hAPP(U_10272,U_10262))
    | U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10262)),U_10261)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10261),U_10276))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10261))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10276))
    | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_10,plain,
    ( hBOOL(hAPP(U_10272,U_10264))
    | U_10274 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10276),U_10264)),U_10263)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),U_10263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10276),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10272,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10274),U_10276))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_14,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_15,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_19,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_20,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_24,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_25,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_29,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_30,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_34,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_35,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_39,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_40,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | U_10277 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_44,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_45,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10277),sK240(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_49,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_50,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK240(U_10277,U_10275,U_10273)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_54,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_55,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK239(U_10277,U_10275,U_10273))),sK240(U_10277,U_10275,U_10273))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK238(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK238(U_10277,U_10275,U_10273)),U_10277))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_59,plain,
    ( U_10275 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10277),sK237(U_10277,U_10275,U_10273))),sK238(U_10277,U_10275,U_10273))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

cnf(f_2536_60,plain,
    ( ~ hBOOL(hAPP(U_10273,sK237(U_10277,U_10275,U_10273)))
    | ~ hBOOL(hAPP(U_10273,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10273,sK239(U_10277,U_10275,U_10273)))
    | hBOOL(hAPP(U_10273,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10275),U_10277))) ),
    inference(clausify,[status(thm)],[f_2536_7]) ).

fof(f_2537_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_2537_2,plain,
    ! [U_10279,U_10278] :
      ( ( c_SMT_Oz3div(U_10279,U_10278) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10279),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10278)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10278)) )
      & ( c_SMT_Oz3div(U_10279,U_10278) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10279),U_10278)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10278)) ) ),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

fof(f_2537_3,plain,
    ( ! [U_10283,U_10281] :
        ( c_SMT_Oz3div(U_10283,U_10281) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10283),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10281)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10281)) )
    & ! [U_10282,U_10280] :
        ( c_SMT_Oz3div(U_10282,U_10280) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10282),U_10280)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10280)) ) ),
    inference(miniscope,[status(thm)],[f_2537_2]) ).

cnf(f_2537_4,plain,
    ( c_SMT_Oz3div(U_10282,U_10280) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10282),U_10280)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10280)) ),
    inference(clausify,[status(thm)],[f_2537_3]) ).

cnf(f_2537_5,plain,
    ( c_SMT_Oz3div(U_10283,U_10281) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10283),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10281)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10281)) ),
    inference(clausify,[status(thm)],[f_2537_3]) ).

fof(f_2538_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).

fof(f_2538_2,plain,
    ! [U_10288,U_10287,U_10286] :
      ( hAPP(U_10287,c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),U_10288)) = c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),hAPP(c_Set_Oimage(U_10286,U_10286,U_10287),U_10288))
      | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10286,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10286),U_10288))
      | ? [U_10285,U_10284] : hAPP(U_10287,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),U_10285),U_10284)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),hAPP(U_10287,U_10285)),hAPP(U_10287,U_10284))
      | ~ class_Orderings_Olinorder(U_10286) ),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

fof(f_2538_3,plain,
    ! [U_10288,U_10287,U_10286] :
      ( hAPP(U_10287,c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),U_10288)) = c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),hAPP(c_Set_Oimage(U_10286,U_10286,U_10287),U_10288))
      | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10286,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10286),U_10288))
      | ? [U_10284] : hAPP(U_10287,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),sK241(U_10288,U_10287,U_10286)),U_10284)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),hAPP(U_10287,sK241(U_10288,U_10287,U_10286))),hAPP(U_10287,U_10284))
      | ~ class_Orderings_Olinorder(U_10286) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_10285,sK241(U_10288,U_10287,U_10286))],[f_2538_2]) ).

fof(f_2538_4,plain,
    ! [U_10288,U_10287,U_10286] :
      ( hAPP(U_10287,c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),U_10288)) = c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),hAPP(c_Set_Oimage(U_10286,U_10286,U_10287),U_10288))
      | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10286,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10286),U_10288))
      | hAPP(U_10287,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),sK241(U_10288,U_10287,U_10286)),sK242(U_10288,U_10287,U_10286))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),hAPP(U_10287,sK241(U_10288,U_10287,U_10286))),hAPP(U_10287,sK242(U_10288,U_10287,U_10286)))
      | ~ class_Orderings_Olinorder(U_10286) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_10284,sK242(U_10288,U_10287,U_10286))],[f_2538_3]) ).

cnf(f_2538_5,plain,
    ( hAPP(U_10287,c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),U_10288)) = c_Big__Operators_Olattice_OSup__fin(U_10286,c_Orderings_Oord__class_Omax(U_10286),hAPP(c_Set_Oimage(U_10286,U_10286,U_10287),U_10288))
    | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10286,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10286),U_10288))
    | hAPP(U_10287,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),sK241(U_10288,U_10287,U_10286)),sK242(U_10288,U_10287,U_10286))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10286),hAPP(U_10287,sK241(U_10288,U_10287,U_10286))),hAPP(U_10287,sK242(U_10288,U_10287,U_10286)))
    | ~ class_Orderings_Olinorder(U_10286) ),
    inference(clausify,[status(thm)],[f_2538_4]) ).

fof(f_2539_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).

fof(f_2539_2,plain,
    ! [U_10293,U_10292,U_10291] :
      ( hAPP(U_10292,c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),U_10293)) = c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),hAPP(c_Set_Oimage(U_10291,U_10291,U_10292),U_10293))
      | U_10293 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10293))
      | ? [U_10290,U_10289] : hAPP(U_10292,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),U_10290),U_10289)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),hAPP(U_10292,U_10290)),hAPP(U_10292,U_10289))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

fof(f_2539_3,plain,
    ! [U_10293,U_10292,U_10291] :
      ( hAPP(U_10292,c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),U_10293)) = c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),hAPP(c_Set_Oimage(U_10291,U_10291,U_10292),U_10293))
      | U_10293 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10293))
      | ? [U_10289] : hAPP(U_10292,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK243(U_10293,U_10292,U_10291)),U_10289)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),hAPP(U_10292,sK243(U_10293,U_10292,U_10291))),hAPP(U_10292,U_10289))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_10290,sK243(U_10293,U_10292,U_10291))],[f_2539_2]) ).

fof(f_2539_4,plain,
    ! [U_10293,U_10292,U_10291] :
      ( hAPP(U_10292,c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),U_10293)) = c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),hAPP(c_Set_Oimage(U_10291,U_10291,U_10292),U_10293))
      | U_10293 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10293))
      | hAPP(U_10292,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK243(U_10293,U_10292,U_10291)),sK244(U_10293,U_10292,U_10291))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),hAPP(U_10292,sK243(U_10293,U_10292,U_10291))),hAPP(U_10292,sK244(U_10293,U_10292,U_10291)))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_10289,sK244(U_10293,U_10292,U_10291))],[f_2539_3]) ).

cnf(f_2539_5,plain,
    ( hAPP(U_10292,c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),U_10293)) = c_Big__Operators_Olattice_OInf__fin(U_10291,c_Orderings_Oord__class_Omin(U_10291),hAPP(c_Set_Oimage(U_10291,U_10291,U_10292),U_10293))
    | U_10293 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10293))
    | hAPP(U_10292,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK243(U_10293,U_10292,U_10291)),sK244(U_10293,U_10292,U_10291))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),hAPP(U_10292,sK243(U_10293,U_10292,U_10291))),hAPP(U_10292,sK244(U_10293,U_10292,U_10291)))
    | ~ class_Orderings_Olinorder(U_10291) ),
    inference(clausify,[status(thm)],[f_2539_4]) ).

fof(f_2540_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).

fof(f_2540_2,plain,
    ! [U_10298,U_10297,U_10296] :
      ( hAPP(U_10297,c_Big__Operators_Olinorder__class_OMax(U_10296,U_10298)) = c_Big__Operators_Olinorder__class_OMax(U_10296,hAPP(c_Set_Oimage(U_10296,U_10296,U_10297),U_10298))
      | U_10298 = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10298))
      | ? [U_10295,U_10294] : hAPP(U_10297,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),U_10295),U_10294)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),hAPP(U_10297,U_10295)),hAPP(U_10297,U_10294))
      | ~ class_Orderings_Olinorder(U_10296) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

fof(f_2540_3,plain,
    ! [U_10298,U_10297,U_10296] :
      ( hAPP(U_10297,c_Big__Operators_Olinorder__class_OMax(U_10296,U_10298)) = c_Big__Operators_Olinorder__class_OMax(U_10296,hAPP(c_Set_Oimage(U_10296,U_10296,U_10297),U_10298))
      | U_10298 = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10298))
      | ? [U_10294] : hAPP(U_10297,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),sK245(U_10298,U_10297,U_10296)),U_10294)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),hAPP(U_10297,sK245(U_10298,U_10297,U_10296))),hAPP(U_10297,U_10294))
      | ~ class_Orderings_Olinorder(U_10296) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_10295,sK245(U_10298,U_10297,U_10296))],[f_2540_2]) ).

fof(f_2540_4,plain,
    ! [U_10298,U_10297,U_10296] :
      ( hAPP(U_10297,c_Big__Operators_Olinorder__class_OMax(U_10296,U_10298)) = c_Big__Operators_Olinorder__class_OMax(U_10296,hAPP(c_Set_Oimage(U_10296,U_10296,U_10297),U_10298))
      | U_10298 = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10298))
      | hAPP(U_10297,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),sK245(U_10298,U_10297,U_10296)),sK246(U_10298,U_10297,U_10296))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),hAPP(U_10297,sK245(U_10298,U_10297,U_10296))),hAPP(U_10297,sK246(U_10298,U_10297,U_10296)))
      | ~ class_Orderings_Olinorder(U_10296) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_10294,sK246(U_10298,U_10297,U_10296))],[f_2540_3]) ).

cnf(f_2540_5,plain,
    ( hAPP(U_10297,c_Big__Operators_Olinorder__class_OMax(U_10296,U_10298)) = c_Big__Operators_Olinorder__class_OMax(U_10296,hAPP(c_Set_Oimage(U_10296,U_10296,U_10297),U_10298))
    | U_10298 = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10298))
    | hAPP(U_10297,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),sK245(U_10298,U_10297,U_10296)),sK246(U_10298,U_10297,U_10296))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10296),hAPP(U_10297,sK245(U_10298,U_10297,U_10296))),hAPP(U_10297,sK246(U_10298,U_10297,U_10296)))
    | ~ class_Orderings_Olinorder(U_10296) ),
    inference(clausify,[status(thm)],[f_2540_4]) ).

fof(f_2541_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_2541_2,plain,
    ! [U_10300,U_10299] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10299),U_10300)),U_10299)),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

cnf(f_2541_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10299),U_10300)),U_10299)),
    inference(clausify,[status(thm)],[f_2541_2]) ).

fof(f_2542_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_2542_2,plain,
    ! [U_10303,U_10302,U_10301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10301),U_10303)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10302),U_10303)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302)) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

cnf(f_2542_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10301),U_10303)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10302),U_10303)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10301),U_10302)) ),
    inference(clausify,[status(thm)],[f_2542_2]) ).

fof(f_2543_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_2543_2,plain,
    ! [U_10306,U_10305,U_10304] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10305),U_10306)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10304),U_10305)),U_10306),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

cnf(f_2543_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10305),U_10306)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10304),U_10305)),U_10306),
    inference(clausify,[status(thm)],[f_2543_2]) ).

fof(f_2544_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_2544_2,plain,
    ! [U_10307] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10307),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_10307,
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

cnf(f_2544_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10307),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_10307,
    inference(clausify,[status(thm)],[f_2544_2]) ).

fof(f_2545_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_2545_2,plain,
    ! [U_10309,U_10308] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10308),U_10309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10308),U_10309)) ),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

cnf(f_2545_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10308),U_10309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10308),U_10309)) ),
    inference(clausify,[status(thm)],[f_2545_2]) ).

fof(f_2546_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_2546_2,plain,
    ! [U_10312,U_10311,U_10310] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10310),U_10311)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10310),U_10312)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10311),U_10312)
        | U_10310 = 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_10310),U_10311)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10310),U_10312)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_10310 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

fof(f_2546_3,plain,
    ( ! [U_10318,U_10316,U_10314] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10314),U_10316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10314),U_10318)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10316),U_10318)
        | U_10314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_10317,U_10315,U_10313] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10313),U_10315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10313),U_10317)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_10313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2546_2]) ).

cnf(f_2546_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10313),U_10315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10313),U_10317)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_10313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2546_3]) ).

cnf(f_2546_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10314),U_10316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10314),U_10318)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10316),U_10318)
    | U_10314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2546_3]) ).

fof(f_2547_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_2547_2,plain,
    ! [U_10320,U_10319] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10319),U_10320)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10320)),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

cnf(f_2547_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10319),U_10320)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10320)),
    inference(clausify,[status(thm)],[f_2547_2]) ).

fof(f_2548_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_2548_2,plain,
    ! [U_10322,U_10321] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10321)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10322)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10321),U_10322)),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

cnf(f_2548_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10321)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10322)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10321),U_10322)),
    inference(clausify,[status(thm)],[f_2548_2]) ).

fof(f_2549_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_2549_2,plain,
    ! [U_10325,U_10324,U_10323] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10325),U_10324)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10325),U_10323)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10323),U_10324))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10323)) ),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

cnf(f_2549_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10325),U_10324)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10325),U_10323)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10323),U_10324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10323)) ),
    inference(clausify,[status(thm)],[f_2549_2]) ).

fof(f_2550_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_2550_2,plain,
    ! [U_10327,U_10326] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10326),U_10327)),U_10326) = U_10327
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10326)) ),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

cnf(f_2550_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10326),U_10327)),U_10326) = U_10327
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10326)) ),
    inference(clausify,[status(thm)],[f_2550_2]) ).

fof(f_2551_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_2551_2,plain,
    ! [U_10329,U_10328] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10329),U_10328)),U_10328) = U_10329
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10328)) ),
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

cnf(f_2551_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10329),U_10328)),U_10328) = U_10329
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10328)) ),
    inference(clausify,[status(thm)],[f_2551_2]) ).

fof(f_2552_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_2552_2,plain,
    ! [U_10332,U_10331,U_10330] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10330),U_10331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10330),U_10332)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10331),U_10332)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10330)) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

cnf(f_2552_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10330),U_10331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10330),U_10332)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10331),U_10332)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10330)) ),
    inference(clausify,[status(thm)],[f_2552_2]) ).

fof(f_2553_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_2553_2,plain,
    ! [U_10334,U_10333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10334),U_10333)),U_10334))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10334))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10333)) ),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

cnf(f_2553_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10334),U_10333)),U_10334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10333)) ),
    inference(clausify,[status(thm)],[f_2553_2]) ).

fof(f_2554_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_2554_2,plain,
    ! [U_10336,U_10335] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10336),U_10335) = 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_10336),U_10335)),U_10335))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10336),U_10335)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10336),U_10335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10336),U_10335)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10335)) ),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

cnf(f_2554_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10336),U_10335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10336),U_10335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10335)) ),
    inference(clausify,[status(thm)],[f_2554_2]) ).

cnf(f_2554_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10336),U_10335) = 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_10336),U_10335)),U_10335))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10336),U_10335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10335)) ),
    inference(clausify,[status(thm)],[f_2554_2]) ).

fof(f_2555_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_2555_2,plain,
    ! [U_10338,U_10337] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10338),U_10337) = 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_10338),U_10337)),U_10337))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10338),U_10337))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10337)) ),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

cnf(f_2555_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10338),U_10337) = 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_10338),U_10337)),U_10337))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10338),U_10337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10337)) ),
    inference(clausify,[status(thm)],[f_2555_2]) ).

fof(f_2556_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div]) ).

fof(f_2556_2,plain,
    ! [U_10345,U_10344,U_10343] :
      ( ( hBOOL(hAPP(U_10343,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10344),U_10345)))
        | ( ? [U_10342,U_10341] :
              ( ~ hBOOL(hAPP(U_10343,U_10342))
              & U_10344 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10345),U_10342)),U_10341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10341),U_10345)) )
          & U_10345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_10340,U_10339] :
                ( hBOOL(hAPP(U_10343,U_10340))
                | U_10344 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10345),U_10340)),U_10339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10339),U_10345)) )
            | U_10345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10343,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10344),U_10345))) ) ),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

fof(f_2556_3,plain,
    ( ! [U_10351,U_10349,U_10347] :
        ( hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351)))
        | ( ? [U_10342,U_10341] :
              ( ~ hBOOL(hAPP(U_10347,U_10342))
              & U_10349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10351),U_10342)),U_10341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10341),U_10351)) )
          & U_10351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10350,U_10348,U_10346] :
        ( ( ( ! [U_10340,U_10339] :
                ( hBOOL(hAPP(U_10346,U_10340))
                | U_10348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10350),U_10340)),U_10339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10339),U_10350)) )
            | U_10350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10348),U_10350))) ) ),
    inference(miniscope,[status(thm)],[f_2556_2]) ).

fof(f_2556_4,plain,
    ( ! [U_10351,U_10349,U_10347] :
        ( hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351)))
        | ( ? [U_10341] :
              ( ~ hBOOL(hAPP(U_10347,sK247(U_10351,U_10349,U_10347)))
              & U_10349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10351),sK247(U_10351,U_10349,U_10347))),U_10341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10341),U_10351)) )
          & U_10351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10350,U_10348,U_10346] :
        ( ( ( ! [U_10340,U_10339] :
                ( hBOOL(hAPP(U_10346,U_10340))
                | U_10348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10350),U_10340)),U_10339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10339),U_10350)) )
            | U_10350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10348),U_10350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_10342,sK247(U_10351,U_10349,U_10347))],[f_2556_3]) ).

fof(f_2556_5,plain,
    ( ! [U_10351,U_10349,U_10347] :
        ( hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351)))
        | ( ~ hBOOL(hAPP(U_10347,sK247(U_10351,U_10349,U_10347)))
          & U_10349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10351),sK247(U_10351,U_10349,U_10347))),sK248(U_10351,U_10349,U_10347))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK248(U_10351,U_10349,U_10347)),U_10351))
          & U_10351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10350,U_10348,U_10346] :
        ( ( ( ! [U_10340,U_10339] :
                ( hBOOL(hAPP(U_10346,U_10340))
                | U_10348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10350),U_10340)),U_10339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10339),U_10350)) )
            | U_10350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10348),U_10350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_10341,sK248(U_10351,U_10349,U_10347))],[f_2556_4]) ).

cnf(f_2556_6,plain,
    ( hBOOL(hAPP(U_10346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_10350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10348),U_10350))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_7,plain,
    ( hBOOL(hAPP(U_10346,U_10340))
    | U_10348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10350),U_10340)),U_10339)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10339),U_10350))
    | U_10350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10348),U_10350))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_8,plain,
    ( U_10351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK248(U_10351,U_10349,U_10347)),U_10351))
    | U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_10,plain,
    ( U_10349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10351),sK247(U_10351,U_10349,U_10347))),sK248(U_10351,U_10349,U_10347))
    | U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_11,plain,
    ( ~ hBOOL(hAPP(U_10347,sK247(U_10351,U_10349,U_10347)))
    | U_10351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_12,plain,
    ( U_10351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK248(U_10351,U_10349,U_10347)),U_10351))
    | ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_14,plain,
    ( U_10349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10351),sK247(U_10351,U_10349,U_10347))),sK248(U_10351,U_10349,U_10347))
    | ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

cnf(f_2556_15,plain,
    ( ~ hBOOL(hAPP(U_10347,sK247(U_10351,U_10349,U_10347)))
    | ~ hBOOL(hAPP(U_10347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_10347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10349),U_10351))) ),
    inference(clausify,[status(thm)],[f_2556_5]) ).

fof(f_2557_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_2557_2,plain,
    ! [U_10353,U_10352] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_10352)),hAPP(c_Int_Onat,U_10353)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10352),U_10353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10352)) ),
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

cnf(f_2557_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_10352)),hAPP(c_Int_Onat,U_10353)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10352),U_10353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10352)) ),
    inference(clausify,[status(thm)],[f_2557_2]) ).

fof(f_2558_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_2558_2,plain,
    ! [U_10355,U_10354] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10354),U_10355)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_10354)),hAPP(c_Int_Onat,U_10355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10354)) ),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

cnf(f_2558_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10354),U_10355)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_10354)),hAPP(c_Int_Onat,U_10355))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10354)) ),
    inference(clausify,[status(thm)],[f_2558_2]) ).

fof(f_2559_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_2559_2,plain,
    ! [U_10357,U_10356] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10357),U_10356) = 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_10357),U_10356)),U_10356))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10356),U_10357))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10356)) ),
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

cnf(f_2559_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10357),U_10356) = 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_10357),U_10356)),U_10356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10356),U_10357))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10356)) ),
    inference(clausify,[status(thm)],[f_2559_2]) ).

fof(f_2560_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_2560_2,plain,
    ! [U_10360,U_10359,U_10358] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),hAPP(c_Nat_OSuc,U_10359))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),U_10359)),U_10360)) )
          | U_10359 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10360),U_10358) )
        & ( U_10359 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10360),U_10358)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),hAPP(c_Nat_OSuc,U_10359))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),U_10359)),U_10360)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10358)) ),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

cnf(f_2560_3,plain,
    ( U_10359 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10360),U_10358)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),hAPP(c_Nat_OSuc,U_10359))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),U_10359)),U_10360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10358)) ),
    inference(clausify,[status(thm)],[f_2560_2]) ).

cnf(f_2560_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_10358),U_10359)),U_10360))
    | U_10359 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10360),U_10358)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10358)) ),
    inference(clausify,[status(thm)],[f_2560_2]) ).

cnf(f_2560_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10358),hAPP(c_Nat_OSuc,U_10359))))
    | U_10359 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10360),U_10358)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10358)) ),
    inference(clausify,[status(thm)],[f_2560_2]) ).

fof(f_2561_1,plain,
    ! [V_n_2,V_m_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_P_2,B_q))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
          & ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).

fof(f_2561_2,plain,
    ! [U_10365,U_10364,U_10363] :
      ( ( hBOOL(hAPP(U_10363,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10364),U_10365)))
        | ( ! [U_10362] :
              ( ~ hBOOL(hAPP(U_10363,U_10362))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10365),hAPP(c_Nat_OSuc,U_10362))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10365),U_10362)),U_10364)) )
          & ( ~ hBOOL(hAPP(U_10363,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10365 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_10361] :
            ( hBOOL(hAPP(U_10363,U_10361))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10365),hAPP(c_Nat_OSuc,U_10361))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10365),U_10361)),U_10364)) )
        | ( hBOOL(hAPP(U_10363,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_10363,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10364),U_10365))) ) ),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ( ! [U_10371,U_10369,U_10367] :
        ( hBOOL(hAPP(U_10367,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10369),U_10371)))
        | ( ! [U_10362] :
              ( ~ hBOOL(hAPP(U_10367,U_10362))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),hAPP(c_Nat_OSuc,U_10362))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),U_10362)),U_10369)) )
          & ( ~ hBOOL(hAPP(U_10367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_10370,U_10368,U_10366] :
        ( ? [U_10361] :
            ( hBOOL(hAPP(U_10366,U_10361))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),hAPP(c_Nat_OSuc,U_10361))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),U_10361)),U_10368)) )
        | ( hBOOL(hAPP(U_10366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ) ),
    inference(miniscope,[status(thm)],[f_2561_2]) ).

fof(f_2561_4,plain,
    ( ! [U_10371,U_10369,U_10367] :
        ( hBOOL(hAPP(U_10367,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10369),U_10371)))
        | ( ! [U_10362] :
              ( ~ hBOOL(hAPP(U_10367,U_10362))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),hAPP(c_Nat_OSuc,U_10362))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),U_10362)),U_10369)) )
          & ( ~ hBOOL(hAPP(U_10367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_10371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_10370,U_10368,U_10366] :
        ( ( hBOOL(hAPP(U_10366,sK249(U_10370,U_10368,U_10366)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),hAPP(c_Nat_OSuc,sK249(U_10370,U_10368,U_10366)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),sK249(U_10370,U_10368,U_10366))),U_10368)) )
        | ( hBOOL(hAPP(U_10366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_10370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_10361,sK249(U_10370,U_10368,U_10366))],[f_2561_3]) ).

cnf(f_2561_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),sK249(U_10370,U_10368,U_10366))),U_10368))
    | U_10370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),hAPP(c_Nat_OSuc,sK249(U_10370,U_10368,U_10366)))))
    | U_10370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_7,plain,
    ( hBOOL(hAPP(U_10366,sK249(U_10370,U_10368,U_10366)))
    | U_10370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),sK249(U_10370,U_10368,U_10366))),U_10368))
    | hBOOL(hAPP(U_10366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10370),hAPP(c_Nat_OSuc,sK249(U_10370,U_10368,U_10366)))))
    | hBOOL(hAPP(U_10366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_10,plain,
    ( hBOOL(hAPP(U_10366,sK249(U_10370,U_10368,U_10366)))
    | hBOOL(hAPP(U_10366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_10366,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10368),U_10370))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_11,plain,
    ( ~ hBOOL(hAPP(U_10367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_10371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10367,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10369),U_10371))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

cnf(f_2561_12,plain,
    ( ~ hBOOL(hAPP(U_10367,U_10362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),hAPP(c_Nat_OSuc,U_10362))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10371),U_10362)),U_10369))
    | hBOOL(hAPP(U_10367,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10369),U_10371))) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

fof(f_2562_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_2562_2,plain,
    ! [U_10373,U_10372] : c_Nitpick_Onat__lcm(U_10372,U_10373) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10372),U_10373)),c_Nitpick_Onat__gcd(U_10372,U_10373)),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

cnf(f_2562_3,plain,
    c_Nitpick_Onat__lcm(U_10372,U_10373) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10372),U_10373)),c_Nitpick_Onat__gcd(U_10372,U_10373)),
    inference(clausify,[status(thm)],[f_2562_2]) ).

fof(f_2563_1,plain,
    ! [V_N_2,V_h_2,T_a] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).

fof(f_2563_2,plain,
    ! [U_10378,U_10377,U_10376] :
      ( hAPP(U_10377,c_Big__Operators_Olinorder__class_OMin(U_10376,U_10378)) = c_Big__Operators_Olinorder__class_OMin(U_10376,hAPP(c_Set_Oimage(U_10376,U_10376,U_10377),U_10378))
      | U_10378 = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10378))
      | ? [U_10375,U_10374] : hAPP(U_10377,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),U_10375),U_10374)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),hAPP(U_10377,U_10375)),hAPP(U_10377,U_10374))
      | ~ class_Orderings_Olinorder(U_10376) ),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

fof(f_2563_3,plain,
    ! [U_10378,U_10377,U_10376] :
      ( hAPP(U_10377,c_Big__Operators_Olinorder__class_OMin(U_10376,U_10378)) = c_Big__Operators_Olinorder__class_OMin(U_10376,hAPP(c_Set_Oimage(U_10376,U_10376,U_10377),U_10378))
      | U_10378 = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10378))
      | ? [U_10374] : hAPP(U_10377,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),sK250(U_10378,U_10377,U_10376)),U_10374)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),hAPP(U_10377,sK250(U_10378,U_10377,U_10376))),hAPP(U_10377,U_10374))
      | ~ class_Orderings_Olinorder(U_10376) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_10375,sK250(U_10378,U_10377,U_10376))],[f_2563_2]) ).

fof(f_2563_4,plain,
    ! [U_10378,U_10377,U_10376] :
      ( hAPP(U_10377,c_Big__Operators_Olinorder__class_OMin(U_10376,U_10378)) = c_Big__Operators_Olinorder__class_OMin(U_10376,hAPP(c_Set_Oimage(U_10376,U_10376,U_10377),U_10378))
      | U_10378 = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10378))
      | hAPP(U_10377,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),sK250(U_10378,U_10377,U_10376)),sK251(U_10378,U_10377,U_10376))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),hAPP(U_10377,sK250(U_10378,U_10377,U_10376))),hAPP(U_10377,sK251(U_10378,U_10377,U_10376)))
      | ~ class_Orderings_Olinorder(U_10376) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_10374,sK251(U_10378,U_10377,U_10376))],[f_2563_3]) ).

cnf(f_2563_5,plain,
    ( hAPP(U_10377,c_Big__Operators_Olinorder__class_OMin(U_10376,U_10378)) = c_Big__Operators_Olinorder__class_OMin(U_10376,hAPP(c_Set_Oimage(U_10376,U_10376,U_10377),U_10378))
    | U_10378 = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10378))
    | hAPP(U_10377,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),sK250(U_10378,U_10377,U_10376)),sK251(U_10378,U_10377,U_10376))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10376),hAPP(U_10377,sK250(U_10378,U_10377,U_10376))),hAPP(U_10377,sK251(U_10378,U_10377,U_10376)))
    | ~ class_Orderings_Olinorder(U_10376) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

fof(f_2564_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_2564_2,plain,
    ! [U_10380] :
      ( ? [U_10379] : U_10380 = 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_10379)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10380),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

fof(f_2564_3,plain,
    ! [U_10380] :
      ( U_10380 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK252(U_10380))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10380),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_10379,sK252(U_10380))],[f_2564_2]) ).

cnf(f_2564_4,plain,
    ( U_10380 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK252(U_10380))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10380),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

fof(f_2565_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong]) ).

fof(f_2565_2,plain,
    ! [U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10384,U_10382),U_10389),U_10387) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10383,U_10382),U_10388),U_10386)
      | ? [U_10381] :
          ( hAPP(U_10388,U_10381) != hAPP(hAPP(c_Fun_Ocomp(U_10384,U_10382,U_10383,U_10389),U_10385),U_10381)
          & hBOOL(hAPP(hAPP(c_member(U_10383),U_10381),U_10386)) )
      | U_10387 != hAPP(c_Set_Oimage(U_10383,U_10384,U_10385),U_10386)
      | ~ c_Fun_Oinj__on(U_10383,U_10384,U_10385,U_10386)
      | ~ class_Groups_Ocomm__monoid__mult(U_10382) ),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

fof(f_2565_3,plain,
    ! [U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10384,U_10382),U_10389),U_10387) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10383,U_10382),U_10388),U_10386)
      | ( hAPP(U_10388,sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382)) != hAPP(hAPP(c_Fun_Ocomp(U_10384,U_10382,U_10383,U_10389),U_10385),sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382))
        & hBOOL(hAPP(hAPP(c_member(U_10383),sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382)),U_10386)) )
      | U_10387 != hAPP(c_Set_Oimage(U_10383,U_10384,U_10385),U_10386)
      | ~ c_Fun_Oinj__on(U_10383,U_10384,U_10385,U_10386)
      | ~ class_Groups_Ocomm__monoid__mult(U_10382) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_10381,sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382))],[f_2565_2]) ).

cnf(f_2565_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10383),sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382)),U_10386))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10384,U_10382),U_10389),U_10387) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10383,U_10382),U_10388),U_10386)
    | U_10387 != hAPP(c_Set_Oimage(U_10383,U_10384,U_10385),U_10386)
    | ~ c_Fun_Oinj__on(U_10383,U_10384,U_10385,U_10386)
    | ~ class_Groups_Ocomm__monoid__mult(U_10382) ),
    inference(clausify,[status(thm)],[f_2565_3]) ).

cnf(f_2565_5,plain,
    ( hAPP(U_10388,sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382)) != hAPP(hAPP(c_Fun_Ocomp(U_10384,U_10382,U_10383,U_10389),U_10385),sK253(U_10389,U_10388,U_10387,U_10386,U_10385,U_10384,U_10383,U_10382))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10384,U_10382),U_10389),U_10387) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10383,U_10382),U_10388),U_10386)
    | U_10387 != hAPP(c_Set_Oimage(U_10383,U_10384,U_10385),U_10386)
    | ~ c_Fun_Oinj__on(U_10383,U_10384,U_10385,U_10386)
    | ~ class_Groups_Ocomm__monoid__mult(U_10382) ),
    inference(clausify,[status(thm)],[f_2565_3]) ).

fof(f_2566_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_2566_2,plain,
    ! [U_10391,U_10390] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_10390),U_10391) = 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_10390)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10391)))),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

cnf(f_2566_3,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_10390),U_10391) = 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_10390)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10391)))),
    inference(clausify,[status(thm)],[f_2566_2]) ).

fof(f_2567_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).

fof(f_2567_2,plain,
    ! [U_10397,U_10396,U_10395,U_10394,U_10393] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10396) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10395)
      | ? [U_10392] :
          ( hAPP(U_10397,U_10392) != c_Groups_Oone__class_Oone(U_10393)
          & hBOOL(hAPP(hAPP(c_member(U_10394),U_10392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10394,tc_HOL_Obool)),U_10395),U_10396))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10394,tc_HOL_Obool)),U_10396),U_10395))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10394),U_10395))
      | ~ class_Groups_Ocomm__monoid__mult(U_10393) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

fof(f_2567_3,plain,
    ! [U_10397,U_10396,U_10395,U_10394,U_10393] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10396) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10395)
      | ( hAPP(U_10397,sK254(U_10397,U_10396,U_10395,U_10394,U_10393)) != c_Groups_Oone__class_Oone(U_10393)
        & hBOOL(hAPP(hAPP(c_member(U_10394),sK254(U_10397,U_10396,U_10395,U_10394,U_10393)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10394,tc_HOL_Obool)),U_10395),U_10396))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10394,tc_HOL_Obool)),U_10396),U_10395))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10394),U_10395))
      | ~ class_Groups_Ocomm__monoid__mult(U_10393) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_10392,sK254(U_10397,U_10396,U_10395,U_10394,U_10393))],[f_2567_2]) ).

cnf(f_2567_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10394),sK254(U_10397,U_10396,U_10395,U_10394,U_10393)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10394,tc_HOL_Obool)),U_10395),U_10396)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10396) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10395)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10394,tc_HOL_Obool)),U_10396),U_10395))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10394),U_10395))
    | ~ class_Groups_Ocomm__monoid__mult(U_10393) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

cnf(f_2567_5,plain,
    ( hAPP(U_10397,sK254(U_10397,U_10396,U_10395,U_10394,U_10393)) != c_Groups_Oone__class_Oone(U_10393)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10396) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10394,U_10393),U_10397),U_10395)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10394,tc_HOL_Obool)),U_10396),U_10395))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10394),U_10395))
    | ~ class_Groups_Ocomm__monoid__mult(U_10393) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

fof(f_2568_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).

fof(f_2568_2,plain,
    ! [U_10403,U_10402,U_10401,U_10400,U_10399] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10402)
      | ? [U_10398] :
          ( hAPP(U_10403,U_10398) != c_Groups_Oone__class_Oone(U_10399)
          & hBOOL(hAPP(hAPP(c_member(U_10400),U_10398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10400,tc_HOL_Obool)),U_10401),U_10402))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10400,tc_HOL_Obool)),U_10402),U_10401))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10400),U_10401))
      | ~ class_Groups_Ocomm__monoid__mult(U_10399) ),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

fof(f_2568_3,plain,
    ! [U_10403,U_10402,U_10401,U_10400,U_10399] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10402)
      | ( hAPP(U_10403,sK255(U_10403,U_10402,U_10401,U_10400,U_10399)) != c_Groups_Oone__class_Oone(U_10399)
        & hBOOL(hAPP(hAPP(c_member(U_10400),sK255(U_10403,U_10402,U_10401,U_10400,U_10399)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10400,tc_HOL_Obool)),U_10401),U_10402))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10400,tc_HOL_Obool)),U_10402),U_10401))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10400),U_10401))
      | ~ class_Groups_Ocomm__monoid__mult(U_10399) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_10398,sK255(U_10403,U_10402,U_10401,U_10400,U_10399))],[f_2568_2]) ).

cnf(f_2568_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10400),sK255(U_10403,U_10402,U_10401,U_10400,U_10399)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10400,tc_HOL_Obool)),U_10401),U_10402)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10402)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10400,tc_HOL_Obool)),U_10402),U_10401))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10400),U_10401))
    | ~ class_Groups_Ocomm__monoid__mult(U_10399) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

cnf(f_2568_5,plain,
    ( hAPP(U_10403,sK255(U_10403,U_10402,U_10401,U_10400,U_10399)) != c_Groups_Oone__class_Oone(U_10399)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10400,U_10399),U_10403),U_10402)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10400,tc_HOL_Obool)),U_10402),U_10401))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10400),U_10401))
    | ~ class_Groups_Ocomm__monoid__mult(U_10399) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

fof(f_2569_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_2569_2,plain,
    ! [U_10407,U_10406,U_10405] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),U_10406),U_10407))
      | ? [U_10404] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10405),U_10404),U_10406)),U_10407))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),U_10404),c_Groups_Oone__class_Oone(U_10405)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),c_Groups_Ozero__class_Ozero(U_10405)),U_10404)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_10405) ),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

fof(f_2569_3,plain,
    ! [U_10407,U_10406,U_10405] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),U_10406),U_10407))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10405),sK256(U_10407,U_10406,U_10405)),U_10406)),U_10407))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),sK256(U_10407,U_10406,U_10405)),c_Groups_Oone__class_Oone(U_10405)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),c_Groups_Ozero__class_Ozero(U_10405)),sK256(U_10407,U_10406,U_10405))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_10405) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_10404,sK256(U_10407,U_10406,U_10405))],[f_2569_2]) ).

cnf(f_2569_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),c_Groups_Ozero__class_Ozero(U_10405)),sK256(U_10407,U_10406,U_10405)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),U_10406),U_10407))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_10405) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

cnf(f_2569_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10405),sK256(U_10407,U_10406,U_10405)),c_Groups_Oone__class_Oone(U_10405)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),U_10406),U_10407))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_10405) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

cnf(f_2569_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10405),sK256(U_10407,U_10406,U_10405)),U_10406)),U_10407))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10405),U_10406),U_10407))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_10405) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

fof(f_2570_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),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_a)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).

fof(f_2570_2,plain,
    ! [U_10413,U_10412,U_10411,U_10410,U_10409] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10412),U_10410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10413),U_10411)
      | ? [U_10408] :
          ( hAPP(U_10412,U_10408) != hAPP(U_10413,U_10408)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10408)) )
      | ~ c_Nat__Transfer_Onat__set(U_10411)
      | U_10410 != U_10411
      | ~ class_Groups_Ocomm__monoid__mult(U_10409)
      | ~ class_Groups_Ocomm__monoid__add(U_10409) ),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

fof(f_2570_3,plain,
    ! [U_10413,U_10412,U_10411,U_10410,U_10409] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10412),U_10410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10413),U_10411)
      | ( hAPP(U_10412,sK257(U_10413,U_10412,U_10411,U_10410,U_10409)) != hAPP(U_10413,sK257(U_10413,U_10412,U_10411,U_10410,U_10409))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK257(U_10413,U_10412,U_10411,U_10410,U_10409))) )
      | ~ c_Nat__Transfer_Onat__set(U_10411)
      | U_10410 != U_10411
      | ~ class_Groups_Ocomm__monoid__mult(U_10409)
      | ~ class_Groups_Ocomm__monoid__add(U_10409) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_10408,sK257(U_10413,U_10412,U_10411,U_10410,U_10409))],[f_2570_2]) ).

cnf(f_2570_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK257(U_10413,U_10412,U_10411,U_10410,U_10409)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10412),U_10410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10413),U_10411)
    | ~ c_Nat__Transfer_Onat__set(U_10411)
    | U_10410 != U_10411
    | ~ class_Groups_Ocomm__monoid__mult(U_10409)
    | ~ class_Groups_Ocomm__monoid__add(U_10409) ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

cnf(f_2570_5,plain,
    ( hAPP(U_10412,sK257(U_10413,U_10412,U_10411,U_10410,U_10409)) != hAPP(U_10413,sK257(U_10413,U_10412,U_10411,U_10410,U_10409))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10412),U_10410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10409),U_10413),U_10411)
    | ~ c_Nat__Transfer_Onat__set(U_10411)
    | U_10410 != U_10411
    | ~ class_Groups_Ocomm__monoid__mult(U_10409)
    | ~ class_Groups_Ocomm__monoid__add(U_10409) ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

fof(f_2571_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_split__pos__lemma]) ).

fof(f_2571_2,plain,
    ! [U_10420,U_10419,U_10418] :
      ( ( ( hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
          | ? [U_10417,U_10416] :
              ( ~ hBOOL(hAPP(hAPP(U_10419,U_10417),U_10416))
              & U_10420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),U_10417)),U_10416)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10416),U_10418))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10416)) ) )
        & ( ! [U_10415,U_10414] :
              ( hBOOL(hAPP(hAPP(U_10419,U_10415),U_10414))
              | U_10420 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),U_10415)),U_10414)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10414),U_10418))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10414)) )
          | ~ hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(variable_rename,[status(thm)],[f_2571_1]) ).

fof(f_2571_3,plain,
    ! [U_10420,U_10419,U_10418] :
      ( ( ( hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
          | ? [U_10416] :
              ( ~ hBOOL(hAPP(hAPP(U_10419,sK258(U_10420,U_10419,U_10418)),U_10416))
              & U_10420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),sK258(U_10420,U_10419,U_10418))),U_10416)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10416),U_10418))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10416)) ) )
        & ( ! [U_10415,U_10414] :
              ( hBOOL(hAPP(hAPP(U_10419,U_10415),U_10414))
              | U_10420 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),U_10415)),U_10414)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10414),U_10418))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10414)) )
          | ~ hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_10417,sK258(U_10420,U_10419,U_10418))],[f_2571_2]) ).

fof(f_2571_4,plain,
    ! [U_10420,U_10419,U_10418] :
      ( ( ( hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
          | ( ~ hBOOL(hAPP(hAPP(U_10419,sK258(U_10420,U_10419,U_10418)),sK259(U_10420,U_10419,U_10418)))
            & U_10420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),sK258(U_10420,U_10419,U_10418))),sK259(U_10420,U_10419,U_10418))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK259(U_10420,U_10419,U_10418)),U_10418))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK259(U_10420,U_10419,U_10418))) ) )
        & ( ! [U_10415,U_10414] :
              ( hBOOL(hAPP(hAPP(U_10419,U_10415),U_10414))
              | U_10420 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),U_10415)),U_10414)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10414),U_10418))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10414)) )
          | ~ hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_10416,sK259(U_10420,U_10419,U_10418))],[f_2571_3]) ).

cnf(f_2571_5,plain,
    ( hBOOL(hAPP(hAPP(U_10419,U_10415),U_10414))
    | U_10420 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),U_10415)),U_10414)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10414),U_10418))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10414))
    | ~ hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(clausify,[status(thm)],[f_2571_4]) ).

cnf(f_2571_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK259(U_10420,U_10419,U_10418)))
    | hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(clausify,[status(thm)],[f_2571_4]) ).

cnf(f_2571_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK259(U_10420,U_10419,U_10418)),U_10418))
    | hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(clausify,[status(thm)],[f_2571_4]) ).

cnf(f_2571_8,plain,
    ( U_10420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10418),sK258(U_10420,U_10419,U_10418))),sK259(U_10420,U_10419,U_10418))
    | hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(clausify,[status(thm)],[f_2571_4]) ).

cnf(f_2571_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_10419,sK258(U_10420,U_10419,U_10418)),sK259(U_10420,U_10419,U_10418)))
    | hBOOL(hAPP(hAPP(U_10419,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10420),U_10418)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10420,U_10418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10418)) ),
    inference(clausify,[status(thm)],[f_2571_4]) ).

fof(f_2572_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).

fof(f_2572_2,plain,
    ! [U_10427,U_10426,U_10425] :
      ( ( ( hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
          | ? [U_10424,U_10423] :
              ( ~ hBOOL(hAPP(hAPP(U_10426,U_10424),U_10423))
              & U_10427 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),U_10424)),U_10423)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10423),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10423)) ) )
        & ( ! [U_10422,U_10421] :
              ( hBOOL(hAPP(hAPP(U_10426,U_10422),U_10421))
              | U_10427 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),U_10422)),U_10421)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10421),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10421)) )
          | ~ hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

fof(f_2572_3,plain,
    ! [U_10427,U_10426,U_10425] :
      ( ( ( hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
          | ? [U_10423] :
              ( ~ hBOOL(hAPP(hAPP(U_10426,sK260(U_10427,U_10426,U_10425)),U_10423))
              & U_10427 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),sK260(U_10427,U_10426,U_10425))),U_10423)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10423),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10423)) ) )
        & ( ! [U_10422,U_10421] :
              ( hBOOL(hAPP(hAPP(U_10426,U_10422),U_10421))
              | U_10427 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),U_10422)),U_10421)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10421),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10421)) )
          | ~ hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_10424,sK260(U_10427,U_10426,U_10425))],[f_2572_2]) ).

fof(f_2572_4,plain,
    ! [U_10427,U_10426,U_10425] :
      ( ( ( hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
          | ( ~ hBOOL(hAPP(hAPP(U_10426,sK260(U_10427,U_10426,U_10425)),sK261(U_10427,U_10426,U_10425)))
            & U_10427 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),sK260(U_10427,U_10426,U_10425))),sK261(U_10427,U_10426,U_10425))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK261(U_10427,U_10426,U_10425)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),sK261(U_10427,U_10426,U_10425))) ) )
        & ( ! [U_10422,U_10421] :
              ( hBOOL(hAPP(hAPP(U_10426,U_10422),U_10421))
              | U_10427 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),U_10422)),U_10421)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10421),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10421)) )
          | ~ hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_10423,sK261(U_10427,U_10426,U_10425))],[f_2572_3]) ).

cnf(f_2572_5,plain,
    ( hBOOL(hAPP(hAPP(U_10426,U_10422),U_10421))
    | U_10427 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),U_10422)),U_10421)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10421),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),U_10421))
    | ~ hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2572_4]) ).

cnf(f_2572_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),sK261(U_10427,U_10426,U_10425)))
    | hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2572_4]) ).

cnf(f_2572_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK261(U_10427,U_10426,U_10425)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2572_4]) ).

cnf(f_2572_8,plain,
    ( U_10427 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10425),sK260(U_10427,U_10426,U_10425))),sK261(U_10427,U_10426,U_10425))
    | hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2572_4]) ).

cnf(f_2572_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_10426,sK260(U_10427,U_10426,U_10425)),sK261(U_10427,U_10426,U_10425)))
    | hBOOL(hAPP(hAPP(U_10426,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10427),U_10425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10427,U_10425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2572_4]) ).

fof(f_2573_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_2573_2,plain,
    ! [U_10429,U_10428] :
      ( c_Groups_Osgn__class_Osgn(U_10428,U_10429) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10428),c_Groups_Oone__class_Oone(U_10428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10428),U_10429),c_Groups_Ozero__class_Ozero(U_10428)))
      | ~ class_Rings_Olinordered__idom(U_10428) ),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

cnf(f_2573_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10428,U_10429) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10428),c_Groups_Oone__class_Oone(U_10428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10428),U_10429),c_Groups_Ozero__class_Ozero(U_10428)))
    | ~ class_Rings_Olinordered__idom(U_10428) ),
    inference(clausify,[status(thm)],[f_2573_2]) ).

fof(f_2574_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_2574_2,plain,
    ! [U_10431,U_10430] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10430,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10431)) = 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_10430),U_10431)),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

cnf(f_2574_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10430,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10431)) = 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_10430),U_10431)),
    inference(clausify,[status(thm)],[f_2574_2]) ).

fof(f_2575_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_2575_2,plain,
    ! [U_10434,U_10433,U_10432] :
      ( c_Divides_Odiv__class_Omod(U_10432,hAPP(c_Groups_Ouminus__class_Ouminus(U_10432),U_10433),U_10434) = c_Divides_Odiv__class_Omod(U_10432,hAPP(c_Groups_Ouminus__class_Ouminus(U_10432),c_Divides_Odiv__class_Omod(U_10432,U_10433,U_10434)),U_10434)
      | ~ class_Divides_Oring__div(U_10432) ),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

cnf(f_2575_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10432,hAPP(c_Groups_Ouminus__class_Ouminus(U_10432),U_10433),U_10434) = c_Divides_Odiv__class_Omod(U_10432,hAPP(c_Groups_Ouminus__class_Ouminus(U_10432),c_Divides_Odiv__class_Omod(U_10432,U_10433,U_10434)),U_10434)
    | ~ class_Divides_Oring__div(U_10432) ),
    inference(clausify,[status(thm)],[f_2575_2]) ).

fof(f_2576_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_2576_2,plain,
    ! [U_10436,U_10435] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10436)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10435,U_10436)),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

cnf(f_2576_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10436)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10435,U_10436)),
    inference(clausify,[status(thm)],[f_2576_2]) ).

fof(f_2577_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_2577_2,plain,
    ! [U_10438,U_10437] : 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_10437,U_10438)),U_10438) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10437),U_10438),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

cnf(f_2577_3,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_10437,U_10438)),U_10438) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10437),U_10438),
    inference(clausify,[status(thm)],[f_2577_2]) ).

fof(f_2578_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_2578_2,plain,
    ! [U_10442,U_10441,U_10440,U_10439] :
      ( c_Divides_Odiv__class_Omod(U_10439,hAPP(c_Groups_Ouminus__class_Ouminus(U_10439),U_10440),U_10441) = c_Divides_Odiv__class_Omod(U_10439,hAPP(c_Groups_Ouminus__class_Ouminus(U_10439),U_10442),U_10441)
      | c_Divides_Odiv__class_Omod(U_10439,U_10440,U_10441) != c_Divides_Odiv__class_Omod(U_10439,U_10442,U_10441)
      | ~ class_Divides_Oring__div(U_10439) ),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

cnf(f_2578_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10439,hAPP(c_Groups_Ouminus__class_Ouminus(U_10439),U_10440),U_10441) = c_Divides_Odiv__class_Omod(U_10439,hAPP(c_Groups_Ouminus__class_Ouminus(U_10439),U_10442),U_10441)
    | c_Divides_Odiv__class_Omod(U_10439,U_10440,U_10441) != c_Divides_Odiv__class_Omod(U_10439,U_10442,U_10441)
    | ~ class_Divides_Oring__div(U_10439) ),
    inference(clausify,[status(thm)],[f_2578_2]) ).

fof(f_2579_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_2579_2,plain,
    ! [U_10445,U_10444,U_10443] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10443),U_10444),U_10445) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10443),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10444,U_10445)),U_10445),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

cnf(f_2579_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10443),U_10444),U_10445) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10443),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10444,U_10445)),U_10445),
    inference(clausify,[status(thm)],[f_2579_2]) ).

fof(f_2580_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_2580_2,plain,
    ! [U_10448,U_10447,U_10446] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10446),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10447,U_10448)),U_10448) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10446),U_10447),U_10448),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

cnf(f_2580_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10446),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10447,U_10448)),U_10448) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10446),U_10447),U_10448),
    inference(clausify,[status(thm)],[f_2580_2]) ).

fof(f_2581_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_2581_2,plain,
    ! [U_10454,U_10453,U_10452,U_10451,U_10450,U_10449] :
      ( c_Divides_Odiv__class_Omod(U_10449,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10449),U_10450),U_10453),U_10451) = c_Divides_Odiv__class_Omod(U_10449,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10449),U_10452),U_10454),U_10451)
      | c_Divides_Odiv__class_Omod(U_10449,U_10453,U_10451) != c_Divides_Odiv__class_Omod(U_10449,U_10454,U_10451)
      | c_Divides_Odiv__class_Omod(U_10449,U_10450,U_10451) != c_Divides_Odiv__class_Omod(U_10449,U_10452,U_10451)
      | ~ class_Divides_Osemiring__div(U_10449) ),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

cnf(f_2581_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10449,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10449),U_10450),U_10453),U_10451) = c_Divides_Odiv__class_Omod(U_10449,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10449),U_10452),U_10454),U_10451)
    | c_Divides_Odiv__class_Omod(U_10449,U_10453,U_10451) != c_Divides_Odiv__class_Omod(U_10449,U_10454,U_10451)
    | c_Divides_Odiv__class_Omod(U_10449,U_10450,U_10451) != c_Divides_Odiv__class_Omod(U_10449,U_10452,U_10451)
    | ~ class_Divides_Osemiring__div(U_10449) ),
    inference(clausify,[status(thm)],[f_2581_2]) ).

fof(f_2582_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_2582_2,plain,
    ! [U_10458,U_10457,U_10456,U_10455] :
      ( c_Divides_Odiv__class_Omod(U_10455,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10455),c_Divides_Odiv__class_Omod(U_10455,U_10456,U_10457)),U_10458),U_10457) = c_Divides_Odiv__class_Omod(U_10455,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10455),U_10456),U_10458),U_10457)
      | ~ class_Divides_Osemiring__div(U_10455) ),
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

cnf(f_2582_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10455,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10455),c_Divides_Odiv__class_Omod(U_10455,U_10456,U_10457)),U_10458),U_10457) = c_Divides_Odiv__class_Omod(U_10455,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10455),U_10456),U_10458),U_10457)
    | ~ class_Divides_Osemiring__div(U_10455) ),
    inference(clausify,[status(thm)],[f_2582_2]) ).

fof(f_2583_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_2583_2,plain,
    ! [U_10462,U_10461,U_10460,U_10459] :
      ( c_Divides_Odiv__class_Omod(U_10459,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10459),U_10460),c_Divides_Odiv__class_Omod(U_10459,U_10461,U_10462)),U_10462) = c_Divides_Odiv__class_Omod(U_10459,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10459),U_10460),U_10461),U_10462)
      | ~ class_Divides_Osemiring__div(U_10459) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

cnf(f_2583_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10459,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10459),U_10460),c_Divides_Odiv__class_Omod(U_10459,U_10461,U_10462)),U_10462) = c_Divides_Odiv__class_Omod(U_10459,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10459),U_10460),U_10461),U_10462)
    | ~ class_Divides_Osemiring__div(U_10459) ),
    inference(clausify,[status(thm)],[f_2583_2]) ).

fof(f_2584_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_2584_2,plain,
    ! [U_10466,U_10465,U_10464,U_10463] :
      ( c_Divides_Odiv__class_Omod(U_10463,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10463),U_10464),U_10465),U_10466) = c_Divides_Odiv__class_Omod(U_10463,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10463),c_Divides_Odiv__class_Omod(U_10463,U_10464,U_10466)),c_Divides_Odiv__class_Omod(U_10463,U_10465,U_10466)),U_10466)
      | ~ class_Divides_Osemiring__div(U_10463) ),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

cnf(f_2584_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10463,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10463),U_10464),U_10465),U_10466) = c_Divides_Odiv__class_Omod(U_10463,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10463),c_Divides_Odiv__class_Omod(U_10463,U_10464,U_10466)),c_Divides_Odiv__class_Omod(U_10463,U_10465,U_10466)),U_10466)
    | ~ class_Divides_Osemiring__div(U_10463) ),
    inference(clausify,[status(thm)],[f_2584_2]) ).

fof(f_2585_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_2585_2,plain,
    ! [U_10470,U_10469,U_10468,U_10467] :
      ( c_Divides_Odiv__class_Omod(U_10467,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10467),U_10468),U_10469),U_10470) = c_Divides_Odiv__class_Omod(U_10467,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10467),c_Divides_Odiv__class_Omod(U_10467,U_10468,U_10470)),U_10469),U_10470)
      | ~ class_Divides_Osemiring__div(U_10467) ),
    inference(variable_rename,[status(thm)],[f_2585_1]) ).

cnf(f_2585_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10467,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10467),U_10468),U_10469),U_10470) = c_Divides_Odiv__class_Omod(U_10467,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10467),c_Divides_Odiv__class_Omod(U_10467,U_10468,U_10470)),U_10469),U_10470)
    | ~ class_Divides_Osemiring__div(U_10467) ),
    inference(clausify,[status(thm)],[f_2585_2]) ).

fof(f_2586_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_2586_2,plain,
    ! [U_10474,U_10473,U_10472,U_10471] :
      ( c_Divides_Odiv__class_Omod(U_10471,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10471),U_10472),U_10473),U_10474) = c_Divides_Odiv__class_Omod(U_10471,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10471),U_10472),c_Divides_Odiv__class_Omod(U_10471,U_10473,U_10474)),U_10474)
      | ~ class_Divides_Osemiring__div(U_10471) ),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

cnf(f_2586_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10471,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10471),U_10472),U_10473),U_10474) = c_Divides_Odiv__class_Omod(U_10471,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10471),U_10472),c_Divides_Odiv__class_Omod(U_10471,U_10473,U_10474)),U_10474)
    | ~ class_Divides_Osemiring__div(U_10471) ),
    inference(clausify,[status(thm)],[f_2586_2]) ).

fof(f_2587_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_2587_2,plain,
    ! [U_10477,U_10476,U_10475] :
      ( c_Divides_Odiv__class_Omod(U_10475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10475),U_10476),U_10477),U_10476) = c_Divides_Odiv__class_Omod(U_10475,U_10477,U_10476)
      | ~ class_Divides_Osemiring__div(U_10475) ),
    inference(variable_rename,[status(thm)],[f_2587_1]) ).

cnf(f_2587_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10475),U_10476),U_10477),U_10476) = c_Divides_Odiv__class_Omod(U_10475,U_10477,U_10476)
    | ~ class_Divides_Osemiring__div(U_10475) ),
    inference(clausify,[status(thm)],[f_2587_2]) ).

fof(f_2588_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_2588_2,plain,
    ! [U_10480,U_10479,U_10478] :
      ( c_Divides_Odiv__class_Omod(U_10478,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10478),U_10479),U_10480),U_10480) = c_Divides_Odiv__class_Omod(U_10478,U_10479,U_10480)
      | ~ class_Divides_Osemiring__div(U_10478) ),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

cnf(f_2588_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10478,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10478),U_10479),U_10480),U_10480) = c_Divides_Odiv__class_Omod(U_10478,U_10479,U_10480)
    | ~ class_Divides_Osemiring__div(U_10478) ),
    inference(clausify,[status(thm)],[f_2588_2]) ).

fof(f_2589_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_2589_2,plain,
    ! [U_10484,U_10483,U_10482,U_10481] :
      ( c_Divides_Odiv__class_Omod(U_10481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10481),U_10482),U_10483),U_10484) = c_Divides_Odiv__class_Omod(U_10481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10481),U_10482),c_Divides_Odiv__class_Omod(U_10481,U_10483,U_10484)),U_10484)
      | ~ class_Divides_Osemiring__div(U_10481) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

cnf(f_2589_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10481),U_10482),U_10483),U_10484) = c_Divides_Odiv__class_Omod(U_10481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10481),U_10482),c_Divides_Odiv__class_Omod(U_10481,U_10483,U_10484)),U_10484)
    | ~ class_Divides_Osemiring__div(U_10481) ),
    inference(clausify,[status(thm)],[f_2589_2]) ).

fof(f_2590_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_2590_2,plain,
    ! [U_10488,U_10487,U_10486,U_10485] :
      ( c_Divides_Odiv__class_Omod(U_10485,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),U_10486),U_10487),U_10488) = c_Divides_Odiv__class_Omod(U_10485,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),c_Divides_Odiv__class_Omod(U_10485,U_10486,U_10488)),U_10487),U_10488)
      | ~ class_Divides_Osemiring__div(U_10485) ),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

cnf(f_2590_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10485,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),U_10486),U_10487),U_10488) = c_Divides_Odiv__class_Omod(U_10485,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),c_Divides_Odiv__class_Omod(U_10485,U_10486,U_10488)),U_10487),U_10488)
    | ~ class_Divides_Osemiring__div(U_10485) ),
    inference(clausify,[status(thm)],[f_2590_2]) ).

fof(f_2591_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_2591_2,plain,
    ! [U_10492,U_10491,U_10490,U_10489] :
      ( c_Divides_Odiv__class_Omod(U_10489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10489),U_10490),U_10491),U_10492) = c_Divides_Odiv__class_Omod(U_10489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10489),c_Divides_Odiv__class_Omod(U_10489,U_10490,U_10492)),c_Divides_Odiv__class_Omod(U_10489,U_10491,U_10492)),U_10492)
      | ~ class_Divides_Osemiring__div(U_10489) ),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

cnf(f_2591_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10489),U_10490),U_10491),U_10492) = c_Divides_Odiv__class_Omod(U_10489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10489),c_Divides_Odiv__class_Omod(U_10489,U_10490,U_10492)),c_Divides_Odiv__class_Omod(U_10489,U_10491,U_10492)),U_10492)
    | ~ class_Divides_Osemiring__div(U_10489) ),
    inference(clausify,[status(thm)],[f_2591_2]) ).

fof(f_2592_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_2592_2,plain,
    ! [U_10496,U_10495,U_10494,U_10493] :
      ( c_Divides_Odiv__class_Omod(U_10493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),U_10495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),U_10496)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),c_Divides_Odiv__class_Omod(U_10493,U_10495,U_10496))
      | ~ class_Divides_Osemiring__div(U_10493) ),
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

cnf(f_2592_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),U_10495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),U_10496)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),U_10494),c_Divides_Odiv__class_Omod(U_10493,U_10495,U_10496))
    | ~ class_Divides_Osemiring__div(U_10493) ),
    inference(clausify,[status(thm)],[f_2592_2]) ).

fof(f_2593_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_2593_2,plain,
    ! [U_10500,U_10499,U_10498,U_10497] :
      ( c_Divides_Odiv__class_Omod(U_10497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),U_10498),U_10499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),U_10500),U_10499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),c_Divides_Odiv__class_Omod(U_10497,U_10498,U_10500)),U_10499)
      | ~ class_Divides_Osemiring__div(U_10497) ),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

cnf(f_2593_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),U_10498),U_10499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),U_10500),U_10499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10497),c_Divides_Odiv__class_Omod(U_10497,U_10498,U_10500)),U_10499)
    | ~ class_Divides_Osemiring__div(U_10497) ),
    inference(clausify,[status(thm)],[f_2593_2]) ).

fof(f_2594_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_2594_2,plain,
    ! [U_10504,U_10503,U_10502,U_10501] :
      ( c_Divides_Odiv__class_Omod(U_10501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10501),c_Divides_Odiv__class_Omod(U_10501,U_10502,U_10503)),U_10504),U_10503) = c_Divides_Odiv__class_Omod(U_10501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10501),U_10502),U_10504),U_10503)
      | ~ class_Divides_Osemiring__div(U_10501) ),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

cnf(f_2594_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10501),c_Divides_Odiv__class_Omod(U_10501,U_10502,U_10503)),U_10504),U_10503) = c_Divides_Odiv__class_Omod(U_10501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10501),U_10502),U_10504),U_10503)
    | ~ class_Divides_Osemiring__div(U_10501) ),
    inference(clausify,[status(thm)],[f_2594_2]) ).

fof(f_2595_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_2595_2,plain,
    ! [U_10510,U_10509,U_10508,U_10507,U_10506,U_10505] :
      ( c_Divides_Odiv__class_Omod(U_10505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10505),U_10506),U_10509),U_10507) = c_Divides_Odiv__class_Omod(U_10505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10505),U_10508),U_10510),U_10507)
      | c_Divides_Odiv__class_Omod(U_10505,U_10509,U_10507) != c_Divides_Odiv__class_Omod(U_10505,U_10510,U_10507)
      | c_Divides_Odiv__class_Omod(U_10505,U_10506,U_10507) != c_Divides_Odiv__class_Omod(U_10505,U_10508,U_10507)
      | ~ class_Divides_Osemiring__div(U_10505) ),
    inference(variable_rename,[status(thm)],[f_2595_1]) ).

cnf(f_2595_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10505),U_10506),U_10509),U_10507) = c_Divides_Odiv__class_Omod(U_10505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10505),U_10508),U_10510),U_10507)
    | c_Divides_Odiv__class_Omod(U_10505,U_10509,U_10507) != c_Divides_Odiv__class_Omod(U_10505,U_10510,U_10507)
    | c_Divides_Odiv__class_Omod(U_10505,U_10506,U_10507) != c_Divides_Odiv__class_Omod(U_10505,U_10508,U_10507)
    | ~ class_Divides_Osemiring__div(U_10505) ),
    inference(clausify,[status(thm)],[f_2595_2]) ).

fof(f_2596_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_2596_2,plain,
    ! [U_10516,U_10515,U_10514,U_10513,U_10512,U_10511] :
      ( c_Divides_Odiv__class_Omod(U_10511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10511),U_10512),U_10515),U_10513) = c_Divides_Odiv__class_Omod(U_10511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10511),U_10514),U_10516),U_10513)
      | c_Divides_Odiv__class_Omod(U_10511,U_10515,U_10513) != c_Divides_Odiv__class_Omod(U_10511,U_10516,U_10513)
      | c_Divides_Odiv__class_Omod(U_10511,U_10512,U_10513) != c_Divides_Odiv__class_Omod(U_10511,U_10514,U_10513)
      | ~ class_Divides_Oring__div(U_10511) ),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

cnf(f_2596_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10511),U_10512),U_10515),U_10513) = c_Divides_Odiv__class_Omod(U_10511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10511),U_10514),U_10516),U_10513)
    | c_Divides_Odiv__class_Omod(U_10511,U_10515,U_10513) != c_Divides_Odiv__class_Omod(U_10511,U_10516,U_10513)
    | c_Divides_Odiv__class_Omod(U_10511,U_10512,U_10513) != c_Divides_Odiv__class_Omod(U_10511,U_10514,U_10513)
    | ~ class_Divides_Oring__div(U_10511) ),
    inference(clausify,[status(thm)],[f_2596_2]) ).

fof(f_2597_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_2597_2,plain,
    ! [U_10520,U_10519,U_10518,U_10517] :
      ( c_Divides_Odiv__class_Omod(U_10517,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10517),U_10518),U_10519),U_10520) = c_Divides_Odiv__class_Omod(U_10517,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10517),c_Divides_Odiv__class_Omod(U_10517,U_10518,U_10520)),c_Divides_Odiv__class_Omod(U_10517,U_10519,U_10520)),U_10520)
      | ~ class_Divides_Oring__div(U_10517) ),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

cnf(f_2597_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10517,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10517),U_10518),U_10519),U_10520) = c_Divides_Odiv__class_Omod(U_10517,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10517),c_Divides_Odiv__class_Omod(U_10517,U_10518,U_10520)),c_Divides_Odiv__class_Omod(U_10517,U_10519,U_10520)),U_10520)
    | ~ class_Divides_Oring__div(U_10517) ),
    inference(clausify,[status(thm)],[f_2597_2]) ).

fof(f_2598_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_2598_2,plain,
    ! [U_10524,U_10523,U_10522,U_10521] :
      ( c_Divides_Odiv__class_Omod(U_10521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10521),U_10522),U_10523),U_10524) = c_Divides_Odiv__class_Omod(U_10521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10521),c_Divides_Odiv__class_Omod(U_10521,U_10522,U_10524)),U_10523),U_10524)
      | ~ class_Divides_Oring__div(U_10521) ),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

cnf(f_2598_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10521),U_10522),U_10523),U_10524) = c_Divides_Odiv__class_Omod(U_10521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10521),c_Divides_Odiv__class_Omod(U_10521,U_10522,U_10524)),U_10523),U_10524)
    | ~ class_Divides_Oring__div(U_10521) ),
    inference(clausify,[status(thm)],[f_2598_2]) ).

fof(f_2599_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_2599_2,plain,
    ! [U_10528,U_10527,U_10526,U_10525] :
      ( c_Divides_Odiv__class_Omod(U_10525,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10525),U_10526),U_10527),U_10528) = c_Divides_Odiv__class_Omod(U_10525,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10525),U_10526),c_Divides_Odiv__class_Omod(U_10525,U_10527,U_10528)),U_10528)
      | ~ class_Divides_Oring__div(U_10525) ),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

cnf(f_2599_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10525,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10525),U_10526),U_10527),U_10528) = c_Divides_Odiv__class_Omod(U_10525,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10525),U_10526),c_Divides_Odiv__class_Omod(U_10525,U_10527,U_10528)),U_10528)
    | ~ class_Divides_Oring__div(U_10525) ),
    inference(clausify,[status(thm)],[f_2599_2]) ).

fof(f_2600_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_2600_2,plain,
    ! [U_10531,U_10530,U_10529] :
      ( c_Divides_Odiv__class_Omod(U_10529,c_Divides_Odiv__class_Omod(U_10529,U_10530,U_10531),U_10531) = c_Divides_Odiv__class_Omod(U_10529,U_10530,U_10531)
      | ~ class_Divides_Osemiring__div(U_10529) ),
    inference(variable_rename,[status(thm)],[f_2600_1]) ).

cnf(f_2600_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10529,c_Divides_Odiv__class_Omod(U_10529,U_10530,U_10531),U_10531) = c_Divides_Odiv__class_Omod(U_10529,U_10530,U_10531)
    | ~ class_Divides_Osemiring__div(U_10529) ),
    inference(clausify,[status(thm)],[f_2600_2]) ).

fof(f_2601_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_2601_2,plain,
    ! [U_10533,U_10532] :
      ( c_Groups_Osgn__class_Osgn(U_10532,c_Groups_Osgn__class_Osgn(U_10532,U_10533)) = c_Groups_Osgn__class_Osgn(U_10532,U_10533)
      | ~ class_Rings_Olinordered__idom(U_10532) ),
    inference(variable_rename,[status(thm)],[f_2601_1]) ).

cnf(f_2601_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10532,c_Groups_Osgn__class_Osgn(U_10532,U_10533)) = c_Groups_Osgn__class_Osgn(U_10532,U_10533)
    | ~ class_Rings_Olinordered__idom(U_10532) ),
    inference(clausify,[status(thm)],[f_2601_2]) ).

fof(f_2602_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_2602_2,plain,
    ! [U_10535,U_10534] :
      ( c_Divides_Odiv__class_Omod(U_10534,c_Groups_Ozero__class_Ozero(U_10534),U_10535) = c_Groups_Ozero__class_Ozero(U_10534)
      | ~ class_Divides_Osemiring__div(U_10534) ),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

cnf(f_2602_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10534,c_Groups_Ozero__class_Ozero(U_10534),U_10535) = c_Groups_Ozero__class_Ozero(U_10534)
    | ~ class_Divides_Osemiring__div(U_10534) ),
    inference(clausify,[status(thm)],[f_2602_2]) ).

fof(f_2603_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_2603_2,plain,
    ! [U_10537,U_10536] :
      ( c_Divides_Odiv__class_Omod(U_10536,U_10537,c_Groups_Ozero__class_Ozero(U_10536)) = U_10537
      | ~ class_Divides_Osemiring__div(U_10536) ),
    inference(variable_rename,[status(thm)],[f_2603_1]) ).

cnf(f_2603_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10536,U_10537,c_Groups_Ozero__class_Ozero(U_10536)) = U_10537
    | ~ class_Divides_Osemiring__div(U_10536) ),
    inference(clausify,[status(thm)],[f_2603_2]) ).

fof(f_2604_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_2604_2,plain,
    ! [U_10539,U_10538] :
      ( c_Divides_Odiv__class_Omod(U_10538,U_10539,U_10539) = c_Groups_Ozero__class_Ozero(U_10538)
      | ~ class_Divides_Osemiring__div(U_10538) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

cnf(f_2604_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10538,U_10539,U_10539) = c_Groups_Ozero__class_Ozero(U_10538)
    | ~ class_Divides_Osemiring__div(U_10538) ),
    inference(clausify,[status(thm)],[f_2604_2]) ).

fof(f_2605_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_2605_2,plain,
    ! [U_10540] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10540) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

cnf(f_2605_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10540) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2605_2]) ).

fof(f_2606_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_2606_2,plain,
    ! [U_10541] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10541,U_10541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2606_1]) ).

cnf(f_2606_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10541,U_10541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2606_2]) ).

fof(f_2607_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_2607_2,plain,
    ! [U_10544,U_10543,U_10542] : 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_10542,U_10543)),U_10544),U_10543) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10542),U_10544),U_10543),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

cnf(f_2607_3,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_10542,U_10543)),U_10544),U_10543) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10542),U_10544),U_10543),
    inference(clausify,[status(thm)],[f_2607_2]) ).

fof(f_2608_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_2608_2,plain,
    ! [U_10547,U_10546,U_10545] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10545),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10546,U_10547)),U_10547) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10545),U_10546),U_10547),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

cnf(f_2608_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10545),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10546,U_10547)),U_10547) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10545),U_10546),U_10547),
    inference(clausify,[status(thm)],[f_2608_2]) ).

fof(f_2609_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_2609_2,plain,
    ! [U_10549,U_10548] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10548,U_10549))
      | ~ c_Nat__Transfer_Ois__nat(U_10549)
      | ~ c_Nat__Transfer_Ois__nat(U_10548) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

cnf(f_2609_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10548,U_10549))
    | ~ c_Nat__Transfer_Ois__nat(U_10549)
    | ~ c_Nat__Transfer_Ois__nat(U_10548) ),
    inference(clausify,[status(thm)],[f_2609_2]) ).

fof(f_2610_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_2610_2,plain,
    ! [U_10552,U_10551,U_10550] : 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_10550,U_10551)),U_10552),U_10551) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10550),U_10552),U_10551),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

cnf(f_2610_3,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_10550,U_10551)),U_10552),U_10551) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10550),U_10552),U_10551),
    inference(clausify,[status(thm)],[f_2610_2]) ).

fof(f_2611_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_2611_2,plain,
    ! [U_10553] :
      ( c_Groups_Osgn__class_Osgn(U_10553,c_Groups_Ozero__class_Ozero(U_10553)) = c_Groups_Ozero__class_Ozero(U_10553)
      | ~ class_Groups_Osgn__if(U_10553) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

cnf(f_2611_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10553,c_Groups_Ozero__class_Ozero(U_10553)) = c_Groups_Ozero__class_Ozero(U_10553)
    | ~ class_Groups_Osgn__if(U_10553) ),
    inference(clausify,[status(thm)],[f_2611_2]) ).

fof(f_2612_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).

fof(f_2612_2,plain,
    ! [U_10555,U_10554] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_10554,U_10555) = c_Groups_Ozero__class_Ozero(U_10554)
          | U_10555 != c_Groups_Ozero__class_Ozero(U_10554) )
        & ( U_10555 = c_Groups_Ozero__class_Ozero(U_10554)
          | c_Groups_Osgn__class_Osgn(U_10554,U_10555) != c_Groups_Ozero__class_Ozero(U_10554) ) )
      | ~ class_Rings_Olinordered__idom(U_10554) ),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

cnf(f_2612_3,plain,
    ( U_10555 = c_Groups_Ozero__class_Ozero(U_10554)
    | c_Groups_Osgn__class_Osgn(U_10554,U_10555) != c_Groups_Ozero__class_Ozero(U_10554)
    | ~ class_Rings_Olinordered__idom(U_10554) ),
    inference(clausify,[status(thm)],[f_2612_2]) ).

cnf(f_2612_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_10554,U_10555) = c_Groups_Ozero__class_Ozero(U_10554)
    | U_10555 != c_Groups_Ozero__class_Ozero(U_10554)
    | ~ class_Rings_Olinordered__idom(U_10554) ),
    inference(clausify,[status(thm)],[f_2612_2]) ).

fof(f_2613_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_2613_2,plain,
    ! [U_10558,U_10557,U_10556] :
      ( c_Groups_Osgn__class_Osgn(U_10556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10556),U_10557),U_10558)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10556),c_Groups_Osgn__class_Osgn(U_10556,U_10557)),c_Groups_Osgn__class_Osgn(U_10556,U_10558))
      | ~ class_Rings_Olinordered__idom(U_10556) ),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

cnf(f_2613_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10556),U_10557),U_10558)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10556),c_Groups_Osgn__class_Osgn(U_10556,U_10557)),c_Groups_Osgn__class_Osgn(U_10556,U_10558))
    | ~ class_Rings_Olinordered__idom(U_10556) ),
    inference(clausify,[status(thm)],[f_2613_2]) ).

fof(f_2614_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_2614_2,plain,
    ! [U_10561,U_10560,U_10559] :
      ( c_Divides_Odiv__class_Omod(U_10559,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10559),U_10560),U_10561),U_10561) = c_Groups_Ozero__class_Ozero(U_10559)
      | ~ class_Divides_Osemiring__div(U_10559) ),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

cnf(f_2614_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10559,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10559),U_10560),U_10561),U_10561) = c_Groups_Ozero__class_Ozero(U_10559)
    | ~ class_Divides_Osemiring__div(U_10559) ),
    inference(clausify,[status(thm)],[f_2614_2]) ).

fof(f_2615_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_2615_2,plain,
    ! [U_10564,U_10563,U_10562] :
      ( c_Divides_Odiv__class_Omod(U_10562,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10562),U_10563),U_10564),U_10563) = c_Groups_Ozero__class_Ozero(U_10562)
      | ~ class_Divides_Osemiring__div(U_10562) ),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

cnf(f_2615_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10562,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10562),U_10563),U_10564),U_10563) = c_Groups_Ozero__class_Ozero(U_10562)
    | ~ class_Divides_Osemiring__div(U_10562) ),
    inference(clausify,[status(thm)],[f_2615_2]) ).

fof(f_2616_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_2616_2,plain,
    ! [U_10568,U_10567,U_10566,U_10565] :
      ( c_Divides_Odiv__class_Omod(U_10565,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10565),U_10566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10565),U_10567),U_10568)),U_10567) = c_Divides_Odiv__class_Omod(U_10565,U_10566,U_10567)
      | ~ class_Divides_Osemiring__div(U_10565) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

cnf(f_2616_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10565,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10565),U_10566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10565),U_10567),U_10568)),U_10567) = c_Divides_Odiv__class_Omod(U_10565,U_10566,U_10567)
    | ~ class_Divides_Osemiring__div(U_10565) ),
    inference(clausify,[status(thm)],[f_2616_2]) ).

fof(f_2617_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_2617_2,plain,
    ! [U_10572,U_10571,U_10570,U_10569] :
      ( c_Divides_Odiv__class_Omod(U_10569,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10569),U_10570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10569),U_10571),U_10572)),U_10572) = c_Divides_Odiv__class_Omod(U_10569,U_10570,U_10572)
      | ~ class_Divides_Osemiring__div(U_10569) ),
    inference(variable_rename,[status(thm)],[f_2617_1]) ).

cnf(f_2617_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10569,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10569),U_10570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10569),U_10571),U_10572)),U_10572) = c_Divides_Odiv__class_Omod(U_10569,U_10570,U_10572)
    | ~ class_Divides_Osemiring__div(U_10569) ),
    inference(clausify,[status(thm)],[f_2617_2]) ).

fof(f_2618_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_2618_2,plain,
    ! [U_10574,U_10573] :
      ( c_Divides_Odiv__class_Omod(U_10573,U_10574,c_Groups_Oone__class_Oone(U_10573)) = c_Groups_Ozero__class_Ozero(U_10573)
      | ~ class_Divides_Osemiring__div(U_10573) ),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

cnf(f_2618_3,plain,
    ( c_Divides_Odiv__class_Omod(U_10573,U_10574,c_Groups_Oone__class_Oone(U_10573)) = c_Groups_Ozero__class_Ozero(U_10573)
    | ~ class_Divides_Osemiring__div(U_10573) ),
    inference(clausify,[status(thm)],[f_2618_2]) ).

fof(f_2619_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_2619_2,plain,
    ! [U_10577,U_10576,U_10575] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10575),c_Divides_Odiv__class_Omod(U_10575,U_10576,U_10577)),U_10577) = c_Groups_Ozero__class_Ozero(U_10575)
      | ~ class_Divides_Osemiring__div(U_10575) ),
    inference(variable_rename,[status(thm)],[f_2619_1]) ).

cnf(f_2619_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10575),c_Divides_Odiv__class_Omod(U_10575,U_10576,U_10577)),U_10577) = c_Groups_Ozero__class_Ozero(U_10575)
    | ~ class_Divides_Osemiring__div(U_10575) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

fof(f_2620_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_2620_2,plain,
    ! [U_10579,U_10578] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10578,U_10579)),U_10578))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10578)) ),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

cnf(f_2620_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10578,U_10579)),U_10578))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10578)) ),
    inference(clausify,[status(thm)],[f_2620_2]) ).

fof(f_2621_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_2621_2,plain,
    ! [U_10581,U_10580] :
      ( 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_10580,U_10581)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10581))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10580)) ),
    inference(variable_rename,[status(thm)],[f_2621_1]) ).

cnf(f_2621_3,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_10580,U_10581)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10581))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10580)) ),
    inference(clausify,[status(thm)],[f_2621_2]) ).

fof(f_2622_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_2622_2,plain,
    ! [U_10583,U_10582] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10583,U_10582)),U_10582))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10582)) ),
    inference(variable_rename,[status(thm)],[f_2622_1]) ).

cnf(f_2622_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10583,U_10582)),U_10582))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10582)) ),
    inference(clausify,[status(thm)],[f_2622_2]) ).

fof(f_2623_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_2623_2,plain,
    ! [U_10585,U_10584] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10584),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10585,U_10584)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

cnf(f_2623_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10584),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10585,U_10584)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2623_2]) ).

fof(f_2624_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_2624_2,plain,
    ! [U_10589,U_10588] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10588,U_10589) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_10587] : U_10588 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10589),U_10587) )
      & ( ? [U_10586] : U_10588 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10589),U_10586)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10588,U_10589) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2624_1]) ).

fof(f_2624_3,plain,
    ( ! [U_10593,U_10591] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10591,U_10593) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_10587] : U_10591 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10593),U_10587) )
    & ! [U_10592,U_10590] :
        ( ? [U_10586] : U_10590 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10592),U_10586)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10590,U_10592) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2624_2]) ).

fof(f_2624_4,plain,
    ( ! [U_10593,U_10591] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10591,U_10593) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_10587] : U_10591 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10593),U_10587) )
    & ! [U_10592,U_10590] :
        ( U_10590 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10592),sK262(U_10592,U_10590))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10590,U_10592) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_10586,sK262(U_10592,U_10590))],[f_2624_3]) ).

cnf(f_2624_5,plain,
    ( U_10590 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10592),sK262(U_10592,U_10590))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10590,U_10592) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

cnf(f_2624_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10591,U_10593) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10591 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10593),U_10587) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

fof(f_2625_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_2625_2,plain,
    ! [U_10595,U_10594] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10594,U_10595) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10594,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10595)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

cnf(f_2625_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10594,U_10595) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10594,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10595)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2625_2]) ).

fof(f_2626_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_2626_2,plain,
    ! [U_10597,U_10596] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10596,U_10597) != 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_10596),U_10597) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

cnf(f_2626_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10596,U_10597) != 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_10596),U_10597) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2626_2]) ).

fof(f_2627_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_2627_2,plain,
    ! [U_10598] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10598,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_10598
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10598),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

fof(f_2627_3,plain,
    ( ! [U_10600] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10600,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_10600
    & ! [U_10599] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10599),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_2627_2]) ).

cnf(f_2627_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10599),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2627_3]) ).

cnf(f_2627_5,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10600,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_10600,
    inference(clausify,[status(thm)],[f_2627_3]) ).

fof(f_2628_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_2628_2,plain,
    ! [U_10602,U_10601] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10601,U_10602)),U_10602) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

cnf(f_2628_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10601,U_10602)),U_10602) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2628_2]) ).

fof(f_2629_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_2629_2,plain,
    ! [U_10605,U_10604,U_10603] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10603),U_10604)),U_10605) = 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_10603),U_10605)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10604),U_10605))),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_10603,U_10605)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10604,U_10605))),U_10605)),
    inference(variable_rename,[status(thm)],[f_2629_1]) ).

cnf(f_2629_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10603),U_10604)),U_10605) = 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_10603),U_10605)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10604),U_10605))),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_10603,U_10605)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10604,U_10605))),U_10605)),
    inference(clausify,[status(thm)],[f_2629_2]) ).

fof(f_2630_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_2630_2,plain,
    ! [U_10609,U_10608,U_10607,U_10606] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10606),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10606),U_10607),U_10608)),U_10608)),c_Divides_Odiv__class_Omod(U_10606,U_10607,U_10608))),U_10609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),U_10607),U_10609)
      | ~ class_Divides_Osemiring__div(U_10606) ),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

cnf(f_2630_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10606),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10606),U_10607),U_10608)),U_10608)),c_Divides_Odiv__class_Omod(U_10606,U_10607,U_10608))),U_10609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10606),U_10607),U_10609)
    | ~ class_Divides_Osemiring__div(U_10606) ),
    inference(clausify,[status(thm)],[f_2630_2]) ).

fof(f_2631_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_2631_2,plain,
    ! [U_10613,U_10612,U_10611,U_10610] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10610),U_10611),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10610),U_10612),U_10611))),c_Divides_Odiv__class_Omod(U_10610,U_10612,U_10611))),U_10613) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),U_10612),U_10613)
      | ~ class_Divides_Osemiring__div(U_10610) ),
    inference(variable_rename,[status(thm)],[f_2631_1]) ).

cnf(f_2631_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10610),U_10611),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10610),U_10612),U_10611))),c_Divides_Odiv__class_Omod(U_10610,U_10612,U_10611))),U_10613) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10610),U_10612),U_10613)
    | ~ class_Divides_Osemiring__div(U_10610) ),
    inference(clausify,[status(thm)],[f_2631_2]) ).

fof(f_2632_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_2632_2,plain,
    ! [U_10616,U_10615,U_10614] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10614),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10614),U_10615),U_10616)),U_10616)),c_Divides_Odiv__class_Omod(U_10614,U_10615,U_10616)) = U_10615
      | ~ class_Divides_Osemiring__div(U_10614) ),
    inference(variable_rename,[status(thm)],[f_2632_1]) ).

cnf(f_2632_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10614),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10614),U_10615),U_10616)),U_10616)),c_Divides_Odiv__class_Omod(U_10614,U_10615,U_10616)) = U_10615
    | ~ class_Divides_Osemiring__div(U_10614) ),
    inference(clausify,[status(thm)],[f_2632_2]) ).

fof(f_2633_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_2633_2,plain,
    ! [U_10619,U_10618,U_10617] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10617),U_10618),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10617),U_10619),U_10618))),c_Divides_Odiv__class_Omod(U_10617,U_10619,U_10618)) = U_10619
      | ~ class_Divides_Osemiring__div(U_10617) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

cnf(f_2633_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10617),U_10618),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10617),U_10619),U_10618))),c_Divides_Odiv__class_Omod(U_10617,U_10619,U_10618)) = U_10619
    | ~ class_Divides_Osemiring__div(U_10617) ),
    inference(clausify,[status(thm)],[f_2633_2]) ).

fof(f_2634_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_2634_2,plain,
    ! [U_10622,U_10621,U_10620] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10620),c_Divides_Odiv__class_Omod(U_10620,U_10621,U_10622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10620),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10620),U_10621),U_10622)),U_10622)) = U_10621
      | ~ class_Divides_Osemiring__div(U_10620) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

cnf(f_2634_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10620),c_Divides_Odiv__class_Omod(U_10620,U_10621,U_10622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10620),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_10620),U_10621),U_10622)),U_10622)) = U_10621
    | ~ class_Divides_Osemiring__div(U_10620) ),
    inference(clausify,[status(thm)],[f_2634_2]) ).

fof(f_2635_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_2635_2,plain,
    ! [U_10624,U_10623] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10623,U_10624) = U_10623
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10624),U_10623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10623),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

cnf(f_2635_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10623,U_10624) = U_10623
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10624),U_10623))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10623),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

fof(f_2636_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_2636_2,plain,
    ! [U_10626,U_10625] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10626,U_10625)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10626,U_10625)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

cnf(f_2636_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10626,U_10625)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2636_2]) ).

cnf(f_2636_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10626,U_10625)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10625),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2636_2]) ).

fof(f_2637_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_2637_2,plain,
    ! [U_10628,U_10627] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10628,U_10627)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10627),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

cnf(f_2637_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10628,U_10627)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10627),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2637_2]) ).

fof(f_2638_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_2638_2,plain,
    ! [U_10630,U_10629] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10629,U_10630) = U_10629
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10629),U_10630))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10629)) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

cnf(f_2638_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10629,U_10630) = U_10629
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10629),U_10630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10629)) ),
    inference(clausify,[status(thm)],[f_2638_2]) ).

fof(f_2639_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_2639_2,plain,
    ! [U_10632,U_10631] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10632,U_10631)),U_10631))
        & 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_10632,U_10631))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10631)) ),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

cnf(f_2639_3,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_10632,U_10631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10631)) ),
    inference(clausify,[status(thm)],[f_2639_2]) ).

cnf(f_2639_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10632,U_10631)),U_10631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10631)) ),
    inference(clausify,[status(thm)],[f_2639_2]) ).

fof(f_2640_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_2640_2,plain,
    ! [U_10634,U_10633] :
      ( 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_10634,U_10633)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10633)) ),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

cnf(f_2640_3,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_10634,U_10633)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10633)) ),
    inference(clausify,[status(thm)],[f_2640_2]) ).

fof(f_2641_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).

fof(f_2641_2,plain,
    ! [U_10636,U_10635] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),c_Groups_Osgn__class_Osgn(U_10635,U_10636)),c_Groups_Ozero__class_Ozero(U_10635)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),U_10636),c_Groups_Ozero__class_Ozero(U_10635))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),U_10636),c_Groups_Ozero__class_Ozero(U_10635)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),c_Groups_Osgn__class_Osgn(U_10635,U_10636)),c_Groups_Ozero__class_Ozero(U_10635))) ) )
      | ~ class_Rings_Olinordered__idom(U_10635) ),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

cnf(f_2641_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),U_10636),c_Groups_Ozero__class_Ozero(U_10635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),c_Groups_Osgn__class_Osgn(U_10635,U_10636)),c_Groups_Ozero__class_Ozero(U_10635)))
    | ~ class_Rings_Olinordered__idom(U_10635) ),
    inference(clausify,[status(thm)],[f_2641_2]) ).

cnf(f_2641_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),c_Groups_Osgn__class_Osgn(U_10635,U_10636)),c_Groups_Ozero__class_Ozero(U_10635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10635),U_10636),c_Groups_Ozero__class_Ozero(U_10635)))
    | ~ class_Rings_Olinordered__idom(U_10635) ),
    inference(clausify,[status(thm)],[f_2641_2]) ).

fof(f_2642_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).

fof(f_2642_2,plain,
    ! [U_10638,U_10637] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),c_Groups_Osgn__class_Osgn(U_10637,U_10638)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),U_10638)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),U_10638))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),c_Groups_Osgn__class_Osgn(U_10637,U_10638))) ) )
      | ~ class_Rings_Olinordered__idom(U_10637) ),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

cnf(f_2642_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),U_10638))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),c_Groups_Osgn__class_Osgn(U_10637,U_10638)))
    | ~ class_Rings_Olinordered__idom(U_10637) ),
    inference(clausify,[status(thm)],[f_2642_2]) ).

cnf(f_2642_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),c_Groups_Osgn__class_Osgn(U_10637,U_10638)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10637),c_Groups_Ozero__class_Ozero(U_10637)),U_10638))
    | ~ class_Rings_Olinordered__idom(U_10637) ),
    inference(clausify,[status(thm)],[f_2642_2]) ).

fof(f_2643_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_2643_2,plain,
    ! [U_10640,U_10639] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10639),U_10640) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10640),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10639,U_10640))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10639,U_10640) = 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_10639),U_10640) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10639,U_10640) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

fof(f_2643_3,plain,
    ( ! [U_10644,U_10642] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10642),U_10644) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10644),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10642,U_10644))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10642,U_10644) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10643,U_10641] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10641),U_10643) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10641,U_10643) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2643_2]) ).

cnf(f_2643_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10641),U_10643) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10641,U_10643) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2643_3]) ).

cnf(f_2643_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10642),U_10644) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10644),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10642,U_10644))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10642,U_10644) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2643_3]) ).

fof(f_2644_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_2644_2,plain,
    ! [U_10646,U_10645] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10645,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10646)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10645,U_10646)),U_10646)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10645,U_10646) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10645,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10646)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10645,U_10646) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

fof(f_2644_3,plain,
    ( ! [U_10650,U_10648] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,U_10650)),U_10650)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,U_10650) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10649,U_10647] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10647,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10649)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10647,U_10649) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2644_2]) ).

cnf(f_2644_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10647,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10649)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10647,U_10649) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2644_3]) ).

cnf(f_2644_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,U_10650)),U_10650)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10648,U_10650) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2644_3]) ).

fof(f_2645_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_2645_2,plain,
    ! [U_10652,U_10651] : U_10651 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10652),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10651),U_10652))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10651,U_10652)),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

cnf(f_2645_3,plain,
    U_10651 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10652),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10651),U_10652))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10651,U_10652)),
    inference(clausify,[status(thm)],[f_2645_2]) ).

fof(f_2646_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_2646_2,plain,
    ! [U_10655,U_10654,U_10653] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),U_10654)),U_10655) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10654),U_10655))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10654,U_10655))),U_10655)),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

cnf(f_2646_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),U_10654)),U_10655) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10654),U_10655))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10653),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10654,U_10655))),U_10655)),
    inference(clausify,[status(thm)],[f_2646_2]) ).

fof(f_2647_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_2647_2,plain,
    ! [U_10658,U_10657,U_10656] : 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_10656),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10657),U_10656))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10657,U_10656))),U_10658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10657),U_10658),
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

cnf(f_2647_3,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_10656),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10657),U_10656))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10657,U_10656))),U_10658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10657),U_10658),
    inference(clausify,[status(thm)],[f_2647_2]) ).

fof(f_2648_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_2648_2,plain,
    ! [U_10661,U_10660,U_10659] : 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_10659),U_10660)),U_10660)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10659,U_10660))),U_10661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10659),U_10661),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

cnf(f_2648_3,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_10659),U_10660)),U_10660)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10659,U_10660))),U_10661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10659),U_10661),
    inference(clausify,[status(thm)],[f_2648_2]) ).

fof(f_2649_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_2649_2,plain,
    ! [U_10663,U_10662] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10662,U_10663) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10662),U_10663)),U_10663)),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

cnf(f_2649_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10662,U_10663) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10662),U_10663)),U_10663)),
    inference(clausify,[status(thm)],[f_2649_2]) ).

fof(f_2650_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_2650_2,plain,
    ! [U_10665,U_10664] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10664),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10665),U_10664)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10665),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10665,U_10664)),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

cnf(f_2650_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10664),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10665),U_10664)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10665),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10665,U_10664)),
    inference(clausify,[status(thm)],[f_2650_2]) ).

fof(f_2651_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_2651_2,plain,
    ! [U_10667,U_10666] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10666),U_10667) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10666),U_10667),c_Groups_Osgn__class_Osgn(U_10666,U_10667))
      | ~ class_Rings_Olinordered__idom(U_10666) ),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

cnf(f_2651_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10666),U_10667) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10666),U_10667),c_Groups_Osgn__class_Osgn(U_10666,U_10667))
    | ~ class_Rings_Olinordered__idom(U_10666) ),
    inference(clausify,[status(thm)],[f_2651_2]) ).

fof(f_2652_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_2652_2,plain,
    ! [U_10669,U_10668] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10668),c_Groups_Osgn__class_Osgn(U_10668,U_10669)),hAPP(c_Groups_Oabs__class_Oabs(U_10668),U_10669)) = U_10669
      | ~ class_Rings_Olinordered__idom(U_10668) ),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

cnf(f_2652_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10668),c_Groups_Osgn__class_Osgn(U_10668,U_10669)),hAPP(c_Groups_Oabs__class_Oabs(U_10668),U_10669)) = U_10669
    | ~ class_Rings_Olinordered__idom(U_10668) ),
    inference(clausify,[status(thm)],[f_2652_2]) ).

fof(f_2653_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_2653_2,plain,
    ! [U_10671,U_10670] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10670,U_10671) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10670),U_10671)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10670),U_10671)),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_10670)) ),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

cnf(f_2653_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10670,U_10671) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10670),U_10671)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10670),U_10671)),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_10670)) ),
    inference(clausify,[status(thm)],[f_2653_2]) ).

fof(f_2654_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_2654_2,plain,
    ! [U_10673,U_10672] :
      ( c_Groups_Osgn__class_Osgn(U_10672,U_10673) = c_Groups_Oone__class_Oone(U_10672)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10672),c_Groups_Ozero__class_Ozero(U_10672)),U_10673))
      | ~ class_Rings_Olinordered__idom(U_10672) ),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

cnf(f_2654_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10672,U_10673) = c_Groups_Oone__class_Oone(U_10672)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10672),c_Groups_Ozero__class_Ozero(U_10672)),U_10673))
    | ~ class_Rings_Olinordered__idom(U_10672) ),
    inference(clausify,[status(thm)],[f_2654_2]) ).

fof(f_2655_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = 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_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
          | c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Oone__class_Oone(T_a) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).

fof(f_2655_2,plain,
    ! [U_10675,U_10674] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_10674,U_10675) = c_Groups_Oone__class_Oone(U_10674)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10674),c_Groups_Ozero__class_Ozero(U_10674)),U_10675)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10674),c_Groups_Ozero__class_Ozero(U_10674)),U_10675))
          | c_Groups_Osgn__class_Osgn(U_10674,U_10675) != c_Groups_Oone__class_Oone(U_10674) ) )
      | ~ class_Rings_Olinordered__idom(U_10674) ),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

cnf(f_2655_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10674),c_Groups_Ozero__class_Ozero(U_10674)),U_10675))
    | c_Groups_Osgn__class_Osgn(U_10674,U_10675) != c_Groups_Oone__class_Oone(U_10674)
    | ~ class_Rings_Olinordered__idom(U_10674) ),
    inference(clausify,[status(thm)],[f_2655_2]) ).

cnf(f_2655_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_10674,U_10675) = c_Groups_Oone__class_Oone(U_10674)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10674),c_Groups_Ozero__class_Ozero(U_10674)),U_10675))
    | ~ class_Rings_Olinordered__idom(U_10674) ),
    inference(clausify,[status(thm)],[f_2655_2]) ).

fof(f_2656_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_2656_2,plain,
    ! [U_10679,U_10678,U_10677,U_10676] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10676,U_10677) = U_10679
      | U_10677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10679),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10679),U_10677))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10679)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677)) )
      | U_10676 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10677),U_10678)),U_10679) ),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

cnf(f_2656_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10676,U_10677) = U_10679
    | U_10677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10676 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10677),U_10678)),U_10679) ),
    inference(clausify,[status(thm)],[f_2656_2]) ).

cnf(f_2656_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10679),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10676,U_10677) = U_10679
    | U_10677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10676 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10677),U_10678)),U_10679) ),
    inference(clausify,[status(thm)],[f_2656_2]) ).

cnf(f_2656_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10679),U_10677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10679))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10676,U_10677) = U_10679
    | U_10677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10676 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10677),U_10678)),U_10679) ),
    inference(clausify,[status(thm)],[f_2656_2]) ).

cnf(f_2656_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10679),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10679),U_10677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10679))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10676,U_10677) = U_10679
    | U_10677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10676 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10677),U_10678)),U_10679) ),
    inference(clausify,[status(thm)],[f_2656_2]) ).

fof(f_2657_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_2657_2,plain,
    ! [U_10683,U_10682,U_10681,U_10680] :
      ( 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_10681),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10683,U_10680))),U_10682)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10682),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10681),U_10682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10680)) ),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

cnf(f_2657_3,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_10681),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10683,U_10680))),U_10682)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10682),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10681),U_10682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10680)) ),
    inference(clausify,[status(thm)],[f_2657_2]) ).

fof(f_2658_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_2658_2,plain,
    ! [U_10687,U_10686,U_10685,U_10684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10685),U_10684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10685),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10687,U_10684))),U_10686)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10686),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10685),U_10686))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10684)) ),
    inference(variable_rename,[status(thm)],[f_2658_1]) ).

cnf(f_2658_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10685),U_10684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10685),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10687,U_10684))),U_10686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10686),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10685),U_10686))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10684)) ),
    inference(clausify,[status(thm)],[f_2658_2]) ).

fof(f_2659_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_2659_2,plain,
    ! [U_10691,U_10690,U_10689,U_10688] :
      ( 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_10690),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10691,U_10688))),U_10689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10690),U_10688)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10689),U_10690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10688)) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

cnf(f_2659_3,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_10690),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10691,U_10688))),U_10689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10690),U_10688)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10689),U_10690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10688)) ),
    inference(clausify,[status(thm)],[f_2659_2]) ).

fof(f_2660_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_2660_2,plain,
    ! [U_10695,U_10694,U_10693,U_10692] :
      ( 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_10694),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10695,U_10692))),U_10693)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10693),U_10694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10693))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10692)) ),
    inference(variable_rename,[status(thm)],[f_2660_1]) ).

cnf(f_2660_3,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_10694),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10695,U_10692))),U_10693)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10693),U_10694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10692)) ),
    inference(clausify,[status(thm)],[f_2660_2]) ).

fof(f_2661_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).

fof(f_2661_2,plain,
    ! [U_10706,U_10705,U_10704] :
      ( ( hBOOL(hAPP(U_10704,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10705,U_10706)))
        | ( ? [U_10703,U_10702] :
              ( ~ hBOOL(hAPP(U_10704,U_10702))
              & U_10705 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10706),U_10703)),U_10702)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10702),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10706),U_10702)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10706),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_10701,U_10700] :
              ( ~ hBOOL(hAPP(U_10704,U_10700))
              & U_10705 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10706),U_10701)),U_10700)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),U_10706))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10700)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10706)) )
        | ( ~ hBOOL(hAPP(U_10704,U_10705))
          & U_10706 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10704,U_10698))
                | U_10705 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10706),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10706),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10706),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10704,U_10696))
                | U_10705 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10706),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10706))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10706)) )
          & ( hBOOL(hAPP(U_10704,U_10705))
            | U_10706 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10704,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10705,U_10706))) ) ),
    inference(variable_rename,[status(thm)],[f_2661_1]) ).

fof(f_2661_3,plain,
    ( ! [U_10712,U_10710,U_10708] :
        ( hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712)))
        | ( ? [U_10703,U_10702] :
              ( ~ hBOOL(hAPP(U_10708,U_10702))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),U_10703)),U_10702)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10702),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),U_10702)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_10701,U_10700] :
              ( ~ hBOOL(hAPP(U_10708,U_10700))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),U_10701)),U_10700)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),U_10712))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10700)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712)) )
        | ( ~ hBOOL(hAPP(U_10708,U_10710))
          & U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10711,U_10709,U_10707] :
        ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10707,U_10698))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10707,U_10696))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711)) )
          & ( hBOOL(hAPP(U_10707,U_10709))
            | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ) ),
    inference(miniscope,[status(thm)],[f_2661_2]) ).

fof(f_2661_4,plain,
    ( ! [U_10712,U_10710,U_10708] :
        ( hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712)))
        | ( ? [U_10703,U_10702] :
              ( ~ hBOOL(hAPP(U_10708,U_10702))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),U_10703)),U_10702)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10702),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),U_10702)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_10700] :
              ( ~ hBOOL(hAPP(U_10708,U_10700))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),U_10700)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),U_10712))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10700)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712)) )
        | ( ~ hBOOL(hAPP(U_10708,U_10710))
          & U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10711,U_10709,U_10707] :
        ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10707,U_10698))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10707,U_10696))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711)) )
          & ( hBOOL(hAPP(U_10707,U_10709))
            | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_10701,sK263(U_10712,U_10710,U_10708))],[f_2661_3]) ).

fof(f_2661_5,plain,
    ( ! [U_10712,U_10710,U_10708] :
        ( hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712)))
        | ( ? [U_10703,U_10702] :
              ( ~ hBOOL(hAPP(U_10708,U_10702))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),U_10703)),U_10702)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10702),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),U_10702)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
          & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712)) )
        | ( ~ hBOOL(hAPP(U_10708,U_10710))
          & U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10711,U_10709,U_10707] :
        ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10707,U_10698))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10707,U_10696))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711)) )
          & ( hBOOL(hAPP(U_10707,U_10709))
            | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_10700,sK264(U_10712,U_10710,U_10708))],[f_2661_4]) ).

fof(f_2661_6,plain,
    ( ! [U_10712,U_10710,U_10708] :
        ( hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712)))
        | ( ? [U_10702] :
              ( ~ hBOOL(hAPP(U_10708,U_10702))
              & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),U_10702)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10702),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),U_10702)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
          & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712)) )
        | ( ~ hBOOL(hAPP(U_10708,U_10710))
          & U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10711,U_10709,U_10707] :
        ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10707,U_10698))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10707,U_10696))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711)) )
          & ( hBOOL(hAPP(U_10707,U_10709))
            | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_10703,sK265(U_10712,U_10710,U_10708))],[f_2661_5]) ).

fof(f_2661_7,plain,
    ( ! [U_10712,U_10710,U_10708] :
        ( hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712)))
        | ( ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
          & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
          & U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712)) )
        | ( ~ hBOOL(hAPP(U_10708,U_10710))
          & U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_10711,U_10709,U_10707] :
        ( ( ( ! [U_10699,U_10698] :
                ( hBOOL(hAPP(U_10707,U_10698))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_10697,U_10696] :
                ( hBOOL(hAPP(U_10707,U_10696))
                | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711)) )
          & ( hBOOL(hAPP(U_10707,U_10709))
            | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_10702,sK266(U_10712,U_10710,U_10708))],[f_2661_6]) ).

cnf(f_2661_8,plain,
    ( hBOOL(hAPP(U_10707,U_10709))
    | U_10711 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_9,plain,
    ( hBOOL(hAPP(U_10707,U_10696))
    | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10697)),U_10696)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10696),U_10711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10711))
    | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_10,plain,
    ( hBOOL(hAPP(U_10707,U_10698))
    | U_10709 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10711),U_10699)),U_10698)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),U_10698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10711),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_10707,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10709,U_10711))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_14,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_15,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_19,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_20,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_24,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_25,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_29,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_30,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_34,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_35,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_39,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_40,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | U_10712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_44,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_45,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10712),sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_49,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_50,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK266(U_10712,U_10710,U_10708)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_54,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_55,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK265(U_10712,U_10710,U_10708))),sK266(U_10712,U_10710,U_10708))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK264(U_10712,U_10710,U_10708)),U_10712))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_59,plain,
    ( U_10710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10712),sK263(U_10712,U_10710,U_10708))),sK264(U_10712,U_10710,U_10708))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

cnf(f_2661_60,plain,
    ( ~ hBOOL(hAPP(U_10708,sK264(U_10712,U_10710,U_10708)))
    | ~ hBOOL(hAPP(U_10708,U_10710))
    | ~ hBOOL(hAPP(U_10708,sK266(U_10712,U_10710,U_10708)))
    | hBOOL(hAPP(U_10708,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10710,U_10712))) ),
    inference(clausify,[status(thm)],[f_2661_7]) ).

fof(f_2662_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_2662_2,plain,
    ! [U_10715,U_10714,U_10713] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10715),U_10713)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10715),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10714),U_10715),U_10713))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10714,U_10715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10713)) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

cnf(f_2662_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10715),U_10713)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10715),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10714),U_10715),U_10713))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10714,U_10715))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10713)) ),
    inference(clausify,[status(thm)],[f_2662_2]) ).

fof(f_2663_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_2663_2,plain,
    ! [U_10717,U_10716] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10716)) = 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_10717),U_10716))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10717,U_10716) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10716)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),U_10716))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10717,U_10716) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_10716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

cnf(f_2663_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10716)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),U_10716))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10717,U_10716) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2663_2]) ).

cnf(f_2663_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10716)) = 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_10717),U_10716))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10717,U_10716) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2663_2]) ).

fof(f_2664_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_2664_2,plain,
    ! [U_10719,U_10718] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10719)),U_10718) = 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_10719),U_10718))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10719,U_10718) = 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_10719)),U_10718) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10719),U_10718))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10719,U_10718) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_10718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2664_1]) ).

cnf(f_2664_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10719)),U_10718) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10719),U_10718))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10719,U_10718) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2664_2]) ).

cnf(f_2664_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10719)),U_10718) = 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_10719),U_10718))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10719,U_10718) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2664_2]) ).

fof(f_2665_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_2665_2,plain,
    ! [U_10720] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10720) = 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_10720)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10720) = 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_10720)) ) )
        | U_10720 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10720) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_10720 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2665_1]) ).

fof(f_2665_3,plain,
    ( ! [U_10722] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10722) = 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_10722)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10722) = 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_10722)) ) )
        | U_10722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10721] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_10721 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2665_2]) ).

cnf(f_2665_4,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10721 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2665_3]) ).

cnf(f_2665_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10722) = 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_10722))
    | U_10722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2665_3]) ).

cnf(f_2665_6,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10722) = 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_10722))
    | U_10722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2665_3]) ).

fof(f_2666_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_2666_2,plain,
    ! [U_10724,U_10723] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10723),c_Groups_Oone__class_Oone(U_10723))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10723),c_Groups_Ozero__class_Ozero(U_10723)),U_10724)) )
            & ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = c_Groups_Oone__class_Oone(U_10723)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10723),c_Groups_Ozero__class_Ozero(U_10723)),U_10724)) ) )
          | U_10724 = c_Groups_Ozero__class_Ozero(U_10723) )
        & ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = c_Groups_Ozero__class_Ozero(U_10723)
          | U_10724 != c_Groups_Ozero__class_Ozero(U_10723) ) )
      | ~ class_Groups_Osgn__if(U_10723) ),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

cnf(f_2666_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = c_Groups_Ozero__class_Ozero(U_10723)
    | U_10724 != c_Groups_Ozero__class_Ozero(U_10723)
    | ~ class_Groups_Osgn__if(U_10723) ),
    inference(clausify,[status(thm)],[f_2666_2]) ).

cnf(f_2666_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = c_Groups_Oone__class_Oone(U_10723)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10723),c_Groups_Ozero__class_Ozero(U_10723)),U_10724))
    | U_10724 = c_Groups_Ozero__class_Ozero(U_10723)
    | ~ class_Groups_Osgn__if(U_10723) ),
    inference(clausify,[status(thm)],[f_2666_2]) ).

cnf(f_2666_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_10723,U_10724) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10723),c_Groups_Oone__class_Oone(U_10723))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10723),c_Groups_Ozero__class_Ozero(U_10723)),U_10724))
    | U_10724 = c_Groups_Ozero__class_Ozero(U_10723)
    | ~ class_Groups_Osgn__if(U_10723) ),
    inference(clausify,[status(thm)],[f_2666_2]) ).

fof(f_2667_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = 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_2),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
          | c_Groups_Osgn__class_Osgn(T_a,V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).

fof(f_2667_2,plain,
    ! [U_10726,U_10725] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_10725,U_10726) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10725),c_Groups_Oone__class_Oone(U_10725))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10725),U_10726),c_Groups_Ozero__class_Ozero(U_10725))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10725),U_10726),c_Groups_Ozero__class_Ozero(U_10725)))
          | c_Groups_Osgn__class_Osgn(U_10725,U_10726) != hAPP(c_Groups_Ouminus__class_Ouminus(U_10725),c_Groups_Oone__class_Oone(U_10725)) ) )
      | ~ class_Rings_Olinordered__idom(U_10725) ),
    inference(variable_rename,[status(thm)],[f_2667_1]) ).

cnf(f_2667_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10725),U_10726),c_Groups_Ozero__class_Ozero(U_10725)))
    | c_Groups_Osgn__class_Osgn(U_10725,U_10726) != hAPP(c_Groups_Ouminus__class_Ouminus(U_10725),c_Groups_Oone__class_Oone(U_10725))
    | ~ class_Rings_Olinordered__idom(U_10725) ),
    inference(clausify,[status(thm)],[f_2667_2]) ).

cnf(f_2667_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_10725,U_10726) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10725),c_Groups_Oone__class_Oone(U_10725))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10725),U_10726),c_Groups_Ozero__class_Ozero(U_10725)))
    | ~ class_Rings_Olinordered__idom(U_10725) ),
    inference(clausify,[status(thm)],[f_2667_2]) ).

fof(f_2668_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_2668_2,plain,
    ! [U_10728,U_10727] :
      ( ( c_SMT_Oz3mod(U_10728,U_10727) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10728,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10727))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10727)) )
      & ( c_SMT_Oz3mod(U_10728,U_10727) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10728,U_10727)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10727)) ) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

fof(f_2668_3,plain,
    ( ! [U_10732,U_10730] :
        ( c_SMT_Oz3mod(U_10732,U_10730) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10732,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10730))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10730)) )
    & ! [U_10731,U_10729] :
        ( c_SMT_Oz3mod(U_10731,U_10729) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10731,U_10729)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10729)) ) ),
    inference(miniscope,[status(thm)],[f_2668_2]) ).

cnf(f_2668_4,plain,
    ( c_SMT_Oz3mod(U_10731,U_10729) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10731,U_10729)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10729)) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

cnf(f_2668_5,plain,
    ( c_SMT_Oz3mod(U_10732,U_10730) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10732,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10730))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10730)) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

fof(f_2669_1,plain,
    ! [V_f_2,V_S_2,T_a] :
      ( 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_a,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_a),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).

fof(f_2669_2,plain,
    ! [U_10736,U_10735,U_10734] :
      ( 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_10734,tc_Nat_Onat),U_10736),U_10735)))
      | ? [U_10733] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10736,U_10733)))
          & hBOOL(hAPP(hAPP(c_member(U_10734),U_10733),U_10735)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10734),U_10735)) ),
    inference(variable_rename,[status(thm)],[f_2669_1]) ).

fof(f_2669_3,plain,
    ! [U_10736,U_10735,U_10734] :
      ( 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_10734,tc_Nat_Onat),U_10736),U_10735)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10736,sK267(U_10736,U_10735,U_10734))))
        & hBOOL(hAPP(hAPP(c_member(U_10734),sK267(U_10736,U_10735,U_10734)),U_10735)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10734),U_10735)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_10733,sK267(U_10736,U_10735,U_10734))],[f_2669_2]) ).

cnf(f_2669_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10734),sK267(U_10736,U_10735,U_10734)),U_10735))
    | 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_10734,tc_Nat_Onat),U_10736),U_10735)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10734),U_10735)) ),
    inference(clausify,[status(thm)],[f_2669_3]) ).

cnf(f_2669_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10736,sK267(U_10736,U_10735,U_10734))))
    | 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_10734,tc_Nat_Onat),U_10736),U_10735)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10734),U_10735)) ),
    inference(clausify,[status(thm)],[f_2669_3]) ).

fof(f_2670_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint]) ).

fof(f_2670_2,plain,
    ! [U_10739,U_10738,U_10737] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_10737,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10737),U_10738),U_10739)) = hAPP(c_Finite__Set_Ocard(U_10737),U_10738)
      | ~ c_Fun_Oinj__on(U_10737,tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10737,tc_fun(tc_prod(U_10737,U_10737),tc_HOL_Obool),tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10737,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10737,U_10737),tc_HOL_Obool),tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool)),U_10737),c_Equiv__Relations_Oquotient(U_10737)),hAPP(hAPP(c_COMBC(U_10737,tc_fun(U_10737,tc_HOL_Obool),tc_fun(U_10737,tc_HOL_Obool)),c_Set_Oinsert(U_10737)),c_Orderings_Obot__class_Obot(tc_fun(U_10737,tc_HOL_Obool))))),U_10739),U_10738)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10737),U_10738)) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

cnf(f_2670_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_10737,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10737),U_10738),U_10739)) = hAPP(c_Finite__Set_Ocard(U_10737),U_10738)
    | ~ c_Fun_Oinj__on(U_10737,tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10737,tc_fun(tc_prod(U_10737,U_10737),tc_HOL_Obool),tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10737,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10737,U_10737),tc_HOL_Obool),tc_fun(tc_fun(U_10737,tc_HOL_Obool),tc_HOL_Obool)),U_10737),c_Equiv__Relations_Oquotient(U_10737)),hAPP(hAPP(c_COMBC(U_10737,tc_fun(U_10737,tc_HOL_Obool),tc_fun(U_10737,tc_HOL_Obool)),c_Set_Oinsert(U_10737)),c_Orderings_Obot__class_Obot(tc_fun(U_10737,tc_HOL_Obool))))),U_10739),U_10738)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10737),U_10738)) ),
    inference(clausify,[status(thm)],[f_2670_2]) ).

fof(f_2671_1,plain,
    ! [V_f_2,V_S_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_b)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).

fof(f_2671_2,plain,
    ! [U_10744,U_10743,U_10742,U_10741] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10741,U_10742,c_Groups_Otimes__class_Otimes(U_10741)),U_10744),c_Groups_Oone__class_Oone(U_10741)),U_10743) = c_Groups_Oone__class_Oone(U_10741)
      | ? [U_10740] :
          ( hAPP(U_10744,U_10740) != c_Groups_Oone__class_Oone(U_10741)
          & hBOOL(hAPP(hAPP(c_member(U_10742),U_10740),U_10743)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10742),U_10743))
      | ~ class_Groups_Ocomm__monoid__mult(U_10741) ),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

fof(f_2671_3,plain,
    ! [U_10744,U_10743,U_10742,U_10741] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10741,U_10742,c_Groups_Otimes__class_Otimes(U_10741)),U_10744),c_Groups_Oone__class_Oone(U_10741)),U_10743) = c_Groups_Oone__class_Oone(U_10741)
      | ( hAPP(U_10744,sK268(U_10744,U_10743,U_10742,U_10741)) != c_Groups_Oone__class_Oone(U_10741)
        & hBOOL(hAPP(hAPP(c_member(U_10742),sK268(U_10744,U_10743,U_10742,U_10741)),U_10743)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10742),U_10743))
      | ~ class_Groups_Ocomm__monoid__mult(U_10741) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_10740,sK268(U_10744,U_10743,U_10742,U_10741))],[f_2671_2]) ).

cnf(f_2671_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10742),sK268(U_10744,U_10743,U_10742,U_10741)),U_10743))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10741,U_10742,c_Groups_Otimes__class_Otimes(U_10741)),U_10744),c_Groups_Oone__class_Oone(U_10741)),U_10743) = c_Groups_Oone__class_Oone(U_10741)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10742),U_10743))
    | ~ class_Groups_Ocomm__monoid__mult(U_10741) ),
    inference(clausify,[status(thm)],[f_2671_3]) ).

cnf(f_2671_5,plain,
    ( hAPP(U_10744,sK268(U_10744,U_10743,U_10742,U_10741)) != c_Groups_Oone__class_Oone(U_10741)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10741,U_10742,c_Groups_Otimes__class_Otimes(U_10741)),U_10744),c_Groups_Oone__class_Oone(U_10741)),U_10743) = c_Groups_Oone__class_Oone(U_10741)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10742),U_10743))
    | ~ class_Groups_Ocomm__monoid__mult(U_10741) ),
    inference(clausify,[status(thm)],[f_2671_3]) ).

fof(f_2672_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_2672_2,plain,
    ! [U_10747,U_10746,U_10745] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10746,U_10747)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),U_10746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),U_10747)),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

cnf(f_2672_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10746,U_10747)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),U_10746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10745),U_10747)),
    inference(clausify,[status(thm)],[f_2672_2]) ).

fof(f_2673_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_2673_2,plain,
    ! [U_10750,U_10749,U_10748] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10748,U_10749)),U_10750) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10748),U_10750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10749),U_10750)),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

cnf(f_2673_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10748,U_10749)),U_10750) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10748),U_10750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10749),U_10750)),
    inference(clausify,[status(thm)],[f_2673_2]) ).

fof(f_2674_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_2674_2,plain,
    ! [U_10752,U_10751] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,U_10752)),U_10751)),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

cnf(f_2674_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,U_10752)),U_10751)),
    inference(clausify,[status(thm)],[f_2674_2]) ).

fof(f_2675_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_2675_2,plain,
    ! [U_10754,U_10753] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10753,U_10754) = U_10753
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10753),U_10754)) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

cnf(f_2675_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10753,U_10754) = U_10753
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10753),U_10754)) ),
    inference(clausify,[status(thm)],[f_2675_2]) ).

fof(f_2676_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_2676_2,plain,
    ! [U_10756,U_10755] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10755),U_10756) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10755,U_10756)),U_10756),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

cnf(f_2676_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10755),U_10756) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10755,U_10756)),U_10756),
    inference(clausify,[status(thm)],[f_2676_2]) ).

fof(f_2677_1,plain,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_quotient__empty]) ).

fof(f_2677_2,plain,
    ! [U_10758,U_10757] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10757),c_Orderings_Obot__class_Obot(tc_fun(U_10757,tc_HOL_Obool))),U_10758) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10757,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

cnf(f_2677_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10757),c_Orderings_Obot__class_Obot(tc_fun(U_10757,tc_HOL_Obool))),U_10758) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10757,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2677_2]) ).

fof(f_2678_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2]) ).

fof(f_2678_2,plain,
    ! [U_10761,U_10760,U_10759] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10759,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10759),U_10760),U_10761)
        | U_10760 != c_Orderings_Obot__class_Obot(tc_fun(U_10759,tc_HOL_Obool)) )
      & ( U_10760 = c_Orderings_Obot__class_Obot(tc_fun(U_10759,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10759,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10759),U_10760),U_10761) ) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ( ! [U_10767,U_10765,U_10763] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10763,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10763),U_10765),U_10767)
        | U_10765 != c_Orderings_Obot__class_Obot(tc_fun(U_10763,tc_HOL_Obool)) )
    & ! [U_10766,U_10764,U_10762] :
        ( U_10764 = c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10762,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10762),U_10764),U_10766) ) ),
    inference(miniscope,[status(thm)],[f_2678_2]) ).

cnf(f_2678_4,plain,
    ( U_10764 = c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10762,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10762),U_10764),U_10766) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

cnf(f_2678_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10763,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10763),U_10765),U_10767)
    | U_10765 != c_Orderings_Obot__class_Obot(tc_fun(U_10763,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

fof(f_2679_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty]) ).

fof(f_2679_2,plain,
    ! [U_10770,U_10769,U_10768] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10768),U_10769),U_10770) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10768,tc_HOL_Obool),tc_HOL_Obool))
        | U_10769 != c_Orderings_Obot__class_Obot(tc_fun(U_10768,tc_HOL_Obool)) )
      & ( U_10769 = c_Orderings_Obot__class_Obot(tc_fun(U_10768,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10768),U_10769),U_10770) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10768,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

fof(f_2679_3,plain,
    ( ! [U_10776,U_10774,U_10772] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10772),U_10774),U_10776) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10772,tc_HOL_Obool),tc_HOL_Obool))
        | U_10774 != c_Orderings_Obot__class_Obot(tc_fun(U_10772,tc_HOL_Obool)) )
    & ! [U_10775,U_10773,U_10771] :
        ( U_10773 = c_Orderings_Obot__class_Obot(tc_fun(U_10771,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10771),U_10773),U_10775) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10771,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2679_2]) ).

cnf(f_2679_4,plain,
    ( U_10773 = c_Orderings_Obot__class_Obot(tc_fun(U_10771,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10771),U_10773),U_10775) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10771,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

cnf(f_2679_5,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10772),U_10774),U_10776) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10772,tc_HOL_Obool),tc_HOL_Obool))
    | U_10774 != c_Orderings_Obot__class_Obot(tc_fun(U_10772,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

fof(f_2680_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_2680_2,plain,
    ! [U_10778,U_10777] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10777),U_10778) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10777,U_10778))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10777,U_10778)) = U_10778 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10777),U_10778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10777,U_10778)) != U_10778 ) ),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

fof(f_2680_3,plain,
    ( ! [U_10782,U_10780] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10780),U_10782) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10780,U_10782))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10780,U_10782)) = U_10782 )
    & ! [U_10781,U_10779] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10779),U_10781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10779,U_10781)) != U_10781 ) ),
    inference(miniscope,[status(thm)],[f_2680_2]) ).

cnf(f_2680_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10779),U_10781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10779,U_10781)) != U_10781 ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

cnf(f_2680_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10780),U_10782) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10780,U_10782))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10780,U_10782)) = U_10782 ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

fof(f_2681_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_2681_2,plain,
    ! [U_10783] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10783,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_2681_1]) ).

cnf(f_2681_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10783,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_2681_2]) ).

fof(f_2682_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_2682_2,plain,
    ! [U_10785,U_10784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10785,U_10784)),U_10784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10784)) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

cnf(f_2682_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10785,U_10784)),U_10784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10784)) ),
    inference(clausify,[status(thm)],[f_2682_2]) ).

fof(f_2683_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_2683_2,plain,
    ! [U_10789,U_10788] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10788,U_10789) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_10787] : U_10788 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10789),U_10787) )
      & ( ? [U_10786] : U_10788 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10789),U_10786)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10788,U_10789) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

fof(f_2683_3,plain,
    ( ! [U_10793,U_10791] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10791,U_10793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_10787] : U_10791 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10793),U_10787) )
    & ! [U_10792,U_10790] :
        ( ? [U_10786] : U_10790 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10792),U_10786)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10790,U_10792) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2683_2]) ).

fof(f_2683_4,plain,
    ( ! [U_10793,U_10791] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10791,U_10793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_10787] : U_10791 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10793),U_10787) )
    & ! [U_10792,U_10790] :
        ( U_10790 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10792),sK269(U_10792,U_10790))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10790,U_10792) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_10786,sK269(U_10792,U_10790))],[f_2683_3]) ).

cnf(f_2683_5,plain,
    ( U_10790 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10792),sK269(U_10792,U_10790))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10790,U_10792) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10791,U_10793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_10791 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10793),U_10787) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

fof(f_2684_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_2684_2,plain,
    ! [U_10795,U_10794] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10794,U_10795) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10794),U_10795),U_10795)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10794),U_10795)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10794,U_10795) = U_10794
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10794),U_10795)) ) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

fof(f_2684_3,plain,
    ( ! [U_10799,U_10797] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10797,U_10799) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10797),U_10799),U_10799)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10797),U_10799)) )
    & ! [U_10798,U_10796] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10796,U_10798) = U_10796
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10796),U_10798)) ) ),
    inference(miniscope,[status(thm)],[f_2684_2]) ).

cnf(f_2684_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10796,U_10798) = U_10796
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10796),U_10798)) ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

cnf(f_2684_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10797,U_10799) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10797),U_10799),U_10799)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10797),U_10799)) ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

fof(f_2685_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_2685_2,plain,
    ! [U_10801,U_10800] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10800,U_10801) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10800),U_10801),U_10801)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10800),U_10801)) ),
    inference(variable_rename,[status(thm)],[f_2685_1]) ).

cnf(f_2685_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10800,U_10801) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10800),U_10801),U_10801)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10800),U_10801)) ),
    inference(clausify,[status(thm)],[f_2685_2]) ).

fof(f_2686_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_2686_2,plain,
    ! [U_10804,U_10803,U_10802] : 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_10802),U_10803)),U_10804),U_10803) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10804,U_10803),
    inference(variable_rename,[status(thm)],[f_2686_1]) ).

cnf(f_2686_3,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_10802),U_10803)),U_10804),U_10803) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10804,U_10803),
    inference(clausify,[status(thm)],[f_2686_2]) ).

fof(f_2687_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_2687_2,plain,
    ! [U_10806,U_10805] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10806,U_10805) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10806),U_10805),U_10805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10805),U_10806)) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

cnf(f_2687_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10806,U_10805) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10806),U_10805),U_10805)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10805),U_10806)) ),
    inference(clausify,[status(thm)],[f_2687_2]) ).

fof(f_2688_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_2688_2,plain,
    ! [U_10808,U_10807] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10807,U_10808)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10807),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10808)),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

cnf(f_2688_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10807,U_10808)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10807),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10808)),
    inference(clausify,[status(thm)],[f_2688_2]) ).

fof(f_2689_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_2689_2,plain,
    ! [U_10810,U_10809] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10809),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10810)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10809,U_10810)),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

cnf(f_2689_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10809),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10810)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10809,U_10810)),
    inference(clausify,[status(thm)],[f_2689_2]) ).

fof(f_2690_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_2690_2,plain,
    ! [U_10813,U_10812,U_10811] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10811),U_10812)),U_10813) = 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_10811),U_10813)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10812),U_10813))),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_10811,U_10813)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10812,U_10813))),U_10813)),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

cnf(f_2690_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10811),U_10812)),U_10813) = 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_10811),U_10813)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10812),U_10813))),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_10811,U_10813)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10812,U_10813))),U_10813)),
    inference(clausify,[status(thm)],[f_2690_2]) ).

fof(f_2691_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_2691_2,plain,
    ! [U_10815,U_10814] :
      ( ( c_Nitpick_Onat__gcd(U_10815,U_10814) = c_Nitpick_Onat__gcd(U_10814,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10815,U_10814))
        | U_10814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_10815,U_10814) = U_10815
        | U_10814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

fof(f_2691_3,plain,
    ( ! [U_10819,U_10817] :
        ( c_Nitpick_Onat__gcd(U_10819,U_10817) = c_Nitpick_Onat__gcd(U_10817,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10819,U_10817))
        | U_10817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_10818,U_10816] :
        ( c_Nitpick_Onat__gcd(U_10818,U_10816) = U_10818
        | U_10816 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2691_2]) ).

cnf(f_2691_4,plain,
    ( c_Nitpick_Onat__gcd(U_10818,U_10816) = U_10818
    | U_10816 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

cnf(f_2691_5,plain,
    ( c_Nitpick_Onat__gcd(U_10819,U_10817) = c_Nitpick_Onat__gcd(U_10817,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10819,U_10817))
    | U_10817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

fof(f_2692_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_2692_2,plain,
    ! [U_10821,U_10820] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10821,U_10820)),U_10820))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10820)) ),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

cnf(f_2692_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10821,U_10820)),U_10820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10820)) ),
    inference(clausify,[status(thm)],[f_2692_2]) ).

fof(f_2693_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_2693_2,plain,
    ! [U_10824,U_10823,U_10822] : 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_10822),U_10823)),U_10824)),U_10823) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10824),U_10823),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

cnf(f_2693_3,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_10822),U_10823)),U_10824)),U_10823) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10824),U_10823),
    inference(clausify,[status(thm)],[f_2693_2]) ).

fof(f_2694_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_2694_2,plain,
    ! [U_10827,U_10826,U_10825] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10825,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10826),U_10827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10826),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10825),U_10826),U_10827))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10825,U_10826)),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

cnf(f_2694_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10825,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10826),U_10827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10826),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10825),U_10826),U_10827))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10825,U_10826)),
    inference(clausify,[status(thm)],[f_2694_2]) ).

fof(f_2695_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_2695_2,plain,
    ! [U_10830,U_10829,U_10828] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),U_10829)),U_10830) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10829),U_10830))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10829,U_10830))),U_10830)),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

cnf(f_2695_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),U_10829)),U_10830) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10829),U_10830))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10828),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10829,U_10830))),U_10830)),
    inference(clausify,[status(thm)],[f_2695_2]) ).

fof(f_2696_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_2696_2,plain,
    ! [U_10832,U_10831] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10831,U_10832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10831),U_10832)),U_10832)),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

cnf(f_2696_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10831,U_10832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10831),U_10832)),U_10832)),
    inference(clausify,[status(thm)],[f_2696_2]) ).

fof(f_2697_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_2697_2,plain,
    ! [U_10834,U_10833] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10833),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10834),U_10833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10834),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10834,U_10833)),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

cnf(f_2697_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10833),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10834),U_10833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10834),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10834,U_10833)),
    inference(clausify,[status(thm)],[f_2697_2]) ).

fof(f_2698_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_2698_2,plain,
    ! [U_10836,U_10835] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10835),U_10836)),U_10836) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10835),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10835,U_10836)),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

cnf(f_2698_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10835),U_10836)),U_10836) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10835),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10835,U_10836)),
    inference(clausify,[status(thm)],[f_2698_2]) ).

fof(f_2699_1,plain,
    ! [V_a_2,V_A_2,V_r_2,T_a] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__diff1]) ).

fof(f_2699_2,plain,
    ! [U_10840,U_10839,U_10838,U_10837] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10837,tc_HOL_Obool)),U_10839),hAPP(hAPP(c_Set_Oinsert(U_10837),U_10840),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool))))),U_10838) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),U_10839),U_10838)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),hAPP(hAPP(c_Set_Oinsert(U_10837),U_10840),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool)))),U_10838))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10837),U_10840),U_10839))
      | ~ c_Fun_Oinj__on(U_10837,tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10837,tc_fun(tc_prod(U_10837,U_10837),tc_HOL_Obool),tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10837,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10837,U_10837),tc_HOL_Obool),tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),U_10837),c_Equiv__Relations_Oquotient(U_10837)),hAPP(hAPP(c_COMBC(U_10837,tc_fun(U_10837,tc_HOL_Obool),tc_fun(U_10837,tc_HOL_Obool)),c_Set_Oinsert(U_10837)),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool))))),U_10838),U_10839) ),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

cnf(f_2699_3,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10837,tc_HOL_Obool)),U_10839),hAPP(hAPP(c_Set_Oinsert(U_10837),U_10840),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool))))),U_10838) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),U_10839),U_10838)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10837),hAPP(hAPP(c_Set_Oinsert(U_10837),U_10840),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool)))),U_10838))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10837),U_10840),U_10839))
    | ~ c_Fun_Oinj__on(U_10837,tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10837,tc_fun(tc_prod(U_10837,U_10837),tc_HOL_Obool),tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10837,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10837,U_10837),tc_HOL_Obool),tc_fun(tc_fun(U_10837,tc_HOL_Obool),tc_HOL_Obool)),U_10837),c_Equiv__Relations_Oquotient(U_10837)),hAPP(hAPP(c_COMBC(U_10837,tc_fun(U_10837,tc_HOL_Obool),tc_fun(U_10837,tc_HOL_Obool)),c_Set_Oinsert(U_10837)),c_Orderings_Obot__class_Obot(tc_fun(U_10837,tc_HOL_Obool))))),U_10838),U_10839) ),
    inference(clausify,[status(thm)],[f_2699_2]) ).

fof(f_2700_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_2700_2,plain,
    ! [U_10844,U_10843,U_10842,U_10841] :
      ( 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_10843),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10844,U_10841))),U_10842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10843),U_10841)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10842),U_10843))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10841)) ),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

cnf(f_2700_3,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_10843),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10844,U_10841))),U_10842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10843),U_10841)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10842),U_10843))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10841)) ),
    inference(clausify,[status(thm)],[f_2700_2]) ).

fof(f_2701_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__mod]) ).

fof(f_2701_2,plain,
    ! [U_10851,U_10850,U_10849] :
      ( ( hBOOL(hAPP(U_10849,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10850,U_10851)))
        | ( ? [U_10848,U_10847] :
              ( ~ hBOOL(hAPP(U_10849,U_10847))
              & U_10850 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10851),U_10848)),U_10847)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10847),U_10851)) )
          & U_10851 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10849,U_10850))
          & U_10851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_10846,U_10845] :
                ( hBOOL(hAPP(U_10849,U_10845))
                | U_10850 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10851),U_10846)),U_10845)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10845),U_10851)) )
            | U_10851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10849,U_10850))
            | U_10851 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10849,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10850,U_10851))) ) ),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

fof(f_2701_3,plain,
    ( ! [U_10857,U_10855,U_10853] :
        ( hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857)))
        | ( ? [U_10848,U_10847] :
              ( ~ hBOOL(hAPP(U_10853,U_10847))
              & U_10855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10857),U_10848)),U_10847)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10847),U_10857)) )
          & U_10857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10853,U_10855))
          & U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10856,U_10854,U_10852] :
        ( ( ( ! [U_10846,U_10845] :
                ( hBOOL(hAPP(U_10852,U_10845))
                | U_10854 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10856),U_10846)),U_10845)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10845),U_10856)) )
            | U_10856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10852,U_10854))
            | U_10856 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10852,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10854,U_10856))) ) ),
    inference(miniscope,[status(thm)],[f_2701_2]) ).

fof(f_2701_4,plain,
    ( ! [U_10857,U_10855,U_10853] :
        ( hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857)))
        | ( ? [U_10847] :
              ( ~ hBOOL(hAPP(U_10853,U_10847))
              & U_10855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10857),sK270(U_10857,U_10855,U_10853))),U_10847)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10847),U_10857)) )
          & U_10857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10853,U_10855))
          & U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10856,U_10854,U_10852] :
        ( ( ( ! [U_10846,U_10845] :
                ( hBOOL(hAPP(U_10852,U_10845))
                | U_10854 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10856),U_10846)),U_10845)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10845),U_10856)) )
            | U_10856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10852,U_10854))
            | U_10856 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10852,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10854,U_10856))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_10848,sK270(U_10857,U_10855,U_10853))],[f_2701_3]) ).

fof(f_2701_5,plain,
    ( ! [U_10857,U_10855,U_10853] :
        ( hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857)))
        | ( ~ hBOOL(hAPP(U_10853,sK271(U_10857,U_10855,U_10853)))
          & U_10855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10857),sK270(U_10857,U_10855,U_10853))),sK271(U_10857,U_10855,U_10853))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK271(U_10857,U_10855,U_10853)),U_10857))
          & U_10857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_10853,U_10855))
          & U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_10856,U_10854,U_10852] :
        ( ( ( ! [U_10846,U_10845] :
                ( hBOOL(hAPP(U_10852,U_10845))
                | U_10854 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10856),U_10846)),U_10845)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10845),U_10856)) )
            | U_10856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_10852,U_10854))
            | U_10856 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_10852,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10854,U_10856))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_10847,sK271(U_10857,U_10855,U_10853))],[f_2701_4]) ).

cnf(f_2701_6,plain,
    ( hBOOL(hAPP(U_10852,U_10854))
    | U_10856 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10852,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10854,U_10856))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_7,plain,
    ( hBOOL(hAPP(U_10852,U_10845))
    | U_10854 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10856),U_10846)),U_10845)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10845),U_10856))
    | U_10856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10852,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10854,U_10856))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_8,plain,
    ( U_10857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK271(U_10857,U_10855,U_10853)),U_10857))
    | U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_10,plain,
    ( U_10855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10857),sK270(U_10857,U_10855,U_10853))),sK271(U_10857,U_10855,U_10853))
    | U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_11,plain,
    ( ~ hBOOL(hAPP(U_10853,sK271(U_10857,U_10855,U_10853)))
    | U_10857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_12,plain,
    ( U_10857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_10853,U_10855))
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK271(U_10857,U_10855,U_10853)),U_10857))
    | ~ hBOOL(hAPP(U_10853,U_10855))
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_14,plain,
    ( U_10855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10857),sK270(U_10857,U_10855,U_10853))),sK271(U_10857,U_10855,U_10853))
    | ~ hBOOL(hAPP(U_10853,U_10855))
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

cnf(f_2701_15,plain,
    ( ~ hBOOL(hAPP(U_10853,sK271(U_10857,U_10855,U_10853)))
    | ~ hBOOL(hAPP(U_10853,U_10855))
    | hBOOL(hAPP(U_10853,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10855,U_10857))) ),
    inference(clausify,[status(thm)],[f_2701_5]) ).

fof(f_2702_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_2702_2,plain,
    ! [U_10859,U_10858] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10858),U_10859)),U_10858) = 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_10858)) ),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

cnf(f_2702_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10858),U_10859)),U_10858) = 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_10858)) ),
    inference(clausify,[status(thm)],[f_2702_2]) ).

fof(f_2703_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_2703_2,plain,
    ! [U_10861,U_10860] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_10860),hAPP(c_Int_Onat,U_10861)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10860,U_10861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10860)) ),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

cnf(f_2703_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_10860),hAPP(c_Int_Onat,U_10861)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10860,U_10861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10860)) ),
    inference(clausify,[status(thm)],[f_2703_2]) ).

fof(f_2704_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_2704_2,plain,
    ! [U_10863,U_10862] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10862,U_10863)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_10862),hAPP(c_Int_Onat,U_10863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10862)) ),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

cnf(f_2704_3,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10862,U_10863)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_10862),hAPP(c_Int_Onat,U_10863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10862)) ),
    inference(clausify,[status(thm)],[f_2704_2]) ).

fof(f_2705_1,plain,
    ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_quotient__def]) ).

fof(f_2705_2,plain,
    ! [U_10866,U_10865,U_10864] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10864),U_10865),U_10866) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),U_10865),hAPP(hAPP(c_COMBC(U_10864,tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10864,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),U_10864),c_Set_Oinsert(tc_fun(U_10864,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10864,tc_HOL_Obool),tc_fun(U_10864,tc_HOL_Obool),U_10864),c_Relation_OImage(U_10864,U_10864,U_10866)),hAPP(hAPP(c_COMBC(U_10864,tc_fun(U_10864,tc_HOL_Obool),tc_fun(U_10864,tc_HOL_Obool)),c_Set_Oinsert(U_10864)),c_Orderings_Obot__class_Obot(tc_fun(U_10864,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

cnf(f_2705_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10864),U_10865),U_10866) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),U_10865),hAPP(hAPP(c_COMBC(U_10864,tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10864,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)),U_10864),c_Set_Oinsert(tc_fun(U_10864,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10864,tc_HOL_Obool),tc_fun(U_10864,tc_HOL_Obool),U_10864),c_Relation_OImage(U_10864,U_10864,U_10866)),hAPP(hAPP(c_COMBC(U_10864,tc_fun(U_10864,tc_HOL_Obool),tc_fun(U_10864,tc_HOL_Obool)),c_Set_Oinsert(U_10864)),c_Orderings_Obot__class_Obot(tc_fun(U_10864,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10864,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2705_2]) ).

fof(f_2706_1,plain,
    ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__quotient]) ).

fof(f_2706_2,plain,
    ! [U_10869,U_10868,U_10867] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),hAPP(hAPP(c_Set_Oinsert(U_10867),U_10868),c_Orderings_Obot__class_Obot(tc_fun(U_10867,tc_HOL_Obool)))),U_10869) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10867,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10867,U_10867,U_10869),hAPP(hAPP(c_Set_Oinsert(U_10867),U_10868),c_Orderings_Obot__class_Obot(tc_fun(U_10867,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10867,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

cnf(f_2706_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10867),hAPP(hAPP(c_Set_Oinsert(U_10867),U_10868),c_Orderings_Obot__class_Obot(tc_fun(U_10867,tc_HOL_Obool)))),U_10869) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10867,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10867,U_10867,U_10869),hAPP(hAPP(c_Set_Oinsert(U_10867),U_10868),c_Orderings_Obot__class_Obot(tc_fun(U_10867,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10867,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2706_2]) ).

fof(f_2707_1,plain,
    ! [V_r_2,V_A_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_quotientI]) ).

fof(f_2707_2,plain,
    ! [U_10873,U_10872,U_10871,U_10870] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10870,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10870,U_10870,U_10873),hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),c_Orderings_Obot__class_Obot(tc_fun(U_10870,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10870),U_10872),U_10873)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10870),U_10871),U_10872)) ),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

cnf(f_2707_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10870,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10870,U_10870,U_10873),hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),c_Orderings_Obot__class_Obot(tc_fun(U_10870,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10870),U_10872),U_10873)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10870),U_10871),U_10872)) ),
    inference(clausify,[status(thm)],[f_2707_2]) ).

fof(f_2708_1,plain,
    ! [V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),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_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).

fof(f_2708_2,plain,
    ! [U_10876,U_10875] :
      ( hAPP(c_Finite__Set_Ocard(U_10875),U_10876) = 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_10874] : hBOOL(hAPP(hAPP(c_member(U_10875),U_10874),U_10876)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10875),U_10876)) ),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

fof(f_2708_3,plain,
    ! [U_10876,U_10875] :
      ( hAPP(c_Finite__Set_Ocard(U_10875),U_10876) = 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_10875),sK272(U_10876,U_10875)),U_10876)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10875),U_10876)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_10874,sK272(U_10876,U_10875))],[f_2708_2]) ).

cnf(f_2708_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10875),sK272(U_10876,U_10875)),U_10876))
    | hAPP(c_Finite__Set_Ocard(U_10875),U_10876) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10875),U_10876)) ),
    inference(clausify,[status(thm)],[f_2708_3]) ).

cnf(f_2708_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_10875),U_10876) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10875),U_10876)) ),
    inference(clausify,[status(thm)],[f_2708_3]) ).

fof(f_2709_1,plain,
    ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,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))))),
    inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).

fof(f_2709_2,plain,
    ! [U_10880,U_10879,U_10878,U_10877] : hAPP(c_Relation_OImage(U_10877,U_10878,U_10879),U_10880) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10877,tc_fun(U_10878,tc_HOL_Obool)),U_10880),hAPP(hAPP(c_COMBB(tc_fun(U_10877,tc_HOL_Obool),tc_fun(U_10878,tc_HOL_Obool),U_10877),c_Relation_OImage(U_10877,U_10878,U_10879)),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,tc_HOL_Obool),tc_fun(U_10877,tc_HOL_Obool)),c_Set_Oinsert(U_10877)),c_Orderings_Obot__class_Obot(tc_fun(U_10877,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

cnf(f_2709_3,plain,
    hAPP(c_Relation_OImage(U_10877,U_10878,U_10879),U_10880) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10877,tc_fun(U_10878,tc_HOL_Obool)),U_10880),hAPP(hAPP(c_COMBB(tc_fun(U_10877,tc_HOL_Obool),tc_fun(U_10878,tc_HOL_Obool),U_10877),c_Relation_OImage(U_10877,U_10878,U_10879)),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,tc_HOL_Obool),tc_fun(U_10877,tc_HOL_Obool)),c_Set_Oinsert(U_10877)),c_Orderings_Obot__class_Obot(tc_fun(U_10877,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2709_2]) ).

fof(f_2710_1,plain,
    ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).

fof(f_2710_2,plain,
    ! [U_10886,U_10885,U_10884,U_10883,U_10882,U_10881] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10881,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10882,U_10881,U_10883),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10884,tc_fun(U_10882,tc_HOL_Obool)),U_10885),U_10886))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10884,tc_fun(U_10881,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_COMBB(tc_fun(U_10882,tc_HOL_Obool),tc_fun(U_10881,tc_HOL_Obool),U_10884),c_Relation_OImage(U_10882,U_10881,U_10883)),U_10886)))),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

cnf(f_2710_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10881,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10882,U_10881,U_10883),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10884,tc_fun(U_10882,tc_HOL_Obool)),U_10885),U_10886))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10884,tc_fun(U_10881,tc_HOL_Obool)),U_10885),hAPP(hAPP(c_COMBB(tc_fun(U_10882,tc_HOL_Obool),tc_fun(U_10881,tc_HOL_Obool),U_10884),c_Relation_OImage(U_10882,U_10881,U_10883)),U_10886)))),
    inference(clausify,[status(thm)],[f_2710_2]) ).

fof(f_2711_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).

fof(f_2711_2,plain,
    ! [U_10891,U_10890,U_10889,U_10888,U_10887] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10887,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10891))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),U_10890)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),U_10891)))),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

cnf(f_2711_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10887,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10891))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),U_10890)),hAPP(c_Relation_OImage(U_10888,U_10887,U_10889),U_10891)))),
    inference(clausify,[status(thm)],[f_2711_2]) ).

fof(f_2712_1,plain,
    ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).

fof(f_2712_2,plain,
    ! [U_10897,U_10896,U_10895,U_10894,U_10893,U_10892] : hAPP(c_Relation_OImage(U_10892,U_10893,U_10894),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10895,tc_fun(U_10892,tc_HOL_Obool)),U_10896),U_10897)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10895,tc_fun(U_10893,tc_HOL_Obool)),U_10896),hAPP(hAPP(c_COMBB(tc_fun(U_10892,tc_HOL_Obool),tc_fun(U_10893,tc_HOL_Obool),U_10895),c_Relation_OImage(U_10892,U_10893,U_10894)),U_10897)),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

cnf(f_2712_3,plain,
    hAPP(c_Relation_OImage(U_10892,U_10893,U_10894),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10895,tc_fun(U_10892,tc_HOL_Obool)),U_10896),U_10897)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10895,tc_fun(U_10893,tc_HOL_Obool)),U_10896),hAPP(hAPP(c_COMBB(tc_fun(U_10892,tc_HOL_Obool),tc_fun(U_10893,tc_HOL_Obool),U_10895),c_Relation_OImage(U_10892,U_10893,U_10894)),U_10897)),
    inference(clausify,[status(thm)],[f_2712_2]) ).

fof(f_2713_1,plain,
    ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).

fof(f_2713_2,plain,
    ! [U_10900,U_10899,U_10898] : hAPP(c_Relation_OImage(U_10898,U_10899,U_10900),c_Orderings_Obot__class_Obot(tc_fun(U_10898,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10899,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

cnf(f_2713_3,plain,
    hAPP(c_Relation_OImage(U_10898,U_10899,U_10900),c_Orderings_Obot__class_Obot(tc_fun(U_10898,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10899,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2713_2]) ).

fof(f_2714_1,plain,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).

fof(f_2714_2,plain,
    ! [U_10906,U_10905,U_10904,U_10903,U_10902,U_10901] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10902,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10901,U_10902,U_10903),U_10905)),hAPP(c_Relation_OImage(U_10901,U_10902,U_10904),U_10906)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10901,tc_HOL_Obool)),U_10905),U_10906))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10901,U_10902),tc_HOL_Obool)),U_10903),U_10904)) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

cnf(f_2714_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10902,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10901,U_10902,U_10903),U_10905)),hAPP(c_Relation_OImage(U_10901,U_10902,U_10904),U_10906)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10901,tc_HOL_Obool)),U_10905),U_10906))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10901,U_10902),tc_HOL_Obool)),U_10903),U_10904)) ),
    inference(clausify,[status(thm)],[f_2714_2]) ).

fof(f_2715_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).

fof(f_2715_2,plain,
    ! [U_10911,U_10910,U_10909,U_10908,U_10907] : hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10907,tc_HOL_Obool)),U_10910),U_10911)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10908,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),U_10910)),hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),U_10911)),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

cnf(f_2715_3,plain,
    hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10907,tc_HOL_Obool)),U_10910),U_10911)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10908,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),U_10910)),hAPP(c_Relation_OImage(U_10907,U_10908,U_10909),U_10911)),
    inference(clausify,[status(thm)],[f_2715_2]) ).

fof(f_2716_1,plain,
    ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).

fof(f_2716_2,plain,
    ! [U_10916,U_10915,U_10914,U_10913,U_10912] : hAPP(c_Relation_OImage(U_10912,U_10913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10912,U_10913),tc_HOL_Obool)),U_10914),U_10915)),U_10916) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10913,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10912,U_10913,U_10914),U_10916)),hAPP(c_Relation_OImage(U_10912,U_10913,U_10915),U_10916)),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

cnf(f_2716_3,plain,
    hAPP(c_Relation_OImage(U_10912,U_10913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10912,U_10913),tc_HOL_Obool)),U_10914),U_10915)),U_10916) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10913,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10912,U_10913,U_10914),U_10916)),hAPP(c_Relation_OImage(U_10912,U_10913,U_10915),U_10916)),
    inference(clausify,[status(thm)],[f_2716_2]) ).

fof(f_2717_1,plain,
    ! [V_r_2,V_A_2,V_X_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
          & V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_quotientE]) ).

fof(f_2717_2,plain,
    ! [U_10921,U_10920,U_10919,U_10918] :
      ( ? [U_10917] :
          ( hBOOL(hAPP(hAPP(c_member(U_10918),U_10917),U_10920))
          & U_10919 = hAPP(c_Relation_OImage(U_10918,U_10918,U_10921),hAPP(hAPP(c_Set_Oinsert(U_10918),U_10917),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10918,tc_HOL_Obool)),U_10919),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10918),U_10920),U_10921))) ),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

fof(f_2717_3,plain,
    ! [U_10921,U_10920,U_10919,U_10918] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10918),sK273(U_10921,U_10920,U_10919,U_10918)),U_10920))
        & U_10919 = hAPP(c_Relation_OImage(U_10918,U_10918,U_10921),hAPP(hAPP(c_Set_Oinsert(U_10918),sK273(U_10921,U_10920,U_10919,U_10918)),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10918,tc_HOL_Obool)),U_10919),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10918),U_10920),U_10921))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_10917,sK273(U_10921,U_10920,U_10919,U_10918))],[f_2717_2]) ).

cnf(f_2717_4,plain,
    ( U_10919 = hAPP(c_Relation_OImage(U_10918,U_10918,U_10921),hAPP(hAPP(c_Set_Oinsert(U_10918),sK273(U_10921,U_10920,U_10919,U_10918)),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10918,tc_HOL_Obool)),U_10919),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10918),U_10920),U_10921))) ),
    inference(clausify,[status(thm)],[f_2717_3]) ).

cnf(f_2717_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10918),sK273(U_10921,U_10920,U_10919,U_10918)),U_10920))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10918,tc_HOL_Obool)),U_10919),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10918),U_10920),U_10921))) ),
    inference(clausify,[status(thm)],[f_2717_3]) ).

fof(f_2718_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_2718_2,plain,
    ! [U_10925,U_10924,U_10923] :
      ( ? [U_10922] : U_10923 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10924),U_10922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10925),U_10923))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10923,U_10924) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10925,U_10924) ),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

fof(f_2718_3,plain,
    ! [U_10925,U_10924,U_10923] :
      ( U_10923 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10924),sK274(U_10925,U_10924,U_10923)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10925),U_10923))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10923,U_10924) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10925,U_10924) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_10922,sK274(U_10925,U_10924,U_10923))],[f_2718_2]) ).

cnf(f_2718_4,plain,
    ( U_10923 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10924),sK274(U_10925,U_10924,U_10923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10925),U_10923))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10923,U_10924) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10925,U_10924) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

fof(f_2719_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).

fof(f_2719_2,plain,
    ! [U_10930,U_10929,U_10928,U_10927] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),hAPP(hAPP(c_Finite__Set_Ofold(U_10927,U_10927,c_Orderings_Oord__class_Omax(U_10927)),U_10930),U_10928)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),U_10929),U_10930)))
      | ? [U_10926] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),U_10926),U_10929))
          & hBOOL(hAPP(hAPP(c_member(U_10927),U_10926),U_10928)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10928))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

fof(f_2719_3,plain,
    ! [U_10930,U_10929,U_10928,U_10927] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),hAPP(hAPP(c_Finite__Set_Ofold(U_10927,U_10927,c_Orderings_Oord__class_Omax(U_10927)),U_10930),U_10928)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),U_10929),U_10930)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),sK275(U_10930,U_10929,U_10928,U_10927)),U_10929))
        & hBOOL(hAPP(hAPP(c_member(U_10927),sK275(U_10930,U_10929,U_10928,U_10927)),U_10928)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10928))
      | ~ class_Orderings_Olinorder(U_10927) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_10926,sK275(U_10930,U_10929,U_10928,U_10927))],[f_2719_2]) ).

cnf(f_2719_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10927),sK275(U_10930,U_10929,U_10928,U_10927)),U_10928))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),hAPP(hAPP(c_Finite__Set_Ofold(U_10927,U_10927,c_Orderings_Oord__class_Omax(U_10927)),U_10930),U_10928)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),U_10929),U_10930)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10928))
    | ~ class_Orderings_Olinorder(U_10927) ),
    inference(clausify,[status(thm)],[f_2719_3]) ).

cnf(f_2719_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),sK275(U_10930,U_10929,U_10928,U_10927)),U_10929))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10927),hAPP(hAPP(c_Finite__Set_Ofold(U_10927,U_10927,c_Orderings_Oord__class_Omax(U_10927)),U_10930),U_10928)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10927),U_10929),U_10930)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10927),U_10928))
    | ~ class_Orderings_Olinorder(U_10927) ),
    inference(clausify,[status(thm)],[f_2719_3]) ).

fof(f_2720_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).

fof(f_2720_2,plain,
    ! [U_10935,U_10934,U_10933,U_10932] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10932),U_10934),U_10935)),hAPP(hAPP(c_Finite__Set_Ofold(U_10932,U_10932,c_Orderings_Oord__class_Omin(U_10932)),U_10935),U_10933)))
      | ? [U_10931] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),U_10934),U_10931))
          & hBOOL(hAPP(hAPP(c_member(U_10932),U_10931),U_10933)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10932),U_10933))
      | ~ class_Orderings_Olinorder(U_10932) ),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

fof(f_2720_3,plain,
    ! [U_10935,U_10934,U_10933,U_10932] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10932),U_10934),U_10935)),hAPP(hAPP(c_Finite__Set_Ofold(U_10932,U_10932,c_Orderings_Oord__class_Omin(U_10932)),U_10935),U_10933)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),U_10934),sK276(U_10935,U_10934,U_10933,U_10932)))
        & hBOOL(hAPP(hAPP(c_member(U_10932),sK276(U_10935,U_10934,U_10933,U_10932)),U_10933)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10932),U_10933))
      | ~ class_Orderings_Olinorder(U_10932) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_10931,sK276(U_10935,U_10934,U_10933,U_10932))],[f_2720_2]) ).

cnf(f_2720_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10932),sK276(U_10935,U_10934,U_10933,U_10932)),U_10933))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10932),U_10934),U_10935)),hAPP(hAPP(c_Finite__Set_Ofold(U_10932,U_10932,c_Orderings_Oord__class_Omin(U_10932)),U_10935),U_10933)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10932),U_10933))
    | ~ class_Orderings_Olinorder(U_10932) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

cnf(f_2720_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),U_10934),sK276(U_10935,U_10934,U_10933,U_10932)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10932),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10932),U_10934),U_10935)),hAPP(hAPP(c_Finite__Set_Ofold(U_10932,U_10932,c_Orderings_Oord__class_Omin(U_10932)),U_10935),U_10933)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10932),U_10933))
    | ~ class_Orderings_Olinorder(U_10932) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

fof(f_2721_1,plain,
    ! [V_B_2,T_a,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).

fof(f_2721_2,plain,
    ! [U_10938,U_10937,U_10936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10937,U_10937),tc_HOL_Obool)),U_10936),U_10938))
      | U_10936 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10937,U_10937),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

cnf(f_2721_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10937,U_10937),tc_HOL_Obool)),U_10936),U_10938))
    | U_10936 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10937,U_10937),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2721_2]) ).

fof(f_2722_1,plain,
    ! [V_i_2,V_P_2,V_p_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
      | ~ hBOOL(hAPP(V_P_2,V_i_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
          & hBOOL(hAPP(V_P_2,B_i))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__induct__0]) ).

fof(f_2722_2,plain,
    ! [U_10942,U_10941,U_10940] :
      ( hBOOL(hAPP(U_10941,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10942),U_10940))
      | ~ hBOOL(hAPP(U_10941,U_10942))
      | ? [U_10939] :
          ( ~ hBOOL(hAPP(U_10941,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10939),U_10940)))
          & hBOOL(hAPP(U_10941,U_10939))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10939),U_10940)) ) ),
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

fof(f_2722_3,plain,
    ! [U_10942,U_10941,U_10940] :
      ( hBOOL(hAPP(U_10941,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10942),U_10940))
      | ~ hBOOL(hAPP(U_10941,U_10942))
      | ( ~ hBOOL(hAPP(U_10941,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK277(U_10942,U_10941,U_10940)),U_10940)))
        & hBOOL(hAPP(U_10941,sK277(U_10942,U_10941,U_10940)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK277(U_10942,U_10941,U_10940)),U_10940)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_10939,sK277(U_10942,U_10941,U_10940))],[f_2722_2]) ).

cnf(f_2722_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK277(U_10942,U_10941,U_10940)),U_10940))
    | hBOOL(hAPP(U_10941,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10942),U_10940))
    | ~ hBOOL(hAPP(U_10941,U_10942)) ),
    inference(clausify,[status(thm)],[f_2722_3]) ).

cnf(f_2722_5,plain,
    ( hBOOL(hAPP(U_10941,sK277(U_10942,U_10941,U_10940)))
    | hBOOL(hAPP(U_10941,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10942),U_10940))
    | ~ hBOOL(hAPP(U_10941,U_10942)) ),
    inference(clausify,[status(thm)],[f_2722_3]) ).

cnf(f_2722_6,plain,
    ( ~ hBOOL(hAPP(U_10941,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK277(U_10942,U_10941,U_10940)),U_10940)))
    | hBOOL(hAPP(U_10941,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10942),U_10940))
    | ~ hBOOL(hAPP(U_10941,U_10942)) ),
    inference(clausify,[status(thm)],[f_2722_3]) ).

fof(f_2723_1,plain,
    ! [V_A_2,V_C_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_InterI]) ).

fof(f_2723_2,plain,
    ! [U_10946,U_10945,U_10944] :
      ( hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10944,tc_HOL_Obool),U_10945)))
      | ? [U_10943] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),U_10943))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10944,tc_HOL_Obool)),U_10943),U_10945)) ) ),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

fof(f_2723_3,plain,
    ! [U_10946,U_10945,U_10944] :
      ( hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10944,tc_HOL_Obool),U_10945)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),sK278(U_10946,U_10945,U_10944)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10944,tc_HOL_Obool)),sK278(U_10946,U_10945,U_10944)),U_10945)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_10943,sK278(U_10946,U_10945,U_10944))],[f_2723_2]) ).

cnf(f_2723_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10944,tc_HOL_Obool)),sK278(U_10946,U_10945,U_10944)),U_10945))
    | hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10944,tc_HOL_Obool),U_10945))) ),
    inference(clausify,[status(thm)],[f_2723_3]) ).

cnf(f_2723_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),sK278(U_10946,U_10945,U_10944)))
    | hBOOL(hAPP(hAPP(c_member(U_10944),U_10946),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10944,tc_HOL_Obool),U_10945))) ),
    inference(clausify,[status(thm)],[f_2723_3]) ).

fof(f_2724_1,plain,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),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_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).

fof(f_2724_2,plain,
    ! [U_10953,U_10952,U_10951,U_10950,U_10949,U_10948] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),U_10953),U_10950) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),U_10953),U_10950)
      | ? [U_10947] :
          ( hAPP(U_10951,U_10947) != hAPP(U_10952,U_10947)
          & hBOOL(hAPP(hAPP(c_member(U_10949),U_10947),U_10950)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
      | ~ class_Groups_Oab__semigroup__mult(U_10948) ),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

fof(f_2724_3,plain,
    ! [U_10953,U_10952,U_10951,U_10950,U_10949,U_10948] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),U_10953),U_10950) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),U_10953),U_10950)
      | ( hAPP(U_10951,sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948)) != hAPP(U_10952,sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948))
        & hBOOL(hAPP(hAPP(c_member(U_10949),sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948)),U_10950)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
      | ~ class_Groups_Oab__semigroup__mult(U_10948) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_10947,sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948))],[f_2724_2]) ).

cnf(f_2724_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10949),sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948)),U_10950))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),U_10953),U_10950) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),U_10953),U_10950)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
    | ~ class_Groups_Oab__semigroup__mult(U_10948) ),
    inference(clausify,[status(thm)],[f_2724_3]) ).

cnf(f_2724_5,plain,
    ( hAPP(U_10951,sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948)) != hAPP(U_10952,sK279(U_10953,U_10952,U_10951,U_10950,U_10949,U_10948))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10951),U_10953),U_10950) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10948,U_10949,c_Groups_Otimes__class_Otimes(U_10948)),U_10952),U_10953),U_10950)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10949),U_10950))
    | ~ class_Groups_Oab__semigroup__mult(U_10948) ),
    inference(clausify,[status(thm)],[f_2724_3]) ).

fof(f_2725_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).

fof(f_2725_2,plain,
    ! [U_10957,U_10956,U_10955] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10955,U_10956) = U_10957
      | ~ hBOOL(hAPP(hAPP(c_member(U_10955),U_10957),U_10956))
      | ? [U_10954] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10955),U_10954),U_10957))
          & hBOOL(hAPP(hAPP(c_member(U_10955),U_10954),U_10956)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10955),U_10956))
      | ~ class_Orderings_Olinorder(U_10955) ),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

fof(f_2725_3,plain,
    ! [U_10957,U_10956,U_10955] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10955,U_10956) = U_10957
      | ~ hBOOL(hAPP(hAPP(c_member(U_10955),U_10957),U_10956))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10955),sK280(U_10957,U_10956,U_10955)),U_10957))
        & hBOOL(hAPP(hAPP(c_member(U_10955),sK280(U_10957,U_10956,U_10955)),U_10956)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10955),U_10956))
      | ~ class_Orderings_Olinorder(U_10955) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_10954,sK280(U_10957,U_10956,U_10955))],[f_2725_2]) ).

cnf(f_2725_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10955),sK280(U_10957,U_10956,U_10955)),U_10956))
    | c_Big__Operators_Olinorder__class_OMax(U_10955,U_10956) = U_10957
    | ~ hBOOL(hAPP(hAPP(c_member(U_10955),U_10957),U_10956))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10955),U_10956))
    | ~ class_Orderings_Olinorder(U_10955) ),
    inference(clausify,[status(thm)],[f_2725_3]) ).

cnf(f_2725_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10955),sK280(U_10957,U_10956,U_10955)),U_10957))
    | c_Big__Operators_Olinorder__class_OMax(U_10955,U_10956) = U_10957
    | ~ hBOOL(hAPP(hAPP(c_member(U_10955),U_10957),U_10956))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10955),U_10956))
    | ~ class_Orderings_Olinorder(U_10955) ),
    inference(clausify,[status(thm)],[f_2725_3]) ).

fof(f_2726_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).

fof(f_2726_2,plain,
    ! [U_10961,U_10960,U_10959] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10959,U_10960) = U_10961
      | ~ hBOOL(hAPP(hAPP(c_member(U_10959),U_10961),U_10960))
      | ? [U_10958] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10959),U_10961),U_10958))
          & hBOOL(hAPP(hAPP(c_member(U_10959),U_10958),U_10960)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10959),U_10960))
      | ~ class_Orderings_Olinorder(U_10959) ),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

fof(f_2726_3,plain,
    ! [U_10961,U_10960,U_10959] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10959,U_10960) = U_10961
      | ~ hBOOL(hAPP(hAPP(c_member(U_10959),U_10961),U_10960))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10959),U_10961),sK281(U_10961,U_10960,U_10959)))
        & hBOOL(hAPP(hAPP(c_member(U_10959),sK281(U_10961,U_10960,U_10959)),U_10960)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10959),U_10960))
      | ~ class_Orderings_Olinorder(U_10959) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_10958,sK281(U_10961,U_10960,U_10959))],[f_2726_2]) ).

cnf(f_2726_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10959),sK281(U_10961,U_10960,U_10959)),U_10960))
    | c_Big__Operators_Olinorder__class_OMin(U_10959,U_10960) = U_10961
    | ~ hBOOL(hAPP(hAPP(c_member(U_10959),U_10961),U_10960))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10959),U_10960))
    | ~ class_Orderings_Olinorder(U_10959) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

cnf(f_2726_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10959),U_10961),sK281(U_10961,U_10960,U_10959)))
    | c_Big__Operators_Olinorder__class_OMin(U_10959,U_10960) = U_10961
    | ~ hBOOL(hAPP(hAPP(c_member(U_10959),U_10961),U_10960))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10959),U_10960))
    | ~ class_Orderings_Olinorder(U_10959) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

fof(f_2727_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).

fof(f_2727_2,plain,
    ! [U_10966,U_10965,U_10964,U_10963] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),U_10965),U_10966)),hAPP(hAPP(c_Finite__Set_Ofold(U_10963,U_10963,c_Lattices_Osemilattice__inf__class_Oinf(U_10963)),U_10966),U_10964)))
      | ? [U_10962] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),U_10965),U_10962))
          & hBOOL(hAPP(hAPP(c_member(U_10963),U_10962),U_10964)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10963),U_10964))
      | ~ class_Lattices_Osemilattice__inf(U_10963) ),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

fof(f_2727_3,plain,
    ! [U_10966,U_10965,U_10964,U_10963] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),U_10965),U_10966)),hAPP(hAPP(c_Finite__Set_Ofold(U_10963,U_10963,c_Lattices_Osemilattice__inf__class_Oinf(U_10963)),U_10966),U_10964)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),U_10965),sK282(U_10966,U_10965,U_10964,U_10963)))
        & hBOOL(hAPP(hAPP(c_member(U_10963),sK282(U_10966,U_10965,U_10964,U_10963)),U_10964)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10963),U_10964))
      | ~ class_Lattices_Osemilattice__inf(U_10963) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_10962,sK282(U_10966,U_10965,U_10964,U_10963))],[f_2727_2]) ).

cnf(f_2727_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10963),sK282(U_10966,U_10965,U_10964,U_10963)),U_10964))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),U_10965),U_10966)),hAPP(hAPP(c_Finite__Set_Ofold(U_10963,U_10963,c_Lattices_Osemilattice__inf__class_Oinf(U_10963)),U_10966),U_10964)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10963),U_10964))
    | ~ class_Lattices_Osemilattice__inf(U_10963) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

cnf(f_2727_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),U_10965),sK282(U_10966,U_10965,U_10964,U_10963)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),U_10965),U_10966)),hAPP(hAPP(c_Finite__Set_Ofold(U_10963,U_10963,c_Lattices_Osemilattice__inf__class_Oinf(U_10963)),U_10966),U_10964)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10963),U_10964))
    | ~ class_Lattices_Osemilattice__inf(U_10963) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

fof(f_2728_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).

fof(f_2728_2,plain,
    ! [U_10971,U_10970,U_10969,U_10968] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),hAPP(hAPP(c_Finite__Set_Ofold(U_10968,U_10968,c_Lattices_Osemilattice__sup__class_Osup(U_10968)),U_10971),U_10969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10968),U_10970),U_10971)))
      | ? [U_10967] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),U_10967),U_10970))
          & hBOOL(hAPP(hAPP(c_member(U_10968),U_10967),U_10969)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10968),U_10969))
      | ~ class_Lattices_Osemilattice__sup(U_10968) ),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

fof(f_2728_3,plain,
    ! [U_10971,U_10970,U_10969,U_10968] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),hAPP(hAPP(c_Finite__Set_Ofold(U_10968,U_10968,c_Lattices_Osemilattice__sup__class_Osup(U_10968)),U_10971),U_10969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10968),U_10970),U_10971)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),sK283(U_10971,U_10970,U_10969,U_10968)),U_10970))
        & hBOOL(hAPP(hAPP(c_member(U_10968),sK283(U_10971,U_10970,U_10969,U_10968)),U_10969)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10968),U_10969))
      | ~ class_Lattices_Osemilattice__sup(U_10968) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_10967,sK283(U_10971,U_10970,U_10969,U_10968))],[f_2728_2]) ).

cnf(f_2728_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10968),sK283(U_10971,U_10970,U_10969,U_10968)),U_10969))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),hAPP(hAPP(c_Finite__Set_Ofold(U_10968,U_10968,c_Lattices_Osemilattice__sup__class_Osup(U_10968)),U_10971),U_10969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10968),U_10970),U_10971)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10968),U_10969))
    | ~ class_Lattices_Osemilattice__sup(U_10968) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

cnf(f_2728_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),sK283(U_10971,U_10970,U_10969,U_10968)),U_10970))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10968),hAPP(hAPP(c_Finite__Set_Ofold(U_10968,U_10968,c_Lattices_Osemilattice__sup__class_Osup(U_10968)),U_10971),U_10969)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10968),U_10970),U_10971)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10968),U_10969))
    | ~ class_Lattices_Osemilattice__sup(U_10968) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

fof(f_2729_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_2729_2,plain,
    ! [U_10972] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10972) = 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_10972)),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_10972))) ),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

cnf(f_2729_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10972) = 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_10972)),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_10972))) ),
    inference(clausify,[status(thm)],[f_2729_2]) ).

fof(f_2730_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) ) )
      | ~ class_Int_Oring__char__0(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).

fof(f_2730_2,plain,
    ! [U_10975,U_10974,U_10973] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10974) = hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10975)
          | U_10974 != U_10975 )
        & ( U_10974 = U_10975
          | hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10974) != hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10975) ) )
      | ~ class_Int_Oring__char__0(U_10973)
      | ~ class_Int_Onumber__ring(U_10973) ),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

cnf(f_2730_3,plain,
    ( U_10974 = U_10975
    | hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10974) != hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10975)
    | ~ class_Int_Oring__char__0(U_10973)
    | ~ class_Int_Onumber__ring(U_10973) ),
    inference(clausify,[status(thm)],[f_2730_2]) ).

cnf(f_2730_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10974) = hAPP(c_Int_Onumber__class_Onumber__of(U_10973),U_10975)
    | U_10974 != U_10975
    | ~ class_Int_Oring__char__0(U_10973)
    | ~ class_Int_Onumber__ring(U_10973) ),
    inference(clausify,[status(thm)],[f_2730_2]) ).

fof(f_2731_1,plain,
    ! [V_x_2,V_w_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
          | V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) )
        & ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
          | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != V_x_2 ) )
      | ~ class_Int_Onumber(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).

fof(f_2731_2,plain,
    ! [U_10978,U_10977,U_10976] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977) = U_10978
          | U_10978 != hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977) )
        & ( U_10978 = hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977) != U_10978 ) )
      | ~ class_Int_Onumber(U_10976) ),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

cnf(f_2731_3,plain,
    ( U_10978 = hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977) != U_10978
    | ~ class_Int_Onumber(U_10976) ),
    inference(clausify,[status(thm)],[f_2731_2]) ).

cnf(f_2731_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977) = U_10978
    | U_10978 != hAPP(c_Int_Onumber__class_Onumber__of(U_10976),U_10977)
    | ~ class_Int_Onumber(U_10976) ),
    inference(clausify,[status(thm)],[f_2731_2]) ).

fof(f_2732_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_2732_2,plain,
    ! [U_10980,U_10979] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10980)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10979),U_10980)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10980))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10980)) = c_Groups_Ozero__class_Ozero(U_10979)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10980))) ) )
      | ~ class_Int_Onumber__ring(U_10979) ),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

cnf(f_2732_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10980)) = c_Groups_Ozero__class_Ozero(U_10979)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10980)))
    | ~ class_Int_Onumber__ring(U_10979) ),
    inference(clausify,[status(thm)],[f_2732_2]) ).

cnf(f_2732_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10979),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10980)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10979),U_10980)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10980)))
    | ~ class_Int_Onumber__ring(U_10979) ),
    inference(clausify,[status(thm)],[f_2732_2]) ).

fof(f_2733_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_2733_2,plain,
    ! [U_10982,U_10981] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10982)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10981),U_10982)
      | ~ class_Int_Onumber__ring(U_10981) ),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

cnf(f_2733_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10982)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10981),U_10982)
    | ~ class_Int_Onumber__ring(U_10981) ),
    inference(clausify,[status(thm)],[f_2733_2]) ).

fof(f_2734_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_2734_2,plain,
    ! [U_10984,U_10983] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_10983),U_10984) = hAPP(c_Int_Oring__1__class_Oof__int(U_10983),U_10984)
      | ~ class_Int_Onumber__ring(U_10983) ),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

cnf(f_2734_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_10983),U_10984) = hAPP(c_Int_Oring__1__class_Oof__int(U_10983),U_10984)
    | ~ class_Int_Onumber__ring(U_10983) ),
    inference(clausify,[status(thm)],[f_2734_2]) ).

fof(f_2735_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_2735_2,plain,
    ! [U_10986,U_10985] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10986)) = c_Groups_Ozero__class_Ozero(U_10985)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_10986))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10986)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10985),U_10986)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_10986))) ) )
      | ~ class_Int_Onumber__ring(U_10985) ),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

cnf(f_2735_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10986)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10985),U_10986)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_10986)))
    | ~ class_Int_Onumber__ring(U_10985) ),
    inference(clausify,[status(thm)],[f_2735_2]) ).

cnf(f_2735_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10986)) = c_Groups_Ozero__class_Ozero(U_10985)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_10986)))
    | ~ class_Int_Onumber__ring(U_10985) ),
    inference(clausify,[status(thm)],[f_2735_2]) ).

fof(f_2736_1,plain,
    ! [V_w_2,V_v_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Int_Onumber(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(f_2736_2,plain,
    ! [U_10989,U_10988,U_10987] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989))) ) )
      | ~ class_Orderings_Olinorder(U_10987)
      | ~ class_Int_Onumber(U_10987) ),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

cnf(f_2736_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)))
    | ~ class_Orderings_Olinorder(U_10987)
    | ~ class_Int_Onumber(U_10987) ),
    inference(clausify,[status(thm)],[f_2736_2]) ).

cnf(f_2736_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10987),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10989)),hAPP(c_Int_Onumber__class_Onumber__of(U_10987),U_10988)))
    | ~ class_Orderings_Olinorder(U_10987)
    | ~ class_Int_Onumber(U_10987) ),
    inference(clausify,[status(thm)],[f_2736_2]) ).

fof(f_2737_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_2737_2,plain,
    ! [U_10993,U_10992,U_10991,U_10990] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10990),U_10991),U_10992)),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),U_10991),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),U_10992),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993)))
      | ~ class_Rings_Osemiring(U_10990)
      | ~ class_Int_Onumber(U_10990) ),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

cnf(f_2737_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10990),U_10991),U_10992)),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),U_10991),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10990),U_10992),hAPP(c_Int_Onumber__class_Onumber__of(U_10990),U_10993)))
    | ~ class_Rings_Osemiring(U_10990)
    | ~ class_Int_Onumber(U_10990) ),
    inference(clausify,[status(thm)],[f_2737_2]) ).

fof(f_2738_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_2738_2,plain,
    ! [U_10997,U_10996,U_10995,U_10994] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10994),U_10996),U_10997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),U_10996)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),U_10997))
      | ~ class_Rings_Osemiring(U_10994)
      | ~ class_Int_Onumber(U_10994) ),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

cnf(f_2738_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10994),U_10996),U_10997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),U_10996)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10994),hAPP(c_Int_Onumber__class_Onumber__of(U_10994),U_10995)),U_10997))
    | ~ class_Rings_Osemiring(U_10994)
    | ~ class_Int_Onumber(U_10994) ),
    inference(clausify,[status(thm)],[f_2738_2]) ).

fof(f_2739_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_2739_2,plain,
    ! [U_11001,U_11000,U_10999,U_10998] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10998),U_11000),U_11001)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),U_11000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),U_11001))
      | ~ class_Rings_Oring(U_10998)
      | ~ class_Int_Onumber(U_10998) ),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

cnf(f_2739_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10998),U_11000),U_11001)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),U_11000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10998),hAPP(c_Int_Onumber__class_Onumber__of(U_10998),U_10999)),U_11001))
    | ~ class_Rings_Oring(U_10998)
    | ~ class_Int_Onumber(U_10998) ),
    inference(clausify,[status(thm)],[f_2739_2]) ).

fof(f_2740_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_2740_2,plain,
    ! [U_11005,U_11004,U_11003,U_11002] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11002),U_11003),U_11004)),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),U_11003),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),U_11004),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005)))
      | ~ class_Rings_Oring(U_11002)
      | ~ class_Int_Onumber(U_11002) ),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

cnf(f_2740_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11002),U_11003),U_11004)),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),U_11003),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11002),U_11004),hAPP(c_Int_Onumber__class_Onumber__of(U_11002),U_11005)))
    | ~ class_Rings_Oring(U_11002)
    | ~ class_Int_Onumber(U_11002) ),
    inference(clausify,[status(thm)],[f_2740_2]) ).

fof(f_2741_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).

fof(f_2741_2,plain,
    ! [U_11008,U_11007,U_11006] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11006),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11007)),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11008)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),U_11008)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),U_11008))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11006),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11007)),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11008))) ) )
      | ~ class_Rings_Olinordered__idom(U_11006)
      | ~ class_Int_Onumber__ring(U_11006) ),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

cnf(f_2741_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),U_11008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11006),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11007)),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11008)))
    | ~ class_Rings_Olinordered__idom(U_11006)
    | ~ class_Int_Onumber__ring(U_11006) ),
    inference(clausify,[status(thm)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11006),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11007)),hAPP(c_Int_Onumber__class_Onumber__of(U_11006),U_11008)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),U_11008))
    | ~ class_Rings_Olinordered__idom(U_11006)
    | ~ class_Int_Onumber__ring(U_11006) ),
    inference(clausify,[status(thm)],[f_2741_2]) ).

fof(f_2742_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).

fof(f_2742_2,plain,
    ! [U_11011,U_11010,U_11009] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11010)),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11011)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11010),U_11011)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11010),U_11011))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11010)),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11011))) ) )
      | ~ class_Rings_Olinordered__idom(U_11009)
      | ~ class_Int_Onumber__ring(U_11009) ),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

cnf(f_2742_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11010),U_11011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11010)),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11011)))
    | ~ class_Rings_Olinordered__idom(U_11009)
    | ~ class_Int_Onumber__ring(U_11009) ),
    inference(clausify,[status(thm)],[f_2742_2]) ).

cnf(f_2742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11010)),hAPP(c_Int_Onumber__class_Onumber__of(U_11009),U_11011)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11010),U_11011))
    | ~ class_Rings_Olinordered__idom(U_11009)
    | ~ class_Int_Onumber__ring(U_11009) ),
    inference(clausify,[status(thm)],[f_2742_2]) ).

fof(f_2743_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_2743_2,plain,
    ! [U_11014,U_11013,U_11012] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014))) ) )
      | ~ class_Orderings_Oord(U_11012)
      | ~ class_Int_Onumber(U_11012) ),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

cnf(f_2743_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)))
    | ~ class_Orderings_Oord(U_11012)
    | ~ class_Int_Onumber(U_11012) ),
    inference(clausify,[status(thm)],[f_2743_2]) ).

cnf(f_2743_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11013)),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),U_11014)))
    | ~ class_Orderings_Oord(U_11012)
    | ~ class_Int_Onumber(U_11012) ),
    inference(clausify,[status(thm)],[f_2743_2]) ).

fof(f_2744_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_2744_2,plain,
    ! [U_11017,U_11016,U_11015] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017))) ) )
      | ~ class_Orderings_Oord(U_11015)
      | ~ class_Int_Onumber(U_11015) ),
    inference(variable_rename,[status(thm)],[f_2744_1]) ).

cnf(f_2744_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)))
    | ~ class_Orderings_Oord(U_11015)
    | ~ class_Int_Onumber(U_11015) ),
    inference(clausify,[status(thm)],[f_2744_2]) ).

cnf(f_2744_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11016)),hAPP(c_Int_Onumber__class_Onumber__of(U_11015),U_11017)))
    | ~ class_Orderings_Oord(U_11015)
    | ~ class_Int_Onumber(U_11015) ),
    inference(clausify,[status(thm)],[f_2744_2]) ).

fof(f_2745_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_2745_2,plain,
    ! [U_11021,U_11020,U_11019,U_11018] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),U_11019)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),U_11020)),U_11021)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11019),U_11020))),U_11021)
      | ~ class_Int_Onumber__ring(U_11018) ),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

cnf(f_2745_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),U_11019)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),U_11020)),U_11021)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11018),hAPP(c_Int_Onumber__class_Onumber__of(U_11018),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11019),U_11020))),U_11021)
    | ~ class_Int_Onumber__ring(U_11018) ),
    inference(clausify,[status(thm)],[f_2745_2]) ).

fof(f_2746_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_2746_2,plain,
    ! [U_11024,U_11023,U_11022] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11022),hAPP(c_Int_Onumber__class_Onumber__of(U_11022),U_11023)),hAPP(c_Int_Onumber__class_Onumber__of(U_11022),U_11024)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11022),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11023),U_11024))
      | ~ class_Int_Onumber__ring(U_11022) ),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

cnf(f_2746_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11022),hAPP(c_Int_Onumber__class_Onumber__of(U_11022),U_11023)),hAPP(c_Int_Onumber__class_Onumber__of(U_11022),U_11024)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11022),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11023),U_11024))
    | ~ class_Int_Onumber__ring(U_11022) ),
    inference(clausify,[status(thm)],[f_2746_2]) ).

fof(f_2747_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_2747_2,plain,
    ! [U_11027,U_11026,U_11025] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11026),U_11027)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11025),hAPP(c_Int_Onumber__class_Onumber__of(U_11025),U_11026)),hAPP(c_Int_Onumber__class_Onumber__of(U_11025),U_11027))
      | ~ class_Int_Onumber__ring(U_11025) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

cnf(f_2747_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11026),U_11027)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11025),hAPP(c_Int_Onumber__class_Onumber__of(U_11025),U_11026)),hAPP(c_Int_Onumber__class_Onumber__of(U_11025),U_11027))
    | ~ class_Int_Onumber__ring(U_11025) ),
    inference(clausify,[status(thm)],[f_2747_2]) ).

fof(f_2748_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_2748_2,plain,
    ! [U_11031,U_11030,U_11029,U_11028] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),U_11029)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),U_11030)),U_11031)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11029),U_11030))),U_11031)
      | ~ class_Int_Onumber__ring(U_11028) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

cnf(f_2748_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),U_11029)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),U_11030)),U_11031)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11028),hAPP(c_Int_Onumber__class_Onumber__of(U_11028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11029),U_11030))),U_11031)
    | ~ class_Int_Onumber__ring(U_11028) ),
    inference(clausify,[status(thm)],[f_2748_2]) ).

fof(f_2749_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_2749_2,plain,
    ! [U_11034,U_11033,U_11032] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11032),hAPP(c_Int_Onumber__class_Onumber__of(U_11032),U_11033)),hAPP(c_Int_Onumber__class_Onumber__of(U_11032),U_11034)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11033),U_11034))
      | ~ class_Int_Onumber__ring(U_11032) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

cnf(f_2749_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11032),hAPP(c_Int_Onumber__class_Onumber__of(U_11032),U_11033)),hAPP(c_Int_Onumber__class_Onumber__of(U_11032),U_11034)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11033),U_11034))
    | ~ class_Int_Onumber__ring(U_11032) ),
    inference(clausify,[status(thm)],[f_2749_2]) ).

fof(f_2750_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_2750_2,plain,
    ! [U_11037,U_11036,U_11035] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11036),U_11037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11035),hAPP(c_Int_Onumber__class_Onumber__of(U_11035),U_11036)),hAPP(c_Int_Onumber__class_Onumber__of(U_11035),U_11037))
      | ~ class_Int_Onumber__ring(U_11035) ),
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

cnf(f_2750_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11036),U_11037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11035),hAPP(c_Int_Onumber__class_Onumber__of(U_11035),U_11036)),hAPP(c_Int_Onumber__class_Onumber__of(U_11035),U_11037))
    | ~ class_Int_Onumber__ring(U_11035) ),
    inference(clausify,[status(thm)],[f_2750_2]) ).

fof(f_2751_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_2751_2,plain,
    ! [U_11040,U_11039,U_11038] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11039),U_11040)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11038),hAPP(c_Int_Onumber__class_Onumber__of(U_11038),U_11039)),hAPP(c_Int_Onumber__class_Onumber__of(U_11038),U_11040))
      | ~ class_Int_Onumber__ring(U_11038) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

cnf(f_2751_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11039),U_11040)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11038),hAPP(c_Int_Onumber__class_Onumber__of(U_11038),U_11039)),hAPP(c_Int_Onumber__class_Onumber__of(U_11038),U_11040))
    | ~ class_Int_Onumber__ring(U_11038) ),
    inference(clausify,[status(thm)],[f_2751_2]) ).

fof(f_2752_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_2752_2,plain,
    ! [U_11042,U_11041] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11041),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11042)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11041),hAPP(c_Int_Onumber__class_Onumber__of(U_11041),U_11042))
      | ~ class_Int_Onumber__ring(U_11041) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

cnf(f_2752_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11041),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11042)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11041),hAPP(c_Int_Onumber__class_Onumber__of(U_11041),U_11042))
    | ~ class_Int_Onumber__ring(U_11041) ),
    inference(clausify,[status(thm)],[f_2752_2]) ).

fof(f_2753_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_2753_2,plain,
    ! [U_11044,U_11043] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11043),hAPP(c_Int_Onumber__class_Onumber__of(U_11043),U_11044)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11043),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11044))
      | ~ class_Int_Onumber__ring(U_11043) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

cnf(f_2753_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11043),hAPP(c_Int_Onumber__class_Onumber__of(U_11043),U_11044)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11043),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11044))
    | ~ class_Int_Onumber__ring(U_11043) ),
    inference(clausify,[status(thm)],[f_2753_2]) ).

fof(f_2754_1,plain,
    ! [V_w_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).

fof(f_2754_2,plain,
    ! [U_11046,U_11045] :
      ( hBOOL(hAPP(hAPP(c_member(U_11045),hAPP(c_Int_Onumber__class_Onumber__of(U_11045),U_11046)),c_Int_Oring__1__class_OInts(U_11045)))
      | ~ class_Int_Onumber__ring(U_11045) ),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

cnf(f_2754_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11045),hAPP(c_Int_Onumber__class_Onumber__of(U_11045),U_11046)),c_Int_Oring__1__class_OInts(U_11045)))
    | ~ class_Int_Onumber__ring(U_11045) ),
    inference(clausify,[status(thm)],[f_2754_2]) ).

fof(f_2755_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) != V_b_2
            & hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2
              | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).

fof(f_2755_2,plain,
    ! [U_11050,U_11049,U_11048,U_11047] :
      ( ( ( U_11048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
          | ( U_11048 != c_Groups_Ozero__class_Ozero(U_11047)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) = c_Groups_Ozero__class_Ozero(U_11047) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11047),U_11048),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) != U_11049
            & hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) != c_Groups_Ozero__class_Ozero(U_11047) ) )
        & ( ( ( U_11048 = c_Groups_Ozero__class_Ozero(U_11047)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) != c_Groups_Ozero__class_Ozero(U_11047) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11047),U_11048),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) = U_11049
              | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) = c_Groups_Ozero__class_Ozero(U_11047) ) )
          | U_11048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) ) )
      | ~ class_Int_Onumber(U_11047)
      | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

cnf(f_2755_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11047),U_11048),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) = U_11049
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) = c_Groups_Ozero__class_Ozero(U_11047)
    | U_11048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

cnf(f_2755_4,plain,
    ( U_11048 = c_Groups_Ozero__class_Ozero(U_11047)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) != c_Groups_Ozero__class_Ozero(U_11047)
    | U_11048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

cnf(f_2755_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) = c_Groups_Ozero__class_Ozero(U_11047)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) != c_Groups_Ozero__class_Ozero(U_11047)
    | U_11048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

cnf(f_2755_6,plain,
    ( U_11048 != c_Groups_Ozero__class_Ozero(U_11047)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) != c_Groups_Ozero__class_Ozero(U_11047)
    | U_11048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

cnf(f_2755_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050) = c_Groups_Ozero__class_Ozero(U_11047)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11047),U_11048),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) != U_11049
    | U_11048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

cnf(f_2755_8,plain,
    ( U_11048 != c_Groups_Ozero__class_Ozero(U_11047)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11047),U_11048),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050)) != U_11049
    | U_11048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11047),U_11049),hAPP(c_Int_Onumber__class_Onumber__of(U_11047),U_11050))
    | ~ class_Int_Onumber(U_11047)
    | ~ class_Fields_Ofield__inverse__zero(U_11047) ),
    inference(clausify,[status(thm)],[f_2755_2]) ).

fof(f_2756_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).

fof(f_2756_2,plain,
    ! [U_11054,U_11053,U_11052,U_11051] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != c_Groups_Ozero__class_Ozero(U_11051)
            & U_11054 = c_Groups_Ozero__class_Ozero(U_11051) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11051),hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052)),U_11054) != U_11053
            & U_11054 != c_Groups_Ozero__class_Ozero(U_11051) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = c_Groups_Ozero__class_Ozero(U_11051)
              | U_11054 != c_Groups_Ozero__class_Ozero(U_11051) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11051),hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052)),U_11054) = U_11053
              | U_11054 = c_Groups_Ozero__class_Ozero(U_11051) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054) ) )
      | ~ class_Int_Onumber(U_11051)
      | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

cnf(f_2756_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11051),hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052)),U_11054) = U_11053
    | U_11054 = c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

cnf(f_2756_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = c_Groups_Ozero__class_Ozero(U_11051)
    | U_11054 != c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

cnf(f_2756_5,plain,
    ( U_11054 = c_Groups_Ozero__class_Ozero(U_11051)
    | U_11054 != c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

cnf(f_2756_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != c_Groups_Ozero__class_Ozero(U_11051)
    | U_11054 != c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

cnf(f_2756_7,plain,
    ( U_11054 = c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11051),hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052)),U_11054) != U_11053
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

cnf(f_2756_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) != c_Groups_Ozero__class_Ozero(U_11051)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11051),hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052)),U_11054) != U_11053
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11051),U_11052) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11051),U_11053),U_11054)
    | ~ class_Int_Onumber(U_11051)
    | ~ class_Fields_Ofield__inverse__zero(U_11051) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

fof(f_2757_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).

fof(f_2757_2,plain,
    ! [U_11058,U_11057,U_11056,U_11055] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) = hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) != c_Groups_Ozero__class_Ozero(U_11055)
            & U_11057 = c_Groups_Ozero__class_Ozero(U_11055) )
          | ( U_11056 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11055),hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)),U_11057)
            & U_11057 != c_Groups_Ozero__class_Ozero(U_11055) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) = c_Groups_Ozero__class_Ozero(U_11055)
              | U_11057 != c_Groups_Ozero__class_Ozero(U_11055) )
            & ( U_11056 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11055),hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)),U_11057)
              | U_11057 = c_Groups_Ozero__class_Ozero(U_11055) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) != hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) ) )
      | ~ class_Int_Onumber(U_11055)
      | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

cnf(f_2757_3,plain,
    ( U_11056 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11055),hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)),U_11057)
    | U_11057 = c_Groups_Ozero__class_Ozero(U_11055)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) != hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

cnf(f_2757_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) = c_Groups_Ozero__class_Ozero(U_11055)
    | U_11057 != c_Groups_Ozero__class_Ozero(U_11055)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) != hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

cnf(f_2757_5,plain,
    ( U_11057 = c_Groups_Ozero__class_Ozero(U_11055)
    | U_11057 != c_Groups_Ozero__class_Ozero(U_11055)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) = hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

cnf(f_2757_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) != c_Groups_Ozero__class_Ozero(U_11055)
    | U_11057 != c_Groups_Ozero__class_Ozero(U_11055)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) = hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

cnf(f_2757_7,plain,
    ( U_11057 = c_Groups_Ozero__class_Ozero(U_11055)
    | U_11056 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11055),hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)),U_11057)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) = hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

cnf(f_2757_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058) != c_Groups_Ozero__class_Ozero(U_11055)
    | U_11056 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11055),hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)),U_11057)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11055),U_11056),U_11057) = hAPP(c_Int_Onumber__class_Onumber__of(U_11055),U_11058)
    | ~ class_Int_Onumber(U_11055)
    | ~ class_Fields_Ofield__inverse__zero(U_11055) ),
    inference(clausify,[status(thm)],[f_2757_2]) ).

fof(f_2758_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
            & hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
              | hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) != V_a_2 ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).

fof(f_2758_2,plain,
    ! [U_11062,U_11061,U_11060,U_11059] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) = U_11062
          | ( U_11062 != c_Groups_Ozero__class_Ozero(U_11059)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) = c_Groups_Ozero__class_Ozero(U_11059) )
          | ( U_11060 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11059),U_11062),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) != c_Groups_Ozero__class_Ozero(U_11059) ) )
        & ( ( ( U_11062 = c_Groups_Ozero__class_Ozero(U_11059)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) != c_Groups_Ozero__class_Ozero(U_11059) )
            & ( U_11060 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11059),U_11062),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) = c_Groups_Ozero__class_Ozero(U_11059) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) != U_11062 ) )
      | ~ class_Int_Onumber(U_11059)
      | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

cnf(f_2758_3,plain,
    ( U_11060 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11059),U_11062),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) = c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) != U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

cnf(f_2758_4,plain,
    ( U_11062 = c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) != c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) != U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

cnf(f_2758_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) = c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) != c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) = U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

cnf(f_2758_6,plain,
    ( U_11062 != c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) != c_Groups_Ozero__class_Ozero(U_11059)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) = U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

cnf(f_2758_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061) = c_Groups_Ozero__class_Ozero(U_11059)
    | U_11060 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11059),U_11062),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) = U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

cnf(f_2758_8,plain,
    ( U_11062 != c_Groups_Ozero__class_Ozero(U_11059)
    | U_11060 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11059),U_11062),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11059),U_11060),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),U_11061)) = U_11062
    | ~ class_Int_Onumber(U_11059)
    | ~ class_Fields_Ofield__inverse__zero(U_11059) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

fof(f_2759_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_2759_2,plain,
    ! [U_11066,U_11065,U_11064,U_11063] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),U_11064)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),U_11065)),U_11066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11064),U_11065))),U_11066)
      | ~ class_Int_Onumber__ring(U_11063) ),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

cnf(f_2759_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),U_11064)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),U_11065)),U_11066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11063),hAPP(c_Int_Onumber__class_Onumber__of(U_11063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11064),U_11065))),U_11066)
    | ~ class_Int_Onumber__ring(U_11063) ),
    inference(clausify,[status(thm)],[f_2759_2]) ).

fof(f_2760_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_2760_2,plain,
    ! [U_11069,U_11068,U_11067] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11067),hAPP(c_Groups_Ouminus__class_Ouminus(U_11067),hAPP(c_Int_Onumber__class_Onumber__of(U_11067),U_11068))),U_11069) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11067),hAPP(c_Int_Onumber__class_Onumber__of(U_11067),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11068))),U_11069)
      | ~ class_Int_Onumber__ring(U_11067) ),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

cnf(f_2760_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11067),hAPP(c_Groups_Ouminus__class_Ouminus(U_11067),hAPP(c_Int_Onumber__class_Onumber__of(U_11067),U_11068))),U_11069) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11067),hAPP(c_Int_Onumber__class_Onumber__of(U_11067),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11068))),U_11069)
    | ~ class_Int_Onumber__ring(U_11067) ),
    inference(clausify,[status(thm)],[f_2760_2]) ).

fof(f_2761_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_2761_2,plain,
    ! [U_11072,U_11071,U_11070] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11070),hAPP(c_Int_Onumber__class_Onumber__of(U_11070),U_11071)),hAPP(c_Int_Onumber__class_Onumber__of(U_11070),U_11072)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11072)))
      | ~ class_Int_Onumber__ring(U_11070) ),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

cnf(f_2761_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11070),hAPP(c_Int_Onumber__class_Onumber__of(U_11070),U_11071)),hAPP(c_Int_Onumber__class_Onumber__of(U_11070),U_11072)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11072)))
    | ~ class_Int_Onumber__ring(U_11070) ),
    inference(clausify,[status(thm)],[f_2761_2]) ).

fof(f_2762_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(f_2762_2,plain,
    ! [U_11076,U_11075,U_11074,U_11073] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))) ) )
      | ~ class_Int_Onumber(U_11073)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

cnf(f_2762_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),c_Groups_Ozero__class_Ozero(U_11073)),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076)),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

cnf(f_2762_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),c_Groups_Ozero__class_Ozero(U_11073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11073),U_11074),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))),U_11075))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11073),U_11074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11073),U_11075),hAPP(c_Int_Onumber__class_Onumber__of(U_11073),U_11076))))
    | ~ class_Int_Onumber(U_11073)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11073) ),
    inference(clausify,[status(thm)],[f_2762_2]) ).

fof(f_2763_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(f_2763_2,plain,
    ! [U_11080,U_11079,U_11078,U_11077] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080))) ) )
      | ~ class_Int_Onumber(U_11077)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(variable_rename,[status(thm)],[f_2763_1]) ).

cnf(f_2763_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),c_Groups_Ozero__class_Ozero(U_11077)),U_11080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11080),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

cnf(f_2763_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),c_Groups_Ozero__class_Ozero(U_11077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),U_11079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),U_11080)),U_11079))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11077),hAPP(c_Int_Onumber__class_Onumber__of(U_11077),U_11078)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11077),U_11079),U_11080)))
    | ~ class_Int_Onumber(U_11077)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11077) ),
    inference(clausify,[status(thm)],[f_2763_2]) ).

fof(f_2764_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(f_2764_2,plain,
    ! [U_11084,U_11083,U_11082,U_11081] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084))) ) )
      | ~ class_Int_Onumber(U_11081)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

cnf(f_2764_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),U_11083))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11083),c_Groups_Ozero__class_Ozero(U_11081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

cnf(f_2764_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),c_Groups_Ozero__class_Ozero(U_11081)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)),U_11082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),U_11082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11081),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)),U_11083)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11081),U_11082),U_11083)),hAPP(c_Int_Onumber__class_Onumber__of(U_11081),U_11084)))
    | ~ class_Int_Onumber(U_11081)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11081) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

fof(f_2765_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(f_2765_2,plain,
    ! [U_11088,U_11087,U_11086,U_11085] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088)) ) )
      | ~ class_Int_Onumber(U_11085)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(variable_rename,[status(thm)],[f_2765_1]) ).

cnf(f_2765_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087)),c_Groups_Ozero__class_Ozero(U_11085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

cnf(f_2765_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),c_Groups_Ozero__class_Ozero(U_11085)),U_11088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11086))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),U_11086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11085),U_11088),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11085),U_11086),hAPP(c_Int_Onumber__class_Onumber__of(U_11085),U_11087))),U_11088))
    | ~ class_Int_Onumber(U_11085)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11085) ),
    inference(clausify,[status(thm)],[f_2765_2]) ).

fof(f_2766_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_2766_2,plain,
    ! [U_11090,U_11089] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)),c_Groups_Ozero__class_Ozero(U_11089))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)),c_Groups_Ozero__class_Ozero(U_11089))) ) )
      | ~ class_Rings_Olinordered__idom(U_11089)
      | ~ class_Int_Onumber__ring(U_11089) ),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

cnf(f_2766_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)),c_Groups_Ozero__class_Ozero(U_11089)))
    | ~ class_Rings_Olinordered__idom(U_11089)
    | ~ class_Int_Onumber__ring(U_11089) ),
    inference(clausify,[status(thm)],[f_2766_2]) ).

cnf(f_2766_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11089),hAPP(c_Int_Onumber__class_Onumber__of(U_11089),U_11090)),c_Groups_Ozero__class_Ozero(U_11089)))
    | ~ class_Rings_Olinordered__idom(U_11089)
    | ~ class_Int_Onumber__ring(U_11089) ),
    inference(clausify,[status(thm)],[f_2766_2]) ).

fof(f_2767_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_2767_2,plain,
    ! [U_11094,U_11093,U_11092,U_11091] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11091),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),U_11092)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11091),U_11093),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),U_11094))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11091),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11092),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11094)))),U_11093)
      | ~ class_Int_Onumber__ring(U_11091) ),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

cnf(f_2767_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11091),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),U_11092)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11091),U_11093),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),U_11094))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11091),hAPP(c_Int_Onumber__class_Onumber__of(U_11091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11092),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11094)))),U_11093)
    | ~ class_Int_Onumber__ring(U_11091) ),
    inference(clausify,[status(thm)],[f_2767_2]) ).

fof(f_2768_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(f_2768_2,plain,
    ! [U_11098,U_11097,U_11096,U_11095] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098)) ) )
      | ~ class_Int_Onumber(U_11095)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

cnf(f_2768_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11095),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097)),c_Groups_Ozero__class_Ozero(U_11095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

cnf(f_2768_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),c_Groups_Ozero__class_Ozero(U_11095)),U_11098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),U_11096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11095),U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11095),U_11096),hAPP(c_Int_Onumber__class_Onumber__of(U_11095),U_11097))),U_11098))
    | ~ class_Int_Onumber(U_11095)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11095) ),
    inference(clausify,[status(thm)],[f_2768_2]) ).

fof(f_2769_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(f_2769_2,plain,
    ! [U_11102,U_11101,U_11100,U_11099] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102))) ) )
      | ~ class_Int_Onumber(U_11099)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

cnf(f_2769_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),U_11101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11099),U_11101),c_Groups_Ozero__class_Ozero(U_11099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

cnf(f_2769_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),c_Groups_Ozero__class_Ozero(U_11099)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)),U_11100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),U_11100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11099),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)),U_11101)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11099),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),U_11101)),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),U_11102)))
    | ~ class_Int_Onumber(U_11099)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11099) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

fof(f_2770_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),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_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(f_2770_2,plain,
    ! [U_11106,U_11105,U_11104,U_11103] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106))) ) )
      | ~ class_Int_Onumber(U_11103)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(variable_rename,[status(thm)],[f_2770_1]) ).

cnf(f_2770_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),c_Groups_Ozero__class_Ozero(U_11103)),U_11106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11103),U_11106),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

cnf(f_2770_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),c_Groups_Ozero__class_Ozero(U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),U_11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),U_11106)),U_11105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11103),hAPP(c_Int_Onumber__class_Onumber__of(U_11103),U_11104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11103),U_11105),U_11106)))
    | ~ class_Int_Onumber(U_11103)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11103) ),
    inference(clausify,[status(thm)],[f_2770_2]) ).

fof(f_2771_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),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(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(f_2771_2,plain,
    ! [U_11110,U_11109,U_11108,U_11107] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))) ) )
      | ~ class_Int_Onumber(U_11107)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

cnf(f_2771_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),c_Groups_Ozero__class_Ozero(U_11107)),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11107),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110)),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

cnf(f_2771_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),c_Groups_Ozero__class_Ozero(U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11107),U_11108),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))),U_11109))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11107),U_11108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11107),U_11109),hAPP(c_Int_Onumber__class_Onumber__of(U_11107),U_11110))))
    | ~ class_Int_Onumber(U_11107)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11107) ),
    inference(clausify,[status(thm)],[f_2771_2]) ).

fof(f_2772_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_2772_2,plain,
    ! [U_11111] :
      ( ( 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_11111)) = 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_11111)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11111))) )
      & ( 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_11111)) = 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_11111))) ) ),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

fof(f_2772_3,plain,
    ( ! [U_11113] :
        ( 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_11113)) = 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_11113)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11113))) )
    & ! [U_11112] :
        ( 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_11112)) = 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_11112))) ) ),
    inference(miniscope,[status(thm)],[f_2772_2]) ).

cnf(f_2772_4,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_11112)) = 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_11112))) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

cnf(f_2772_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_11113)) = 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_11113)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11113))) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

fof(f_2773_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_2773_2,plain,
    ! [U_11114] : 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_11114)) = 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_11114))),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

cnf(f_2773_3,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_11114)) = 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_11114))),
    inference(clausify,[status(thm)],[f_2773_2]) ).

fof(f_2774_1,plain,
    ! [V_v_2,V_w_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_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_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(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_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(f_2774_2,plain,
    ! [U_11117,U_11116,U_11115] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11116))) = c_Groups_Oone__class_Oone(U_11115)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11116))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11116))) = hAPP(hAPP(c_HOL_OLet(U_11115,U_11115),hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11116))),hAPP(hAPP(c_COMBS(U_11115,U_11115,U_11115),hAPP(hAPP(c_COMBB(U_11115,tc_fun(U_11115,U_11115),U_11115),c_Groups_Otimes__class_Otimes(U_11115)),hAPP(c_Groups_Otimes__class_Otimes(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)))),c_COMBI(U_11115)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11116))) ) )
      | ~ class_Int_Onumber__ring(U_11115) ),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

cnf(f_2774_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11116))) = hAPP(hAPP(c_HOL_OLet(U_11115,U_11115),hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11116))),hAPP(hAPP(c_COMBS(U_11115,U_11115,U_11115),hAPP(hAPP(c_COMBB(U_11115,tc_fun(U_11115,U_11115),U_11115),c_Groups_Otimes__class_Otimes(U_11115)),hAPP(c_Groups_Otimes__class_Otimes(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)))),c_COMBI(U_11115)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11116)))
    | ~ class_Int_Onumber__ring(U_11115) ),
    inference(clausify,[status(thm)],[f_2774_2]) ).

cnf(f_2774_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11115),hAPP(c_Int_Onumber__class_Onumber__of(U_11115),U_11117)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11116))) = c_Groups_Oone__class_Oone(U_11115)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11116)))
    | ~ class_Int_Onumber__ring(U_11115) ),
    inference(clausify,[status(thm)],[f_2774_2]) ).

fof(f_2775_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_2775_2,plain,
    ! [U_11119,U_11118] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11118)),U_11119) = 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_11118)),U_11119))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11118))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11118)),U_11119) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11119)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11118))) ) ),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

fof(f_2775_3,plain,
    ( ! [U_11123,U_11121] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11121)),U_11123) = 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_11121)),U_11123))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11121))) )
    & ! [U_11122,U_11120] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11120)),U_11122) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11122)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11120))) ) ),
    inference(miniscope,[status(thm)],[f_2775_2]) ).

cnf(f_2775_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11120)),U_11122) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11122)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11120))) ),
    inference(clausify,[status(thm)],[f_2775_3]) ).

cnf(f_2775_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11121)),U_11123) = 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_11121)),U_11123))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11121))) ),
    inference(clausify,[status(thm)],[f_2775_3]) ).

fof(f_2776_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_2776_2,plain,
    ! [U_11124] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11124)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11124)),
    inference(variable_rename,[status(thm)],[f_2776_1]) ).

cnf(f_2776_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11124)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11124)),
    inference(clausify,[status(thm)],[f_2776_2]) ).

fof(f_2777_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_2777_2,plain,
    ! [U_11126,U_11125] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11125),U_11126)),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

cnf(f_2777_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11125),U_11126)),
    inference(clausify,[status(thm)],[f_2777_2]) ).

fof(f_2778_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_2778_2,plain,
    ! [U_11128,U_11127] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11128)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11127),U_11128)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11127),U_11128))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11128))) ) ),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

fof(f_2778_3,plain,
    ( ! [U_11132,U_11130] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11130)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11132)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11130),U_11132)) )
    & ! [U_11131,U_11129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11129),U_11131))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11129)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11131))) ) ),
    inference(miniscope,[status(thm)],[f_2778_2]) ).

cnf(f_2778_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11129),U_11131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11129)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11131))) ),
    inference(clausify,[status(thm)],[f_2778_3]) ).

cnf(f_2778_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11130)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11130),U_11132)) ),
    inference(clausify,[status(thm)],[f_2778_3]) ).

fof(f_2779_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_2779_2,plain,
    ! [U_11133] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11133) = U_11133,
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

cnf(f_2779_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11133) = U_11133,
    inference(clausify,[status(thm)],[f_2779_2]) ).

fof(f_2780_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_2780_2,plain,
    ! [U_11134] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11134))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11134))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11134)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11134)))) ) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ( ! [U_11136] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11136))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11136))) )
    & ! [U_11135] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11135)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11135)))) ) ),
    inference(miniscope,[status(thm)],[f_2780_2]) ).

cnf(f_2780_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11135)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11135)))) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

cnf(f_2780_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11136))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11136))) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

fof(f_2781_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_2781_2,plain,
    ! [U_11138,U_11137] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11137)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11138)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11137),U_11138)),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

cnf(f_2781_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11137)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11138)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11137),U_11138)),
    inference(clausify,[status(thm)],[f_2781_2]) ).

fof(f_2782_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_2782_2,plain,
    ! [U_11140,U_11139] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11140)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11139),U_11140)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11139),U_11140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11140))) ) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

fof(f_2782_3,plain,
    ( ! [U_11144,U_11142] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11142)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11144)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11142),U_11144)) )
    & ! [U_11143,U_11141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11141),U_11143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11141)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11143))) ) ),
    inference(miniscope,[status(thm)],[f_2782_2]) ).

cnf(f_2782_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11141),U_11143))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11141)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11143))) ),
    inference(clausify,[status(thm)],[f_2782_3]) ).

cnf(f_2782_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11142)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11144)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11142),U_11144)) ),
    inference(clausify,[status(thm)],[f_2782_3]) ).

fof(f_2783_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_2783_2,plain,
    ! [U_11146,U_11145] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11145)),c_Int_OBit1(U_11146)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11145),U_11146)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11145),U_11146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11145)),c_Int_OBit1(U_11146))) ) ),
    inference(variable_rename,[status(thm)],[f_2783_1]) ).

fof(f_2783_3,plain,
    ( ! [U_11150,U_11148] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11148)),c_Int_OBit1(U_11150)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11148),U_11150)) )
    & ! [U_11149,U_11147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11147),U_11149))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11147)),c_Int_OBit1(U_11149))) ) ),
    inference(miniscope,[status(thm)],[f_2783_2]) ).

cnf(f_2783_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11147),U_11149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11147)),c_Int_OBit1(U_11149))) ),
    inference(clausify,[status(thm)],[f_2783_3]) ).

cnf(f_2783_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11148)),c_Int_OBit1(U_11150)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11148),U_11150)) ),
    inference(clausify,[status(thm)],[f_2783_3]) ).

fof(f_2784_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_2784_2,plain,
    ! [U_11152,U_11151] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11151)),c_Int_OBit1(U_11152)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11151),U_11152)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11151),U_11152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11151)),c_Int_OBit1(U_11152))) ) ),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

fof(f_2784_3,plain,
    ( ! [U_11156,U_11154] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11154)),c_Int_OBit1(U_11156)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11154),U_11156)) )
    & ! [U_11155,U_11153] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11153),U_11155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11153)),c_Int_OBit1(U_11155))) ) ),
    inference(miniscope,[status(thm)],[f_2784_2]) ).

cnf(f_2784_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11153),U_11155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11153)),c_Int_OBit1(U_11155))) ),
    inference(clausify,[status(thm)],[f_2784_3]) ).

cnf(f_2784_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11154)),c_Int_OBit1(U_11156)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11154),U_11156)) ),
    inference(clausify,[status(thm)],[f_2784_3]) ).

fof(f_2785_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_2785_2,plain,
    ! [U_11158,U_11157] :
      ( ( c_Int_OBit1(U_11157) = c_Int_OBit1(U_11158)
        | U_11157 != U_11158 )
      & ( U_11157 = U_11158
        | c_Int_OBit1(U_11157) != c_Int_OBit1(U_11158) ) ),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

fof(f_2785_3,plain,
    ( ! [U_11162,U_11160] :
        ( c_Int_OBit1(U_11160) = c_Int_OBit1(U_11162)
        | U_11160 != U_11162 )
    & ! [U_11161,U_11159] :
        ( U_11159 = U_11161
        | c_Int_OBit1(U_11159) != c_Int_OBit1(U_11161) ) ),
    inference(miniscope,[status(thm)],[f_2785_2]) ).

cnf(f_2785_4,plain,
    ( U_11159 = U_11161
    | c_Int_OBit1(U_11159) != c_Int_OBit1(U_11161) ),
    inference(clausify,[status(thm)],[f_2785_3]) ).

cnf(f_2785_5,plain,
    ( c_Int_OBit1(U_11160) = c_Int_OBit1(U_11162)
    | U_11160 != U_11162 ),
    inference(clausify,[status(thm)],[f_2785_3]) ).

fof(f_2786_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_2786_2,plain,
    ! [U_11164,U_11163] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11163)),c_Int_OBit1(U_11164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11163),U_11164)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11163),U_11164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11163)),c_Int_OBit1(U_11164))) ) ),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

fof(f_2786_3,plain,
    ( ! [U_11168,U_11166] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11166)),c_Int_OBit1(U_11168)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11166),U_11168)) )
    & ! [U_11167,U_11165] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11165),U_11167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11165)),c_Int_OBit1(U_11167))) ) ),
    inference(miniscope,[status(thm)],[f_2786_2]) ).

cnf(f_2786_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11165),U_11167))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11165)),c_Int_OBit1(U_11167))) ),
    inference(clausify,[status(thm)],[f_2786_3]) ).

cnf(f_2786_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11166)),c_Int_OBit1(U_11168)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11166),U_11168)) ),
    inference(clausify,[status(thm)],[f_2786_3]) ).

fof(f_2787_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_2787_2,plain,
    ! [U_11170,U_11169] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11169)),c_Int_OBit1(U_11170)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11169),U_11170)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11169),U_11170))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11169)),c_Int_OBit1(U_11170))) ) ),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

fof(f_2787_3,plain,
    ( ! [U_11174,U_11172] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11172)),c_Int_OBit1(U_11174)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11172),U_11174)) )
    & ! [U_11173,U_11171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11171),U_11173))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11171)),c_Int_OBit1(U_11173))) ) ),
    inference(miniscope,[status(thm)],[f_2787_2]) ).

cnf(f_2787_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11171),U_11173))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11171)),c_Int_OBit1(U_11173))) ),
    inference(clausify,[status(thm)],[f_2787_3]) ).

cnf(f_2787_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11172)),c_Int_OBit1(U_11174)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11172),U_11174)) ),
    inference(clausify,[status(thm)],[f_2787_3]) ).

fof(f_2788_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_2788_2,plain,
    ! [U_11175] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11175) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_11175),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

cnf(f_2788_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11175) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_11175),
    inference(clausify,[status(thm)],[f_2788_2]) ).

fof(f_2789_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_2789_2,plain,
    ! [U_11176] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11176)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11176),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11176),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11176)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

fof(f_2789_3,plain,
    ( ! [U_11178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11178)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_11177] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11177),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11177)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2789_2]) ).

cnf(f_2789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11177),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11177)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2789_3]) ).

cnf(f_2789_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11178)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2789_3]) ).

fof(f_2790_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_2790_2,plain,
    ! [U_11179] : c_Int_OBit1(U_11179) = 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_11179)),U_11179),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

cnf(f_2790_3,plain,
    c_Int_OBit1(U_11179) = 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_11179)),U_11179),
    inference(clausify,[status(thm)],[f_2790_2]) ).

fof(f_2791_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_2791_2,plain,
    ! [U_11180] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11180),
    inference(variable_rename,[status(thm)],[f_2791_1]) ).

cnf(f_2791_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11180),
    inference(clausify,[status(thm)],[f_2791_2]) ).

fof(f_2792_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_2792_2,plain,
    ! [U_11181] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11181) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11181)),
    inference(variable_rename,[status(thm)],[f_2792_1]) ).

cnf(f_2792_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11181) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11181)),
    inference(clausify,[status(thm)],[f_2792_2]) ).

fof(f_2793_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_2793_2,plain,
    ! [U_11182] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11182)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11182)),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_11182))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11182)) = 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_11182))) ) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

fof(f_2793_3,plain,
    ( ! [U_11184] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11184)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11184)),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_11184))) )
    & ! [U_11183] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11183)) = 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_11183))) ) ),
    inference(miniscope,[status(thm)],[f_2793_2]) ).

cnf(f_2793_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11183)) = 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_11183))) ),
    inference(clausify,[status(thm)],[f_2793_3]) ).

cnf(f_2793_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11184)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11184)),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_11184))) ),
    inference(clausify,[status(thm)],[f_2793_3]) ).

fof(f_2794_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_2794_2,plain,
    ! [U_11186,U_11185] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11185),c_Int_OBit1(U_11186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11185),c_Groups_Oone__class_Oone(U_11185)),hAPP(c_Int_Onumber__class_Onumber__of(U_11185),U_11186))),hAPP(c_Int_Onumber__class_Onumber__of(U_11185),U_11186))
      | ~ class_Int_Onumber__ring(U_11185) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

cnf(f_2794_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11185),c_Int_OBit1(U_11186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11185),c_Groups_Oone__class_Oone(U_11185)),hAPP(c_Int_Onumber__class_Onumber__of(U_11185),U_11186))),hAPP(c_Int_Onumber__class_Onumber__of(U_11185),U_11186))
    | ~ class_Int_Onumber__ring(U_11185) ),
    inference(clausify,[status(thm)],[f_2794_2]) ).

fof(f_2795_1,plain,
    ! [V_z_2,V_w_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_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_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(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_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).

fof(f_2795_2,plain,
    ! [U_11189,U_11188,U_11187] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11188))) = c_Groups_Oone__class_Oone(U_11187)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11188))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11188))) = hAPP(hAPP(c_HOL_OLet(U_11187,U_11187),hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11188))),hAPP(hAPP(c_COMBS(U_11187,U_11187,U_11187),hAPP(hAPP(c_COMBB(U_11187,tc_fun(U_11187,U_11187),U_11187),c_Groups_Otimes__class_Otimes(U_11187)),hAPP(c_Groups_Otimes__class_Otimes(U_11187),U_11189))),c_COMBI(U_11187)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11188))) ) )
      | ~ class_Int_Onumber__ring(U_11187) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

cnf(f_2795_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11188))) = hAPP(hAPP(c_HOL_OLet(U_11187,U_11187),hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11188))),hAPP(hAPP(c_COMBS(U_11187,U_11187,U_11187),hAPP(hAPP(c_COMBB(U_11187,tc_fun(U_11187,U_11187),U_11187),c_Groups_Otimes__class_Otimes(U_11187)),hAPP(c_Groups_Otimes__class_Otimes(U_11187),U_11189))),c_COMBI(U_11187)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11188)))
    | ~ class_Int_Onumber__ring(U_11187) ),
    inference(clausify,[status(thm)],[f_2795_2]) ).

cnf(f_2795_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11187),U_11189),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11188))) = c_Groups_Oone__class_Oone(U_11187)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11188)))
    | ~ class_Int_Onumber__ring(U_11187) ),
    inference(clausify,[status(thm)],[f_2795_2]) ).

fof(f_2796_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_2796_2,plain,
    ! [U_11191,U_11190] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11191),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11190))) = 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_11190))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11191),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11190))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11191),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11190))),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_11191))),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_11190))) ) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

fof(f_2796_3,plain,
    ( ! [U_11195,U_11193] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11193))) = 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_11193))) )
    & ! [U_11194,U_11192] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11192))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11192))),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_11194))),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_11192))) ) ),
    inference(miniscope,[status(thm)],[f_2796_2]) ).

cnf(f_2796_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11192))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11192))),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_11194))),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_11192))) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

cnf(f_2796_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_11193))) = 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_11193))) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

fof(f_2797_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_2797_2,plain,
    ! [U_11197,U_11196] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11196)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11197)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11196),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11197))),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

cnf(f_2797_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11196)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11197)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11196),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11197))),
    inference(clausify,[status(thm)],[f_2797_2]) ).

fof(f_2798_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_2798_2,plain,
    ! [U_11198] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11198) = 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_11198))) ),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

cnf(f_2798_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11198) = 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_11198))) ),
    inference(clausify,[status(thm)],[f_2798_2]) ).

fof(f_2799_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_2799_2,plain,
    ! [U_11200,U_11199] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11199) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11200)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11200)))
        | U_11199 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11200)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11200)))
          & U_11199 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11200)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11199) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11200) ) ),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

fof(f_2799_3,plain,
    ( ! [U_11204,U_11202] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11202) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11204)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11204)))
        | U_11202 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11204)) )
    & ! [U_11203,U_11201] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11203)))
          & U_11201 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11203)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11201) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11203) ) ),
    inference(miniscope,[status(thm)],[f_2799_2]) ).

cnf(f_2799_4,plain,
    ( U_11201 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11203))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11201) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11203) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

cnf(f_2799_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),U_11203)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11201) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11203) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

cnf(f_2799_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11202) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11204)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11204)))
    | U_11202 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11204)) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

fof(f_2800_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_2800_2,plain,
    ! [U_11206,U_11205] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11205) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11206)
        | ( ( ( U_11205 != U_11206
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11206))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11205) != 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_11206))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11205))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11206)),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_11205))) ) )
      & ( ( ( ( ( U_11205 = U_11206
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11206))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11205) = 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_11206))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11205))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11206)),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_11205))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11205) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11206) ) ),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

fof(f_2800_3,plain,
    ( ! [U_11210,U_11208] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210)
        | ( ( ( U_11208 != U_11210
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208) != 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_11210))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)),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_11208))) ) )
    & ! [U_11209,U_11207] :
        ( ( ( ( ( U_11207 = U_11209
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11209))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11207) = 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_11209))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11207))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11209)),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_11207))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11207) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11209) ) ),
    inference(miniscope,[status(thm)],[f_2800_2]) ).

cnf(f_2800_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11209)),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_11207)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11207) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11209) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11207) = 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_11209)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11207)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11207) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11209) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_6,plain,
    ( U_11207 = U_11209
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11209)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11207)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11207) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11209) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_7,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_8,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_9,plain,
    ( U_11208 != U_11210
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_10,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208) != 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_11208)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_11,plain,
    ( U_11208 != U_11210
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208) != 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_11208)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_12,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_14,plain,
    ( U_11208 != U_11210
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_15,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11210)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208) != c_Groups_Ozero__class_Ozero(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_11210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

cnf(f_2800_16,plain,
    ( U_11208 != U_11210
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11208) != c_Groups_Ozero__class_Ozero(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_11210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11208) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11210) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

fof(f_2801_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_2801_2,plain,
    ! [U_11213,U_11212,U_11211] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11212)),U_11213)) = 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_11211),U_11212))),U_11213)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11212))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11212)),U_11213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11211)),U_11213)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11212))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11211))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11212)),U_11213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11212)),U_11213)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11211))) ) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

fof(f_2801_3,plain,
    ( ! [U_11219,U_11217,U_11215] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11217)),U_11219)) = 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_11215),U_11217))),U_11219)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11217))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11217)),U_11219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),U_11219)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11217))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11215))) )
    & ! [U_11218,U_11216,U_11214] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11216)),U_11218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11216)),U_11218)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11214))) ) ),
    inference(miniscope,[status(thm)],[f_2801_2]) ).

cnf(f_2801_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11216)),U_11218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11216)),U_11218)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11214))) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

cnf(f_2801_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11217)),U_11219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),U_11219)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11217)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11215))) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

cnf(f_2801_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11217)),U_11219)) = 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_11215),U_11217))),U_11219)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11217)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11215))) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

fof(f_2802_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_2802_2,plain,
    ! [U_11220] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11220)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11220)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11220))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11220)) = 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_11220))) ) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ( ! [U_11222] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11222)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11222)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11222))) )
    & ! [U_11221] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11221)) = 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_11221))) ) ),
    inference(miniscope,[status(thm)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11221)) = 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_11221))) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

cnf(f_2802_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11222)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11222)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11222))) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_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_2803_2,plain,
    ! [U_11224,U_11223] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11223),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11224)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11223),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11224)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11224))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11223),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11224)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11223)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11224))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11223))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11223),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11224)) = 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_11223))) ) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

fof(f_2803_3,plain,
    ( ! [U_11228,U_11226] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11228)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11228)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11226))) )
    & ! [U_11227,U_11225] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11225),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11227)) = 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_11225))) ) ),
    inference(miniscope,[status(thm)],[f_2803_2]) ).

cnf(f_2803_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11225),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11227)) = 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_11225))) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

cnf(f_2803_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11228)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11226))) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

cnf(f_2803_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11228)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11226),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11228)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11226))) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

fof(f_2804_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_2804_2,plain,
    ! [U_11230,U_11229] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11229)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11230)) = 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_11229)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11230)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11229))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11229)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11230)) = 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_11229))) ) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

fof(f_2804_3,plain,
    ( ! [U_11234,U_11232] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11232)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11234)) = 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_11232)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11234)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11232))) )
    & ! [U_11233,U_11231] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11231)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11233)) = 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_11231))) ) ),
    inference(miniscope,[status(thm)],[f_2804_2]) ).

cnf(f_2804_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11231)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11233)) = 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_11231))) ),
    inference(clausify,[status(thm)],[f_2804_3]) ).

cnf(f_2804_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11232)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11234)) = 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_11232)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11234)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11232))) ),
    inference(clausify,[status(thm)],[f_2804_3]) ).

fof(f_2805_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_2805_2,plain,
    ! [U_11236,U_11235] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11236)) = 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_11235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11236)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11235))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11236)) = 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_11236))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11235))) ) ),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

fof(f_2805_3,plain,
    ( ! [U_11240,U_11238] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11238)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11240)) = 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_11238)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11240)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11238))) )
    & ! [U_11239,U_11237] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11237)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11239)) = 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_11239))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11237))) ) ),
    inference(miniscope,[status(thm)],[f_2805_2]) ).

cnf(f_2805_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11237)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11239)) = 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_11239))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11237))) ),
    inference(clausify,[status(thm)],[f_2805_3]) ).

cnf(f_2805_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11238)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11240)) = 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_11238)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11240)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11238))) ),
    inference(clausify,[status(thm)],[f_2805_3]) ).

fof(f_2806_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_2806_2,plain,
    ! [U_11242,U_11241] :
      ( ( 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_11241)),U_11242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11241))),U_11242)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11241))) )
      & ( 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_11241)),U_11242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_11242)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11241))) ) ),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

fof(f_2806_3,plain,
    ( ! [U_11246,U_11244] :
        ( 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_11244)),U_11246)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11244))),U_11246)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11244))) )
    & ! [U_11245,U_11243] :
        ( 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_11243)),U_11245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_11245)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11243))) ) ),
    inference(miniscope,[status(thm)],[f_2806_2]) ).

cnf(f_2806_4,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_11243)),U_11245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_11245)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11243))) ),
    inference(clausify,[status(thm)],[f_2806_3]) ).

cnf(f_2806_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_11244)),U_11246)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11244))),U_11246)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11244))) ),
    inference(clausify,[status(thm)],[f_2806_3]) ).

fof(f_2807_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_2807_2,plain,
    ! [U_11248,U_11247] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11248)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11247)) = 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_11248),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11247)))),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_11247),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11248)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11247)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11248)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11247),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

fof(f_2807_3,plain,
    ( ! [U_11252,U_11250] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11252)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11250)) = 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_11252),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11250)))),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_11250),c_Int_OPls)) )
    & ! [U_11251,U_11249] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11251)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11249)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11251)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11249),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11251)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11249)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11251)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11249),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

cnf(f_2807_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11252)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11250)) = 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_11252),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11250)))),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_11250),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

fof(f_2808_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_2808_2,plain,
    ! [U_11254,U_11253] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11253)),hAPP(c_Nat_OSuc,U_11254)) = 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_11253))),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_11254)))),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

cnf(f_2808_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11253)),hAPP(c_Nat_OSuc,U_11254)) = 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_11253))),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_11254)))),
    inference(clausify,[status(thm)],[f_2808_2]) ).

fof(f_2809_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

cnf(f_2809_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_2809_1]) ).

fof(f_2810_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_2810_2,plain,
    ! [U_11255] : c_Int_OPls != c_Int_OBit1(U_11255),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

cnf(f_2810_3,plain,
    c_Int_OPls != c_Int_OBit1(U_11255),
    inference(clausify,[status(thm)],[f_2810_2]) ).

fof(f_2811_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_2811_2,plain,
    ! [U_11256] : c_Int_OBit1(U_11256) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_2811_1]) ).

cnf(f_2811_3,plain,
    c_Int_OBit1(U_11256) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_2811_2]) ).

fof(f_2812_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]) ).

cnf(f_2812_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_2812_1]) ).

fof(f_2813_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

cnf(f_2813_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2813_1]) ).

fof(f_2814_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_2814_2,plain,
    ! [U_11257] : c_Int_Osucc(c_Int_Opred(U_11257)) = U_11257,
    inference(variable_rename,[status(thm)],[f_2814_1]) ).

cnf(f_2814_3,plain,
    c_Int_Osucc(c_Int_Opred(U_11257)) = U_11257,
    inference(clausify,[status(thm)],[f_2814_2]) ).

fof(f_2815_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_2815_2,plain,
    ! [U_11258] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_11258) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

cnf(f_2815_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_11258) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_2815_2]) ).

fof(f_2816_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_2816_2,plain,
    ! [U_11259] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_11259) = U_11259,
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

cnf(f_2816_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_11259) = U_11259,
    inference(clausify,[status(thm)],[f_2816_2]) ).

fof(f_2817_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_2817_2,plain,
    ! [U_11260] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11260),c_Int_OPls) = U_11260,
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

cnf(f_2817_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11260),c_Int_OPls) = U_11260,
    inference(clausify,[status(thm)],[f_2817_2]) ).

fof(f_2818_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]) ).

cnf(f_2818_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2818_1]) ).

fof(f_2819_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_2819_2,plain,
    ! [U_11261] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11261),c_Int_OPls) = U_11261,
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

cnf(f_2819_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11261),c_Int_OPls) = U_11261,
    inference(clausify,[status(thm)],[f_2819_2]) ).

fof(f_2820_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]) ).

cnf(f_2820_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2820_1]) ).

fof(f_2821_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_2821_2,plain,
    ! [U_11262] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11262),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_11262)
      | ~ class_Int_Onumber__ring(U_11262) ),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

cnf(f_2821_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11262),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_11262)
    | ~ class_Int_Onumber__ring(U_11262) ),
    inference(clausify,[status(thm)],[f_2821_2]) ).

fof(f_2822_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_2822_2,plain,
    ! [U_11263] :
      ( c_Groups_Ozero__class_Ozero(U_11263) = hAPP(c_Int_Onumber__class_Onumber__of(U_11263),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_11263) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

cnf(f_2822_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_11263) = hAPP(c_Int_Onumber__class_Onumber__of(U_11263),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_11263) ),
    inference(clausify,[status(thm)],[f_2822_2]) ).

fof(f_2823_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_2823_2,plain,
    ! [U_11265,U_11264] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11264),U_11265),hAPP(c_Int_Onumber__class_Onumber__of(U_11264),c_Int_OPls)) = U_11265
      | ~ class_Int_Onumber__ring(U_11264) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

cnf(f_2823_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11264),U_11265),hAPP(c_Int_Onumber__class_Onumber__of(U_11264),c_Int_OPls)) = U_11265
    | ~ class_Int_Onumber__ring(U_11264) ),
    inference(clausify,[status(thm)],[f_2823_2]) ).

fof(f_2824_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_2824_2,plain,
    ! [U_11267,U_11266] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11266),hAPP(c_Int_Onumber__class_Onumber__of(U_11266),c_Int_OPls)),U_11267) = U_11267
      | ~ class_Int_Onumber__ring(U_11266) ),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

cnf(f_2824_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11266),hAPP(c_Int_Onumber__class_Onumber__of(U_11266),c_Int_OPls)),U_11267) = U_11267
    | ~ class_Int_Onumber__ring(U_11266) ),
    inference(clausify,[status(thm)],[f_2824_2]) ).

fof(f_2825_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]) ).

cnf(f_2825_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(clausify,[status(thm)],[f_2825_1]) ).

fof(f_2826_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]) ).

cnf(f_2826_2,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_2826_1]) ).

fof(f_2827_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]) ).

cnf(f_2827_2,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_2827_1]) ).

fof(f_2828_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]) ).

cnf(f_2828_2,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_2828_1]) ).

fof(f_2829_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_2829_2,plain,
    ! [U_11268] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11268)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11268)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11268))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11268))) ) ),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

fof(f_2829_3,plain,
    ( ! [U_11270] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11270)) )
    & ! [U_11269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11269))) ) ),
    inference(miniscope,[status(thm)],[f_2829_2]) ).

cnf(f_2829_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11269))) ),
    inference(clausify,[status(thm)],[f_2829_3]) ).

cnf(f_2829_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11270)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11270)) ),
    inference(clausify,[status(thm)],[f_2829_3]) ).

fof(f_2830_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_2830_2,plain,
    ! [U_11271] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11271)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11271),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11271),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11271)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

fof(f_2830_3,plain,
    ( ! [U_11273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11273)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11273),c_Int_OPls)) )
    & ! [U_11272] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11272),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11272)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2830_2]) ).

cnf(f_2830_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11272),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11272)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

cnf(f_2830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11273)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11273),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

fof(f_2831_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_2831_2,plain,
    ! [U_11275,U_11274] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11275),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_11274)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11274)) ),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

cnf(f_2831_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11275),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_11274)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11274)) ),
    inference(clausify,[status(thm)],[f_2831_2]) ).

fof(f_2832_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]) ).

cnf(f_2832_2,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_2832_1]) ).

fof(f_2833_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_2833_2,plain,
    ! [U_11276] :
      ( ( 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_11276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11276))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11276),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_11276)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11276),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

fof(f_2833_3,plain,
    ( ! [U_11278] :
        ( 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_11278)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11278))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11278),c_Int_OPls)) )
    & ! [U_11277] :
        ( 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_11277)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11277),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2833_2]) ).

cnf(f_2833_4,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_11277)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11277),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2833_3]) ).

cnf(f_2833_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_11278)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11278))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11278),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2833_3]) ).

fof(f_2834_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_2834_2,plain,
    ! [U_11279] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11279)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11279))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11279),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11279)),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_11279),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

fof(f_2834_3,plain,
    ( ! [U_11281] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11281))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11281),c_Int_OPls)) )
    & ! [U_11280] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11280)),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_11280),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2834_2]) ).

cnf(f_2834_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11280)),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_11280),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

cnf(f_2834_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11281))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11281),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

fof(f_2835_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_2835_2,plain,
    ! [U_11283,U_11282] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11282),U_11283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11282)),U_11283)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11282)),U_11283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11282),U_11283)) ) ),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

fof(f_2835_3,plain,
    ( ! [U_11287,U_11285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11285),U_11287))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11285)),U_11287)) )
    & ! [U_11286,U_11284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11284)),U_11286))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11284),U_11286)) ) ),
    inference(miniscope,[status(thm)],[f_2835_2]) ).

cnf(f_2835_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11284)),U_11286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11284),U_11286)) ),
    inference(clausify,[status(thm)],[f_2835_3]) ).

cnf(f_2835_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11285),U_11287))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_11285)),U_11287)) ),
    inference(clausify,[status(thm)],[f_2835_3]) ).

fof(f_2836_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_2836_2,plain,
    ! [U_11288] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_11288)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11288))),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

cnf(f_2836_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_11288)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11288))),
    inference(clausify,[status(thm)],[f_2836_2]) ).

fof(f_2837_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_2837_2,plain,
    ! [U_11289] : c_Int_Opred(U_11289) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11289),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

cnf(f_2837_3,plain,
    c_Int_Opred(U_11289) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11289),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2837_2]) ).

fof(f_2838_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_2838_2,plain,
    ! [U_11290] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11290)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_11290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11290),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11290)),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_11290),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

fof(f_2838_3,plain,
    ( ! [U_11292] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_11292))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11292),c_Int_OPls)) )
    & ! [U_11291] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11291)),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_11291),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2838_2]) ).

cnf(f_2838_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11291)),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_11291),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

cnf(f_2838_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_11292))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11292),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

fof(f_2839_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_2839_2,plain,
    ! [U_11294,U_11293] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11293),hAPP(c_Int_Onumber__class_Onumber__of(U_11293),c_Int_OBit1(c_Int_OPls))),U_11294) = U_11294
      | ~ class_Int_Onumber__ring(U_11293) ),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

cnf(f_2839_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11293),hAPP(c_Int_Onumber__class_Onumber__of(U_11293),c_Int_OBit1(c_Int_OPls))),U_11294) = U_11294
    | ~ class_Int_Onumber__ring(U_11293) ),
    inference(clausify,[status(thm)],[f_2839_2]) ).

fof(f_2840_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_2840_2,plain,
    ! [U_11296,U_11295] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11295),U_11296),hAPP(c_Int_Onumber__class_Onumber__of(U_11295),c_Int_OBit1(c_Int_OPls))) = U_11296
      | ~ class_Int_Onumber__ring(U_11295) ),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

cnf(f_2840_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11295),U_11296),hAPP(c_Int_Onumber__class_Onumber__of(U_11295),c_Int_OBit1(c_Int_OPls))) = U_11296
    | ~ class_Int_Onumber__ring(U_11295) ),
    inference(clausify,[status(thm)],[f_2840_2]) ).

fof(f_2841_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_2841_2,plain,
    ! [U_11298,U_11297] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11297),U_11298),hAPP(c_Int_Onumber__class_Onumber__of(U_11297),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_11297)
      | ~ class_Int_Onumber__ring(U_11297)
      | ~ class_Fields_Ofield__inverse__zero(U_11297) ),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

cnf(f_2841_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11297),U_11298),hAPP(c_Int_Onumber__class_Onumber__of(U_11297),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_11297)
    | ~ class_Int_Onumber__ring(U_11297)
    | ~ class_Fields_Ofield__inverse__zero(U_11297) ),
    inference(clausify,[status(thm)],[f_2841_2]) ).

fof(f_2842_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_2842_2,plain,
    ! [U_11299] :
      ( c_Groups_Oone__class_Oone(U_11299) = hAPP(c_Int_Onumber__class_Onumber__of(U_11299),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_11299) ),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

cnf(f_2842_3,plain,
    ( c_Groups_Oone__class_Oone(U_11299) = hAPP(c_Int_Onumber__class_Onumber__of(U_11299),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_11299) ),
    inference(clausify,[status(thm)],[f_2842_2]) ).

fof(f_2843_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_2843_2,plain,
    ! [U_11300] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11300),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_11300)
      | ~ class_Int_Onumber__ring(U_11300) ),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

cnf(f_2843_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11300),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_11300)
    | ~ class_Int_Onumber__ring(U_11300) ),
    inference(clausify,[status(thm)],[f_2843_2]) ).

fof(f_2844_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_2844_2,plain,
    ! [U_11301] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11301) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11301),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11301),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11301) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

fof(f_2844_3,plain,
    ( ! [U_11303] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11303) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11303),c_Int_OPls)) )
    & ! [U_11302] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11302),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11302) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2844_2]) ).

cnf(f_2844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11302),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11302) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2844_3]) ).

cnf(f_2844_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11303) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11303),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2844_3]) ).

fof(f_2845_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_2845_2,plain,
    ! [U_11304] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11304)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11304),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11304),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11304) ) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

fof(f_2845_3,plain,
    ( ! [U_11306] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11306)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11306),c_Int_OPls)) )
    & ! [U_11305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11305),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11305) ) ),
    inference(miniscope,[status(thm)],[f_2845_2]) ).

cnf(f_2845_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11305),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11305) ),
    inference(clausify,[status(thm)],[f_2845_3]) ).

cnf(f_2845_5,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11306)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11306),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2845_3]) ).

fof(f_2846_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]) ).

cnf(f_2846_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(clausify,[status(thm)],[f_2846_1]) ).

fof(f_2847_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_2847_2,plain,
    ! [U_11307] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11307)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11307))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11307))) ) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

fof(f_2847_3,plain,
    ( ! [U_11309] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11309)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11309)) )
    & ! [U_11308] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11308))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11308))) ) ),
    inference(miniscope,[status(thm)],[f_2847_2]) ).

cnf(f_2847_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11308))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11308))) ),
    inference(clausify,[status(thm)],[f_2847_3]) ).

cnf(f_2847_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11309)) ),
    inference(clausify,[status(thm)],[f_2847_3]) ).

fof(f_2848_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_2848_2,plain,
    ! [U_11310] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11310)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11310),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11310),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11310)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

fof(f_2848_3,plain,
    ( ! [U_11312] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11312)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11312),c_Int_OPls)) )
    & ! [U_11311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11311),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11311)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2848_2]) ).

cnf(f_2848_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11311),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11311)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2848_3]) ).

cnf(f_2848_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11312)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11312),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2848_3]) ).

fof(f_2849_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_2849_2,plain,
    ! [U_11314,U_11313] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11313)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11314)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11313),U_11314))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11314))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11313),U_11314)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11313),U_11314))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11314))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11313),U_11314)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11313)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11314))) ) ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

fof(f_2849_3,plain,
    ( ! [U_11318,U_11316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11316),U_11318))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11318))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11316),U_11318)) ) )
    & ! [U_11317,U_11315] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11315),U_11317))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11317))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11315),U_11317)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11317))) ) ),
    inference(miniscope,[status(thm)],[f_2849_2]) ).

cnf(f_2849_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11315),U_11317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11317))) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11315),U_11317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11317))) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11316),U_11318))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11316),U_11318))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11318))) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11318))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11316),U_11318))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11318))) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

fof(f_2850_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_2850_2,plain,
    ! [U_11320,U_11319] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11319),U_11320),hAPP(c_Int_Onumber__class_Onumber__of(U_11319),c_Int_OBit1(c_Int_OPls))) = U_11320
      | ~ class_Int_Onumber__ring(U_11319)
      | ~ class_Fields_Ofield(U_11319) ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

cnf(f_2850_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11319),U_11320),hAPP(c_Int_Onumber__class_Onumber__of(U_11319),c_Int_OBit1(c_Int_OPls))) = U_11320
    | ~ class_Int_Onumber__ring(U_11319)
    | ~ class_Fields_Ofield(U_11319) ),
    inference(clausify,[status(thm)],[f_2850_2]) ).

fof(f_2851_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_2851_2,plain,
    ! [U_11322,U_11321] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11321),U_11322),hAPP(c_Int_Onumber__class_Onumber__of(U_11321),c_Int_OBit1(c_Int_OPls))) = U_11322
      | ~ class_Int_Onumber__ring(U_11321)
      | ~ class_Fields_Ofield(U_11321) ),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

cnf(f_2851_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11321),U_11322),hAPP(c_Int_Onumber__class_Onumber__of(U_11321),c_Int_OBit1(c_Int_OPls))) = U_11322
    | ~ class_Int_Onumber__ring(U_11321)
    | ~ class_Fields_Ofield(U_11321) ),
    inference(clausify,[status(thm)],[f_2851_2]) ).

fof(f_2852_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_2852_2,plain,
    ! [U_11324,U_11323] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11323)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11324)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11323),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11323),U_11324)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11323),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11323),U_11324))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11323)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11324))) ) ),
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

fof(f_2852_3,plain,
    ( ! [U_11328,U_11326] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11326)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11328)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11326),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11326),U_11328)) ) )
    & ! [U_11327,U_11325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11325),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11325),U_11327))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11325)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11327))) ) ),
    inference(miniscope,[status(thm)],[f_2852_2]) ).

cnf(f_2852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11325),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11325),U_11327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11325)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11327))) ),
    inference(clausify,[status(thm)],[f_2852_3]) ).

cnf(f_2852_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11326),U_11328))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11326)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11328))) ),
    inference(clausify,[status(thm)],[f_2852_3]) ).

cnf(f_2852_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11326),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11326)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11328))) ),
    inference(clausify,[status(thm)],[f_2852_3]) ).

fof(f_2853_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]) ).

cnf(f_2853_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(clausify,[status(thm)],[f_2853_1]) ).

fof(f_2854_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]) ).

cnf(f_2854_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(clausify,[status(thm)],[f_2854_1]) ).

fof(f_2855_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]) ).

cnf(f_2855_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(clausify,[status(thm)],[f_2855_1]) ).

fof(f_2856_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]) ).

cnf(f_2856_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(clausify,[status(thm)],[f_2856_1]) ).

fof(f_2857_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_2857_2,plain,
    ! [U_11329] : c_Int_Osucc(U_11329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11329),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

cnf(f_2857_3,plain,
    c_Int_Osucc(U_11329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11329),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2857_2]) ).

fof(f_2858_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ 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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),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_le__special_I3_J]) ).

fof(f_2858_2,plain,
    ! [U_11331,U_11330] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11330),hAPP(c_Int_Onumber__class_Onumber__of(U_11330),U_11331)),c_Groups_Ozero__class_Ozero(U_11330)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11331),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11331),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11330),hAPP(c_Int_Onumber__class_Onumber__of(U_11330),U_11331)),c_Groups_Ozero__class_Ozero(U_11330))) ) )
      | ~ class_Rings_Olinordered__idom(U_11330)
      | ~ class_Int_Onumber__ring(U_11330) ),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

cnf(f_2858_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11331),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11330),hAPP(c_Int_Onumber__class_Onumber__of(U_11330),U_11331)),c_Groups_Ozero__class_Ozero(U_11330)))
    | ~ class_Rings_Olinordered__idom(U_11330)
    | ~ class_Int_Onumber__ring(U_11330) ),
    inference(clausify,[status(thm)],[f_2858_2]) ).

cnf(f_2858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11330),hAPP(c_Int_Onumber__class_Onumber__of(U_11330),U_11331)),c_Groups_Ozero__class_Ozero(U_11330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11331),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_11330)
    | ~ class_Int_Onumber__ring(U_11330) ),
    inference(clausify,[status(thm)],[f_2858_2]) ).

fof(f_2859_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).

fof(f_2859_2,plain,
    ! [U_11333,U_11332] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11332),c_Groups_Ozero__class_Ozero(U_11332)),hAPP(c_Int_Onumber__class_Onumber__of(U_11332),U_11333)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11333)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11333))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11332),c_Groups_Ozero__class_Ozero(U_11332)),hAPP(c_Int_Onumber__class_Onumber__of(U_11332),U_11333))) ) )
      | ~ class_Rings_Olinordered__idom(U_11332)
      | ~ class_Int_Onumber__ring(U_11332) ),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

cnf(f_2859_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11333))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11332),c_Groups_Ozero__class_Ozero(U_11332)),hAPP(c_Int_Onumber__class_Onumber__of(U_11332),U_11333)))
    | ~ class_Rings_Olinordered__idom(U_11332)
    | ~ class_Int_Onumber__ring(U_11332) ),
    inference(clausify,[status(thm)],[f_2859_2]) ).

cnf(f_2859_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11332),c_Groups_Ozero__class_Ozero(U_11332)),hAPP(c_Int_Onumber__class_Onumber__of(U_11332),U_11333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11333))
    | ~ class_Rings_Olinordered__idom(U_11332)
    | ~ class_Int_Onumber__ring(U_11332) ),
    inference(clausify,[status(thm)],[f_2859_2]) ).

fof(f_2860_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).

fof(f_2860_2,plain,
    ! [U_11335,U_11334] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11334),c_Groups_Ozero__class_Ozero(U_11334)),hAPP(c_Int_Onumber__class_Onumber__of(U_11334),U_11335)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11335)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11335))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11334),c_Groups_Ozero__class_Ozero(U_11334)),hAPP(c_Int_Onumber__class_Onumber__of(U_11334),U_11335))) ) )
      | ~ class_Rings_Olinordered__idom(U_11334)
      | ~ class_Int_Onumber__ring(U_11334) ),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

cnf(f_2860_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11334),c_Groups_Ozero__class_Ozero(U_11334)),hAPP(c_Int_Onumber__class_Onumber__of(U_11334),U_11335)))
    | ~ class_Rings_Olinordered__idom(U_11334)
    | ~ class_Int_Onumber__ring(U_11334) ),
    inference(clausify,[status(thm)],[f_2860_2]) ).

cnf(f_2860_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11334),c_Groups_Ozero__class_Ozero(U_11334)),hAPP(c_Int_Onumber__class_Onumber__of(U_11334),U_11335)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11335))
    | ~ class_Rings_Olinordered__idom(U_11334)
    | ~ class_Int_Onumber__ring(U_11334) ),
    inference(clausify,[status(thm)],[f_2860_2]) ).

fof(f_2861_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ 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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),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_less__special_I3_J]) ).

fof(f_2861_2,plain,
    ! [U_11337,U_11336] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11336),hAPP(c_Int_Onumber__class_Onumber__of(U_11336),U_11337)),c_Groups_Ozero__class_Ozero(U_11336)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11337),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11337),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11336),hAPP(c_Int_Onumber__class_Onumber__of(U_11336),U_11337)),c_Groups_Ozero__class_Ozero(U_11336))) ) )
      | ~ class_Rings_Olinordered__idom(U_11336)
      | ~ class_Int_Onumber__ring(U_11336) ),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

cnf(f_2861_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11337),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11336),hAPP(c_Int_Onumber__class_Onumber__of(U_11336),U_11337)),c_Groups_Ozero__class_Ozero(U_11336)))
    | ~ class_Rings_Olinordered__idom(U_11336)
    | ~ class_Int_Onumber__ring(U_11336) ),
    inference(clausify,[status(thm)],[f_2861_2]) ).

cnf(f_2861_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11336),hAPP(c_Int_Onumber__class_Onumber__of(U_11336),U_11337)),c_Groups_Ozero__class_Ozero(U_11336)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11337),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_11336)
    | ~ class_Int_Onumber__ring(U_11336) ),
    inference(clausify,[status(thm)],[f_2861_2]) ).

fof(f_2862_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_2862_2,plain,
    ! [U_11338] :
      ( ( 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_11338)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11338)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11338))
        | ~ 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_11338))) ) ),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ( ! [U_11340] :
        ( 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_11340)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11340)) )
    & ! [U_11339] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11339))
        | ~ 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_11339))) ) ),
    inference(miniscope,[status(thm)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11339))
    | ~ 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_11339))) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

cnf(f_2862_5,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_11340)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11340)) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_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]) ).

cnf(f_2863_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(clausify,[status(thm)],[f_2863_1]) ).

fof(f_2864_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]) ).

cnf(f_2864_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(clausify,[status(thm)],[f_2864_1]) ).

fof(f_2865_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_2865_2,plain,
    ! [U_11342,U_11341] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11341),U_11342),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_11341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11341),U_11342),U_11342)),U_11342)
      | ~ class_Groups_Omonoid__mult(U_11341) ),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

cnf(f_2865_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11341),U_11342),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_11341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11341),U_11342),U_11342)),U_11342)
    | ~ class_Groups_Omonoid__mult(U_11341) ),
    inference(clausify,[status(thm)],[f_2865_2]) ).

fof(f_2866_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]) ).

cnf(f_2866_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(clausify,[status(thm)],[f_2866_1]) ).

fof(f_2867_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_2867_2,plain,
    ! [U_11343] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11343))) = 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_11343),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

cnf(f_2867_3,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11343))) = 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_11343),
    inference(clausify,[status(thm)],[f_2867_2]) ).

fof(f_2868_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_2868_2,plain,
    ! [U_11345,U_11344] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11344)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11345)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11344),U_11345))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11345),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11344)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11345)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11344)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11345),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11344),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11344)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11345)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11345)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11344),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

fof(f_2868_3,plain,
    ( ! [U_11349,U_11347] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11349)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11347),U_11349))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11349),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11349)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11349),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11347),c_Int_OPls)) )
    & ! [U_11348,U_11346] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11346)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11348)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11348)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11346),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2868_2]) ).

cnf(f_2868_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11346)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11348)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11348)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11346),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

cnf(f_2868_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11349)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11349),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11347),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

cnf(f_2868_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11347)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11349)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11347),U_11349))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11349),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11347),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

fof(f_2869_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]) ).

cnf(f_2869_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(clausify,[status(thm)],[f_2869_1]) ).

fof(f_2870_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]) ).

cnf(f_2870_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(clausify,[status(thm)],[f_2870_1]) ).

fof(f_2871_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_2871_2,plain,
    ! [U_11351,U_11350] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11350),c_Int_Osucc(U_11351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11350),c_Groups_Oone__class_Oone(U_11350)),hAPP(c_Int_Onumber__class_Onumber__of(U_11350),U_11351))
      | ~ class_Int_Onumber__ring(U_11350) ),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

cnf(f_2871_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11350),c_Int_Osucc(U_11351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11350),c_Groups_Oone__class_Oone(U_11350)),hAPP(c_Int_Onumber__class_Onumber__of(U_11350),U_11351))
    | ~ class_Int_Onumber__ring(U_11350) ),
    inference(clausify,[status(thm)],[f_2871_2]) ).

fof(f_2872_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_2872_2,plain,
    ! [U_11353,U_11352] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11352),c_Int_Opred(U_11353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11352),hAPP(c_Groups_Ouminus__class_Ouminus(U_11352),c_Groups_Oone__class_Oone(U_11352))),hAPP(c_Int_Onumber__class_Onumber__of(U_11352),U_11353))
      | ~ class_Int_Onumber__ring(U_11352) ),
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

cnf(f_2872_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11352),c_Int_Opred(U_11353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11352),hAPP(c_Groups_Ouminus__class_Ouminus(U_11352),c_Groups_Oone__class_Oone(U_11352))),hAPP(c_Int_Onumber__class_Onumber__of(U_11352),U_11353))
    | ~ class_Int_Onumber__ring(U_11352) ),
    inference(clausify,[status(thm)],[f_2872_2]) ).

fof(f_2873_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
          | ~ 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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),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_le__special_I4_J]) ).

fof(f_2873_2,plain,
    ! [U_11355,U_11354] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11354),hAPP(c_Int_Onumber__class_Onumber__of(U_11354),U_11355)),c_Groups_Oone__class_Oone(U_11354)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11355),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11355),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11354),hAPP(c_Int_Onumber__class_Onumber__of(U_11354),U_11355)),c_Groups_Oone__class_Oone(U_11354))) ) )
      | ~ class_Rings_Olinordered__idom(U_11354)
      | ~ class_Int_Onumber__ring(U_11354) ),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

cnf(f_2873_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11355),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11354),hAPP(c_Int_Onumber__class_Onumber__of(U_11354),U_11355)),c_Groups_Oone__class_Oone(U_11354)))
    | ~ class_Rings_Olinordered__idom(U_11354)
    | ~ class_Int_Onumber__ring(U_11354) ),
    inference(clausify,[status(thm)],[f_2873_2]) ).

cnf(f_2873_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11354),hAPP(c_Int_Onumber__class_Onumber__of(U_11354),U_11355)),c_Groups_Oone__class_Oone(U_11354)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11355),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_11354)
    | ~ class_Int_Onumber__ring(U_11354) ),
    inference(clausify,[status(thm)],[f_2873_2]) ).

fof(f_2874_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).

fof(f_2874_2,plain,
    ! [U_11357,U_11356] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11356),c_Groups_Oone__class_Oone(U_11356)),hAPP(c_Int_Onumber__class_Onumber__of(U_11356),U_11357)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11357)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11357))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11356),c_Groups_Oone__class_Oone(U_11356)),hAPP(c_Int_Onumber__class_Onumber__of(U_11356),U_11357))) ) )
      | ~ class_Rings_Olinordered__idom(U_11356)
      | ~ class_Int_Onumber__ring(U_11356) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

cnf(f_2874_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11357))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11356),c_Groups_Oone__class_Oone(U_11356)),hAPP(c_Int_Onumber__class_Onumber__of(U_11356),U_11357)))
    | ~ class_Rings_Olinordered__idom(U_11356)
    | ~ class_Int_Onumber__ring(U_11356) ),
    inference(clausify,[status(thm)],[f_2874_2]) ).

cnf(f_2874_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11356),c_Groups_Oone__class_Oone(U_11356)),hAPP(c_Int_Onumber__class_Onumber__of(U_11356),U_11357)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11357))
    | ~ class_Rings_Olinordered__idom(U_11356)
    | ~ class_Int_Onumber__ring(U_11356) ),
    inference(clausify,[status(thm)],[f_2874_2]) ).

fof(f_2875_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).

fof(f_2875_2,plain,
    ! [U_11359,U_11358] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11358),c_Groups_Oone__class_Oone(U_11358)),hAPP(c_Int_Onumber__class_Onumber__of(U_11358),U_11359)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11359)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11359))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11358),c_Groups_Oone__class_Oone(U_11358)),hAPP(c_Int_Onumber__class_Onumber__of(U_11358),U_11359))) ) )
      | ~ class_Rings_Olinordered__idom(U_11358)
      | ~ class_Int_Onumber__ring(U_11358) ),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

cnf(f_2875_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11359))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11358),c_Groups_Oone__class_Oone(U_11358)),hAPP(c_Int_Onumber__class_Onumber__of(U_11358),U_11359)))
    | ~ class_Rings_Olinordered__idom(U_11358)
    | ~ class_Int_Onumber__ring(U_11358) ),
    inference(clausify,[status(thm)],[f_2875_2]) ).

cnf(f_2875_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11358),c_Groups_Oone__class_Oone(U_11358)),hAPP(c_Int_Onumber__class_Onumber__of(U_11358),U_11359)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11359))
    | ~ class_Rings_Olinordered__idom(U_11358)
    | ~ class_Int_Onumber__ring(U_11358) ),
    inference(clausify,[status(thm)],[f_2875_2]) ).

fof(f_2876_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
          | ~ 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_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),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_less__special_I4_J]) ).

fof(f_2876_2,plain,
    ! [U_11361,U_11360] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11360),hAPP(c_Int_Onumber__class_Onumber__of(U_11360),U_11361)),c_Groups_Oone__class_Oone(U_11360)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11361),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11361),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11360),hAPP(c_Int_Onumber__class_Onumber__of(U_11360),U_11361)),c_Groups_Oone__class_Oone(U_11360))) ) )
      | ~ class_Rings_Olinordered__idom(U_11360)
      | ~ class_Int_Onumber__ring(U_11360) ),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

cnf(f_2876_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11361),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11360),hAPP(c_Int_Onumber__class_Onumber__of(U_11360),U_11361)),c_Groups_Oone__class_Oone(U_11360)))
    | ~ class_Rings_Olinordered__idom(U_11360)
    | ~ class_Int_Onumber__ring(U_11360) ),
    inference(clausify,[status(thm)],[f_2876_2]) ).

cnf(f_2876_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11360),hAPP(c_Int_Onumber__class_Onumber__of(U_11360),U_11361)),c_Groups_Oone__class_Oone(U_11360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11361),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_11360)
    | ~ class_Int_Onumber__ring(U_11360) ),
    inference(clausify,[status(thm)],[f_2876_2]) ).

fof(f_2877_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_2877_2,plain,
    ! [U_11363,U_11362] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11362),hAPP(c_Int_Onumber__class_Onumber__of(U_11362),U_11363)),c_Groups_Oone__class_Oone(U_11362)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11363),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_11362) ),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

cnf(f_2877_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11362),hAPP(c_Int_Onumber__class_Onumber__of(U_11362),U_11363)),c_Groups_Oone__class_Oone(U_11362)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11363),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_11362) ),
    inference(clausify,[status(thm)],[f_2877_2]) ).

fof(f_2878_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_2878_2,plain,
    ! [U_11365,U_11364] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11364),c_Groups_Oone__class_Oone(U_11364)),hAPP(c_Int_Onumber__class_Onumber__of(U_11364),U_11365)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11364),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11365))
      | ~ class_Int_Onumber__ring(U_11364) ),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

cnf(f_2878_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11364),c_Groups_Oone__class_Oone(U_11364)),hAPP(c_Int_Onumber__class_Onumber__of(U_11364),U_11365)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11364),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_11365))
    | ~ class_Int_Onumber__ring(U_11364) ),
    inference(clausify,[status(thm)],[f_2878_2]) ).

fof(f_2879_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_2879_2,plain,
    ! [U_11367,U_11366] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11367)),U_11366) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11366),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_11366)) ),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

cnf(f_2879_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11367)),U_11366) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11366),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_11366)) ),
    inference(clausify,[status(thm)],[f_2879_2]) ).

fof(f_2880_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_2880_2,plain,
    ! [U_11370,U_11369,U_11368] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11368)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11369)),U_11370)) = 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_11368),U_11369))),U_11370)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11368),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11368)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11369)),U_11370)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11368),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

fof(f_2880_3,plain,
    ( ! [U_11376,U_11374,U_11372] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11374)),U_11376)) = 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_11372),U_11374))),U_11376)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11372),c_Int_OPls)) )
    & ! [U_11375,U_11373,U_11371] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11371)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11373)),U_11375)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11371),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2880_2]) ).

cnf(f_2880_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11371)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11373)),U_11375)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11371),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

cnf(f_2880_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11374)),U_11376)) = 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_11372),U_11374))),U_11376)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11372),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

fof(f_2881_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_2881_2,plain,
    ! [U_11378,U_11377] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11377),U_11378))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11377),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11377)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11378)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11377),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

fof(f_2881_3,plain,
    ( ! [U_11382,U_11380] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11380)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11382)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11380),U_11382))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11380),c_Int_OPls)) )
    & ! [U_11381,U_11379] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11379)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11381)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11379),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2881_2]) ).

cnf(f_2881_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11379)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11381)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11379),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2881_3]) ).

cnf(f_2881_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11380)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11382)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11380),U_11382))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11380),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2881_3]) ).

fof(f_2882_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_2882_2,plain,
    ! [U_11383] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11383))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11383) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11383) = 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_11383)))) ) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ( ! [U_11385] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11385))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11385) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_11384] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11384) = 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_11384)))) ) ),
    inference(miniscope,[status(thm)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11384) = 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_11384)))) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

cnf(f_2882_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11385))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11385) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_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_2883_2,plain,
    ! [U_11387,U_11386] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11386,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11387)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11386,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_11387)),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

cnf(f_2883_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11386,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11387)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11386,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_11387)),
    inference(clausify,[status(thm)],[f_2883_2]) ).

fof(f_2884_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_2884_2,plain,
    ! [U_11389,U_11388] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11388))),U_11389) = 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_11388),U_11389),
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

cnf(f_2884_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11388))),U_11389) = 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_11388),U_11389),
    inference(clausify,[status(thm)],[f_2884_2]) ).

fof(f_2885_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_2885_2,plain,
    ! [U_11391,U_11390] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11390))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11391)) = 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_11390),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11391)),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

cnf(f_2885_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11390))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11391)) = 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_11390),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11391)),
    inference(clausify,[status(thm)],[f_2885_2]) ).

fof(f_2886_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_2886_2,plain,
    ! [U_11393,U_11392] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11393)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),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_11393)),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

cnf(f_2886_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11393)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),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_11393)),
    inference(clausify,[status(thm)],[f_2886_2]) ).

fof(f_2887_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_2887_2,plain,
    ! [U_11395,U_11394] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11394)))),U_11395) = 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_11394)),U_11395),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

cnf(f_2887_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11394)))),U_11395) = 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_11394)),U_11395),
    inference(clausify,[status(thm)],[f_2887_2]) ).

fof(f_2888_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_2888_2,plain,
    ! [U_11397,U_11396] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11396)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11397)) = 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_11396)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11397)),
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

cnf(f_2888_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11396)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11397)) = 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_11396)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11397)),
    inference(clausify,[status(thm)],[f_2888_2]) ).

fof(f_2889_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_2889_2,plain,
    ! [U_11399,U_11398] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11398),c_Groups_Oone__class_Oone(U_11398)),hAPP(c_Int_Onumber__class_Onumber__of(U_11398),U_11399)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11398),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_11399)))
      | ~ class_Int_Onumber__ring(U_11398) ),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

cnf(f_2889_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11398),c_Groups_Oone__class_Oone(U_11398)),hAPP(c_Int_Onumber__class_Onumber__of(U_11398),U_11399)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11398),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_11399)))
    | ~ class_Int_Onumber__ring(U_11398) ),
    inference(clausify,[status(thm)],[f_2889_2]) ).

fof(f_2890_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_2890_2,plain,
    ! [U_11401,U_11400] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11400),hAPP(c_Int_Onumber__class_Onumber__of(U_11400),U_11401)),c_Groups_Oone__class_Oone(U_11400)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_11400) ),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

cnf(f_2890_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11400),hAPP(c_Int_Onumber__class_Onumber__of(U_11400),U_11401)),c_Groups_Oone__class_Oone(U_11400)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_11400) ),
    inference(clausify,[status(thm)],[f_2890_2]) ).

fof(f_2891_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_2891_2,plain,
    ! [U_11403,U_11402] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11402) = hAPP(c_Nat_OSuc,U_11403)
        | ~ 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_11402))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11403))))) )
      & ( 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_11402))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11403)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11402) != hAPP(c_Nat_OSuc,U_11403) ) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

fof(f_2891_3,plain,
    ( ! [U_11407,U_11405] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11405) = hAPP(c_Nat_OSuc,U_11407)
        | ~ 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_11405))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11407))))) )
    & ! [U_11406,U_11404] :
        ( 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_11404))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11406)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11404) != hAPP(c_Nat_OSuc,U_11406) ) ),
    inference(miniscope,[status(thm)],[f_2891_2]) ).

cnf(f_2891_4,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_11404))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11406)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11404) != hAPP(c_Nat_OSuc,U_11406) ),
    inference(clausify,[status(thm)],[f_2891_3]) ).

cnf(f_2891_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11405) = hAPP(c_Nat_OSuc,U_11407)
    | ~ 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_11405))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11407))))) ),
    inference(clausify,[status(thm)],[f_2891_3]) ).

fof(f_2892_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_2892_2,plain,
    ! [U_11409,U_11408] :
      ( ( hAPP(c_Nat_OSuc,U_11408) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11409)
        | ~ 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_11409))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11408))))) )
      & ( 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_11409))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11408)))))
        | hAPP(c_Nat_OSuc,U_11408) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11409) ) ),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

fof(f_2892_3,plain,
    ( ! [U_11413,U_11411] :
        ( hAPP(c_Nat_OSuc,U_11411) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11413)
        | ~ 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_11413))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11411))))) )
    & ! [U_11412,U_11410] :
        ( 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_11412))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11410)))))
        | hAPP(c_Nat_OSuc,U_11410) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11412) ) ),
    inference(miniscope,[status(thm)],[f_2892_2]) ).

cnf(f_2892_4,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_11412))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11410)))))
    | hAPP(c_Nat_OSuc,U_11410) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11412) ),
    inference(clausify,[status(thm)],[f_2892_3]) ).

cnf(f_2892_5,plain,
    ( hAPP(c_Nat_OSuc,U_11411) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11413)
    | ~ 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_11413))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11411))))) ),
    inference(clausify,[status(thm)],[f_2892_3]) ).

fof(f_2893_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).

fof(f_2893_2,plain,
    ! [U_11417,U_11416,U_11415,U_11414] : c_Nat_Onat_Onat__case(U_11414,U_11415,U_11416,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11417)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11417))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11414,U_11414),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11414,tc_fun(U_11414,U_11414)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11414,tc_fun(U_11414,U_11414)),tc_Int_Oint),c_If(U_11414)),c_Nat__Numeral_Oneg)),U_11415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11414,tc_Int_Oint),U_11416),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

cnf(f_2893_3,plain,
    c_Nat_Onat_Onat__case(U_11414,U_11415,U_11416,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11417)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11417))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11414,U_11414),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11414,tc_fun(U_11414,U_11414)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11414,tc_fun(U_11414,U_11414)),tc_Int_Oint),c_If(U_11414)),c_Nat__Numeral_Oneg)),U_11415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11414,tc_Int_Oint),U_11416),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_2893_2]) ).

fof(f_2894_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_2894_2,plain,
    ! [U_11419,U_11418] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11418)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11419)))
        | ~ 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_11419))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11418)),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_11419))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11418)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11418)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11419))) ) ),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

fof(f_2894_3,plain,
    ( ! [U_11423,U_11421] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11421)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11423)))
        | ~ 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_11423))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11421)),c_Int_Onat))))) )
    & ! [U_11422,U_11420] :
        ( 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_11422))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11420)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11420)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11422))) ) ),
    inference(miniscope,[status(thm)],[f_2894_2]) ).

cnf(f_2894_4,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_11422))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11420)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11420)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11422))) ),
    inference(clausify,[status(thm)],[f_2894_3]) ).

cnf(f_2894_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11421)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11423)))
    | ~ 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_11423))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11421)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2894_3]) ).

fof(f_2895_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_2895_2,plain,
    ! [U_11425,U_11424] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11424)),hAPP(c_Nat_OSuc,U_11425)))
        | ~ 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_11424))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11425)))) )
      & ( 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_11424))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11425))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11424)),hAPP(c_Nat_OSuc,U_11425))) ) ),
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

fof(f_2895_3,plain,
    ( ! [U_11429,U_11427] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11427)),hAPP(c_Nat_OSuc,U_11429)))
        | ~ 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_11427))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11429)))) )
    & ! [U_11428,U_11426] :
        ( 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_11426))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11428))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11426)),hAPP(c_Nat_OSuc,U_11428))) ) ),
    inference(miniscope,[status(thm)],[f_2895_2]) ).

cnf(f_2895_4,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_11426))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11428))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11426)),hAPP(c_Nat_OSuc,U_11428))) ),
    inference(clausify,[status(thm)],[f_2895_3]) ).

cnf(f_2895_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11427)),hAPP(c_Nat_OSuc,U_11429)))
    | ~ 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_11427))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11429)))) ),
    inference(clausify,[status(thm)],[f_2895_3]) ).

fof(f_2896_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_2896_2,plain,
    ! [U_11431,U_11430] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11430)),hAPP(c_Nat_OSuc,U_11431)))
        | ~ 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_11430))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11431)))) )
      & ( 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_11430))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11431))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11430)),hAPP(c_Nat_OSuc,U_11431))) ) ),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

fof(f_2896_3,plain,
    ( ! [U_11435,U_11433] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11433)),hAPP(c_Nat_OSuc,U_11435)))
        | ~ 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_11433))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11435)))) )
    & ! [U_11434,U_11432] :
        ( 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_11432))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11434))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11432)),hAPP(c_Nat_OSuc,U_11434))) ) ),
    inference(miniscope,[status(thm)],[f_2896_2]) ).

cnf(f_2896_4,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_11432))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11434))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11432)),hAPP(c_Nat_OSuc,U_11434))) ),
    inference(clausify,[status(thm)],[f_2896_3]) ).

cnf(f_2896_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11433)),hAPP(c_Nat_OSuc,U_11435)))
    | ~ 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_11433))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11435)))) ),
    inference(clausify,[status(thm)],[f_2896_3]) ).

fof(f_2897_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_2897_2,plain,
    ! [U_11437,U_11436] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11436)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11437)))
        | ~ 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_11437))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11436)),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_11437))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11436)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11436)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11437))) ) ),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

fof(f_2897_3,plain,
    ( ! [U_11441,U_11439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11439)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11441)))
        | ~ 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_11441))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11439)),c_Int_Onat))))) )
    & ! [U_11440,U_11438] :
        ( 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_11440))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11438)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11440))) ) ),
    inference(miniscope,[status(thm)],[f_2897_2]) ).

cnf(f_2897_4,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_11440))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11438)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11440))) ),
    inference(clausify,[status(thm)],[f_2897_3]) ).

cnf(f_2897_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11439)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11441)))
    | ~ 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_11441))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11439)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2897_3]) ).

fof(f_2898_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_2898_2,plain,
    ! [U_11442] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11442)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11442))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11442))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11442)) = 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_11442))) ) ),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

fof(f_2898_3,plain,
    ( ! [U_11444] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11444)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11444))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11444))) )
    & ! [U_11443] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11443)) = 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_11443))) ) ),
    inference(miniscope,[status(thm)],[f_2898_2]) ).

cnf(f_2898_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11443)) = 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_11443))) ),
    inference(clausify,[status(thm)],[f_2898_3]) ).

cnf(f_2898_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11444)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_11444))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11444))) ),
    inference(clausify,[status(thm)],[f_2898_3]) ).

fof(f_2899_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_2899_2,plain,
    ! [U_11446,U_11445] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11445)),hAPP(c_Nat_OSuc,U_11446)) = 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_11445))),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_11446))),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_11446)))),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

cnf(f_2899_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11445)),hAPP(c_Nat_OSuc,U_11446)) = 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_11445))),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_11446))),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_11446)))),
    inference(clausify,[status(thm)],[f_2899_2]) ).

fof(f_2900_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_2900_2,plain,
    ! [U_11448,U_11447] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11447)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11448)) = 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_11448))),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_11447))),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_11447)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

cnf(f_2900_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11447)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11448)) = 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_11448))),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_11447))),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_11447)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2900_2]) ).

fof(f_2901_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_2901_2,plain,
    ! [U_11453,U_11452,U_11451,U_11450,U_11449] : c_Nat_Onat_Onat__case(U_11449,U_11450,U_11451,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11452)),U_11453)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11449),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11452))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11449,U_11449),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11449,tc_fun(U_11449,U_11449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11449,tc_fun(U_11449,U_11449)),tc_Int_Oint),c_If(U_11449)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_11449,U_11450,U_11451,U_11453))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11449,tc_Int_Oint),U_11451),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_11453)))),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

cnf(f_2901_3,plain,
    c_Nat_Onat_Onat__case(U_11449,U_11450,U_11451,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11452)),U_11453)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11449),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11452))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11449,U_11449),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11449,tc_fun(U_11449,U_11449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11449,tc_fun(U_11449,U_11449)),tc_Int_Oint),c_If(U_11449)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_11449,U_11450,U_11451,U_11453))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11449,tc_Int_Oint),U_11451),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_11453)))),
    inference(clausify,[status(thm)],[f_2901_2]) ).

fof(f_2902_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_2902_2,plain,
    ! [U_11455,U_11454] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11455)) = 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_11455))),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_11454)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

cnf(f_2902_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11455)) = 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_11455))),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_11454)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2902_2]) ).

fof(f_2903_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),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_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,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_2903_2,plain,
    ! [U_11460,U_11459,U_11458,U_11457,U_11456] : hAPP(c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11459)),U_11460)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11456),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11459))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11456,U_11456),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11456,tc_fun(U_11456,U_11456)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11456,tc_fun(U_11456,U_11456)),tc_Int_Oint),c_If(U_11456)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458),U_11460))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11456,U_11456),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11456,U_11456),tc_Int_Oint),U_11458),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_11460))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11456,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458)),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_11460))))),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

cnf(f_2903_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11459)),U_11460)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11456),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11459))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11456,U_11456),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11456,tc_fun(U_11456,U_11456)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11456,tc_fun(U_11456,U_11456)),tc_Int_Oint),c_If(U_11456)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458),U_11460))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11456,U_11456),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11456,U_11456),tc_Int_Oint),U_11458),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_11460))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11456,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11456,U_11457,U_11458)),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_11460))))),
    inference(clausify,[status(thm)],[f_2903_2]) ).

fof(f_2904_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).

fof(f_2904_2,plain,
    ! [U_11462,U_11461] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11461),U_11462) = c_Groups_Oone__class_Oone(U_11461)
          | ~ c_Int_Oiszero(U_11461,hAPP(c_Int_Onumber__class_Onumber__of(U_11461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11462),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_11461,hAPP(c_Int_Onumber__class_Onumber__of(U_11461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11462),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_11461),U_11462) != c_Groups_Oone__class_Oone(U_11461) ) )
      | ~ class_Int_Onumber__ring(U_11461) ),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

cnf(f_2904_3,plain,
    ( c_Int_Oiszero(U_11461,hAPP(c_Int_Onumber__class_Onumber__of(U_11461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11462),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11461),U_11462) != c_Groups_Oone__class_Oone(U_11461)
    | ~ class_Int_Onumber__ring(U_11461) ),
    inference(clausify,[status(thm)],[f_2904_2]) ).

cnf(f_2904_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11461),U_11462) = c_Groups_Oone__class_Oone(U_11461)
    | ~ c_Int_Oiszero(U_11461,hAPP(c_Int_Onumber__class_Onumber__of(U_11461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11462),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Int_Onumber__ring(U_11461) ),
    inference(clausify,[status(thm)],[f_2904_2]) ).

fof(f_2905_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
          | ~ c_Int_Oiszero(T_a,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_y_2)))) )
        & ( c_Int_Oiszero(T_a,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_y_2))))
          | c_Groups_Oone__class_Oone(T_a) != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).

fof(f_2905_2,plain,
    ! [U_11464,U_11463] :
      ( ( ( c_Groups_Oone__class_Oone(U_11463) = hAPP(c_Int_Onumber__class_Onumber__of(U_11463),U_11464)
          | ~ c_Int_Oiszero(U_11463,hAPP(c_Int_Onumber__class_Onumber__of(U_11463),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_11464)))) )
        & ( c_Int_Oiszero(U_11463,hAPP(c_Int_Onumber__class_Onumber__of(U_11463),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_11464))))
          | c_Groups_Oone__class_Oone(U_11463) != hAPP(c_Int_Onumber__class_Onumber__of(U_11463),U_11464) ) )
      | ~ class_Int_Onumber__ring(U_11463) ),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

cnf(f_2905_3,plain,
    ( c_Int_Oiszero(U_11463,hAPP(c_Int_Onumber__class_Onumber__of(U_11463),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_11464))))
    | c_Groups_Oone__class_Oone(U_11463) != hAPP(c_Int_Onumber__class_Onumber__of(U_11463),U_11464)
    | ~ class_Int_Onumber__ring(U_11463) ),
    inference(clausify,[status(thm)],[f_2905_2]) ).

cnf(f_2905_4,plain,
    ( c_Groups_Oone__class_Oone(U_11463) = hAPP(c_Int_Onumber__class_Onumber__of(U_11463),U_11464)
    | ~ c_Int_Oiszero(U_11463,hAPP(c_Int_Onumber__class_Onumber__of(U_11463),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_11464))))
    | ~ class_Int_Onumber__ring(U_11463) ),
    inference(clausify,[status(thm)],[f_2905_2]) ).

fof(f_2906_1,plain,
    ! [V_z_2,T_a] :
      ( ( ( c_Int_Oiszero(T_a,V_z_2)
          | V_z_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Int_Oiszero(T_a,V_z_2) ) )
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).

fof(f_2906_2,plain,
    ! [U_11466,U_11465] :
      ( ( ( c_Int_Oiszero(U_11465,U_11466)
          | U_11466 != c_Groups_Ozero__class_Ozero(U_11465) )
        & ( U_11466 = c_Groups_Ozero__class_Ozero(U_11465)
          | ~ c_Int_Oiszero(U_11465,U_11466) ) )
      | ~ class_Rings_Osemiring__1(U_11465) ),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

cnf(f_2906_3,plain,
    ( U_11466 = c_Groups_Ozero__class_Ozero(U_11465)
    | ~ c_Int_Oiszero(U_11465,U_11466)
    | ~ class_Rings_Osemiring__1(U_11465) ),
    inference(clausify,[status(thm)],[f_2906_2]) ).

cnf(f_2906_4,plain,
    ( c_Int_Oiszero(U_11465,U_11466)
    | U_11466 != c_Groups_Ozero__class_Ozero(U_11465)
    | ~ class_Rings_Osemiring__1(U_11465) ),
    inference(clausify,[status(thm)],[f_2906_2]) ).

fof(f_2907_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_2907_2,plain,
    ! [U_11467] :
      ( c_Int_Oiszero(U_11467,c_Groups_Ozero__class_Ozero(U_11467))
      | ~ class_Rings_Osemiring__1(U_11467) ),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

cnf(f_2907_3,plain,
    ( c_Int_Oiszero(U_11467,c_Groups_Ozero__class_Ozero(U_11467))
    | ~ class_Rings_Osemiring__1(U_11467) ),
    inference(clausify,[status(thm)],[f_2907_2]) ).

fof(f_2908_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_2908_2,plain,
    ! [U_11468] :
      ( ~ c_Int_Oiszero(U_11468,c_Groups_Oone__class_Oone(U_11468))
      | ~ class_Rings_Osemiring__1(U_11468) ),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

cnf(f_2908_3,plain,
    ( ~ c_Int_Oiszero(U_11468,c_Groups_Oone__class_Oone(U_11468))
    | ~ class_Rings_Osemiring__1(U_11468) ),
    inference(clausify,[status(thm)],[f_2908_2]) ).

fof(f_2909_1,plain,
    ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_2909_2,plain,
    ! [U_11471,U_11470,U_11469] : hAPP(c_Nat_Onat_Onat__rec(U_11469,U_11470,U_11471),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_11470,
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

cnf(f_2909_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_11469,U_11470,U_11471),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_11470,
    inference(clausify,[status(thm)],[f_2909_2]) ).

fof(f_2910_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a,V_f1_2,V_f2_2),V_nat_2)),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).

fof(f_2910_2,plain,
    ! [U_11475,U_11474,U_11473,U_11472] : hAPP(c_Nat_Onat_Onat__rec(U_11472,U_11473,U_11474),hAPP(c_Nat_OSuc,U_11475)) = hAPP(hAPP(U_11474,U_11475),hAPP(c_Nat_Onat_Onat__rec(U_11472,U_11473,U_11474),U_11475)),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

cnf(f_2910_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_11472,U_11473,U_11474),hAPP(c_Nat_OSuc,U_11475)) = hAPP(hAPP(U_11474,U_11475),hAPP(c_Nat_Onat_Onat__rec(U_11472,U_11473,U_11474),U_11475)),
    inference(clausify,[status(thm)],[f_2910_2]) ).

fof(f_2911_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_2911_2,plain,
    ! [U_11476] :
      ( c_Int_Oiszero(U_11476,hAPP(c_Int_Onumber__class_Onumber__of(U_11476),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_11476) ),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

cnf(f_2911_3,plain,
    ( c_Int_Oiszero(U_11476,hAPP(c_Int_Onumber__class_Onumber__of(U_11476),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_11476) ),
    inference(clausify,[status(thm)],[f_2911_2]) ).

fof(f_2912_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_2912_2,plain,
    ! [U_11478,U_11477] :
      ( ~ c_Int_Oiszero(U_11477,hAPP(c_Int_Onumber__class_Onumber__of(U_11477),c_Int_OBit1(U_11478)))
      | ~ class_Int_Oring__char__0(U_11477)
      | ~ class_Int_Onumber__ring(U_11477) ),
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

cnf(f_2912_3,plain,
    ( ~ c_Int_Oiszero(U_11477,hAPP(c_Int_Onumber__class_Onumber__of(U_11477),c_Int_OBit1(U_11478)))
    | ~ class_Int_Oring__char__0(U_11477)
    | ~ class_Int_Onumber__ring(U_11477) ),
    inference(clausify,[status(thm)],[f_2912_2]) ).

fof(f_2913_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_2913_2,plain,
    ! [U_11479] :
      ( ~ c_Int_Oiszero(U_11479,hAPP(c_Int_Onumber__class_Onumber__of(U_11479),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_11479) ),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

cnf(f_2913_3,plain,
    ( ~ c_Int_Oiszero(U_11479,hAPP(c_Int_Onumber__class_Onumber__of(U_11479),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_11479) ),
    inference(clausify,[status(thm)],[f_2913_2]) ).

fof(f_2914_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).

fof(f_2914_2,plain,
    ! [U_11482,U_11481,U_11480] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11481) = hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11482)
          | ~ c_Int_Oiszero(U_11480,hAPP(c_Int_Onumber__class_Onumber__of(U_11480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11481),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11482)))) )
        & ( c_Int_Oiszero(U_11480,hAPP(c_Int_Onumber__class_Onumber__of(U_11480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11481),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11482))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11481) != hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11482) ) )
      | ~ class_Int_Onumber__ring(U_11480) ),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

cnf(f_2914_3,plain,
    ( c_Int_Oiszero(U_11480,hAPP(c_Int_Onumber__class_Onumber__of(U_11480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11481),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11482))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11481) != hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11482)
    | ~ class_Int_Onumber__ring(U_11480) ),
    inference(clausify,[status(thm)],[f_2914_2]) ).

cnf(f_2914_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11481) = hAPP(c_Int_Onumber__class_Onumber__of(U_11480),U_11482)
    | ~ c_Int_Oiszero(U_11480,hAPP(c_Int_Onumber__class_Onumber__of(U_11480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11481),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11482))))
    | ~ class_Int_Onumber__ring(U_11480) ),
    inference(clausify,[status(thm)],[f_2914_2]) ).

fof(f_2915_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a) != hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).

fof(f_2915_2,plain,
    ! [U_11484,U_11483] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_11483) = hAPP(c_Int_Onumber__class_Onumber__of(U_11483),U_11484)
          | ~ c_Int_Oiszero(U_11483,hAPP(c_Int_Onumber__class_Onumber__of(U_11483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11484)))) )
        & ( c_Int_Oiszero(U_11483,hAPP(c_Int_Onumber__class_Onumber__of(U_11483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11484))))
          | c_Groups_Ozero__class_Ozero(U_11483) != hAPP(c_Int_Onumber__class_Onumber__of(U_11483),U_11484) ) )
      | ~ class_Int_Onumber__ring(U_11483) ),
    inference(variable_rename,[status(thm)],[f_2915_1]) ).

cnf(f_2915_3,plain,
    ( c_Int_Oiszero(U_11483,hAPP(c_Int_Onumber__class_Onumber__of(U_11483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11484))))
    | c_Groups_Ozero__class_Ozero(U_11483) != hAPP(c_Int_Onumber__class_Onumber__of(U_11483),U_11484)
    | ~ class_Int_Onumber__ring(U_11483) ),
    inference(clausify,[status(thm)],[f_2915_2]) ).

cnf(f_2915_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_11483) = hAPP(c_Int_Onumber__class_Onumber__of(U_11483),U_11484)
    | ~ c_Int_Oiszero(U_11483,hAPP(c_Int_Onumber__class_Onumber__of(U_11483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11484))))
    | ~ class_Int_Onumber__ring(U_11483) ),
    inference(clausify,[status(thm)],[f_2915_2]) ).

fof(f_2916_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a),V_x_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).

fof(f_2916_2,plain,
    ! [U_11486,U_11485] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_11485),U_11486) = c_Groups_Ozero__class_Ozero(U_11485)
          | ~ c_Int_Oiszero(U_11485,hAPP(c_Int_Onumber__class_Onumber__of(U_11485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11486),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_11485,hAPP(c_Int_Onumber__class_Onumber__of(U_11485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11486),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_11485),U_11486) != c_Groups_Ozero__class_Ozero(U_11485) ) )
      | ~ class_Int_Onumber__ring(U_11485) ),
    inference(variable_rename,[status(thm)],[f_2916_1]) ).

cnf(f_2916_3,plain,
    ( c_Int_Oiszero(U_11485,hAPP(c_Int_Onumber__class_Onumber__of(U_11485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11486),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_11485),U_11486) != c_Groups_Ozero__class_Ozero(U_11485)
    | ~ class_Int_Onumber__ring(U_11485) ),
    inference(clausify,[status(thm)],[f_2916_2]) ).

cnf(f_2916_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11485),U_11486) = c_Groups_Ozero__class_Ozero(U_11485)
    | ~ c_Int_Oiszero(U_11485,hAPP(c_Int_Onumber__class_Onumber__of(U_11485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11486),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_11485) ),
    inference(clausify,[status(thm)],[f_2916_2]) ).

fof(f_2917_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).

fof(f_2917_2,plain,
    ! [U_11490,U_11489,U_11488,U_11487] : hAPP(c_Nat_Onat_Onat__rec(U_11487,U_11488,U_11489),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11490)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11487),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11490))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11487,U_11487),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11487,tc_fun(U_11487,U_11487)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11487,tc_fun(U_11487,U_11487)),tc_Int_Oint),c_If(U_11487)),c_Nat__Numeral_Oneg)),U_11488)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11487,U_11487),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11487,U_11487),tc_Int_Oint),U_11489),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11487,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11487,U_11488,U_11489)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

cnf(f_2917_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_11487,U_11488,U_11489),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11490)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11487),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11490))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11487,U_11487),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11487,tc_fun(U_11487,U_11487)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11487,tc_fun(U_11487,U_11487)),tc_Int_Oint),c_If(U_11487)),c_Nat__Numeral_Oneg)),U_11488)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11487,U_11487),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11487,U_11487),tc_Int_Oint),U_11489),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11487,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11487,U_11488,U_11489)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2917_2]) ).

fof(f_2918_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_2918_2,plain,
    ! [U_11492,U_11491] :
      ( 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_11492)),hAPP(hAPP(c_Groups_Otimes__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_11491)) = 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_11492),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11491))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11491),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

cnf(f_2918_3,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_11492)),hAPP(hAPP(c_Groups_Otimes__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_11491)) = 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_11492),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11491))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11491),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2918_2]) ).

fof(f_2919_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_2919_2,plain,
    ! [U_11494,U_11493] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11494)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11493))) = 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_11494)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11493)))),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_11493))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11494)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11493))) = 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_11494),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11493)))),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_11493))) ) ),
    inference(variable_rename,[status(thm)],[f_2919_1]) ).

fof(f_2919_3,plain,
    ( ! [U_11498,U_11496] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11498)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11496))) = 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_11498)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11496)))),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_11496))) )
    & ! [U_11497,U_11495] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11497)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11495))) = 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_11497),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11495)))),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_11495))) ) ),
    inference(miniscope,[status(thm)],[f_2919_2]) ).

cnf(f_2919_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11497)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11495))) = 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_11497),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11495)))),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_11495))) ),
    inference(clausify,[status(thm)],[f_2919_3]) ).

cnf(f_2919_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11498)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11496))) = 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_11498)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11496)))),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_11496))) ),
    inference(clausify,[status(thm)],[f_2919_3]) ).

fof(f_2920_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_2920_2,plain,
    ! [U_11501,U_11500,U_11499] : hAPP(hAPP(c_Groups_Otimes__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_11499)),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_11500))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11501))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11501)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11499),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_11501),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_11500)))),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

cnf(f_2920_3,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_11499)),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_11500))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11501))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11501)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11499),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_11501),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_11500)))),
    inference(clausify,[status(thm)],[f_2920_2]) ).

fof(f_2921_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_2921_2,plain,
    ! [U_11503,U_11502] : c_Int_OBit0(U_11502) != c_Int_OBit1(U_11503),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

cnf(f_2921_3,plain,
    c_Int_OBit0(U_11502) != c_Int_OBit1(U_11503),
    inference(clausify,[status(thm)],[f_2921_2]) ).

fof(f_2922_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_2922_2,plain,
    ! [U_11505,U_11504] : c_Int_OBit1(U_11504) != c_Int_OBit0(U_11505),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

cnf(f_2922_3,plain,
    c_Int_OBit1(U_11504) != c_Int_OBit0(U_11505),
    inference(clausify,[status(thm)],[f_2922_2]) ).

fof(f_2923_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_2923_2,plain,
    ! [U_11506] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_11506)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11506)),
    inference(variable_rename,[status(thm)],[f_2923_1]) ).

cnf(f_2923_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_11506)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11506)),
    inference(clausify,[status(thm)],[f_2923_2]) ).

fof(f_2924_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_2924_2,plain,
    ! [U_11508,U_11507] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_11507)),U_11508) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11507),U_11508)),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

cnf(f_2924_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_11507)),U_11508) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11507),U_11508)),
    inference(clausify,[status(thm)],[f_2924_2]) ).

fof(f_2925_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_2925_2,plain,
    ! [U_11510,U_11509] :
      ( ( c_Int_OBit0(U_11509) = c_Int_OBit0(U_11510)
        | U_11509 != U_11510 )
      & ( U_11509 = U_11510
        | c_Int_OBit0(U_11509) != c_Int_OBit0(U_11510) ) ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

fof(f_2925_3,plain,
    ( ! [U_11514,U_11512] :
        ( c_Int_OBit0(U_11512) = c_Int_OBit0(U_11514)
        | U_11512 != U_11514 )
    & ! [U_11513,U_11511] :
        ( U_11511 = U_11513
        | c_Int_OBit0(U_11511) != c_Int_OBit0(U_11513) ) ),
    inference(miniscope,[status(thm)],[f_2925_2]) ).

cnf(f_2925_4,plain,
    ( U_11511 = U_11513
    | c_Int_OBit0(U_11511) != c_Int_OBit0(U_11513) ),
    inference(clausify,[status(thm)],[f_2925_3]) ).

cnf(f_2925_5,plain,
    ( c_Int_OBit0(U_11512) = c_Int_OBit0(U_11514)
    | U_11512 != U_11514 ),
    inference(clausify,[status(thm)],[f_2925_3]) ).

fof(f_2926_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_2926_2,plain,
    ! [U_11515] : c_Int_OBit0(U_11515) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11515),U_11515),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

cnf(f_2926_3,plain,
    c_Int_OBit0(U_11515) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11515),U_11515),
    inference(clausify,[status(thm)],[f_2926_2]) ).

fof(f_2927_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_2927_2,plain,
    ! [U_11517,U_11516] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_11516)),c_Int_OBit0(U_11517)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11516),U_11517)),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

cnf(f_2927_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_11516)),c_Int_OBit0(U_11517)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11516),U_11517)),
    inference(clausify,[status(thm)],[f_2927_2]) ).

fof(f_2928_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_2928_2,plain,
    ! [U_11519,U_11518] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11518)),c_Int_OBit0(U_11519)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11518),U_11519)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11518),U_11519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11518)),c_Int_OBit0(U_11519))) ) ),
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

fof(f_2928_3,plain,
    ( ! [U_11523,U_11521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11521)),c_Int_OBit0(U_11523)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11521),U_11523)) )
    & ! [U_11522,U_11520] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11520),U_11522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11520)),c_Int_OBit0(U_11522))) ) ),
    inference(miniscope,[status(thm)],[f_2928_2]) ).

cnf(f_2928_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11520),U_11522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11520)),c_Int_OBit0(U_11522))) ),
    inference(clausify,[status(thm)],[f_2928_3]) ).

cnf(f_2928_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11521)),c_Int_OBit0(U_11523)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11521),U_11523)) ),
    inference(clausify,[status(thm)],[f_2928_3]) ).

fof(f_2929_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_2929_2,plain,
    ! [U_11525,U_11524] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11524)),c_Int_OBit0(U_11525)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11524),U_11525)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11524),U_11525))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11524)),c_Int_OBit0(U_11525))) ) ),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

fof(f_2929_3,plain,
    ( ! [U_11529,U_11527] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11527)),c_Int_OBit0(U_11529)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11527),U_11529)) )
    & ! [U_11528,U_11526] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11526),U_11528))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11526)),c_Int_OBit0(U_11528))) ) ),
    inference(miniscope,[status(thm)],[f_2929_2]) ).

cnf(f_2929_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11526),U_11528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11526)),c_Int_OBit0(U_11528))) ),
    inference(clausify,[status(thm)],[f_2929_3]) ).

cnf(f_2929_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11527)),c_Int_OBit0(U_11529)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11527),U_11529)) ),
    inference(clausify,[status(thm)],[f_2929_3]) ).

fof(f_2930_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_2930_2,plain,
    ! [U_11531,U_11530] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_11530)),c_Int_OBit0(U_11531)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11530),U_11531)),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

cnf(f_2930_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_11530)),c_Int_OBit0(U_11531)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11530),U_11531)),
    inference(clausify,[status(thm)],[f_2930_2]) ).

fof(f_2931_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_2931_2,plain,
    ! [U_11533,U_11532] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11532)),c_Int_OBit0(U_11533)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11532),U_11533)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11532),U_11533))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11532)),c_Int_OBit0(U_11533))) ) ),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

fof(f_2931_3,plain,
    ( ! [U_11537,U_11535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11535)),c_Int_OBit0(U_11537)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11535),U_11537)) )
    & ! [U_11536,U_11534] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11534),U_11536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11534)),c_Int_OBit0(U_11536))) ) ),
    inference(miniscope,[status(thm)],[f_2931_2]) ).

cnf(f_2931_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11534),U_11536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11534)),c_Int_OBit0(U_11536))) ),
    inference(clausify,[status(thm)],[f_2931_3]) ).

cnf(f_2931_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11535)),c_Int_OBit0(U_11537)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11535),U_11537)) ),
    inference(clausify,[status(thm)],[f_2931_3]) ).

fof(f_2932_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_2932_2,plain,
    ! [U_11539,U_11538] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11538)),c_Int_OBit0(U_11539)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11538),U_11539)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11538),U_11539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11538)),c_Int_OBit0(U_11539))) ) ),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

fof(f_2932_3,plain,
    ( ! [U_11543,U_11541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11541)),c_Int_OBit0(U_11543)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11541),U_11543)) )
    & ! [U_11542,U_11540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11540),U_11542))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11540)),c_Int_OBit0(U_11542))) ) ),
    inference(miniscope,[status(thm)],[f_2932_2]) ).

cnf(f_2932_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11540),U_11542))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11540)),c_Int_OBit0(U_11542))) ),
    inference(clausify,[status(thm)],[f_2932_3]) ).

cnf(f_2932_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11541)),c_Int_OBit0(U_11543)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11541),U_11543)) ),
    inference(clausify,[status(thm)],[f_2932_3]) ).

fof(f_2933_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

cnf(f_2933_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_2933_1]) ).

fof(f_2934_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_2934_2,plain,
    ! [U_11544] :
      ( ( c_Int_OPls = c_Int_OBit0(U_11544)
        | c_Int_OPls != U_11544 )
      & ( c_Int_OPls = U_11544
        | c_Int_OPls != c_Int_OBit0(U_11544) ) ),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

fof(f_2934_3,plain,
    ( ! [U_11546] :
        ( c_Int_OPls = c_Int_OBit0(U_11546)
        | c_Int_OPls != U_11546 )
    & ! [U_11545] :
        ( c_Int_OPls = U_11545
        | c_Int_OPls != c_Int_OBit0(U_11545) ) ),
    inference(miniscope,[status(thm)],[f_2934_2]) ).

cnf(f_2934_4,plain,
    ( c_Int_OPls = U_11545
    | c_Int_OPls != c_Int_OBit0(U_11545) ),
    inference(clausify,[status(thm)],[f_2934_3]) ).

cnf(f_2934_5,plain,
    ( c_Int_OPls = c_Int_OBit0(U_11546)
    | c_Int_OPls != U_11546 ),
    inference(clausify,[status(thm)],[f_2934_3]) ).

fof(f_2935_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_2935_2,plain,
    ! [U_11547] :
      ( ( c_Int_OBit0(U_11547) = c_Int_OPls
        | U_11547 != c_Int_OPls )
      & ( U_11547 = c_Int_OPls
        | c_Int_OBit0(U_11547) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

fof(f_2935_3,plain,
    ( ! [U_11549] :
        ( c_Int_OBit0(U_11549) = c_Int_OPls
        | U_11549 != c_Int_OPls )
    & ! [U_11548] :
        ( U_11548 = c_Int_OPls
        | c_Int_OBit0(U_11548) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_2935_2]) ).

cnf(f_2935_4,plain,
    ( U_11548 = c_Int_OPls
    | c_Int_OBit0(U_11548) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_2935_3]) ).

cnf(f_2935_5,plain,
    ( c_Int_OBit0(U_11549) = c_Int_OPls
    | U_11549 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_2935_3]) ).

fof(f_2936_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_2936_2,plain,
    ! [U_11550] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11550)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11550),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11550),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11550)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2936_1]) ).

fof(f_2936_3,plain,
    ( ! [U_11552] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11552)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11552),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_11551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11551),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11551)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2936_2]) ).

cnf(f_2936_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11551),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11551)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2936_3]) ).

cnf(f_2936_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11552)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11552),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2936_3]) ).

fof(f_2937_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_2937_2,plain,
    ! [U_11553] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11553)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11553)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11553))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11553))) ) ),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

fof(f_2937_3,plain,
    ( ! [U_11555] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11555)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11555)) )
    & ! [U_11554] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11554))) ) ),
    inference(miniscope,[status(thm)],[f_2937_2]) ).

cnf(f_2937_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11554))) ),
    inference(clausify,[status(thm)],[f_2937_3]) ).

cnf(f_2937_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11555)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11555)) ),
    inference(clausify,[status(thm)],[f_2937_3]) ).

fof(f_2938_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_2938_2,plain,
    ! [U_11556] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11556)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11556),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11556),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11556)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

fof(f_2938_3,plain,
    ( ! [U_11558] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11558)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11558),c_Int_OPls)) )
    & ! [U_11557] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11557),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11557)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2938_2]) ).

cnf(f_2938_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11557),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11557)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2938_3]) ).

cnf(f_2938_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11558)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11558),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2938_3]) ).

fof(f_2939_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_2939_2,plain,
    ! [U_11560,U_11559] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11559)),c_Int_OBit1(U_11560)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11559),U_11560)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11559),U_11560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11559)),c_Int_OBit1(U_11560))) ) ),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

fof(f_2939_3,plain,
    ( ! [U_11564,U_11562] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11562)),c_Int_OBit1(U_11564)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11562),U_11564)) )
    & ! [U_11563,U_11561] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11561),U_11563))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11561)),c_Int_OBit1(U_11563))) ) ),
    inference(miniscope,[status(thm)],[f_2939_2]) ).

cnf(f_2939_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11561),U_11563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11561)),c_Int_OBit1(U_11563))) ),
    inference(clausify,[status(thm)],[f_2939_3]) ).

cnf(f_2939_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11562)),c_Int_OBit1(U_11564)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11562),U_11564)) ),
    inference(clausify,[status(thm)],[f_2939_3]) ).

fof(f_2940_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_2940_2,plain,
    ! [U_11566,U_11565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11565)),c_Int_OBit1(U_11566)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11565),U_11566)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11565),U_11566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11565)),c_Int_OBit1(U_11566))) ) ),
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

fof(f_2940_3,plain,
    ( ! [U_11570,U_11568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11568)),c_Int_OBit1(U_11570)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11568),U_11570)) )
    & ! [U_11569,U_11567] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11567),U_11569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11567)),c_Int_OBit1(U_11569))) ) ),
    inference(miniscope,[status(thm)],[f_2940_2]) ).

cnf(f_2940_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11567),U_11569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11567)),c_Int_OBit1(U_11569))) ),
    inference(clausify,[status(thm)],[f_2940_3]) ).

cnf(f_2940_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11568)),c_Int_OBit1(U_11570)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11568),U_11570)) ),
    inference(clausify,[status(thm)],[f_2940_3]) ).

fof(f_2941_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_2941_2,plain,
    ! [U_11571] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11571)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11571),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11571),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11571)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

fof(f_2941_3,plain,
    ( ! [U_11573] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11573)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11573),c_Int_OPls)) )
    & ! [U_11572] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11572),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11572)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2941_2]) ).

cnf(f_2941_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11572),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11572)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2941_3]) ).

cnf(f_2941_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11573)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11573),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2941_3]) ).

fof(f_2942_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_2942_2,plain,
    ! [U_11574] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11574)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11574)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11574))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11574))) ) ),
    inference(variable_rename,[status(thm)],[f_2942_1]) ).

fof(f_2942_3,plain,
    ( ! [U_11576] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11576)) )
    & ! [U_11575] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11575))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11575))) ) ),
    inference(miniscope,[status(thm)],[f_2942_2]) ).

cnf(f_2942_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11575))) ),
    inference(clausify,[status(thm)],[f_2942_3]) ).

cnf(f_2942_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11576)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_11576)) ),
    inference(clausify,[status(thm)],[f_2942_3]) ).

fof(f_2943_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_2943_2,plain,
    ! [U_11578,U_11577] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11577)),c_Int_OBit0(U_11578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11577),U_11578)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11577),U_11578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11577)),c_Int_OBit0(U_11578))) ) ),
    inference(variable_rename,[status(thm)],[f_2943_1]) ).

fof(f_2943_3,plain,
    ( ! [U_11582,U_11580] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11580)),c_Int_OBit0(U_11582)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11580),U_11582)) )
    & ! [U_11581,U_11579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11579),U_11581))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11579)),c_Int_OBit0(U_11581))) ) ),
    inference(miniscope,[status(thm)],[f_2943_2]) ).

cnf(f_2943_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11579),U_11581))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11579)),c_Int_OBit0(U_11581))) ),
    inference(clausify,[status(thm)],[f_2943_3]) ).

cnf(f_2943_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11580)),c_Int_OBit0(U_11582)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11580),U_11582)) ),
    inference(clausify,[status(thm)],[f_2943_3]) ).

fof(f_2944_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_2944_2,plain,
    ! [U_11584,U_11583] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11583)),c_Int_OBit0(U_11584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11583),U_11584)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11583),U_11584))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11583)),c_Int_OBit0(U_11584))) ) ),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

fof(f_2944_3,plain,
    ( ! [U_11588,U_11586] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11586)),c_Int_OBit0(U_11588)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11586),U_11588)) )
    & ! [U_11587,U_11585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11585),U_11587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11585)),c_Int_OBit0(U_11587))) ) ),
    inference(miniscope,[status(thm)],[f_2944_2]) ).

cnf(f_2944_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11585),U_11587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11585)),c_Int_OBit0(U_11587))) ),
    inference(clausify,[status(thm)],[f_2944_3]) ).

cnf(f_2944_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11586)),c_Int_OBit0(U_11588)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11586),U_11588)) ),
    inference(clausify,[status(thm)],[f_2944_3]) ).

fof(f_2945_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_2945_2,plain,
    ! [U_11590,U_11589] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_11589)),c_Int_OBit1(U_11590)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11589),U_11590)),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

cnf(f_2945_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_11589)),c_Int_OBit1(U_11590)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11589),U_11590)),
    inference(clausify,[status(thm)],[f_2945_2]) ).

fof(f_2946_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_2946_2,plain,
    ! [U_11592,U_11591] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_11591)),c_Int_OBit0(U_11592)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11591),U_11592)),
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

cnf(f_2946_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_11591)),c_Int_OBit0(U_11592)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11591),U_11592)),
    inference(clausify,[status(thm)],[f_2946_2]) ).

fof(f_2947_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_2947_2,plain,
    ! [U_11593] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11593)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_11593)),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

cnf(f_2947_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_11593)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_11593)),
    inference(clausify,[status(thm)],[f_2947_2]) ).

fof(f_2948_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_2948_2,plain,
    ! [U_11595,U_11594] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_11594)),c_Int_OBit1(U_11595)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11594),U_11595)),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

cnf(f_2948_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_11594)),c_Int_OBit1(U_11595)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11594),U_11595)),
    inference(clausify,[status(thm)],[f_2948_2]) ).

fof(f_2949_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_2949_2,plain,
    ! [U_11597,U_11596] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_11596)),c_Int_OBit0(U_11597)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11596),U_11597)),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

cnf(f_2949_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_11596)),c_Int_OBit0(U_11597)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11596),U_11597)),
    inference(clausify,[status(thm)],[f_2949_2]) ).

fof(f_2950_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_2950_2,plain,
    ! [U_11599,U_11598] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11598))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11599))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11598)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11599)),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

cnf(f_2950_3,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_11598))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11599))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11598)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11599)),
    inference(clausify,[status(thm)],[f_2950_2]) ).

fof(f_2951_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_2951_2,plain,
    ! [U_11600] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11600))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11600))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11600)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11600)))) ) ),
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

fof(f_2951_3,plain,
    ( ! [U_11602] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11602))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11602))) )
    & ! [U_11601] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11601)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11601)))) ) ),
    inference(miniscope,[status(thm)],[f_2951_2]) ).

cnf(f_2951_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11601)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11601)))) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

cnf(f_2951_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11602))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11602))) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

fof(f_2952_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_2952_2,plain,
    ! [U_11603] : c_Int_Opred(c_Int_OBit1(U_11603)) = c_Int_OBit0(U_11603),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

cnf(f_2952_3,plain,
    c_Int_Opred(c_Int_OBit1(U_11603)) = c_Int_OBit0(U_11603),
    inference(clausify,[status(thm)],[f_2952_2]) ).

fof(f_2953_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_2953_2,plain,
    ! [U_11604] : c_Int_Opred(c_Int_OBit0(U_11604)) = c_Int_OBit1(c_Int_Opred(U_11604)),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

cnf(f_2953_3,plain,
    c_Int_Opred(c_Int_OBit0(U_11604)) = c_Int_OBit1(c_Int_Opred(U_11604)),
    inference(clausify,[status(thm)],[f_2953_2]) ).

fof(f_2954_1,plain,
    ! [V_w_2,T_a] :
      ( ( ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) )
        & ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
          | ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) ) )
      | ~ class_Int_Oring__char__0(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).

fof(f_2954_2,plain,
    ! [U_11606,U_11605] :
      ( ( ( c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),c_Int_OBit0(U_11606)))
          | ~ c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),U_11606)) )
        & ( c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),U_11606))
          | ~ c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),c_Int_OBit0(U_11606))) ) )
      | ~ class_Int_Oring__char__0(U_11605)
      | ~ class_Int_Onumber__ring(U_11605) ),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

cnf(f_2954_3,plain,
    ( c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),U_11606))
    | ~ c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),c_Int_OBit0(U_11606)))
    | ~ class_Int_Oring__char__0(U_11605)
    | ~ class_Int_Onumber__ring(U_11605) ),
    inference(clausify,[status(thm)],[f_2954_2]) ).

cnf(f_2954_4,plain,
    ( c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),c_Int_OBit0(U_11606)))
    | ~ c_Int_Oiszero(U_11605,hAPP(c_Int_Onumber__class_Onumber__of(U_11605),U_11606))
    | ~ class_Int_Oring__char__0(U_11605)
    | ~ class_Int_Onumber__ring(U_11605) ),
    inference(clausify,[status(thm)],[f_2954_2]) ).

fof(f_2955_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_2955_2,plain,
    ! [U_11607] : c_Int_Osucc(c_Int_OBit0(U_11607)) = c_Int_OBit1(U_11607),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

cnf(f_2955_3,plain,
    c_Int_Osucc(c_Int_OBit0(U_11607)) = c_Int_OBit1(U_11607),
    inference(clausify,[status(thm)],[f_2955_2]) ).

fof(f_2956_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_2956_2,plain,
    ! [U_11608] : c_Int_Osucc(c_Int_OBit1(U_11608)) = c_Int_OBit0(c_Int_Osucc(U_11608)),
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

cnf(f_2956_3,plain,
    c_Int_Osucc(c_Int_OBit1(U_11608)) = c_Int_OBit0(c_Int_Osucc(U_11608)),
    inference(clausify,[status(thm)],[f_2956_2]) ).

fof(f_2957_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_2957_2,plain,
    ! [U_11609] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11609)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11609)),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_2957_1]) ).

cnf(f_2957_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11609)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11609)),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_2957_2]) ).

fof(f_2958_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_2958_2,plain,
    ! [U_11611,U_11610] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11610),c_Int_OBit0(U_11611)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11610),c_Groups_Ozero__class_Ozero(U_11610)),hAPP(c_Int_Onumber__class_Onumber__of(U_11610),U_11611))),hAPP(c_Int_Onumber__class_Onumber__of(U_11610),U_11611))
      | ~ class_Int_Onumber__ring(U_11610) ),
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

cnf(f_2958_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11610),c_Int_OBit0(U_11611)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11610),c_Groups_Ozero__class_Ozero(U_11610)),hAPP(c_Int_Onumber__class_Onumber__of(U_11610),U_11611))),hAPP(c_Int_Onumber__class_Onumber__of(U_11610),U_11611))
    | ~ class_Int_Onumber__ring(U_11610) ),
    inference(clausify,[status(thm)],[f_2958_2]) ).

fof(f_2959_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_2959_2,plain,
    ! [U_11613,U_11612] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11612)),c_Int_OBit0(U_11613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11612),U_11613)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11612),U_11613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11612)),c_Int_OBit0(U_11613))) ) ),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

fof(f_2959_3,plain,
    ( ! [U_11617,U_11615] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11615)),c_Int_OBit0(U_11617)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11615),U_11617)) )
    & ! [U_11616,U_11614] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11614),U_11616))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11614)),c_Int_OBit0(U_11616))) ) ),
    inference(miniscope,[status(thm)],[f_2959_2]) ).

cnf(f_2959_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11614),U_11616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11614)),c_Int_OBit0(U_11616))) ),
    inference(clausify,[status(thm)],[f_2959_3]) ).

cnf(f_2959_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11615)),c_Int_OBit0(U_11617)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11615),U_11617)) ),
    inference(clausify,[status(thm)],[f_2959_3]) ).

fof(f_2960_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_2960_2,plain,
    ! [U_11619,U_11618] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11618)),c_Int_OBit0(U_11619)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11618),U_11619)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11618),U_11619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11618)),c_Int_OBit0(U_11619))) ) ),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

fof(f_2960_3,plain,
    ( ! [U_11623,U_11621] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11621)),c_Int_OBit0(U_11623)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11621),U_11623)) )
    & ! [U_11622,U_11620] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11620),U_11622))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11620)),c_Int_OBit0(U_11622))) ) ),
    inference(miniscope,[status(thm)],[f_2960_2]) ).

cnf(f_2960_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11620),U_11622))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11620)),c_Int_OBit0(U_11622))) ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

cnf(f_2960_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11621)),c_Int_OBit0(U_11623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11621),U_11623)) ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

fof(f_2961_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_2961_2,plain,
    ! [U_11625,U_11624] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11624)),c_Int_OBit1(U_11625)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11624),U_11625)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11624),U_11625))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11624)),c_Int_OBit1(U_11625))) ) ),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

fof(f_2961_3,plain,
    ( ! [U_11629,U_11627] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11627)),c_Int_OBit1(U_11629)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11627),U_11629)) )
    & ! [U_11628,U_11626] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11626),U_11628))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11626)),c_Int_OBit1(U_11628))) ) ),
    inference(miniscope,[status(thm)],[f_2961_2]) ).

cnf(f_2961_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11626),U_11628))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11626)),c_Int_OBit1(U_11628))) ),
    inference(clausify,[status(thm)],[f_2961_3]) ).

cnf(f_2961_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11627)),c_Int_OBit1(U_11629)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11627),U_11629)) ),
    inference(clausify,[status(thm)],[f_2961_3]) ).

fof(f_2962_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_2962_2,plain,
    ! [U_11631,U_11630] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11630)),c_Int_OBit1(U_11631)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11630),U_11631)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11630),U_11631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11630)),c_Int_OBit1(U_11631))) ) ),
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

fof(f_2962_3,plain,
    ( ! [U_11635,U_11633] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11633)),c_Int_OBit1(U_11635)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11633),U_11635)) )
    & ! [U_11634,U_11632] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11632),U_11634))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11632)),c_Int_OBit1(U_11634))) ) ),
    inference(miniscope,[status(thm)],[f_2962_2]) ).

cnf(f_2962_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11632),U_11634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11632)),c_Int_OBit1(U_11634))) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

cnf(f_2962_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11633)),c_Int_OBit1(U_11635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11633),U_11635)) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

fof(f_2963_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]) ).

cnf(f_2963_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(clausify,[status(thm)],[f_2963_1]) ).

fof(f_2964_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_2964_2,plain,
    ! [U_11637,U_11636] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_11636)),U_11637) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11636),U_11637))),U_11637),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

cnf(f_2964_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_11636)),U_11637) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11636),U_11637))),U_11637),
    inference(clausify,[status(thm)],[f_2964_2]) ).

fof(f_2965_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_2965_2,plain,
    ! [U_11639,U_11638] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_11638)),c_Int_OBit1(U_11639)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_11638)),U_11639)),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

cnf(f_2965_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_11638)),c_Int_OBit1(U_11639)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_11638)),U_11639)),
    inference(clausify,[status(thm)],[f_2965_2]) ).

fof(f_2966_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_2966_2,plain,
    ! [U_11641,U_11640] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_11640)),c_Int_OBit1(U_11641)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11640),c_Int_Osucc(U_11641))),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

cnf(f_2966_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_11640)),c_Int_OBit1(U_11641)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11640),c_Int_Osucc(U_11641))),
    inference(clausify,[status(thm)],[f_2966_2]) ).

fof(f_2967_1,plain,
    ! [V_w_2,V_z_2,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).

fof(f_2967_2,plain,
    ! [U_11644,U_11643,U_11642] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11642),U_11643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11644))) = hAPP(hAPP(c_HOL_OLet(U_11642,U_11642),hAPP(hAPP(c_Power_Opower__class_Opower(U_11642),U_11643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11644))),hAPP(hAPP(c_COMBS(U_11642,U_11642,U_11642),c_Groups_Otimes__class_Otimes(U_11642)),c_COMBI(U_11642)))
      | ~ class_Int_Onumber__ring(U_11642) ),
    inference(variable_rename,[status(thm)],[f_2967_1]) ).

cnf(f_2967_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11642),U_11643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11644))) = hAPP(hAPP(c_HOL_OLet(U_11642,U_11642),hAPP(hAPP(c_Power_Opower__class_Opower(U_11642),U_11643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11644))),hAPP(hAPP(c_COMBS(U_11642,U_11642,U_11642),c_Groups_Otimes__class_Otimes(U_11642)),c_COMBI(U_11642)))
    | ~ class_Int_Onumber__ring(U_11642) ),
    inference(clausify,[status(thm)],[f_2967_2]) ).

fof(f_2968_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_2968_2,plain,
    ! [U_11646,U_11645] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11646))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11646))),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_2968_1]) ).

cnf(f_2968_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11646))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_11645),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11646))),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_2968_2]) ).

fof(f_2969_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_2969_2,plain,
    ! [U_11648,U_11647] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11647),c_Groups_Oone__class_Oone(U_11647)),c_Groups_Oone__class_Oone(U_11647))),hAPP(c_Int_Onumber__class_Onumber__of(U_11647),U_11648)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11647),c_Int_OBit0(U_11648))
      | ~ class_Int_Onumber__ring(U_11647) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

cnf(f_2969_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11647),c_Groups_Oone__class_Oone(U_11647)),c_Groups_Oone__class_Oone(U_11647))),hAPP(c_Int_Onumber__class_Onumber__of(U_11647),U_11648)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11647),c_Int_OBit0(U_11648))
    | ~ class_Int_Onumber__ring(U_11647) ),
    inference(clausify,[status(thm)],[f_2969_2]) ).

fof(f_2970_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_2970_2,plain,
    ! [U_11649] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11649))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11649)))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11649))) ),
    inference(variable_rename,[status(thm)],[f_2970_1]) ).

cnf(f_2970_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(U_11649))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11649))) ),
    inference(clausify,[status(thm)],[f_2970_2]) ).

cnf(f_2970_4,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_11649))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11649))) ),
    inference(clausify,[status(thm)],[f_2970_2]) ).

fof(f_2971_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]) ).

cnf(f_2971_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(clausify,[status(thm)],[f_2971_1]) ).

fof(f_2972_1,plain,
    ! [V_w_2,V_v_2,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).

fof(f_2972_2,plain,
    ! [U_11652,U_11651,U_11650] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11650),hAPP(c_Int_Onumber__class_Onumber__of(U_11650),U_11651)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11652))) = hAPP(hAPP(c_HOL_OLet(U_11650,U_11650),hAPP(hAPP(c_Power_Opower__class_Opower(U_11650),hAPP(c_Int_Onumber__class_Onumber__of(U_11650),U_11651)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11652))),hAPP(hAPP(c_COMBS(U_11650,U_11650,U_11650),c_Groups_Otimes__class_Otimes(U_11650)),c_COMBI(U_11650)))
      | ~ class_Int_Onumber__ring(U_11650) ),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

cnf(f_2972_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11650),hAPP(c_Int_Onumber__class_Onumber__of(U_11650),U_11651)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_11652))) = hAPP(hAPP(c_HOL_OLet(U_11650,U_11650),hAPP(hAPP(c_Power_Opower__class_Opower(U_11650),hAPP(c_Int_Onumber__class_Onumber__of(U_11650),U_11651)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11652))),hAPP(hAPP(c_COMBS(U_11650,U_11650,U_11650),c_Groups_Otimes__class_Otimes(U_11650)),c_COMBI(U_11650)))
    | ~ class_Int_Onumber__ring(U_11650) ),
    inference(clausify,[status(thm)],[f_2972_2]) ).

fof(f_2973_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_2973_2,plain,
    ! [U_11654,U_11653] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11653),hAPP(c_Int_Onumber__class_Onumber__of(U_11653),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11653),U_11654),U_11654)
      | ~ class_Int_Onumber__ring(U_11653) ),
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

cnf(f_2973_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11653),hAPP(c_Int_Onumber__class_Onumber__of(U_11653),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11653),U_11654),U_11654)
    | ~ class_Int_Onumber__ring(U_11653) ),
    inference(clausify,[status(thm)],[f_2973_2]) ).

fof(f_2974_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_2974_2,plain,
    ! [U_11656,U_11655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11655),U_11656),hAPP(c_Int_Onumber__class_Onumber__of(U_11655),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11655),U_11656),U_11656)
      | ~ class_Int_Onumber__ring(U_11655) ),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

cnf(f_2974_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11655),U_11656),hAPP(c_Int_Onumber__class_Onumber__of(U_11655),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11655),U_11656),U_11656)
    | ~ class_Int_Onumber__ring(U_11655) ),
    inference(clausify,[status(thm)],[f_2974_2]) ).

fof(f_2975_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_2975_2,plain,
    ! [U_11657] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11657),c_Groups_Oone__class_Oone(U_11657)),c_Groups_Oone__class_Oone(U_11657)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11657),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_11657) ),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

cnf(f_2975_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11657),c_Groups_Oone__class_Oone(U_11657)),c_Groups_Oone__class_Oone(U_11657)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11657),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_11657) ),
    inference(clausify,[status(thm)],[f_2975_2]) ).

fof(f_2976_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).

fof(f_2976_2,plain,
    ! [U_11659,U_11658] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11658),U_11659),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_11658)
          | U_11659 != c_Groups_Ozero__class_Ozero(U_11658) )
        & ( U_11659 = c_Groups_Ozero__class_Ozero(U_11658)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_11658),U_11659),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_11658) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_11658) ),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

cnf(f_2976_3,plain,
    ( U_11659 = c_Groups_Ozero__class_Ozero(U_11658)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_11658),U_11659),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_11658)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_11658) ),
    inference(clausify,[status(thm)],[f_2976_2]) ).

cnf(f_2976_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11658),U_11659),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_11658)
    | U_11659 != c_Groups_Ozero__class_Ozero(U_11658)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_11658) ),
    inference(clausify,[status(thm)],[f_2976_2]) ).

fof(f_2977_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_2977_2,plain,
    ! [U_11660] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11660),c_Groups_Ozero__class_Ozero(U_11660)),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_11660)
      | ~ class_Rings_Osemiring__1(U_11660) ),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

cnf(f_2977_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11660),c_Groups_Ozero__class_Ozero(U_11660)),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_11660)
    | ~ class_Rings_Osemiring__1(U_11660) ),
    inference(clausify,[status(thm)],[f_2977_2]) ).

fof(f_2978_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]) ).

cnf(f_2978_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(clausify,[status(thm)],[f_2978_1]) ).

fof(f_2979_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]) ).

cnf(f_2979_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(clausify,[status(thm)],[f_2979_1]) ).

fof(f_2980_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_2980_2,plain,
    ! [U_11662,U_11661] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11661),U_11662),U_11662) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11661),U_11662),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_11661) ),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

cnf(f_2980_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11661),U_11662),U_11662) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11661),U_11662),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_11661) ),
    inference(clausify,[status(thm)],[f_2980_2]) ).

fof(f_2981_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_2981_2,plain,
    ! [U_11664,U_11663] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11663),U_11664),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_11663),U_11664),U_11664)
      | ~ class_Groups_Omonoid__mult(U_11663) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

cnf(f_2981_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11663),U_11664),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_11663),U_11664),U_11664)
    | ~ class_Groups_Omonoid__mult(U_11663) ),
    inference(clausify,[status(thm)],[f_2981_2]) ).

fof(f_2982_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]) ).

cnf(f_2982_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(clausify,[status(thm)],[f_2982_1]) ).

fof(f_2983_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_2983_2,plain,
    ! [U_11665] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11665),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_11665)),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

cnf(f_2983_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11665),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_11665)),
    inference(clausify,[status(thm)],[f_2983_2]) ).

fof(f_2984_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_2984_2,plain,
    ! [U_11666] : 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_11666) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11666)),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

cnf(f_2984_3,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_11666) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11666)),
    inference(clausify,[status(thm)],[f_2984_2]) ).

fof(f_2985_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_2985_2,plain,
    ! [U_11667] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11667),c_Groups_Oone__class_Oone(U_11667)),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_11667)
      | ~ class_Rings_Osemiring__1(U_11667) ),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

cnf(f_2985_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11667),c_Groups_Oone__class_Oone(U_11667)),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_11667)
    | ~ class_Rings_Osemiring__1(U_11667) ),
    inference(clausify,[status(thm)],[f_2985_2]) ).

fof(f_2986_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_2986_2,plain,
    ! [U_11669,U_11668] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11668),hAPP(c_Groups_Ouminus__class_Ouminus(U_11668),U_11669)),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_11668),U_11669),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_11668) ),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

cnf(f_2986_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11668),hAPP(c_Groups_Ouminus__class_Ouminus(U_11668),U_11669)),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_11668),U_11669),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_11668) ),
    inference(clausify,[status(thm)],[f_2986_2]) ).

fof(f_2987_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_2987_2,plain,
    ! [U_11670] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11670),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_11670),U_11670),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

cnf(f_2987_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11670),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_11670),U_11670),
    inference(clausify,[status(thm)],[f_2987_2]) ).

fof(f_2988_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_2988_2,plain,
    ! [U_11671] : 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_11671) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11671),U_11671),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

cnf(f_2988_3,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_11671) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11671),U_11671),
    inference(clausify,[status(thm)],[f_2988_2]) ).

fof(f_2989_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_2989_2,plain,
    ! [U_11674,U_11673,U_11672] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),U_11673),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_11674)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),U_11673),U_11674)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_11672) ),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

cnf(f_2989_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),U_11673),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_11674)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),hAPP(hAPP(c_Power_Opower__class_Opower(U_11672),U_11673),U_11674)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_11672) ),
    inference(clausify,[status(thm)],[f_2989_2]) ).

fof(f_2990_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]) ).

cnf(f_2990_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(clausify,[status(thm)],[f_2990_1]) ).

fof(f_2991_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]) ).

cnf(f_2991_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(clausify,[status(thm)],[f_2991_1]) ).

fof(f_2992_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_2992_2,plain,
    ! [U_11676,U_11675] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_11675),hAPP(hAPP(c_Power_Opower__class_Opower(U_11675),U_11676),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_11675),U_11676),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_11675) ),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

cnf(f_2992_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_11675),hAPP(hAPP(c_Power_Opower__class_Opower(U_11675),U_11676),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_11675),U_11676),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_11675) ),
    inference(clausify,[status(thm)],[f_2992_2]) ).

fof(f_2993_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_2993_2,plain,
    ! [U_11678,U_11677] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11677),hAPP(c_Groups_Oabs__class_Oabs(U_11677),U_11678)),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_11677),U_11678),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_11677) ),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

cnf(f_2993_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11677),hAPP(c_Groups_Oabs__class_Oabs(U_11677),U_11678)),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_11677),U_11678),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_11677) ),
    inference(clausify,[status(thm)],[f_2993_2]) ).

fof(f_2994_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]) ).

cnf(f_2994_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(clausify,[status(thm)],[f_2994_1]) ).

fof(f_2995_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_2995_2,plain,
    ! [U_11679] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11679)),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_11679,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_2995_1]) ).

cnf(f_2995_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11679)),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_11679,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2995_2]) ).

fof(f_2996_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_2996_2,plain,
    ! [U_11680] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11680))),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_11680),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_2996_1]) ).

cnf(f_2996_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_11680))),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_11680),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_2996_2]) ).

fof(f_2997_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_2997_2,plain,
    ! [U_11682,U_11681] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11682))) = hAPP(hAPP(c_Groups_Otimes__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_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11682))),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

cnf(f_2997_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11682))) = hAPP(hAPP(c_Groups_Otimes__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_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11682))),
    inference(clausify,[status(thm)],[f_2997_2]) ).

fof(f_2998_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_2998_2,plain,
    ! [U_11683] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11683),U_11683)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_11683,
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

cnf(f_2998_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11683),U_11683)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_11683,
    inference(clausify,[status(thm)],[f_2998_2]) ).

fof(f_2999_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_2999_2,plain,
    ! [U_11685,U_11684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11684),c_Groups_Ozero__class_Ozero(U_11684)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11684),U_11685),hAPP(c_Int_Onumber__class_Onumber__of(U_11684),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11684),c_Groups_Ozero__class_Ozero(U_11684)),U_11685))
      | ~ class_Int_Onumber__ring(U_11684)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11684) ),
    inference(variable_rename,[status(thm)],[f_2999_1]) ).

cnf(f_2999_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11684),c_Groups_Ozero__class_Ozero(U_11684)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11684),U_11685),hAPP(c_Int_Onumber__class_Onumber__of(U_11684),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11684),c_Groups_Ozero__class_Ozero(U_11684)),U_11685))
    | ~ class_Int_Onumber__ring(U_11684)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11684) ),
    inference(clausify,[status(thm)],[f_2999_2]) ).

fof(f_3000_1,plain,
    ! [V_r_2,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_2),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_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2))
          | ~ 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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).

fof(f_3000_2,plain,
    ! [U_11687,U_11686] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11686),U_11687),hAPP(c_Int_Onumber__class_Onumber__of(U_11686),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),U_11687)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),U_11687))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11686),U_11687),hAPP(c_Int_Onumber__class_Onumber__of(U_11686),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_11686)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_11686) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

cnf(f_3000_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),U_11687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11686),U_11687),hAPP(c_Int_Onumber__class_Onumber__of(U_11686),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Int_Onumber__ring(U_11686)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11686) ),
    inference(clausify,[status(thm)],[f_3000_2]) ).

cnf(f_3000_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11686),U_11687),hAPP(c_Int_Onumber__class_Onumber__of(U_11686),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11686),c_Groups_Ozero__class_Ozero(U_11686)),U_11687))
    | ~ class_Int_Onumber__ring(U_11686)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_11686) ),
    inference(clausify,[status(thm)],[f_3000_2]) ).

fof(f_3001_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_3001_2,plain,
    ! [U_11690,U_11689,U_11688] :
      ( U_11689 = U_11690
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11688),c_Groups_Ozero__class_Ozero(U_11688)),U_11690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11688),c_Groups_Ozero__class_Ozero(U_11688)),U_11689))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_11688),U_11689),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_11688),U_11690),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_11688) ),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

cnf(f_3001_3,plain,
    ( U_11689 = U_11690
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11688),c_Groups_Ozero__class_Ozero(U_11688)),U_11690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11688),c_Groups_Ozero__class_Ozero(U_11688)),U_11689))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_11688),U_11689),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_11688),U_11690),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(U_11688) ),
    inference(clausify,[status(thm)],[f_3001_2]) ).

fof(f_3002_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_3002_2,plain,
    ! [U_11693,U_11692,U_11691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),U_11692),U_11693))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),c_Groups_Ozero__class_Ozero(U_11691)),U_11693))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),hAPP(hAPP(c_Power_Opower__class_Opower(U_11691),U_11692),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_11691),U_11693),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_11691) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

cnf(f_3002_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),U_11692),U_11693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),c_Groups_Ozero__class_Ozero(U_11691)),U_11693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11691),hAPP(hAPP(c_Power_Opower__class_Opower(U_11691),U_11692),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_11691),U_11693),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_11691) ),
    inference(clausify,[status(thm)],[f_3002_2]) ).

fof(f_3003_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_3003_2,plain,
    ! [U_11695,U_11694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11694),c_Groups_Ozero__class_Ozero(U_11694)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11694),U_11695),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_11694) ),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

cnf(f_3003_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11694),c_Groups_Ozero__class_Ozero(U_11694)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11694),U_11695),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_11694) ),
    inference(clausify,[status(thm)],[f_3003_2]) ).

fof(f_3004_1,plain,
    ! [V_a_2,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_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_a) )
        & ( V_a_2 != 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_Power_Opower__class_Opower(T_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).

fof(f_3004_2,plain,
    ! [U_11697,U_11696] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11696),c_Groups_Ozero__class_Ozero(U_11696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11696),U_11697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_11697 = c_Groups_Ozero__class_Ozero(U_11696) )
        & ( U_11697 != c_Groups_Ozero__class_Ozero(U_11696)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11696),c_Groups_Ozero__class_Ozero(U_11696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11696),U_11697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_11696) ),
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

cnf(f_3004_3,plain,
    ( U_11697 != c_Groups_Ozero__class_Ozero(U_11696)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11696),c_Groups_Ozero__class_Ozero(U_11696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11696),U_11697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_11696) ),
    inference(clausify,[status(thm)],[f_3004_2]) ).

cnf(f_3004_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11696),c_Groups_Ozero__class_Ozero(U_11696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11696),U_11697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_11697 = c_Groups_Ozero__class_Ozero(U_11696)
    | ~ class_Rings_Olinordered__idom(U_11696) ),
    inference(clausify,[status(thm)],[f_3004_2]) ).

fof(f_3005_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_3005_2,plain,
    ! [U_11699,U_11698] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11698),hAPP(hAPP(c_Power_Opower__class_Opower(U_11698),U_11699),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_11698)))
      | ~ class_Rings_Olinordered__idom(U_11698) ),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

cnf(f_3005_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11698),hAPP(hAPP(c_Power_Opower__class_Opower(U_11698),U_11699),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_11698)))
    | ~ class_Rings_Olinordered__idom(U_11698) ),
    inference(clausify,[status(thm)],[f_3005_2]) ).

fof(f_3006_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = 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_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_a),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_a) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).

fof(f_3006_2,plain,
    ! [U_11702,U_11701,U_11700] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11700),hAPP(hAPP(c_Power_Opower__class_Opower(U_11700),U_11701),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_11700),U_11702),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_11700)
          | U_11702 != c_Groups_Ozero__class_Ozero(U_11700)
          | U_11701 != c_Groups_Ozero__class_Ozero(U_11700) )
        & ( ( U_11702 = c_Groups_Ozero__class_Ozero(U_11700)
            & U_11701 = c_Groups_Ozero__class_Ozero(U_11700) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11700),hAPP(hAPP(c_Power_Opower__class_Opower(U_11700),U_11701),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_11700),U_11702),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_11700) ) )
      | ~ class_Rings_Olinordered__idom(U_11700) ),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

cnf(f_3006_3,plain,
    ( U_11701 = c_Groups_Ozero__class_Ozero(U_11700)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11700),hAPP(hAPP(c_Power_Opower__class_Opower(U_11700),U_11701),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_11700),U_11702),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_11700)
    | ~ class_Rings_Olinordered__idom(U_11700) ),
    inference(clausify,[status(thm)],[f_3006_2]) ).

cnf(f_3006_4,plain,
    ( U_11702 = c_Groups_Ozero__class_Ozero(U_11700)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11700),hAPP(hAPP(c_Power_Opower__class_Opower(U_11700),U_11701),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_11700),U_11702),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_11700)
    | ~ class_Rings_Olinordered__idom(U_11700) ),
    inference(clausify,[status(thm)],[f_3006_2]) ).

cnf(f_3006_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11700),hAPP(hAPP(c_Power_Opower__class_Opower(U_11700),U_11701),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_11700),U_11702),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_11700)
    | U_11702 != c_Groups_Ozero__class_Ozero(U_11700)
    | U_11701 != c_Groups_Ozero__class_Ozero(U_11700)
    | ~ class_Rings_Olinordered__idom(U_11700) ),
    inference(clausify,[status(thm)],[f_3006_2]) ).

fof(f_3007_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_3007_2,plain,
    ! [U_11704,U_11703] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11703),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704)),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_11703),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704)),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704))
      | ~ class_Int_Onumber(U_11703)
      | ~ class_Groups_Omonoid__mult(U_11703) ),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

cnf(f_3007_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11703),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704)),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_11703),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704)),hAPP(c_Int_Onumber__class_Onumber__of(U_11703),U_11704))
    | ~ class_Int_Onumber(U_11703)
    | ~ class_Groups_Omonoid__mult(U_11703) ),
    inference(clausify,[status(thm)],[f_3007_2]) ).

fof(f_3008_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_3008_2,plain,
    ! [U_11705] :
      ( U_11705 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_11705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11705),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_3008_1]) ).

cnf(f_3008_3,plain,
    ( U_11705 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_11705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11705),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_3008_2]) ).

fof(f_3009_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]) ).

cnf(f_3009_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(clausify,[status(thm)],[f_3009_1]) ).

fof(f_3010_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
            & V_a_2 != c_Groups_Oone__class_Oone(T_a) ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
          | V_a_2 = c_Groups_Oone__class_Oone(T_a)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).

fof(f_3010_2,plain,
    ! [U_11707,U_11706] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11706),U_11707),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_11706)
          | ( U_11707 != hAPP(c_Groups_Ouminus__class_Ouminus(U_11706),c_Groups_Oone__class_Oone(U_11706))
            & U_11707 != c_Groups_Oone__class_Oone(U_11706) ) )
        & ( U_11707 = hAPP(c_Groups_Ouminus__class_Ouminus(U_11706),c_Groups_Oone__class_Oone(U_11706))
          | U_11707 = c_Groups_Oone__class_Oone(U_11706)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_11706),U_11707),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_11706) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_11706) ),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

cnf(f_3010_3,plain,
    ( U_11707 = hAPP(c_Groups_Ouminus__class_Ouminus(U_11706),c_Groups_Oone__class_Oone(U_11706))
    | U_11707 = c_Groups_Oone__class_Oone(U_11706)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_11706),U_11707),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_11706)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_11706) ),
    inference(clausify,[status(thm)],[f_3010_2]) ).

cnf(f_3010_4,plain,
    ( U_11707 != c_Groups_Oone__class_Oone(U_11706)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_11706),U_11707),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_11706)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_11706) ),
    inference(clausify,[status(thm)],[f_3010_2]) ).

cnf(f_3010_5,plain,
    ( U_11707 != hAPP(c_Groups_Ouminus__class_Ouminus(U_11706),c_Groups_Oone__class_Oone(U_11706))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_11706),U_11707),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_11706)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_11706) ),
    inference(clausify,[status(thm)],[f_3010_2]) ).

fof(f_3011_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_3011_2,plain,
    ! [U_11710,U_11709,U_11708] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),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_11710)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11708),hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),U_11710)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),U_11710))
      | ~ class_Rings_Ocomm__semiring__1(U_11708) ),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

cnf(f_3011_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),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_11710)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11708),hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),U_11710)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11708),U_11709),U_11710))
    | ~ class_Rings_Ocomm__semiring__1(U_11708) ),
    inference(clausify,[status(thm)],[f_3011_2]) ).

fof(f_3012_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_3012_2,plain,
    ! [U_11713,U_11712,U_11711] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11711),hAPP(c_Groups_Ouminus__class_Ouminus(U_11711),U_11712)),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_11713)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11711),U_11712),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_11713))
      | ~ class_Rings_Oring__1(U_11711) ),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

cnf(f_3012_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11711),hAPP(c_Groups_Ouminus__class_Ouminus(U_11711),U_11712)),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_11713)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_11711),U_11712),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_11713))
    | ~ class_Rings_Oring__1(U_11711) ),
    inference(clausify,[status(thm)],[f_3012_2]) ).

fof(f_3013_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_3013_2,plain,
    ! [U_11716,U_11715,U_11714] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11714),U_11715),U_11716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11714),c_Groups_Ozero__class_Ozero(U_11714)),U_11716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11714),hAPP(hAPP(c_Power_Opower__class_Opower(U_11714),U_11715),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_11714),U_11716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_11714) ),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

cnf(f_3013_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11714),U_11715),U_11716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11714),c_Groups_Ozero__class_Ozero(U_11714)),U_11716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11714),hAPP(hAPP(c_Power_Opower__class_Opower(U_11714),U_11715),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_11714),U_11716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_11714) ),
    inference(clausify,[status(thm)],[f_3013_2]) ).

fof(f_3014_1,plain,
    ! [V_y_2,V_x_2,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_Power_Opower__class_Opower(T_a),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_a),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_a)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).

fof(f_3014_2,plain,
    ! [U_11719,U_11718,U_11717] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11717),hAPP(hAPP(c_Power_Opower__class_Opower(U_11717),U_11718),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_11717),U_11719),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_11717)))
          | U_11719 != c_Groups_Ozero__class_Ozero(U_11717)
          | U_11718 != c_Groups_Ozero__class_Ozero(U_11717) )
        & ( ( U_11719 = c_Groups_Ozero__class_Ozero(U_11717)
            & U_11718 = c_Groups_Ozero__class_Ozero(U_11717) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11717),hAPP(hAPP(c_Power_Opower__class_Opower(U_11717),U_11718),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_11717),U_11719),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_11717))) ) )
      | ~ class_Rings_Olinordered__idom(U_11717) ),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

cnf(f_3014_3,plain,
    ( U_11718 = c_Groups_Ozero__class_Ozero(U_11717)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11717),hAPP(hAPP(c_Power_Opower__class_Opower(U_11717),U_11718),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_11717),U_11719),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_11717)))
    | ~ class_Rings_Olinordered__idom(U_11717) ),
    inference(clausify,[status(thm)],[f_3014_2]) ).

cnf(f_3014_4,plain,
    ( U_11719 = c_Groups_Ozero__class_Ozero(U_11717)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11717),hAPP(hAPP(c_Power_Opower__class_Opower(U_11717),U_11718),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_11717),U_11719),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_11717)))
    | ~ class_Rings_Olinordered__idom(U_11717) ),
    inference(clausify,[status(thm)],[f_3014_2]) ).

cnf(f_3014_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11717),hAPP(hAPP(c_Power_Opower__class_Opower(U_11717),U_11718),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_11717),U_11719),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_11717)))
    | U_11719 != c_Groups_Ozero__class_Ozero(U_11717)
    | U_11718 != c_Groups_Ozero__class_Ozero(U_11717)
    | ~ class_Rings_Olinordered__idom(U_11717) ),
    inference(clausify,[status(thm)],[f_3014_2]) ).

fof(f_3015_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_3015_2,plain,
    ! [U_11722,U_11721,U_11720] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11720),c_Groups_Ozero__class_Ozero(U_11720)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11720),hAPP(hAPP(c_Power_Opower__class_Opower(U_11720),U_11721),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_11720),U_11722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_11720) ),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

cnf(f_3015_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11720),c_Groups_Ozero__class_Ozero(U_11720)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11720),hAPP(hAPP(c_Power_Opower__class_Opower(U_11720),U_11721),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_11720),U_11722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_11720) ),
    inference(clausify,[status(thm)],[f_3015_2]) ).

fof(f_3016_1,plain,
    ! [V_y_2,V_x_2,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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != 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_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).

fof(f_3016_2,plain,
    ! [U_11725,U_11724,U_11723] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11723),c_Groups_Ozero__class_Ozero(U_11723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11723),hAPP(hAPP(c_Power_Opower__class_Opower(U_11723),U_11724),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_11723),U_11725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_11725 = c_Groups_Ozero__class_Ozero(U_11723)
            & U_11724 = c_Groups_Ozero__class_Ozero(U_11723) ) )
        & ( U_11725 != c_Groups_Ozero__class_Ozero(U_11723)
          | U_11724 != c_Groups_Ozero__class_Ozero(U_11723)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11723),c_Groups_Ozero__class_Ozero(U_11723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11723),hAPP(hAPP(c_Power_Opower__class_Opower(U_11723),U_11724),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_11723),U_11725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_11723) ),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

cnf(f_3016_3,plain,
    ( U_11725 != c_Groups_Ozero__class_Ozero(U_11723)
    | U_11724 != c_Groups_Ozero__class_Ozero(U_11723)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11723),c_Groups_Ozero__class_Ozero(U_11723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11723),hAPP(hAPP(c_Power_Opower__class_Opower(U_11723),U_11724),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_11723),U_11725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_11723) ),
    inference(clausify,[status(thm)],[f_3016_2]) ).

cnf(f_3016_4,plain,
    ( U_11724 = c_Groups_Ozero__class_Ozero(U_11723)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11723),c_Groups_Ozero__class_Ozero(U_11723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11723),hAPP(hAPP(c_Power_Opower__class_Opower(U_11723),U_11724),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_11723),U_11725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_11723) ),
    inference(clausify,[status(thm)],[f_3016_2]) ).

cnf(f_3016_5,plain,
    ( U_11725 = c_Groups_Ozero__class_Ozero(U_11723)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11723),c_Groups_Ozero__class_Ozero(U_11723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11723),hAPP(hAPP(c_Power_Opower__class_Opower(U_11723),U_11724),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_11723),U_11725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_11723) ),
    inference(clausify,[status(thm)],[f_3016_2]) ).

fof(f_3017_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_3017_2,plain,
    ! [U_11728,U_11727,U_11726] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11726),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11726),hAPP(hAPP(c_Power_Opower__class_Opower(U_11726),U_11727),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_11726),U_11728),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_11726)))
      | ~ class_Rings_Olinordered__idom(U_11726) ),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

cnf(f_3017_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11726),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11726),hAPP(hAPP(c_Power_Opower__class_Opower(U_11726),U_11727),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_11726),U_11728),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_11726)))
    | ~ class_Rings_Olinordered__idom(U_11726) ),
    inference(clausify,[status(thm)],[f_3017_2]) ).

fof(f_3018_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_3018_2,plain,
    ! [U_11731,U_11730,U_11729] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11729),U_11730),U_11731)),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_11729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11729),hAPP(hAPP(c_Power_Opower__class_Opower(U_11729),U_11730),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_11729),U_11731),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_11729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11729),hAPP(c_Int_Onumber__class_Onumber__of(U_11729),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11730)),U_11731))
      | ~ class_Int_Onumber__ring(U_11729) ),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

cnf(f_3018_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11729),U_11730),U_11731)),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_11729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11729),hAPP(hAPP(c_Power_Opower__class_Opower(U_11729),U_11730),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_11729),U_11731),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_11729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11729),hAPP(c_Int_Onumber__class_Onumber__of(U_11729),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11730)),U_11731))
    | ~ class_Int_Onumber__ring(U_11729) ),
    inference(clausify,[status(thm)],[f_3018_2]) ).

fof(f_3019_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_3019_2,plain,
    ! [U_11734,U_11733,U_11732] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11732),c_Groups_Ozero__class_Ozero(U_11732)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11732),U_11733),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_11734))))
      | ~ class_Rings_Olinordered__idom(U_11732) ),
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

cnf(f_3019_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11732),c_Groups_Ozero__class_Ozero(U_11732)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11732),U_11733),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_11734))))
    | ~ class_Rings_Olinordered__idom(U_11732) ),
    inference(clausify,[status(thm)],[f_3019_2]) ).

fof(f_3020_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_3020_2,plain,
    ! [U_11737,U_11736,U_11735] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),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_11737))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11735),U_11736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11735),hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),U_11737)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),U_11737)))
      | ~ class_Rings_Ocomm__semiring__1(U_11735) ),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

cnf(f_3020_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),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_11737))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11735),U_11736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11735),hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),U_11737)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11735),U_11736),U_11737)))
    | ~ class_Rings_Ocomm__semiring__1(U_11735) ),
    inference(clausify,[status(thm)],[f_3020_2]) ).

fof(f_3021_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_3021_2,plain,
    ! [U_11740,U_11739,U_11738] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),U_11739),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_11740))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11738),U_11739),hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),U_11739),U_11740)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_11738) ),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

cnf(f_3021_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),U_11739),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_11740))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11738),U_11739),hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),hAPP(hAPP(c_Power_Opower__class_Opower(U_11738),U_11739),U_11740)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_11738) ),
    inference(clausify,[status(thm)],[f_3021_2]) ).

fof(f_3022_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_3022_2,plain,
    ! [U_11742,U_11741] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11741),hAPP(c_Groups_Ouminus__class_Ouminus(U_11741),c_Groups_Oone__class_Oone(U_11741))),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_11742)) = c_Groups_Oone__class_Oone(U_11741)
      | ~ class_Rings_Oring__1(U_11741) ),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

cnf(f_3022_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11741),hAPP(c_Groups_Ouminus__class_Ouminus(U_11741),c_Groups_Oone__class_Oone(U_11741))),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_11742)) = c_Groups_Oone__class_Oone(U_11741)
    | ~ class_Rings_Oring__1(U_11741) ),
    inference(clausify,[status(thm)],[f_3022_2]) ).

fof(f_3023_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_3023_2,plain,
    ! [U_11744,U_11743] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11744))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11743))) = 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_11744)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11743))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11744))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11743))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11744)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11743))) ) ),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

fof(f_3023_3,plain,
    ( ! [U_11748,U_11746] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11748))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11746))) = 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_11748)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11746))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11746))) )
    & ! [U_11747,U_11745] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11747))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11745))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11747)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11745))) ) ),
    inference(miniscope,[status(thm)],[f_3023_2]) ).

cnf(f_3023_4,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_11747))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11745))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11747)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11745))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11745))) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

cnf(f_3023_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_11748))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11746))) = 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_11748)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11746))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__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_11746))) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

fof(f_3024_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_3024_2,plain,
    ! [U_11749] :
      ( ( 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_11749,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_11749,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_11749,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_11749,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_3024_1]) ).

fof(f_3024_3,plain,
    ( ! [U_11751] :
        ( 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_11751,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_11751,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_11750] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11750,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_11750,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_3024_2]) ).

cnf(f_3024_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11750,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_11750,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_3024_3]) ).

cnf(f_3024_5,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_11751,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_11751,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_3024_3]) ).

fof(f_3025_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_3025_2,plain,
    ! [U_11752] :
      ( 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_11752),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_11752)) ),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

cnf(f_3025_3,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_11752),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_11752)) ),
    inference(clausify,[status(thm)],[f_3025_2]) ).

fof(f_3026_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_3026_2,plain,
    ! [U_11755,U_11754,U_11753] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11753),U_11754),U_11755)),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_11753),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11753),hAPP(hAPP(c_Power_Opower__class_Opower(U_11753),U_11754),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_11753),U_11755),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_11753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11753),hAPP(c_Int_Onumber__class_Onumber__of(U_11753),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11754)),U_11755))
      | ~ class_Int_Onumber__ring(U_11753) ),
    inference(variable_rename,[status(thm)],[f_3026_1]) ).

cnf(f_3026_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11753),U_11754),U_11755)),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_11753),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11753),hAPP(hAPP(c_Power_Opower__class_Opower(U_11753),U_11754),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_11753),U_11755),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_11753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11753),hAPP(c_Int_Onumber__class_Onumber__of(U_11753),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11754)),U_11755))
    | ~ class_Int_Onumber__ring(U_11753) ),
    inference(clausify,[status(thm)],[f_3026_2]) ).

fof(f_3027_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_3027_2,plain,
    ! [U_11758,U_11757,U_11756] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11756),c_Groups_Ozero__class_Ozero(U_11756)),U_11757))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11756),c_Groups_Ozero__class_Ozero(U_11756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11756),U_11757),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_11758)))))
      | ~ class_Rings_Olinordered__idom(U_11756) ),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

cnf(f_3027_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11756),c_Groups_Ozero__class_Ozero(U_11756)),U_11757))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11756),c_Groups_Ozero__class_Ozero(U_11756)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11756),U_11757),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_11758)))))
    | ~ class_Rings_Olinordered__idom(U_11756) ),
    inference(clausify,[status(thm)],[f_3027_2]) ).

fof(f_3028_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_3028_2,plain,
    ! [U_11761,U_11760,U_11759] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11759),hAPP(hAPP(c_Power_Opower__class_Opower(U_11759),U_11760),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_11761)))),c_Groups_Ozero__class_Ozero(U_11759)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11759),U_11760),c_Groups_Ozero__class_Ozero(U_11759)))
      | ~ class_Rings_Olinordered__idom(U_11759) ),
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

cnf(f_3028_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11759),hAPP(hAPP(c_Power_Opower__class_Opower(U_11759),U_11760),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_11761)))),c_Groups_Ozero__class_Ozero(U_11759)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11759),U_11760),c_Groups_Ozero__class_Ozero(U_11759)))
    | ~ class_Rings_Olinordered__idom(U_11759) ),
    inference(clausify,[status(thm)],[f_3028_2]) ).

fof(f_3029_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_3029_2,plain,
    ! [U_11763,U_11762] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11762),hAPP(c_Groups_Ouminus__class_Ouminus(U_11762),c_Groups_Oone__class_Oone(U_11762))),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_11763))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11762),c_Groups_Oone__class_Oone(U_11762))
      | ~ class_Rings_Oring__1(U_11762) ),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

cnf(f_3029_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11762),hAPP(c_Groups_Ouminus__class_Ouminus(U_11762),c_Groups_Oone__class_Oone(U_11762))),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_11763))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11762),c_Groups_Oone__class_Oone(U_11762))
    | ~ class_Rings_Oring__1(U_11762) ),
    inference(clausify,[status(thm)],[f_3029_2]) ).

fof(f_3030_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_3030_2,plain,
    ! [U_11764] :
      ( 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_11764),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_11764)) ),
    inference(variable_rename,[status(thm)],[f_3030_1]) ).

cnf(f_3030_3,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_11764),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_11764)) ),
    inference(clausify,[status(thm)],[f_3030_2]) ).

fof(f_3031_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_3031_2,plain,
    ! [U_11766,U_11765] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),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_11766))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11765),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),hAPP(c_Int_Onat,U_11766))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),hAPP(c_Int_Onat,U_11766)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11766))
      | ~ class_Rings_Osemiring__1(U_11765) ),
    inference(variable_rename,[status(thm)],[f_3031_1]) ).

cnf(f_3031_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),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_11766))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11765),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),hAPP(c_Int_Onat,U_11766))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11765),hAPP(c_Int_Onat,U_11766)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11766))
    | ~ class_Rings_Osemiring__1(U_11765) ),
    inference(clausify,[status(thm)],[f_3031_2]) ).

fof(f_3032_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_3032_2,plain,
    ! [U_11768,U_11767] :
      ( 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_11768)),hAPP(hAPP(c_Groups_Otimes__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_11767)) = 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_11768,U_11767)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11767)) ),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

cnf(f_3032_3,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_11768)),hAPP(hAPP(c_Groups_Otimes__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_11767)) = 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_11768,U_11767)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11767)) ),
    inference(clausify,[status(thm)],[f_3032_2]) ).

fof(f_3033_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_3033_2,plain,
    ! [U_11770,U_11769] :
      ( 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_11770))),hAPP(hAPP(c_Groups_Otimes__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_11769)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11770),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11769)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

cnf(f_3033_3,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_11770))),hAPP(hAPP(c_Groups_Otimes__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_11769)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11770),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11769)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3033_2]) ).

fof(f_3034_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_3034_2,plain,
    ! [U_11772,U_11771] :
      ( 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_11772))),hAPP(hAPP(c_Groups_Otimes__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_11771)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11772),U_11771)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11771)) ),
    inference(variable_rename,[status(thm)],[f_3034_1]) ).

cnf(f_3034_3,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_11772))),hAPP(hAPP(c_Groups_Otimes__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_11771)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11772),U_11771)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11771)) ),
    inference(clausify,[status(thm)],[f_3034_2]) ).

fof(f_3035_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_3035_2,plain,
    ! [U_11773] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_11773) = 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_11773),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_11773,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_11773) = hAPP(hAPP(c_Groups_Otimes__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_11773),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_11773,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_11773 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_11773) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_11773 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

fof(f_3035_3,plain,
    ( ! [U_11775] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_11775) = 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_11775),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_11775,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_11775) = hAPP(hAPP(c_Groups_Otimes__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_11775),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_11775,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_11775 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_11774] :
        ( hAPP(c_Code__Numeral_Oint__of,U_11774) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_11774 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3035_2]) ).

cnf(f_3035_4,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_11774) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_11774 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

cnf(f_3035_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_11775) = hAPP(hAPP(c_Groups_Otimes__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_11775),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_11775,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_11775 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

cnf(f_3035_6,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_11775) = 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_11775),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_11775,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_11775 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

fof(f_3036_1,plain,
    ! [V_k_2,T_a] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),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_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),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_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).

fof(f_3036_2,plain,
    ! [U_11777,U_11776] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_11776),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_11776,U_11776)),tc_fun(tc_Int_Oint,U_11776)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11776,U_11776),U_11776),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_11776,U_11776)),tc_fun(tc_Int_Oint,U_11776)),tc_Int_Oint),c_COMBB(tc_fun(U_11776,U_11776),U_11776,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_11776,tc_fun(tc_fun(U_11776,U_11776),U_11776),tc_Int_Oint),c_HOL_OLet(U_11776,U_11776)),c_Int_Oring__1__class_Oof__int(U_11776)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11776,U_11776),tc_fun(U_11776,U_11776)),hAPP(hAPP(c_COMBB(tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_fun(tc_fun(U_11776,U_11776),tc_fun(U_11776,U_11776)),tc_Int_Oint),c_COMBS(U_11776,U_11776,U_11776)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11776,U_11776),tc_fun(U_11776,tc_fun(U_11776,U_11776))),hAPP(hAPP(c_COMBB(tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_fun(tc_fun(U_11776,U_11776),tc_fun(U_11776,tc_fun(U_11776,U_11776))),tc_Int_Oint),c_COMBB(U_11776,tc_fun(U_11776,U_11776),U_11776)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_Int_Oint),c_If(U_11776)),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_11776,U_11776,U_11776),c_Groups_Oplus__class_Oplus(U_11776)),c_COMBI(U_11776))))),hAPP(hAPP(c_COMBC(U_11776,U_11776,U_11776),hAPP(hAPP(c_COMBB(U_11776,tc_fun(U_11776,U_11776),U_11776),c_Groups_Oplus__class_Oplus(U_11776)),hAPP(hAPP(c_COMBS(U_11776,U_11776,U_11776),c_Groups_Oplus__class_Oplus(U_11776)),c_COMBI(U_11776)))),c_Groups_Oone__class_Oone(U_11776))))),c_Divides_Odivmod__int(U_11777,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_11777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11776),hAPP(c_Int_Oring__1__class_Oof__int(U_11776),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11777)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_11777 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = c_Groups_Ozero__class_Ozero(U_11776)
          | U_11777 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_11776) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

cnf(f_3036_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = c_Groups_Ozero__class_Ozero(U_11776)
    | U_11777 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_11776) ),
    inference(clausify,[status(thm)],[f_3036_2]) ).

cnf(f_3036_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11776),hAPP(c_Int_Oring__1__class_Oof__int(U_11776),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11777)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11777),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_11777 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_11776) ),
    inference(clausify,[status(thm)],[f_3036_2]) ).

cnf(f_3036_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11776),U_11777) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_11776),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_11776,U_11776)),tc_fun(tc_Int_Oint,U_11776)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11776,U_11776),U_11776),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_11776,U_11776)),tc_fun(tc_Int_Oint,U_11776)),tc_Int_Oint),c_COMBB(tc_fun(U_11776,U_11776),U_11776,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_11776,tc_fun(tc_fun(U_11776,U_11776),U_11776),tc_Int_Oint),c_HOL_OLet(U_11776,U_11776)),c_Int_Oring__1__class_Oof__int(U_11776)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11776,U_11776),tc_fun(U_11776,U_11776)),hAPP(hAPP(c_COMBB(tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_fun(tc_fun(U_11776,U_11776),tc_fun(U_11776,U_11776)),tc_Int_Oint),c_COMBS(U_11776,U_11776,U_11776)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11776,U_11776),tc_fun(U_11776,tc_fun(U_11776,U_11776))),hAPP(hAPP(c_COMBB(tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_fun(tc_fun(U_11776,U_11776),tc_fun(U_11776,tc_fun(U_11776,U_11776))),tc_Int_Oint),c_COMBB(U_11776,tc_fun(U_11776,U_11776),U_11776)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11776,tc_fun(U_11776,U_11776)),tc_Int_Oint),c_If(U_11776)),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_11776,U_11776,U_11776),c_Groups_Oplus__class_Oplus(U_11776)),c_COMBI(U_11776))))),hAPP(hAPP(c_COMBC(U_11776,U_11776,U_11776),hAPP(hAPP(c_COMBB(U_11776,tc_fun(U_11776,U_11776),U_11776),c_Groups_Oplus__class_Oplus(U_11776)),hAPP(hAPP(c_COMBS(U_11776,U_11776,U_11776),c_Groups_Oplus__class_Oplus(U_11776)),c_COMBI(U_11776)))),c_Groups_Oone__class_Oone(U_11776))))),c_Divides_Odivmod__int(U_11777,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_11777),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_11777 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_11776) ),
    inference(clausify,[status(thm)],[f_3036_2]) ).

fof(f_3037_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_3037_2,plain,
    ! [U_11779,U_11778] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11778),hAPP(c_Int_Onumber__class_Onumber__of(U_11778),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_11779))) = hAPP(c_Int_Onumber__class_Onumber__of(U_11778),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_11778) ),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

cnf(f_3037_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11778),hAPP(c_Int_Onumber__class_Onumber__of(U_11778),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_11779))) = hAPP(c_Int_Onumber__class_Onumber__of(U_11778),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_11778) ),
    inference(clausify,[status(thm)],[f_3037_2]) ).

fof(f_3038_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_3038_2,plain,
    ! [U_11780] : c_Int_OBit0(U_11780) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

cnf(f_3038_3,plain,
    c_Int_OBit0(U_11780) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_3038_2]) ).

fof(f_3039_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_3039_2,plain,
    ! [U_11781] : c_Int_OMin != c_Int_OBit0(U_11781),
    inference(variable_rename,[status(thm)],[f_3039_1]) ).

cnf(f_3039_3,plain,
    c_Int_OMin != c_Int_OBit0(U_11781),
    inference(clausify,[status(thm)],[f_3039_2]) ).

fof(f_3040_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

cnf(f_3040_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_3040_1]) ).

fof(f_3041_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

cnf(f_3041_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_3041_1]) ).

fof(f_3042_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]) ).

cnf(f_3042_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_3042_1]) ).

fof(f_3043_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]) ).

cnf(f_3043_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(clausify,[status(thm)],[f_3043_1]) ).

fof(f_3044_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]) ).

cnf(f_3044_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_3044_1]) ).

fof(f_3045_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_3045_2,plain,
    ! [U_11782] :
      ( ( c_Int_OBit1(U_11782) = c_Int_OMin
        | U_11782 != c_Int_OMin )
      & ( U_11782 = c_Int_OMin
        | c_Int_OBit1(U_11782) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

fof(f_3045_3,plain,
    ( ! [U_11784] :
        ( c_Int_OBit1(U_11784) = c_Int_OMin
        | U_11784 != c_Int_OMin )
    & ! [U_11783] :
        ( U_11783 = c_Int_OMin
        | c_Int_OBit1(U_11783) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_3045_2]) ).

cnf(f_3045_4,plain,
    ( U_11783 = c_Int_OMin
    | c_Int_OBit1(U_11783) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_3045_3]) ).

cnf(f_3045_5,plain,
    ( c_Int_OBit1(U_11784) = c_Int_OMin
    | U_11784 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_3045_3]) ).

fof(f_3046_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_3046_2,plain,
    ! [U_11785] :
      ( ( c_Int_OMin = c_Int_OBit1(U_11785)
        | c_Int_OMin != U_11785 )
      & ( c_Int_OMin = U_11785
        | c_Int_OMin != c_Int_OBit1(U_11785) ) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

fof(f_3046_3,plain,
    ( ! [U_11787] :
        ( c_Int_OMin = c_Int_OBit1(U_11787)
        | c_Int_OMin != U_11787 )
    & ! [U_11786] :
        ( c_Int_OMin = U_11786
        | c_Int_OMin != c_Int_OBit1(U_11786) ) ),
    inference(miniscope,[status(thm)],[f_3046_2]) ).

cnf(f_3046_4,plain,
    ( c_Int_OMin = U_11786
    | c_Int_OMin != c_Int_OBit1(U_11786) ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

cnf(f_3046_5,plain,
    ( c_Int_OMin = c_Int_OBit1(U_11787)
    | c_Int_OMin != U_11787 ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

fof(f_3047_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

cnf(f_3047_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_3047_1]) ).

fof(f_3048_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]) ).

cnf(f_3048_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(clausify,[status(thm)],[f_3048_1]) ).

fof(f_3049_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]) ).

cnf(f_3049_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_3049_1]) ).

fof(f_3050_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]) ).

cnf(f_3050_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_3050_1]) ).

fof(f_3051_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_3051_2,plain,
    ! [U_11788] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11788)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11788),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11788),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11788)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

fof(f_3051_3,plain,
    ( ! [U_11790] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11790)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11790),c_Int_OMin)) )
    & ! [U_11789] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11789),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11789)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_3051_2]) ).

cnf(f_3051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11789),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11789)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3051_3]) ).

cnf(f_3051_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11790)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11790),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3051_3]) ).

fof(f_3052_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_3052_2,plain,
    ! [U_11791] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11791)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11791)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11791))) ) ),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

fof(f_3052_3,plain,
    ( ! [U_11793] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11793)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11793)) )
    & ! [U_11792] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11792))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11792))) ) ),
    inference(miniscope,[status(thm)],[f_3052_2]) ).

cnf(f_3052_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11792))) ),
    inference(clausify,[status(thm)],[f_3052_3]) ).

cnf(f_3052_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11793)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11793)) ),
    inference(clausify,[status(thm)],[f_3052_3]) ).

fof(f_3053_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]) ).

cnf(f_3053_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_3053_1]) ).

fof(f_3054_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]) ).

cnf(f_3054_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_3054_1]) ).

fof(f_3055_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_3055_2,plain,
    ! [U_11794] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11794)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11794)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11794))) ) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

fof(f_3055_3,plain,
    ( ! [U_11796] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11796)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11796)) )
    & ! [U_11795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11795))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11795))) ) ),
    inference(miniscope,[status(thm)],[f_3055_2]) ).

cnf(f_3055_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11795))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11795))) ),
    inference(clausify,[status(thm)],[f_3055_3]) ).

cnf(f_3055_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11796)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11796)) ),
    inference(clausify,[status(thm)],[f_3055_3]) ).

fof(f_3056_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_3056_2,plain,
    ! [U_11797] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11797)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11797),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11797),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11797)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

fof(f_3056_3,plain,
    ( ! [U_11799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11799)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11799),c_Int_OMin)) )
    & ! [U_11798] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11798),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11798)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_3056_2]) ).

cnf(f_3056_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11798),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11798)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3056_3]) ).

cnf(f_3056_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11799)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11799),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3056_3]) ).

fof(f_3057_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_3057_2,plain,
    ! [U_11800] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11800)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11800),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11800),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11800)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

fof(f_3057_3,plain,
    ( ! [U_11802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11802)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11802),c_Int_OMin)) )
    & ! [U_11801] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11801),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11801)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_3057_2]) ).

cnf(f_3057_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11801),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11801)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3057_3]) ).

cnf(f_3057_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11802)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11802),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3057_3]) ).

fof(f_3058_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_3058_2,plain,
    ! [U_11803] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11803)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11803)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11803))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11803))) ) ),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

fof(f_3058_3,plain,
    ( ! [U_11805] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11805)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11805)) )
    & ! [U_11804] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11804))) ) ),
    inference(miniscope,[status(thm)],[f_3058_2]) ).

cnf(f_3058_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11804))) ),
    inference(clausify,[status(thm)],[f_3058_3]) ).

cnf(f_3058_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11805)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11805)) ),
    inference(clausify,[status(thm)],[f_3058_3]) ).

fof(f_3059_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]) ).

cnf(f_3059_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(clausify,[status(thm)],[f_3059_1]) ).

fof(f_3060_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]) ).

cnf(f_3060_2,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_3060_1]) ).

fof(f_3061_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_3061_2,plain,
    ! [U_11806] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_11806) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11806),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

cnf(f_3061_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_11806) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11806),
    inference(clausify,[status(thm)],[f_3061_2]) ).

fof(f_3062_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]) ).

cnf(f_3062_2,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_3062_1]) ).

fof(f_3063_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

cnf(f_3063_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_3063_1]) ).

fof(f_3064_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_3064_2,plain,
    ! [U_11807] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11807),c_Int_OMin) = c_Int_Opred(U_11807),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

cnf(f_3064_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11807),c_Int_OMin) = c_Int_Opred(U_11807),
    inference(clausify,[status(thm)],[f_3064_2]) ).

fof(f_3065_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_3065_2,plain,
    ! [U_11808] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_11808) = c_Int_Opred(U_11808),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

cnf(f_3065_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_11808) = c_Int_Opred(U_11808),
    inference(clausify,[status(thm)],[f_3065_2]) ).

fof(f_3066_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

cnf(f_3066_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_3066_1]) ).

fof(f_3067_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_3067_2,plain,
    ! [U_11809] :
      ( ~ c_Int_Oiszero(U_11809,hAPP(c_Int_Onumber__class_Onumber__of(U_11809),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_11809) ),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

cnf(f_3067_3,plain,
    ( ~ c_Int_Oiszero(U_11809,hAPP(c_Int_Onumber__class_Onumber__of(U_11809),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_11809) ),
    inference(clausify,[status(thm)],[f_3067_2]) ).

fof(f_3068_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

cnf(f_3068_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_3068_1]) ).

fof(f_3069_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_3069_2,plain,
    ! [U_11810] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11810),c_Int_OMin) = c_Int_Osucc(U_11810),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

cnf(f_3069_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11810),c_Int_OMin) = c_Int_Osucc(U_11810),
    inference(clausify,[status(thm)],[f_3069_2]) ).

fof(f_3070_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_3070_2,plain,
    ! [U_11812,U_11811] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11811),U_11812),hAPP(c_Int_Onumber__class_Onumber__of(U_11811),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11811),U_11812)
      | ~ class_Int_Onumber__ring(U_11811) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

cnf(f_3070_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11811),U_11812),hAPP(c_Int_Onumber__class_Onumber__of(U_11811),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11811),U_11812)
    | ~ class_Int_Onumber__ring(U_11811) ),
    inference(clausify,[status(thm)],[f_3070_2]) ).

fof(f_3071_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_3071_2,plain,
    ! [U_11814,U_11813] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11813),hAPP(c_Int_Onumber__class_Onumber__of(U_11813),c_Int_OMin)),U_11814) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11813),U_11814)
      | ~ class_Int_Onumber__ring(U_11813) ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

cnf(f_3071_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11813),hAPP(c_Int_Onumber__class_Onumber__of(U_11813),c_Int_OMin)),U_11814) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11813),U_11814)
    | ~ class_Int_Onumber__ring(U_11813) ),
    inference(clausify,[status(thm)],[f_3071_2]) ).

fof(f_3072_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_3072_2,plain,
    ! [U_11815] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_11815),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11815),c_Groups_Oone__class_Oone(U_11815))
      | ~ class_Int_Onumber__ring(U_11815) ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

cnf(f_3072_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_11815),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11815),c_Groups_Oone__class_Oone(U_11815))
    | ~ class_Int_Onumber__ring(U_11815) ),
    inference(clausify,[status(thm)],[f_3072_2]) ).

fof(f_3073_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_3073_2,plain,
    ! [U_11816] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11816),c_Groups_Oone__class_Oone(U_11816)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11816),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_11816) ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

cnf(f_3073_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11816),c_Groups_Oone__class_Oone(U_11816)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11816),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_11816) ),
    inference(clausify,[status(thm)],[f_3073_2]) ).

fof(f_3074_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_3074_2,plain,
    ! [U_11817] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_11817),hAPP(c_Int_Onumber__class_Onumber__of(U_11817),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_11817)
      | ~ class_Rings_Olinordered__idom(U_11817)
      | ~ class_Int_Onumber__ring(U_11817) ),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

cnf(f_3074_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_11817),hAPP(c_Int_Onumber__class_Onumber__of(U_11817),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_11817)
    | ~ class_Rings_Olinordered__idom(U_11817)
    | ~ class_Int_Onumber__ring(U_11817) ),
    inference(clausify,[status(thm)],[f_3074_2]) ).

fof(f_3075_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_3075_2,plain,
    ! [U_11819,U_11818] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11818),U_11819),hAPP(c_Int_Onumber__class_Onumber__of(U_11818),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11818),U_11819)
      | ~ class_Int_Onumber__ring(U_11818)
      | ~ class_Fields_Ofield__inverse__zero(U_11818) ),
    inference(variable_rename,[status(thm)],[f_3075_1]) ).

cnf(f_3075_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11818),U_11819),hAPP(c_Int_Onumber__class_Onumber__of(U_11818),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11818),U_11819)
    | ~ class_Int_Onumber__ring(U_11818)
    | ~ class_Fields_Ofield__inverse__zero(U_11818) ),
    inference(clausify,[status(thm)],[f_3075_2]) ).

fof(f_3076_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_3076_2,plain,
    ! [U_11820] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11820)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11820)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11820))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11820))) ) ),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

fof(f_3076_3,plain,
    ( ! [U_11822] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11822)) )
    & ! [U_11821] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11821))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11821))) ) ),
    inference(miniscope,[status(thm)],[f_3076_2]) ).

cnf(f_3076_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11821))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11821))) ),
    inference(clausify,[status(thm)],[f_3076_3]) ).

cnf(f_3076_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11822)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11822)) ),
    inference(clausify,[status(thm)],[f_3076_3]) ).

fof(f_3077_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_3077_2,plain,
    ! [U_11823] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11823)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11823),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11823),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11823)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

fof(f_3077_3,plain,
    ( ! [U_11825] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11825)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11825),c_Int_OMin)) )
    & ! [U_11824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11824),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11824)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_3077_2]) ).

cnf(f_3077_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11824),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11824)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3077_3]) ).

cnf(f_3077_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11825)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11825),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_3077_3]) ).

fof(f_3078_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_3078_2,plain,
    ! [U_11826] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11826,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_3078_1]) ).

cnf(f_3078_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11826,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_3078_2]) ).

fof(f_3079_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_3079_2,plain,
    ! [U_11827] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11827)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11827)),
    inference(variable_rename,[status(thm)],[f_3079_1]) ).

cnf(f_3079_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11827)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11827)),
    inference(clausify,[status(thm)],[f_3079_2]) ).

fof(f_3080_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]) ).

cnf(f_3080_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_3080_1]) ).

fof(f_3081_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_3081_2,plain,
    ! [U_11829,U_11828] :
      ( U_11828 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_11828 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11828),U_11829) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_3081_1]) ).

cnf(f_3081_3,plain,
    ( U_11828 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11828 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11828),U_11829) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3081_2]) ).

fof(f_3082_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_3082_2,plain,
    ! [U_11831,U_11830] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11830),U_11831) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_11831 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_11830 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_11831 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_11830 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_11831 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_11830 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_11831 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_11830 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11830),U_11831) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_3082_1]) ).

fof(f_3082_3,plain,
    ( ! [U_11835,U_11833] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11833),U_11835) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_11835 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_11833 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_11835 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_11833 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_11834,U_11832] :
        ( ( U_11834 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_11832 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_11834 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_11832 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11832),U_11834) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_3082_2]) ).

cnf(f_3082_4,plain,
    ( U_11832 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11832 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11832),U_11834) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_5,plain,
    ( U_11834 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11832 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11832),U_11834) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_6,plain,
    ( U_11832 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11834 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11832),U_11834) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_7,plain,
    ( U_11834 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11834 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11832),U_11834) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_8,plain,
    ( U_11835 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_11833 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11833),U_11835) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

cnf(f_3082_9,plain,
    ( U_11835 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_11833 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11833),U_11835) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

fof(f_3083_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_3083_2,plain,
    ! [U_11836] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11836)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11836)),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

cnf(f_3083_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11836)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11836)),
    inference(clausify,[status(thm)],[f_3083_2]) ).

fof(f_3084_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_3084_2,plain,
    ! [U_11837] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11837)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11837)),
    inference(variable_rename,[status(thm)],[f_3084_1]) ).

cnf(f_3084_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11837)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11837)),
    inference(clausify,[status(thm)],[f_3084_2]) ).

fof(f_3085_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_3085_2,plain,
    ! [U_11838] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_11838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11838),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_11838) ),
    inference(variable_rename,[status(thm)],[f_3085_1]) ).

cnf(f_3085_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11838),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_11838) ),
    inference(clausify,[status(thm)],[f_3085_2]) ).

fof(f_3086_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_3086_2,plain,
    ! [U_11839] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11839),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11839),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

cnf(f_3086_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11839),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11839),
    inference(clausify,[status(thm)],[f_3086_2]) ).

fof(f_3087_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]) ).

cnf(f_3087_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(clausify,[status(thm)],[f_3087_1]) ).

fof(f_3088_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_3088_2,plain,
    ! [U_11841,U_11840] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11840),hAPP(c_Int_Onumber__class_Onumber__of(U_11840),c_Int_OMin)),U_11841) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11840),c_Groups_Oone__class_Oone(U_11840)),U_11841))
      | ~ class_Int_Onumber__ring(U_11840)
      | ~ class_Fields_Ofield__inverse__zero(U_11840) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

cnf(f_3088_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11840),hAPP(c_Int_Onumber__class_Onumber__of(U_11840),c_Int_OMin)),U_11841) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11840),c_Groups_Oone__class_Oone(U_11840)),U_11841))
    | ~ class_Int_Onumber__ring(U_11840)
    | ~ class_Fields_Ofield__inverse__zero(U_11840) ),
    inference(clausify,[status(thm)],[f_3088_2]) ).

fof(f_3089_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_3089_2,plain,
    ! [U_11843,U_11842] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_11842),hAPP(hAPP(c_Power_Opower__class_Opower(U_11842),hAPP(c_Int_Onumber__class_Onumber__of(U_11842),c_Int_OMin)),U_11843)) = c_Groups_Oone__class_Oone(U_11842)
      | ~ class_Rings_Olinordered__idom(U_11842)
      | ~ class_Int_Onumber__ring(U_11842) ),
    inference(variable_rename,[status(thm)],[f_3089_1]) ).

cnf(f_3089_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_11842),hAPP(hAPP(c_Power_Opower__class_Opower(U_11842),hAPP(c_Int_Onumber__class_Onumber__of(U_11842),c_Int_OMin)),U_11843)) = c_Groups_Oone__class_Oone(U_11842)
    | ~ class_Rings_Olinordered__idom(U_11842)
    | ~ class_Int_Onumber__ring(U_11842) ),
    inference(clausify,[status(thm)],[f_3089_2]) ).

fof(f_3090_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_3090_2,plain,
    ! [U_11844] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_11844) = 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_11844)) ),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

cnf(f_3090_3,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_11844) = 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_11844)) ),
    inference(clausify,[status(thm)],[f_3090_2]) ).

fof(f_3091_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_3091_2,plain,
    ! [U_11846,U_11845] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11845),U_11846) = 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_11845),U_11846)),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_11845)) ),
    inference(variable_rename,[status(thm)],[f_3091_1]) ).

cnf(f_3091_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11845),U_11846) = 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_11845),U_11846)),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_11845)) ),
    inference(clausify,[status(thm)],[f_3091_2]) ).

fof(f_3092_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_3092_2,plain,
    ! [U_11847] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11847) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11847),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_11847)) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

cnf(f_3092_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11847) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11847),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_11847)) ),
    inference(clausify,[status(thm)],[f_3092_2]) ).

fof(f_3093_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]) ).

cnf(f_3093_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(clausify,[status(thm)],[f_3093_1]) ).

fof(f_3094_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_3094_2,plain,
    ! [U_11849,U_11848] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11848),hAPP(c_Int_Onumber__class_Onumber__of(U_11848),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_11849)) = c_Groups_Oone__class_Oone(U_11848)
      | ~ class_Int_Onumber__ring(U_11848) ),
    inference(variable_rename,[status(thm)],[f_3094_1]) ).

cnf(f_3094_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_11848),hAPP(c_Int_Onumber__class_Onumber__of(U_11848),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_11849)) = c_Groups_Oone__class_Oone(U_11848)
    | ~ class_Int_Onumber__ring(U_11848) ),
    inference(clausify,[status(thm)],[f_3094_2]) ).

fof(f_3095_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]) ).

cnf(f_3095_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(clausify,[status(thm)],[f_3095_1]) ).

fof(f_3096_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_3096_2,plain,
    ! [U_11850] : c_Int_Oint__ge__less__than(U_11850) = 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_11850)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

cnf(f_3096_3,plain,
    c_Int_Oint__ge__less__than(U_11850) = 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_11850)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3096_2]) ).

fof(f_3097_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_3097_2,plain,
    ! [U_11851] : c_Int_Oint__ge__less__than2(U_11851) = 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_11851)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

cnf(f_3097_3,plain,
    c_Int_Oint__ge__less__than2(U_11851) = 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_11851)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3097_2]) ).

fof(f_3098_1,plain,
    ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__graph]) ).

fof(f_3098_2,plain,
    ! [U_11853,U_11852] : c_Fun_Oinj__on(tc_fun(U_11852,U_11853),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(U_11852,U_11853)),c_Set_OCollect(tc_prod(U_11852,U_11853))),hAPP(hAPP(c_COMBB(tc_fun(U_11852,tc_fun(U_11853,tc_HOL_Obool)),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(U_11852,U_11853)),c_Product__Type_Oprod_Oprod__case(U_11852,U_11853,tc_HOL_Obool)),hAPP(c_COMBB(U_11853,tc_fun(U_11853,tc_HOL_Obool),U_11852),hAPP(c_COMBC(U_11853,U_11853,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11852,U_11853),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

cnf(f_3098_3,plain,
    c_Fun_Oinj__on(tc_fun(U_11852,U_11853),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(U_11852,U_11853)),c_Set_OCollect(tc_prod(U_11852,U_11853))),hAPP(hAPP(c_COMBB(tc_fun(U_11852,tc_fun(U_11853,tc_HOL_Obool)),tc_fun(tc_prod(U_11852,U_11853),tc_HOL_Obool),tc_fun(U_11852,U_11853)),c_Product__Type_Oprod_Oprod__case(U_11852,U_11853,tc_HOL_Obool)),hAPP(c_COMBB(U_11853,tc_fun(U_11853,tc_HOL_Obool),U_11852),hAPP(c_COMBC(U_11853,U_11853,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11852,U_11853),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3098_2]) ).

fof(f_3099_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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_Nitpick_Oprod__def]) ).

fof(f_3099_2,plain,
    ! [U_11857,U_11856,U_11855,U_11854] : c_Nitpick_Oprod(U_11854,U_11855,U_11856,U_11857) = hAPP(c_Set_OCollect(tc_prod(U_11854,U_11855)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11854,U_11855,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11854,tc_fun(U_11855,tc_HOL_Obool),tc_fun(U_11855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11855,tc_HOL_Obool),tc_fun(U_11855,tc_HOL_Obool)),U_11854),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11855)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11854),c_fconj),hAPP(hAPP(c_COMBC(U_11854,tc_fun(U_11854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11854)),U_11856)))),hAPP(hAPP(c_COMBC(U_11855,tc_fun(U_11855,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11855)),U_11857)))),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

cnf(f_3099_3,plain,
    c_Nitpick_Oprod(U_11854,U_11855,U_11856,U_11857) = hAPP(c_Set_OCollect(tc_prod(U_11854,U_11855)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11854,U_11855,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11854,tc_fun(U_11855,tc_HOL_Obool),tc_fun(U_11855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11855,tc_HOL_Obool),tc_fun(U_11855,tc_HOL_Obool)),U_11854),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11855)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11854),c_fconj),hAPP(hAPP(c_COMBC(U_11854,tc_fun(U_11854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11854)),U_11856)))),hAPP(hAPP(c_COMBC(U_11855,tc_fun(U_11855,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11855)),U_11857)))),
    inference(clausify,[status(thm)],[f_3099_2]) ).

fof(f_3100_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_3100_2,plain,
    ! [U_11859,U_11858] :
      ( ( c_Code__Numeral_Onat__of__aux(U_11858,U_11859) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11858),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11859))
        | U_11858 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_11858,U_11859) = U_11859
        | U_11858 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

fof(f_3100_3,plain,
    ( ! [U_11863,U_11861] :
        ( c_Code__Numeral_Onat__of__aux(U_11861,U_11863) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11861),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11863))
        | U_11861 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_11862,U_11860] :
        ( c_Code__Numeral_Onat__of__aux(U_11860,U_11862) = U_11862
        | U_11860 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3100_2]) ).

cnf(f_3100_4,plain,
    ( c_Code__Numeral_Onat__of__aux(U_11860,U_11862) = U_11862
    | U_11860 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

cnf(f_3100_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_11861,U_11863) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11861),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11863))
    | U_11861 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

fof(f_3101_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_3101_2,plain,
    ! [U_11865,U_11864] : c_Divides_Odivmod__int__rel(U_11864,U_11865) = 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_11864))),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_11865)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))))),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_11865)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))),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_3101_1]) ).

cnf(f_3101_3,plain,
    c_Divides_Odivmod__int__rel(U_11864,U_11865) = 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_11864))),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_11865)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))))),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_11865)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,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_11865))),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_3101_2]) ).

fof(f_3102_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_3102_2,plain,
    ! [U_11867,U_11866] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11867,U_11866),c_Divides_Odivmod__int(U_11867,U_11866)))
      | U_11866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

cnf(f_3102_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11867,U_11866),c_Divides_Odivmod__int(U_11867,U_11866)))
    | U_11866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3102_2]) ).

fof(f_3103_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_3103_2,plain,
    ! [U_11872,U_11871,U_11870,U_11869,U_11868] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11869),U_11872)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11870),U_11872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11869),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11870,U_11872))),U_11871))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11872))
      | U_11869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11868,U_11869),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11870),U_11871))) ),
    inference(variable_rename,[status(thm)],[f_3103_1]) ).

cnf(f_3103_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11869),U_11872)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11870),U_11872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11869),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11870,U_11872))),U_11871))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11872))
    | U_11869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11868,U_11869),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11870),U_11871))) ),
    inference(clausify,[status(thm)],[f_3103_2]) ).

fof(f_3104_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]) ).

cnf(f_3104_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(clausify,[status(thm)],[f_3104_1]) ).

fof(f_3105_1,plain,
    ! [V_w_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).

fof(f_3105_2,plain,
    ! [U_11874,U_11873] :
      ( hBOOL(hAPP(hAPP(c_member(U_11873),hAPP(c_Int_Onumber__class_Onumber__of(U_11873),U_11874)),c_Nat_Osemiring__1__class_ONats(U_11873)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11874))
      | ~ class_Int_Onumber__ring(U_11873) ),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

cnf(f_3105_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11873),hAPP(c_Int_Onumber__class_Onumber__of(U_11873),U_11874)),c_Nat_Osemiring__1__class_ONats(U_11873)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11874))
    | ~ class_Int_Onumber__ring(U_11873) ),
    inference(clausify,[status(thm)],[f_3105_2]) ).

fof(f_3106_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).

fof(f_3106_2,plain,
    ! [U_11880,U_11879,U_11878,U_11877,U_11876,U_11875] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11875,tc_fun(U_11876,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11875,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),U_11875),c_COMBC(U_11876,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_prod(U_11875,U_11876)),tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),U_11875),hAPP(c_COMBB(tc_prod(U_11875,U_11876),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool),U_11876),c_member(tc_prod(U_11875,U_11876)))),c_Product__Type_OPair(U_11875,U_11876)))),U_11877)),hAPP(hAPP(c_COMBC(U_11875,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),U_11875),c_COMBC(U_11876,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_prod(U_11875,U_11876)),tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),U_11875),hAPP(c_COMBB(tc_prod(U_11875,U_11876),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool),U_11876),c_member(tc_prod(U_11875,U_11876)))),c_Product__Type_OPair(U_11875,U_11876)))),U_11878)),U_11879),U_11880))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11875,U_11876)),hAPP(hAPP(c_Product__Type_OPair(U_11875,U_11876),U_11879),U_11880)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool)),U_11877),U_11878))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11875,U_11876)),hAPP(hAPP(c_Product__Type_OPair(U_11875,U_11876),U_11879),U_11880)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool)),U_11877),U_11878)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11875,tc_fun(U_11876,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11875,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),U_11875),c_COMBC(U_11876,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_prod(U_11875,U_11876)),tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),U_11875),hAPP(c_COMBB(tc_prod(U_11875,U_11876),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool),U_11876),c_member(tc_prod(U_11875,U_11876)))),c_Product__Type_OPair(U_11875,U_11876)))),U_11877)),hAPP(hAPP(c_COMBC(U_11875,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_fun(U_11876,tc_HOL_Obool)),U_11875),c_COMBC(U_11876,tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11876,tc_prod(U_11875,U_11876)),tc_fun(U_11876,tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool)),U_11875),hAPP(c_COMBB(tc_prod(U_11875,U_11876),tc_fun(tc_fun(tc_prod(U_11875,U_11876),tc_HOL_Obool),tc_HOL_Obool),U_11876),c_member(tc_prod(U_11875,U_11876)))),c_Product__Type_OPair(U_11875,U_11876)))),U_11878)),U_11879),U_11880)) ) ),
    inference(variable_rename,[status(thm)],[f_3106_1]) ).

fof(f_3106_3,plain,
    ( ! [U_11892,U_11890,U_11888,U_11886,U_11884,U_11882] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11882,tc_fun(U_11884,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11882,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),U_11882),c_COMBC(U_11884,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_prod(U_11882,U_11884)),tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),U_11882),hAPP(c_COMBB(tc_prod(U_11882,U_11884),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool),U_11884),c_member(tc_prod(U_11882,U_11884)))),c_Product__Type_OPair(U_11882,U_11884)))),U_11886)),hAPP(hAPP(c_COMBC(U_11882,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),U_11882),c_COMBC(U_11884,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_prod(U_11882,U_11884)),tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),U_11882),hAPP(c_COMBB(tc_prod(U_11882,U_11884),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool),U_11884),c_member(tc_prod(U_11882,U_11884)))),c_Product__Type_OPair(U_11882,U_11884)))),U_11888)),U_11890),U_11892))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11882,U_11884)),hAPP(hAPP(c_Product__Type_OPair(U_11882,U_11884),U_11890),U_11892)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool)),U_11886),U_11888))) )
    & ! [U_11891,U_11889,U_11887,U_11885,U_11883,U_11881] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11881,U_11883)),hAPP(hAPP(c_Product__Type_OPair(U_11881,U_11883),U_11889),U_11891)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool)),U_11885),U_11887)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11881,tc_fun(U_11883,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11881,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),U_11881),c_COMBC(U_11883,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_prod(U_11881,U_11883)),tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),U_11881),hAPP(c_COMBB(tc_prod(U_11881,U_11883),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool),U_11883),c_member(tc_prod(U_11881,U_11883)))),c_Product__Type_OPair(U_11881,U_11883)))),U_11885)),hAPP(hAPP(c_COMBC(U_11881,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),U_11881),c_COMBC(U_11883,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_prod(U_11881,U_11883)),tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),U_11881),hAPP(c_COMBB(tc_prod(U_11881,U_11883),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool),U_11883),c_member(tc_prod(U_11881,U_11883)))),c_Product__Type_OPair(U_11881,U_11883)))),U_11887)),U_11889),U_11891)) ) ),
    inference(miniscope,[status(thm)],[f_3106_2]) ).

cnf(f_3106_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11881,U_11883)),hAPP(hAPP(c_Product__Type_OPair(U_11881,U_11883),U_11889),U_11891)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool)),U_11885),U_11887)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11881,tc_fun(U_11883,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11881,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),U_11881),c_COMBC(U_11883,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_prod(U_11881,U_11883)),tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),U_11881),hAPP(c_COMBB(tc_prod(U_11881,U_11883),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool),U_11883),c_member(tc_prod(U_11881,U_11883)))),c_Product__Type_OPair(U_11881,U_11883)))),U_11885)),hAPP(hAPP(c_COMBC(U_11881,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_fun(U_11883,tc_HOL_Obool)),U_11881),c_COMBC(U_11883,tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11883,tc_prod(U_11881,U_11883)),tc_fun(U_11883,tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool)),U_11881),hAPP(c_COMBB(tc_prod(U_11881,U_11883),tc_fun(tc_fun(tc_prod(U_11881,U_11883),tc_HOL_Obool),tc_HOL_Obool),U_11883),c_member(tc_prod(U_11881,U_11883)))),c_Product__Type_OPair(U_11881,U_11883)))),U_11887)),U_11889),U_11891)) ),
    inference(clausify,[status(thm)],[f_3106_3]) ).

cnf(f_3106_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11882,tc_fun(U_11884,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11882,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),U_11882),c_COMBC(U_11884,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_prod(U_11882,U_11884)),tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),U_11882),hAPP(c_COMBB(tc_prod(U_11882,U_11884),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool),U_11884),c_member(tc_prod(U_11882,U_11884)))),c_Product__Type_OPair(U_11882,U_11884)))),U_11886)),hAPP(hAPP(c_COMBC(U_11882,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_fun(U_11884,tc_HOL_Obool)),U_11882),c_COMBC(U_11884,tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11884,tc_prod(U_11882,U_11884)),tc_fun(U_11884,tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool)),U_11882),hAPP(c_COMBB(tc_prod(U_11882,U_11884),tc_fun(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool),tc_HOL_Obool),U_11884),c_member(tc_prod(U_11882,U_11884)))),c_Product__Type_OPair(U_11882,U_11884)))),U_11888)),U_11890),U_11892))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11882,U_11884)),hAPP(hAPP(c_Product__Type_OPair(U_11882,U_11884),U_11890),U_11892)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11882,U_11884),tc_HOL_Obool)),U_11886),U_11888))) ),
    inference(clausify,[status(thm)],[f_3106_3]) ).

fof(f_3107_1,plain,
    ! [V_y_2,V_x_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).

fof(f_3107_2,plain,
    ! [U_11896,U_11895,U_11894,U_11893] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11893,tc_fun(U_11894,tc_HOL_Obool))),U_11895),U_11896))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11893,U_11894)),hAPP(hAPP(c_Product__Type_OPair(U_11893,U_11894),U_11895),U_11896)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11893,U_11894),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11893,U_11894)),hAPP(hAPP(c_Product__Type_OPair(U_11893,U_11894),U_11895),U_11896)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11893,U_11894),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11893,tc_fun(U_11894,tc_HOL_Obool))),U_11895),U_11896)) ) ),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

fof(f_3107_3,plain,
    ( ! [U_11904,U_11902,U_11900,U_11898] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11898,tc_fun(U_11900,tc_HOL_Obool))),U_11902),U_11904))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11898,U_11900)),hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11900),U_11902),U_11904)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11898,U_11900),tc_HOL_Obool)))) )
    & ! [U_11903,U_11901,U_11899,U_11897] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11897,U_11899)),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11899),U_11901),U_11903)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11897,U_11899),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11897,tc_fun(U_11899,tc_HOL_Obool))),U_11901),U_11903)) ) ),
    inference(miniscope,[status(thm)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11897,U_11899)),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11899),U_11901),U_11903)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11897,U_11899),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11897,tc_fun(U_11899,tc_HOL_Obool))),U_11901),U_11903)) ),
    inference(clausify,[status(thm)],[f_3107_3]) ).

cnf(f_3107_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11898,tc_fun(U_11900,tc_HOL_Obool))),U_11902),U_11904))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11898,U_11900)),hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11900),U_11902),U_11904)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11898,U_11900),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3107_3]) ).

fof(f_3108_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).

fof(f_3108_2,plain,
    ! [U_11910,U_11909,U_11908,U_11907,U_11906,U_11905] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11905,tc_fun(U_11906,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11905,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),U_11905),c_COMBC(U_11906,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_prod(U_11905,U_11906)),tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),U_11905),hAPP(c_COMBB(tc_prod(U_11905,U_11906),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool),U_11906),c_member(tc_prod(U_11905,U_11906)))),c_Product__Type_OPair(U_11905,U_11906)))),U_11907)),hAPP(hAPP(c_COMBC(U_11905,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),U_11905),c_COMBC(U_11906,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_prod(U_11905,U_11906)),tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),U_11905),hAPP(c_COMBB(tc_prod(U_11905,U_11906),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool),U_11906),c_member(tc_prod(U_11905,U_11906)))),c_Product__Type_OPair(U_11905,U_11906)))),U_11908)),U_11909),U_11910))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11905,U_11906)),hAPP(hAPP(c_Product__Type_OPair(U_11905,U_11906),U_11909),U_11910)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool)),U_11907),U_11908))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11905,U_11906)),hAPP(hAPP(c_Product__Type_OPair(U_11905,U_11906),U_11909),U_11910)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool)),U_11907),U_11908)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11905,tc_fun(U_11906,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11905,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),U_11905),c_COMBC(U_11906,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_prod(U_11905,U_11906)),tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),U_11905),hAPP(c_COMBB(tc_prod(U_11905,U_11906),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool),U_11906),c_member(tc_prod(U_11905,U_11906)))),c_Product__Type_OPair(U_11905,U_11906)))),U_11907)),hAPP(hAPP(c_COMBC(U_11905,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_fun(U_11906,tc_HOL_Obool)),U_11905),c_COMBC(U_11906,tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11906,tc_prod(U_11905,U_11906)),tc_fun(U_11906,tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool)),U_11905),hAPP(c_COMBB(tc_prod(U_11905,U_11906),tc_fun(tc_fun(tc_prod(U_11905,U_11906),tc_HOL_Obool),tc_HOL_Obool),U_11906),c_member(tc_prod(U_11905,U_11906)))),c_Product__Type_OPair(U_11905,U_11906)))),U_11908)),U_11909),U_11910)) ) ),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

fof(f_3108_3,plain,
    ( ! [U_11922,U_11920,U_11918,U_11916,U_11914,U_11912] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11912,tc_fun(U_11914,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11912,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),U_11912),c_COMBC(U_11914,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_prod(U_11912,U_11914)),tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),U_11912),hAPP(c_COMBB(tc_prod(U_11912,U_11914),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool),U_11914),c_member(tc_prod(U_11912,U_11914)))),c_Product__Type_OPair(U_11912,U_11914)))),U_11916)),hAPP(hAPP(c_COMBC(U_11912,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),U_11912),c_COMBC(U_11914,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_prod(U_11912,U_11914)),tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),U_11912),hAPP(c_COMBB(tc_prod(U_11912,U_11914),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool),U_11914),c_member(tc_prod(U_11912,U_11914)))),c_Product__Type_OPair(U_11912,U_11914)))),U_11918)),U_11920),U_11922))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11912,U_11914)),hAPP(hAPP(c_Product__Type_OPair(U_11912,U_11914),U_11920),U_11922)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool)),U_11916),U_11918))) )
    & ! [U_11921,U_11919,U_11917,U_11915,U_11913,U_11911] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11911,U_11913)),hAPP(hAPP(c_Product__Type_OPair(U_11911,U_11913),U_11919),U_11921)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool)),U_11915),U_11917)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11911,tc_fun(U_11913,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11911,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),U_11911),c_COMBC(U_11913,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_prod(U_11911,U_11913)),tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),U_11911),hAPP(c_COMBB(tc_prod(U_11911,U_11913),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool),U_11913),c_member(tc_prod(U_11911,U_11913)))),c_Product__Type_OPair(U_11911,U_11913)))),U_11915)),hAPP(hAPP(c_COMBC(U_11911,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),U_11911),c_COMBC(U_11913,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_prod(U_11911,U_11913)),tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),U_11911),hAPP(c_COMBB(tc_prod(U_11911,U_11913),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool),U_11913),c_member(tc_prod(U_11911,U_11913)))),c_Product__Type_OPair(U_11911,U_11913)))),U_11917)),U_11919),U_11921)) ) ),
    inference(miniscope,[status(thm)],[f_3108_2]) ).

cnf(f_3108_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11911,U_11913)),hAPP(hAPP(c_Product__Type_OPair(U_11911,U_11913),U_11919),U_11921)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool)),U_11915),U_11917)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11911,tc_fun(U_11913,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11911,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),U_11911),c_COMBC(U_11913,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_prod(U_11911,U_11913)),tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),U_11911),hAPP(c_COMBB(tc_prod(U_11911,U_11913),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool),U_11913),c_member(tc_prod(U_11911,U_11913)))),c_Product__Type_OPair(U_11911,U_11913)))),U_11915)),hAPP(hAPP(c_COMBC(U_11911,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_fun(U_11913,tc_HOL_Obool)),U_11911),c_COMBC(U_11913,tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11913,tc_prod(U_11911,U_11913)),tc_fun(U_11913,tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool)),U_11911),hAPP(c_COMBB(tc_prod(U_11911,U_11913),tc_fun(tc_fun(tc_prod(U_11911,U_11913),tc_HOL_Obool),tc_HOL_Obool),U_11913),c_member(tc_prod(U_11911,U_11913)))),c_Product__Type_OPair(U_11911,U_11913)))),U_11917)),U_11919),U_11921)) ),
    inference(clausify,[status(thm)],[f_3108_3]) ).

cnf(f_3108_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11912,tc_fun(U_11914,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11912,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),U_11912),c_COMBC(U_11914,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_prod(U_11912,U_11914)),tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),U_11912),hAPP(c_COMBB(tc_prod(U_11912,U_11914),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool),U_11914),c_member(tc_prod(U_11912,U_11914)))),c_Product__Type_OPair(U_11912,U_11914)))),U_11916)),hAPP(hAPP(c_COMBC(U_11912,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_fun(U_11914,tc_HOL_Obool)),U_11912),c_COMBC(U_11914,tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11914,tc_prod(U_11912,U_11914)),tc_fun(U_11914,tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool)),U_11912),hAPP(c_COMBB(tc_prod(U_11912,U_11914),tc_fun(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool),tc_HOL_Obool),U_11914),c_member(tc_prod(U_11912,U_11914)))),c_Product__Type_OPair(U_11912,U_11914)))),U_11918)),U_11920),U_11922))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11912,U_11914)),hAPP(hAPP(c_Product__Type_OPair(U_11912,U_11914),U_11920),U_11922)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11912,U_11914),tc_HOL_Obool)),U_11916),U_11918))) ),
    inference(clausify,[status(thm)],[f_3108_3]) ).

fof(f_3109_1,plain,
    ! [V_S_2,V_R_2,T_b,T_a] :
      ( ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) != hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).

fof(f_3109_2,plain,
    ! [U_11926,U_11925,U_11924,U_11923] :
      ( ( hAPP(hAPP(c_COMBC(U_11923,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),U_11923),c_COMBC(U_11924,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_prod(U_11923,U_11924)),tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),U_11923),hAPP(c_COMBB(tc_prod(U_11923,U_11924),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool),U_11924),c_member(tc_prod(U_11923,U_11924)))),c_Product__Type_OPair(U_11923,U_11924)))),U_11925) = hAPP(hAPP(c_COMBC(U_11923,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),U_11923),c_COMBC(U_11924,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_prod(U_11923,U_11924)),tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),U_11923),hAPP(c_COMBB(tc_prod(U_11923,U_11924),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool),U_11924),c_member(tc_prod(U_11923,U_11924)))),c_Product__Type_OPair(U_11923,U_11924)))),U_11926)
        | U_11925 != U_11926 )
      & ( U_11925 = U_11926
        | hAPP(hAPP(c_COMBC(U_11923,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),U_11923),c_COMBC(U_11924,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_prod(U_11923,U_11924)),tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),U_11923),hAPP(c_COMBB(tc_prod(U_11923,U_11924),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool),U_11924),c_member(tc_prod(U_11923,U_11924)))),c_Product__Type_OPair(U_11923,U_11924)))),U_11925) != hAPP(hAPP(c_COMBC(U_11923,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_fun(U_11924,tc_HOL_Obool)),U_11923),c_COMBC(U_11924,tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11924,tc_prod(U_11923,U_11924)),tc_fun(U_11924,tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool)),U_11923),hAPP(c_COMBB(tc_prod(U_11923,U_11924),tc_fun(tc_fun(tc_prod(U_11923,U_11924),tc_HOL_Obool),tc_HOL_Obool),U_11924),c_member(tc_prod(U_11923,U_11924)))),c_Product__Type_OPair(U_11923,U_11924)))),U_11926) ) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

fof(f_3109_3,plain,
    ( ! [U_11934,U_11932] :
        ( ! [U_11930,U_11928] : hAPP(hAPP(c_COMBC(U_11928,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),U_11928),c_COMBC(U_11930,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_prod(U_11928,U_11930)),tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),U_11928),hAPP(c_COMBB(tc_prod(U_11928,U_11930),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool),U_11930),c_member(tc_prod(U_11928,U_11930)))),c_Product__Type_OPair(U_11928,U_11930)))),U_11932) = hAPP(hAPP(c_COMBC(U_11928,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),U_11928),c_COMBC(U_11930,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_prod(U_11928,U_11930)),tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),U_11928),hAPP(c_COMBB(tc_prod(U_11928,U_11930),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool),U_11930),c_member(tc_prod(U_11928,U_11930)))),c_Product__Type_OPair(U_11928,U_11930)))),U_11934)
        | U_11932 != U_11934 )
    & ! [U_11933,U_11931] :
        ( ! [U_11929,U_11927] : hAPP(hAPP(c_COMBC(U_11927,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),U_11927),c_COMBC(U_11929,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_prod(U_11927,U_11929)),tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),U_11927),hAPP(c_COMBB(tc_prod(U_11927,U_11929),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool),U_11929),c_member(tc_prod(U_11927,U_11929)))),c_Product__Type_OPair(U_11927,U_11929)))),U_11931) != hAPP(hAPP(c_COMBC(U_11927,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),U_11927),c_COMBC(U_11929,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_prod(U_11927,U_11929)),tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),U_11927),hAPP(c_COMBB(tc_prod(U_11927,U_11929),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool),U_11929),c_member(tc_prod(U_11927,U_11929)))),c_Product__Type_OPair(U_11927,U_11929)))),U_11933)
        | U_11931 = U_11933 ) ),
    inference(miniscope,[status(thm)],[f_3109_2]) ).

cnf(f_3109_4,plain,
    ( hAPP(hAPP(c_COMBC(U_11927,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),U_11927),c_COMBC(U_11929,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_prod(U_11927,U_11929)),tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),U_11927),hAPP(c_COMBB(tc_prod(U_11927,U_11929),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool),U_11929),c_member(tc_prod(U_11927,U_11929)))),c_Product__Type_OPair(U_11927,U_11929)))),U_11931) != hAPP(hAPP(c_COMBC(U_11927,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_fun(U_11929,tc_HOL_Obool)),U_11927),c_COMBC(U_11929,tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11929,tc_prod(U_11927,U_11929)),tc_fun(U_11929,tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool)),U_11927),hAPP(c_COMBB(tc_prod(U_11927,U_11929),tc_fun(tc_fun(tc_prod(U_11927,U_11929),tc_HOL_Obool),tc_HOL_Obool),U_11929),c_member(tc_prod(U_11927,U_11929)))),c_Product__Type_OPair(U_11927,U_11929)))),U_11933)
    | U_11931 = U_11933 ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

cnf(f_3109_5,plain,
    ( hAPP(hAPP(c_COMBC(U_11928,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),U_11928),c_COMBC(U_11930,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_prod(U_11928,U_11930)),tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),U_11928),hAPP(c_COMBB(tc_prod(U_11928,U_11930),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool),U_11930),c_member(tc_prod(U_11928,U_11930)))),c_Product__Type_OPair(U_11928,U_11930)))),U_11932) = hAPP(hAPP(c_COMBC(U_11928,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_fun(U_11930,tc_HOL_Obool)),U_11928),c_COMBC(U_11930,tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11930,tc_prod(U_11928,U_11930)),tc_fun(U_11930,tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool)),U_11928),hAPP(c_COMBB(tc_prod(U_11928,U_11930),tc_fun(tc_fun(tc_prod(U_11928,U_11930),tc_HOL_Obool),tc_HOL_Obool),U_11930),c_member(tc_prod(U_11928,U_11930)))),c_Product__Type_OPair(U_11928,U_11930)))),U_11934)
    | U_11932 != U_11934 ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

fof(f_3110_1,plain,
    ! [V_S_2,V_R_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).

fof(f_3110_2,plain,
    ! [U_11938,U_11937,U_11936,U_11935] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11935,tc_fun(U_11936,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11935,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),U_11935),c_COMBC(U_11936,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_prod(U_11935,U_11936)),tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),U_11935),hAPP(c_COMBB(tc_prod(U_11935,U_11936),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool),U_11936),c_member(tc_prod(U_11935,U_11936)))),c_Product__Type_OPair(U_11935,U_11936)))),U_11937)),hAPP(hAPP(c_COMBC(U_11935,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),U_11935),c_COMBC(U_11936,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_prod(U_11935,U_11936)),tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),U_11935),hAPP(c_COMBB(tc_prod(U_11935,U_11936),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool),U_11936),c_member(tc_prod(U_11935,U_11936)))),c_Product__Type_OPair(U_11935,U_11936)))),U_11938)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool)),U_11937),U_11938)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool)),U_11937),U_11938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11935,tc_fun(U_11936,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11935,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),U_11935),c_COMBC(U_11936,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_prod(U_11935,U_11936)),tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),U_11935),hAPP(c_COMBB(tc_prod(U_11935,U_11936),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool),U_11936),c_member(tc_prod(U_11935,U_11936)))),c_Product__Type_OPair(U_11935,U_11936)))),U_11937)),hAPP(hAPP(c_COMBC(U_11935,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_fun(U_11936,tc_HOL_Obool)),U_11935),c_COMBC(U_11936,tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11936,tc_prod(U_11935,U_11936)),tc_fun(U_11936,tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool)),U_11935),hAPP(c_COMBB(tc_prod(U_11935,U_11936),tc_fun(tc_fun(tc_prod(U_11935,U_11936),tc_HOL_Obool),tc_HOL_Obool),U_11936),c_member(tc_prod(U_11935,U_11936)))),c_Product__Type_OPair(U_11935,U_11936)))),U_11938))) ) ),
    inference(variable_rename,[status(thm)],[f_3110_1]) ).

fof(f_3110_3,plain,
    ( ! [U_11946,U_11944,U_11942,U_11940] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11940,tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11940,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11940),c_COMBC(U_11942,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_prod(U_11940,U_11942)),tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),U_11940),hAPP(c_COMBB(tc_prod(U_11940,U_11942),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool),U_11942),c_member(tc_prod(U_11940,U_11942)))),c_Product__Type_OPair(U_11940,U_11942)))),U_11944)),hAPP(hAPP(c_COMBC(U_11940,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11940),c_COMBC(U_11942,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_prod(U_11940,U_11942)),tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),U_11940),hAPP(c_COMBB(tc_prod(U_11940,U_11942),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool),U_11942),c_member(tc_prod(U_11940,U_11942)))),c_Product__Type_OPair(U_11940,U_11942)))),U_11946)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool)),U_11944),U_11946)) )
    & ! [U_11945,U_11943,U_11941,U_11939] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool)),U_11943),U_11945))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11939,tc_fun(U_11941,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11939,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),U_11939),c_COMBC(U_11941,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_prod(U_11939,U_11941)),tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),U_11939),hAPP(c_COMBB(tc_prod(U_11939,U_11941),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool),U_11941),c_member(tc_prod(U_11939,U_11941)))),c_Product__Type_OPair(U_11939,U_11941)))),U_11943)),hAPP(hAPP(c_COMBC(U_11939,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),U_11939),c_COMBC(U_11941,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_prod(U_11939,U_11941)),tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),U_11939),hAPP(c_COMBB(tc_prod(U_11939,U_11941),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool),U_11941),c_member(tc_prod(U_11939,U_11941)))),c_Product__Type_OPair(U_11939,U_11941)))),U_11945))) ) ),
    inference(miniscope,[status(thm)],[f_3110_2]) ).

cnf(f_3110_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool)),U_11943),U_11945))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11939,tc_fun(U_11941,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11939,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),U_11939),c_COMBC(U_11941,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_prod(U_11939,U_11941)),tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),U_11939),hAPP(c_COMBB(tc_prod(U_11939,U_11941),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool),U_11941),c_member(tc_prod(U_11939,U_11941)))),c_Product__Type_OPair(U_11939,U_11941)))),U_11943)),hAPP(hAPP(c_COMBC(U_11939,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_fun(U_11941,tc_HOL_Obool)),U_11939),c_COMBC(U_11941,tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11941,tc_prod(U_11939,U_11941)),tc_fun(U_11941,tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool)),U_11939),hAPP(c_COMBB(tc_prod(U_11939,U_11941),tc_fun(tc_fun(tc_prod(U_11939,U_11941),tc_HOL_Obool),tc_HOL_Obool),U_11941),c_member(tc_prod(U_11939,U_11941)))),c_Product__Type_OPair(U_11939,U_11941)))),U_11945))) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

cnf(f_3110_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11940,tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11940,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11940),c_COMBC(U_11942,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_prod(U_11940,U_11942)),tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),U_11940),hAPP(c_COMBB(tc_prod(U_11940,U_11942),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool),U_11942),c_member(tc_prod(U_11940,U_11942)))),c_Product__Type_OPair(U_11940,U_11942)))),U_11944)),hAPP(hAPP(c_COMBC(U_11940,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11940),c_COMBC(U_11942,tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11942,tc_prod(U_11940,U_11942)),tc_fun(U_11942,tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool)),U_11940),hAPP(c_COMBB(tc_prod(U_11940,U_11942),tc_fun(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool),tc_HOL_Obool),U_11942),c_member(tc_prod(U_11940,U_11942)))),c_Product__Type_OPair(U_11940,U_11942)))),U_11946)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11940,U_11942),tc_HOL_Obool)),U_11944),U_11946)) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

fof(f_3111_1,plain,
    ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).

fof(f_3111_2,plain,
    ! [U_11952,U_11951,U_11950,U_11949,U_11948,U_11947] :
      ( hBOOL(hAPP(hAPP(c_member(U_11950),U_11951),hAPP(c_Relation_OImage(U_11947,U_11950,U_11952),U_11949)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11947,U_11950)),hAPP(hAPP(c_Product__Type_OPair(U_11947,U_11950),U_11948),U_11951)),U_11952))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11947),U_11948),U_11949)) ),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

cnf(f_3111_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11950),U_11951),hAPP(c_Relation_OImage(U_11947,U_11950,U_11952),U_11949)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11947,U_11950)),hAPP(hAPP(c_Product__Type_OPair(U_11947,U_11950),U_11948),U_11951)),U_11952))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11947),U_11948),U_11949)) ),
    inference(clausify,[status(thm)],[f_3111_2]) ).

fof(f_3112_1,plain,
    ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).

fof(f_3112_2,plain,
    ! [U_11959,U_11958,U_11957,U_11956,U_11955] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11955),U_11956),hAPP(c_Relation_OImage(U_11957,U_11955,U_11958),U_11959)))
        | ! [U_11954] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11957,U_11955)),hAPP(hAPP(c_Product__Type_OPair(U_11957,U_11955),U_11954),U_11956)),U_11958))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11957),U_11954),U_11959)) ) )
      & ( ? [U_11953] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11957,U_11955)),hAPP(hAPP(c_Product__Type_OPair(U_11957,U_11955),U_11953),U_11956)),U_11958))
            & hBOOL(hAPP(hAPP(c_member(U_11957),U_11953),U_11959)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11955),U_11956),hAPP(c_Relation_OImage(U_11957,U_11955,U_11958),U_11959))) ) ),
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

fof(f_3112_3,plain,
    ( ! [U_11969,U_11967,U_11965,U_11963,U_11961] :
        ( hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),hAPP(c_Relation_OImage(U_11965,U_11961,U_11967),U_11969)))
        | ! [U_11954] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11961)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11961),U_11954),U_11963)),U_11967))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11954),U_11969)) ) )
    & ! [U_11968,U_11966,U_11964,U_11962,U_11960] :
        ( ? [U_11953] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11964,U_11960)),hAPP(hAPP(c_Product__Type_OPair(U_11964,U_11960),U_11953),U_11962)),U_11966))
            & hBOOL(hAPP(hAPP(c_member(U_11964),U_11953),U_11968)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),hAPP(c_Relation_OImage(U_11964,U_11960,U_11966),U_11968))) ) ),
    inference(miniscope,[status(thm)],[f_3112_2]) ).

fof(f_3112_4,plain,
    ( ! [U_11969,U_11967,U_11965,U_11963,U_11961] :
        ( hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),hAPP(c_Relation_OImage(U_11965,U_11961,U_11967),U_11969)))
        | ! [U_11954] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11961)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11961),U_11954),U_11963)),U_11967))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11954),U_11969)) ) )
    & ! [U_11968,U_11966,U_11964,U_11962,U_11960] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11964,U_11960)),hAPP(hAPP(c_Product__Type_OPair(U_11964,U_11960),sK284(U_11968,U_11966,U_11964,U_11962,U_11960)),U_11962)),U_11966))
          & hBOOL(hAPP(hAPP(c_member(U_11964),sK284(U_11968,U_11966,U_11964,U_11962,U_11960)),U_11968)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),hAPP(c_Relation_OImage(U_11964,U_11960,U_11966),U_11968))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_11953,sK284(U_11968,U_11966,U_11964,U_11962,U_11960))],[f_3112_3]) ).

cnf(f_3112_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11964),sK284(U_11968,U_11966,U_11964,U_11962,U_11960)),U_11968))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),hAPP(c_Relation_OImage(U_11964,U_11960,U_11966),U_11968))) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11964,U_11960)),hAPP(hAPP(c_Product__Type_OPair(U_11964,U_11960),sK284(U_11968,U_11966,U_11964,U_11962,U_11960)),U_11962)),U_11966))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11962),hAPP(c_Relation_OImage(U_11964,U_11960,U_11966),U_11968))) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

cnf(f_3112_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11961),U_11963),hAPP(c_Relation_OImage(U_11965,U_11961,U_11967),U_11969)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11961)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11961),U_11954),U_11963)),U_11967))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11954),U_11969)) ),
    inference(clausify,[status(thm)],[f_3112_4]) ).

fof(f_3113_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_3113_2,plain,
    ! [U_11975,U_11974,U_11973,U_11972,U_11971,U_11970] :
      ( U_11973 = U_11975
      | U_11971 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11970,U_11971),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11974),U_11975)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11970,U_11971),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11972),U_11973))) ),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

cnf(f_3113_3,plain,
    ( U_11973 = U_11975
    | U_11971 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11970,U_11971),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11974),U_11975)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11970,U_11971),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11972),U_11973))) ),
    inference(clausify,[status(thm)],[f_3113_2]) ).

fof(f_3114_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_3114_2,plain,
    ! [U_11981,U_11980,U_11979,U_11978,U_11977,U_11976] :
      ( U_11978 = U_11980
      | U_11977 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11976,U_11977),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11980),U_11981)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11976,U_11977),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11978),U_11979))) ),
    inference(variable_rename,[status(thm)],[f_3114_1]) ).

cnf(f_3114_3,plain,
    ( U_11978 = U_11980
    | U_11977 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11976,U_11977),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11980),U_11981)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11976,U_11977),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11978),U_11979))) ),
    inference(clausify,[status(thm)],[f_3114_2]) ).

fof(f_3115_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_3115_2,plain,
    ! [U_11984,U_11983,U_11982] :
      ( U_11984 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_11982 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11982,U_11982),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11983),U_11984))) ),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

cnf(f_3115_3,plain,
    ( U_11984 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_11982 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11982,U_11982),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11983),U_11984))) ),
    inference(clausify,[status(thm)],[f_3115_2]) ).

fof(f_3116_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_3116_2,plain,
    ! [U_11985] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11985),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_11985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

cnf(f_3116_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11985),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_11985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3116_2]) ).

fof(f_3117_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),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)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_SUP__UN__eq2]) ).

fof(f_3117_2,plain,
    ! [U_11991,U_11990,U_11989,U_11988,U_11987,U_11986] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11986,tc_fun(U_11987,tc_fun(U_11988,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11986,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11987,tc_fun(U_11988,tc_HOL_Obool)),U_11986),hAPP(c_COMBC(U_11987,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11988,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11988,tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11988,tc_HOL_Obool)),U_11987),c_COMBC(U_11988,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11988,tc_prod(U_11987,U_11988)),tc_fun(U_11988,tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),U_11987),hAPP(c_COMBB(tc_prod(U_11987,U_11988),tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool),U_11988),c_member(tc_prod(U_11987,U_11988)))),c_Product__Type_OPair(U_11987,U_11988))))),U_11989)),U_11990),U_11991))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11987,U_11988)),hAPP(hAPP(c_Product__Type_OPair(U_11987,U_11988),U_11990),U_11991)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11986,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11986,tc_HOL_Obool))),U_11989))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11987,U_11988)),hAPP(hAPP(c_Product__Type_OPair(U_11987,U_11988),U_11990),U_11991)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11986,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11986,tc_HOL_Obool))),U_11989)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11986,tc_fun(U_11987,tc_fun(U_11988,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11986,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11987,tc_fun(U_11988,tc_HOL_Obool)),U_11986),hAPP(c_COMBC(U_11987,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11988,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11988,tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_fun(U_11988,tc_HOL_Obool)),U_11987),c_COMBC(U_11988,tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11988,tc_prod(U_11987,U_11988)),tc_fun(U_11988,tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool)),U_11987),hAPP(c_COMBB(tc_prod(U_11987,U_11988),tc_fun(tc_fun(tc_prod(U_11987,U_11988),tc_HOL_Obool),tc_HOL_Obool),U_11988),c_member(tc_prod(U_11987,U_11988)))),c_Product__Type_OPair(U_11987,U_11988))))),U_11989)),U_11990),U_11991)) ) ),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

fof(f_3117_3,plain,
    ( ! [U_12003,U_12001,U_11999,U_11997,U_11995,U_11993] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11993,tc_fun(U_11995,tc_fun(U_11997,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11993,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11995,tc_fun(U_11997,tc_HOL_Obool)),U_11993),hAPP(c_COMBC(U_11995,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11997,tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11997,tc_HOL_Obool)),U_11995),c_COMBC(U_11997,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11997,tc_prod(U_11995,U_11997)),tc_fun(U_11997,tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),U_11995),hAPP(c_COMBB(tc_prod(U_11995,U_11997),tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool),U_11997),c_member(tc_prod(U_11995,U_11997)))),c_Product__Type_OPair(U_11995,U_11997))))),U_11999)),U_12001),U_12003))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11995,U_11997)),hAPP(hAPP(c_Product__Type_OPair(U_11995,U_11997),U_12001),U_12003)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11993,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11993,tc_HOL_Obool))),U_11999))) )
    & ! [U_12002,U_12000,U_11998,U_11996,U_11994,U_11992] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11994,U_11996)),hAPP(hAPP(c_Product__Type_OPair(U_11994,U_11996),U_12000),U_12002)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11992,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),U_11998)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11992,tc_fun(U_11994,tc_fun(U_11996,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11994,tc_fun(U_11996,tc_HOL_Obool)),U_11992),hAPP(c_COMBC(U_11994,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11996,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11996,tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11996,tc_HOL_Obool)),U_11994),c_COMBC(U_11996,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11996,tc_prod(U_11994,U_11996)),tc_fun(U_11996,tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),U_11994),hAPP(c_COMBB(tc_prod(U_11994,U_11996),tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool),U_11996),c_member(tc_prod(U_11994,U_11996)))),c_Product__Type_OPair(U_11994,U_11996))))),U_11998)),U_12000),U_12002)) ) ),
    inference(miniscope,[status(thm)],[f_3117_2]) ).

cnf(f_3117_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11994,U_11996)),hAPP(hAPP(c_Product__Type_OPair(U_11994,U_11996),U_12000),U_12002)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11992,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),U_11998)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11992,tc_fun(U_11994,tc_fun(U_11996,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11994,tc_fun(U_11996,tc_HOL_Obool)),U_11992),hAPP(c_COMBC(U_11994,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11996,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11996,tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_fun(U_11996,tc_HOL_Obool)),U_11994),c_COMBC(U_11996,tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11996,tc_prod(U_11994,U_11996)),tc_fun(U_11996,tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool)),U_11994),hAPP(c_COMBB(tc_prod(U_11994,U_11996),tc_fun(tc_fun(tc_prod(U_11994,U_11996),tc_HOL_Obool),tc_HOL_Obool),U_11996),c_member(tc_prod(U_11994,U_11996)))),c_Product__Type_OPair(U_11994,U_11996))))),U_11998)),U_12000),U_12002)) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

cnf(f_3117_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11993,tc_fun(U_11995,tc_fun(U_11997,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11993,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11995,tc_fun(U_11997,tc_HOL_Obool)),U_11993),hAPP(c_COMBC(U_11995,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11997,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11997,tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_fun(U_11997,tc_HOL_Obool)),U_11995),c_COMBC(U_11997,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11997,tc_prod(U_11995,U_11997)),tc_fun(U_11997,tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool)),U_11995),hAPP(c_COMBB(tc_prod(U_11995,U_11997),tc_fun(tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool),tc_HOL_Obool),U_11997),c_member(tc_prod(U_11995,U_11997)))),c_Product__Type_OPair(U_11995,U_11997))))),U_11999)),U_12001),U_12003))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11995,U_11997)),hAPP(hAPP(c_Product__Type_OPair(U_11995,U_11997),U_12001),U_12003)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11993,tc_fun(tc_prod(U_11995,U_11997),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11993,tc_HOL_Obool))),U_11999))) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

fof(f_3118_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),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)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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_INF__INT__eq2]) ).

fof(f_3118_2,plain,
    ! [U_12009,U_12008,U_12007,U_12006,U_12005,U_12004] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(U_12005,tc_fun(U_12006,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12004,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12005,tc_fun(U_12006,tc_HOL_Obool)),U_12004),hAPP(c_COMBC(U_12005,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12006,tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12006,tc_HOL_Obool)),U_12005),c_COMBC(U_12006,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12006,tc_prod(U_12005,U_12006)),tc_fun(U_12006,tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),U_12005),hAPP(c_COMBB(tc_prod(U_12005,U_12006),tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool),U_12006),c_member(tc_prod(U_12005,U_12006)))),c_Product__Type_OPair(U_12005,U_12006))))),U_12007)),U_12008),U_12009))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12005,U_12006)),hAPP(hAPP(c_Product__Type_OPair(U_12005,U_12006),U_12008),U_12009)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12004,tc_HOL_Obool))),U_12007))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12005,U_12006)),hAPP(hAPP(c_Product__Type_OPair(U_12005,U_12006),U_12008),U_12009)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12004,tc_HOL_Obool))),U_12007)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(U_12005,tc_fun(U_12006,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12004,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12005,tc_fun(U_12006,tc_HOL_Obool)),U_12004),hAPP(c_COMBC(U_12005,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12006,tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_fun(U_12006,tc_HOL_Obool)),U_12005),c_COMBC(U_12006,tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12006,tc_prod(U_12005,U_12006)),tc_fun(U_12006,tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool)),U_12005),hAPP(c_COMBB(tc_prod(U_12005,U_12006),tc_fun(tc_fun(tc_prod(U_12005,U_12006),tc_HOL_Obool),tc_HOL_Obool),U_12006),c_member(tc_prod(U_12005,U_12006)))),c_Product__Type_OPair(U_12005,U_12006))))),U_12007)),U_12008),U_12009)) ) ),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

fof(f_3118_3,plain,
    ( ! [U_12021,U_12019,U_12017,U_12015,U_12013,U_12011] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12011,tc_fun(U_12013,tc_fun(U_12015,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12011,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12013,tc_fun(U_12015,tc_HOL_Obool)),U_12011),hAPP(c_COMBC(U_12013,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12015,tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12015,tc_HOL_Obool)),U_12013),c_COMBC(U_12015,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12015,tc_prod(U_12013,U_12015)),tc_fun(U_12015,tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),U_12013),hAPP(c_COMBB(tc_prod(U_12013,U_12015),tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool),U_12015),c_member(tc_prod(U_12013,U_12015)))),c_Product__Type_OPair(U_12013,U_12015))))),U_12017)),U_12019),U_12021))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12013,U_12015)),hAPP(hAPP(c_Product__Type_OPair(U_12013,U_12015),U_12019),U_12021)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12011,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12011,tc_HOL_Obool))),U_12017))) )
    & ! [U_12020,U_12018,U_12016,U_12014,U_12012,U_12010] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12012,U_12014)),hAPP(hAPP(c_Product__Type_OPair(U_12012,U_12014),U_12018),U_12020)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12010,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12010,tc_HOL_Obool))),U_12016)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12010,tc_fun(U_12012,tc_fun(U_12014,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12010,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12012,tc_fun(U_12014,tc_HOL_Obool)),U_12010),hAPP(c_COMBC(U_12012,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12014,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12014,tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12014,tc_HOL_Obool)),U_12012),c_COMBC(U_12014,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12014,tc_prod(U_12012,U_12014)),tc_fun(U_12014,tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),U_12012),hAPP(c_COMBB(tc_prod(U_12012,U_12014),tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool),U_12014),c_member(tc_prod(U_12012,U_12014)))),c_Product__Type_OPair(U_12012,U_12014))))),U_12016)),U_12018),U_12020)) ) ),
    inference(miniscope,[status(thm)],[f_3118_2]) ).

cnf(f_3118_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12012,U_12014)),hAPP(hAPP(c_Product__Type_OPair(U_12012,U_12014),U_12018),U_12020)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12010,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12010,tc_HOL_Obool))),U_12016)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12010,tc_fun(U_12012,tc_fun(U_12014,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12010,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12012,tc_fun(U_12014,tc_HOL_Obool)),U_12010),hAPP(c_COMBC(U_12012,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12014,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12014,tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_fun(U_12014,tc_HOL_Obool)),U_12012),c_COMBC(U_12014,tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12014,tc_prod(U_12012,U_12014)),tc_fun(U_12014,tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool)),U_12012),hAPP(c_COMBB(tc_prod(U_12012,U_12014),tc_fun(tc_fun(tc_prod(U_12012,U_12014),tc_HOL_Obool),tc_HOL_Obool),U_12014),c_member(tc_prod(U_12012,U_12014)))),c_Product__Type_OPair(U_12012,U_12014))))),U_12016)),U_12018),U_12020)) ),
    inference(clausify,[status(thm)],[f_3118_3]) ).

cnf(f_3118_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12011,tc_fun(U_12013,tc_fun(U_12015,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12011,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12013,tc_fun(U_12015,tc_HOL_Obool)),U_12011),hAPP(c_COMBC(U_12013,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12015,tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_fun(U_12015,tc_HOL_Obool)),U_12013),c_COMBC(U_12015,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12015,tc_prod(U_12013,U_12015)),tc_fun(U_12015,tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool)),U_12013),hAPP(c_COMBB(tc_prod(U_12013,U_12015),tc_fun(tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool),tc_HOL_Obool),U_12015),c_member(tc_prod(U_12013,U_12015)))),c_Product__Type_OPair(U_12013,U_12015))))),U_12017)),U_12019),U_12021))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12013,U_12015)),hAPP(hAPP(c_Product__Type_OPair(U_12013,U_12015),U_12019),U_12021)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12011,tc_fun(tc_prod(U_12013,U_12015),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12011,tc_HOL_Obool))),U_12017))) ),
    inference(clausify,[status(thm)],[f_3118_3]) ).

fof(f_3119_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_3119_2,plain,
    ! [U_12024,U_12023,U_12022] :
      ( U_12023 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_12022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12022,U_12022),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12023),U_12024))) ),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

cnf(f_3119_3,plain,
    ( U_12023 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_12022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12022,U_12022),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12023),U_12024))) ),
    inference(clausify,[status(thm)],[f_3119_2]) ).

fof(f_3120_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_3120_2,plain,
    ! [U_12028,U_12027,U_12026,U_12025] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12025,U_12026) = U_12028
      | U_12026 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12025,U_12026),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12027),U_12028))) ),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

cnf(f_3120_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12025,U_12026) = U_12028
    | U_12026 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12025,U_12026),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12027),U_12028))) ),
    inference(clausify,[status(thm)],[f_3120_2]) ).

fof(f_3121_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_3121_2,plain,
    ! [U_12032,U_12031,U_12030,U_12029] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12029),U_12030) = U_12031
      | U_12030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12029,U_12030),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12031),U_12032))) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

cnf(f_3121_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12029),U_12030) = U_12031
    | U_12030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12029,U_12030),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12031),U_12032))) ),
    inference(clausify,[status(thm)],[f_3121_2]) ).

fof(f_3122_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).

fof(f_3122_2,plain,
    ! [U_12033] :
      ( hBOOL(hAPP(hAPP(c_member(U_12033),c_Groups_Ozero__class_Ozero(U_12033)),c_Nat_Osemiring__1__class_ONats(U_12033)))
      | ~ class_Rings_Osemiring__1(U_12033) ),
    inference(variable_rename,[status(thm)],[f_3122_1]) ).

cnf(f_3122_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12033),c_Groups_Ozero__class_Ozero(U_12033)),c_Nat_Osemiring__1__class_ONats(U_12033)))
    | ~ class_Rings_Osemiring__1(U_12033) ),
    inference(clausify,[status(thm)],[f_3122_2]) ).

fof(f_3123_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_3123_2,plain,
    ! [U_12035,U_12034] : c_Divides_Odivmod__int(U_12034,U_12035) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12034),U_12035)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12034,U_12035)),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

cnf(f_3123_3,plain,
    c_Divides_Odivmod__int(U_12034,U_12035) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12034),U_12035)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12034,U_12035)),
    inference(clausify,[status(thm)],[f_3123_2]) ).

fof(f_3124_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).

fof(f_3124_2,plain,
    ! [U_12038,U_12037,U_12036] :
      ( hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12036),U_12037),U_12038)),c_Nat_Osemiring__1__class_ONats(U_12036)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12036),U_12038),c_Nat_Osemiring__1__class_ONats(U_12036)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12036),U_12037),c_Nat_Osemiring__1__class_ONats(U_12036)))
      | ~ class_Rings_Osemiring__1(U_12036) ),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

cnf(f_3124_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12036),U_12037),U_12038)),c_Nat_Osemiring__1__class_ONats(U_12036)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12036),U_12038),c_Nat_Osemiring__1__class_ONats(U_12036)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12036),U_12037),c_Nat_Osemiring__1__class_ONats(U_12036)))
    | ~ class_Rings_Osemiring__1(U_12036) ),
    inference(clausify,[status(thm)],[f_3124_2]) ).

fof(f_3125_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).

fof(f_3125_2,plain,
    ! [U_12041,U_12040,U_12039] :
      ( hBOOL(hAPP(hAPP(c_member(U_12039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12039),U_12040),U_12041)),c_Nat_Osemiring__1__class_ONats(U_12039)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12039),U_12041),c_Nat_Osemiring__1__class_ONats(U_12039)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12039),U_12040),c_Nat_Osemiring__1__class_ONats(U_12039)))
      | ~ class_Rings_Osemiring__1(U_12039) ),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

cnf(f_3125_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12039),U_12040),U_12041)),c_Nat_Osemiring__1__class_ONats(U_12039)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12039),U_12041),c_Nat_Osemiring__1__class_ONats(U_12039)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12039),U_12040),c_Nat_Osemiring__1__class_ONats(U_12039)))
    | ~ class_Rings_Osemiring__1(U_12039) ),
    inference(clausify,[status(thm)],[f_3125_2]) ).

fof(f_3126_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).

fof(f_3126_2,plain,
    ! [U_12042] :
      ( hBOOL(hAPP(hAPP(c_member(U_12042),c_Groups_Oone__class_Oone(U_12042)),c_Nat_Osemiring__1__class_ONats(U_12042)))
      | ~ class_Rings_Osemiring__1(U_12042) ),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

cnf(f_3126_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12042),c_Groups_Oone__class_Oone(U_12042)),c_Nat_Osemiring__1__class_ONats(U_12042)))
    | ~ class_Rings_Osemiring__1(U_12042) ),
    inference(clausify,[status(thm)],[f_3126_2]) ).

fof(f_3127_1,plain,
    ! [V_n_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a)))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).

fof(f_3127_2,plain,
    ! [U_12044,U_12043] :
      ( hBOOL(hAPP(hAPP(c_member(U_12043),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12043),U_12044)),c_Nat_Osemiring__1__class_ONats(U_12043)))
      | ~ class_Rings_Osemiring__1(U_12043) ),
    inference(variable_rename,[status(thm)],[f_3127_1]) ).

cnf(f_3127_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12043),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12043),U_12044)),c_Nat_Osemiring__1__class_ONats(U_12043)))
    | ~ class_Rings_Osemiring__1(U_12043) ),
    inference(clausify,[status(thm)],[f_3127_2]) ).

fof(f_3128_1,plain,
    ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,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(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,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)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).

fof(f_3128_2,plain,
    ! [U_12049,U_12048,U_12047,U_12046,U_12045] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12045),U_12046),hAPP(c_Relation_OImage(U_12047,U_12045,U_12048),hAPP(hAPP(c_Set_Oinsert(U_12047),U_12049),c_Orderings_Obot__class_Obot(tc_fun(U_12047,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12047,U_12045)),hAPP(hAPP(c_Product__Type_OPair(U_12047,U_12045),U_12049),U_12046)),U_12048)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12047,U_12045)),hAPP(hAPP(c_Product__Type_OPair(U_12047,U_12045),U_12049),U_12046)),U_12048))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12046),hAPP(c_Relation_OImage(U_12047,U_12045,U_12048),hAPP(hAPP(c_Set_Oinsert(U_12047),U_12049),c_Orderings_Obot__class_Obot(tc_fun(U_12047,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

fof(f_3128_3,plain,
    ( ! [U_12059,U_12057,U_12055,U_12053,U_12051] :
        ( hBOOL(hAPP(hAPP(c_member(U_12051),U_12053),hAPP(c_Relation_OImage(U_12055,U_12051,U_12057),hAPP(hAPP(c_Set_Oinsert(U_12055),U_12059),c_Orderings_Obot__class_Obot(tc_fun(U_12055,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12055,U_12051)),hAPP(hAPP(c_Product__Type_OPair(U_12055,U_12051),U_12059),U_12053)),U_12057)) )
    & ! [U_12058,U_12056,U_12054,U_12052,U_12050] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12054,U_12050)),hAPP(hAPP(c_Product__Type_OPair(U_12054,U_12050),U_12058),U_12052)),U_12056))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12050),U_12052),hAPP(c_Relation_OImage(U_12054,U_12050,U_12056),hAPP(hAPP(c_Set_Oinsert(U_12054),U_12058),c_Orderings_Obot__class_Obot(tc_fun(U_12054,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_3128_2]) ).

cnf(f_3128_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12054,U_12050)),hAPP(hAPP(c_Product__Type_OPair(U_12054,U_12050),U_12058),U_12052)),U_12056))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12050),U_12052),hAPP(c_Relation_OImage(U_12054,U_12050,U_12056),hAPP(hAPP(c_Set_Oinsert(U_12054),U_12058),c_Orderings_Obot__class_Obot(tc_fun(U_12054,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_3128_3]) ).

cnf(f_3128_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12051),U_12053),hAPP(c_Relation_OImage(U_12055,U_12051,U_12057),hAPP(hAPP(c_Set_Oinsert(U_12055),U_12059),c_Orderings_Obot__class_Obot(tc_fun(U_12055,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12055,U_12051)),hAPP(hAPP(c_Product__Type_OPair(U_12055,U_12051),U_12059),U_12053)),U_12057)) ),
    inference(clausify,[status(thm)],[f_3128_3]) ).

fof(f_3129_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_3129_2,plain,
    ! [U_12061,U_12060] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12061,U_12060),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12061),U_12060)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12061,U_12060))))
      | U_12060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

cnf(f_3129_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12061,U_12060),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12061),U_12060)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12061,U_12060))))
    | U_12060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3129_2]) ).

fof(f_3130_1,plain,
    ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,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_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).

fof(f_3130_2,plain,
    ! [U_12065,U_12064,U_12063,U_12062] : hAPP(c_Relation_OImage(U_12062,U_12063,U_12064),hAPP(hAPP(c_Set_Oinsert(U_12062),U_12065),c_Orderings_Obot__class_Obot(tc_fun(U_12062,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12063),hAPP(hAPP(c_COMBC(U_12063,tc_fun(tc_prod(U_12062,U_12063),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12062,U_12063),tc_fun(tc_fun(tc_prod(U_12062,U_12063),tc_HOL_Obool),tc_HOL_Obool),U_12063),c_member(tc_prod(U_12062,U_12063))),hAPP(c_Product__Type_OPair(U_12062,U_12063),U_12065))),U_12064)),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

cnf(f_3130_3,plain,
    hAPP(c_Relation_OImage(U_12062,U_12063,U_12064),hAPP(hAPP(c_Set_Oinsert(U_12062),U_12065),c_Orderings_Obot__class_Obot(tc_fun(U_12062,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12063),hAPP(hAPP(c_COMBC(U_12063,tc_fun(tc_prod(U_12062,U_12063),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12062,U_12063),tc_fun(tc_fun(tc_prod(U_12062,U_12063),tc_HOL_Obool),tc_HOL_Obool),U_12063),c_member(tc_prod(U_12062,U_12063))),hAPP(c_Product__Type_OPair(U_12062,U_12063),U_12065))),U_12064)),
    inference(clausify,[status(thm)],[f_3130_2]) ).

fof(f_3131_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_3131_2,plain,
    ! [U_12072,U_12071,U_12070,U_12069,U_12068,U_12067,U_12066] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12066),U_12070),U_12067),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_12068),U_12071)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),U_12072)),U_12067))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),U_12072),U_12067))))
      | U_12067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12070,U_12067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12071),U_12072)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12066,U_12067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12068),U_12069))) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

cnf(f_3131_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12066),U_12070),U_12067),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_12068),U_12071)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),U_12072)),U_12067))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),U_12072),U_12067))))
    | U_12067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12070,U_12067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12071),U_12072)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12066,U_12067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12068),U_12069))) ),
    inference(clausify,[status(thm)],[f_3131_2]) ).

fof(f_3132_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_3132_2,plain,
    ! [U_12076,U_12075,U_12074,U_12073] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12073),U_12074),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_12076),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12075)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12075)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_12076),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_12074),U_12076)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12073,U_12074),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12075),U_12076))) ),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

cnf(f_3132_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12073),U_12074),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_12076),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12075)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12075)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_12076),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_12074),U_12076)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12073,U_12074),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12075),U_12076))) ),
    inference(clausify,[status(thm)],[f_3132_2]) ).

fof(f_3133_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_3133_2,plain,
    ! [U_12080,U_12079,U_12078,U_12077] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12077,U_12078),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12079),U_12080)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12080),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12078),U_12080)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12080),U_12078))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12080)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078)) )
      | U_12077 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12078),U_12079)),U_12080) ),
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

cnf(f_3133_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12077,U_12078),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12079),U_12080)))
    | U_12077 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12078),U_12079)),U_12080) ),
    inference(clausify,[status(thm)],[f_3133_2]) ).

cnf(f_3133_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12080),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12078),U_12080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12077,U_12078),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12079),U_12080)))
    | U_12077 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12078),U_12079)),U_12080) ),
    inference(clausify,[status(thm)],[f_3133_2]) ).

cnf(f_3133_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12078))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12080),U_12078))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12080))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12077,U_12078),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12079),U_12080)))
    | U_12077 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12078),U_12079)),U_12080) ),
    inference(clausify,[status(thm)],[f_3133_2]) ).

cnf(f_3133_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12080),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12078),U_12080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12080),U_12078))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12080))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12077,U_12078),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12079),U_12080)))
    | U_12077 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12078),U_12079)),U_12080) ),
    inference(clausify,[status(thm)],[f_3133_2]) ).

fof(f_3134_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_3134_2,plain,
    ! [U_12085,U_12084,U_12083,U_12082,U_12081] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12081),U_12082),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_12085),U_12083)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12084)),U_12082))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12084),U_12082))))
      | U_12082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12081,U_12082),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12083),U_12084))) ),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

cnf(f_3134_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12081),U_12082),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_12085),U_12083)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12084)),U_12082))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_12085),U_12084),U_12082))))
    | U_12082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12081,U_12082),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12083),U_12084))) ),
    inference(clausify,[status(thm)],[f_3134_2]) ).

fof(f_3135_1,plain,
    ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).

fof(f_3135_2,plain,
    ! [U_12092,U_12091,U_12090,U_12089,U_12088,U_12087,U_12086] :
      ( hBOOL(hAPP(hAPP(c_member(U_12091),hAPP(hAPP(U_12092,U_12088),U_12089)),hAPP(c_Set_Oimage(tc_prod(U_12086,U_12087),U_12091,hAPP(c_Product__Type_Oprod_Oprod__case(U_12086,U_12087,U_12091),U_12092)),U_12090)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12086,U_12087)),hAPP(hAPP(c_Product__Type_OPair(U_12086,U_12087),U_12088),U_12089)),U_12090)) ),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

cnf(f_3135_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12091),hAPP(hAPP(U_12092,U_12088),U_12089)),hAPP(c_Set_Oimage(tc_prod(U_12086,U_12087),U_12091,hAPP(c_Product__Type_Oprod_Oprod__case(U_12086,U_12087,U_12091),U_12092)),U_12090)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12086,U_12087)),hAPP(hAPP(c_Product__Type_OPair(U_12086,U_12087),U_12088),U_12089)),U_12090)) ),
    inference(clausify,[status(thm)],[f_3135_2]) ).

fof(f_3136_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_3136_2,plain,
    ! [U_12094,U_12093] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_12094,U_12093) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_12094),U_12093)),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_12094))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12093)))
            | U_12093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_12094 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_12094,U_12093) = 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_12093 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_12094 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12093),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_12094,U_12093) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12094),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12093),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

fof(f_3136_3,plain,
    ( ! [U_12098,U_12096] :
        ( ( ( c_Nitpick_Onorm__frac(U_12098,U_12096) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_12098),U_12096)),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_12098))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12096)))
            | U_12096 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_12098 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_12098,U_12096) = 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_12096 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_12098 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12096),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_12097,U_12095] :
        ( c_Nitpick_Onorm__frac(U_12097,U_12095) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12097),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12095))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_3136_2]) ).

cnf(f_3136_4,plain,
    ( c_Nitpick_Onorm__frac(U_12097,U_12095) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12097),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12095),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_5,plain,
    ( U_12098 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_12098,U_12096) = 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),U_12096),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_6,plain,
    ( U_12096 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_12098,U_12096) = 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),U_12096),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_7,plain,
    ( c_Nitpick_Onorm__frac(U_12098,U_12096) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_12098),U_12096)),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_12098))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12096)))
    | U_12096 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12098 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12096),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

fof(f_3137_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_3137_2,plain,
    ! [U_12101,U_12100,U_12099] : hAPP(c_Divides_Oadjust(U_12099),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12100),U_12101)) = 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_12101),U_12099)),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_12100)),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_12100)),U_12101))),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

cnf(f_3137_3,plain,
    hAPP(c_Divides_Oadjust(U_12099),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12100),U_12101)) = 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_12101),U_12099)),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_12100)),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_12100)),U_12101))),
    inference(clausify,[status(thm)],[f_3137_2]) ).

fof(f_3138_1,plain,
    ! [T_b,T_a,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_a,tc_fun(T_b,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_3138_2,plain,
    ! [U_12107,U_12106,U_12105,U_12104,U_12103,U_12102] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12106,tc_fun(U_12107,tc_HOL_Obool))),U_12105),U_12102),U_12103),U_12104))
      | ( ~ hBOOL(hAPP(hAPP(U_12105,U_12103),U_12104))
        & ~ hBOOL(hAPP(hAPP(U_12102,U_12103),U_12104)) ) ),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

cnf(f_3138_3,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12102,U_12103),U_12104))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12106,tc_fun(U_12107,tc_HOL_Obool))),U_12105),U_12102),U_12103),U_12104)) ),
    inference(clausify,[status(thm)],[f_3138_2]) ).

cnf(f_3138_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12105,U_12103),U_12104))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12106,tc_fun(U_12107,tc_HOL_Obool))),U_12105),U_12102),U_12103),U_12104)) ),
    inference(clausify,[status(thm)],[f_3138_2]) ).

fof(f_3139_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( 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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2E]) ).

fof(f_3139_2,plain,
    ! [U_12113,U_12112,U_12111,U_12110,U_12109,U_12108] :
      ( hBOOL(hAPP(hAPP(U_12111,U_12112),U_12113))
      | hBOOL(hAPP(hAPP(U_12110,U_12112),U_12113))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12108,tc_fun(U_12109,tc_HOL_Obool))),U_12110),U_12111),U_12112),U_12113)) ),
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

fof(f_3139_3,plain,
    ! [U_12113,U_12112,U_12111,U_12110] :
      ( ! [U_12109,U_12108] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12108,tc_fun(U_12109,tc_HOL_Obool))),U_12110),U_12111),U_12112),U_12113))
      | hBOOL(hAPP(hAPP(U_12111,U_12112),U_12113))
      | hBOOL(hAPP(hAPP(U_12110,U_12112),U_12113)) ),
    inference(miniscope,[status(thm)],[f_3139_2]) ).

cnf(f_3139_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12108,tc_fun(U_12109,tc_HOL_Obool))),U_12110),U_12111),U_12112),U_12113))
    | hBOOL(hAPP(hAPP(U_12111,U_12112),U_12113))
    | hBOOL(hAPP(hAPP(U_12110,U_12112),U_12113)) ),
    inference(clausify,[status(thm)],[f_3139_3]) ).

fof(f_3140_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( ( 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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2E]) ).

fof(f_3140_2,plain,
    ! [U_12119,U_12118,U_12117,U_12116,U_12115,U_12114] :
      ( ( hBOOL(hAPP(hAPP(U_12117,U_12118),U_12119))
        & hBOOL(hAPP(hAPP(U_12116,U_12118),U_12119)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12114,tc_fun(U_12115,tc_HOL_Obool))),U_12116),U_12117),U_12118),U_12119)) ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

fof(f_3140_3,plain,
    ! [U_12119,U_12118,U_12117,U_12116] :
      ( ! [U_12115,U_12114] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12114,tc_fun(U_12115,tc_HOL_Obool))),U_12116),U_12117),U_12118),U_12119))
      | ( hBOOL(hAPP(hAPP(U_12117,U_12118),U_12119))
        & hBOOL(hAPP(hAPP(U_12116,U_12118),U_12119)) ) ),
    inference(miniscope,[status(thm)],[f_3140_2]) ).

cnf(f_3140_4,plain,
    ( hBOOL(hAPP(hAPP(U_12116,U_12118),U_12119))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12114,tc_fun(U_12115,tc_HOL_Obool))),U_12116),U_12117),U_12118),U_12119)) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

cnf(f_3140_5,plain,
    ( hBOOL(hAPP(hAPP(U_12117,U_12118),U_12119))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12114,tc_fun(U_12115,tc_HOL_Obool))),U_12116),U_12117),U_12118),U_12119)) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

fof(f_3141_1,plain,
    ! [T_b,T_a,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_a,tc_fun(T_b,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_3141_2,plain,
    ! [U_12125,U_12124,U_12123,U_12122,U_12121,U_12120] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12124,tc_fun(U_12125,tc_HOL_Obool))),U_12120),U_12123),U_12121),U_12122))
      | ~ hBOOL(hAPP(hAPP(U_12123,U_12121),U_12122))
      | ~ hBOOL(hAPP(hAPP(U_12120,U_12121),U_12122)) ),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

cnf(f_3141_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12124,tc_fun(U_12125,tc_HOL_Obool))),U_12120),U_12123),U_12121),U_12122))
    | ~ hBOOL(hAPP(hAPP(U_12123,U_12121),U_12122))
    | ~ hBOOL(hAPP(hAPP(U_12120,U_12121),U_12122)) ),
    inference(clausify,[status(thm)],[f_3141_2]) ).

fof(f_3142_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).

fof(f_3142_2,plain,
    ! [U_12132,U_12131,U_12130,U_12129,U_12128,U_12127,U_12126] :
      ( hBOOL(hAPP(hAPP(c_member(U_12126),U_12127),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12131,U_12132,tc_fun(U_12126,tc_HOL_Obool)),U_12128),hAPP(hAPP(c_Product__Type_OPair(U_12131,U_12132),U_12129),U_12130))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12126),U_12127),hAPP(hAPP(U_12128,U_12129),U_12130))) ),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

cnf(f_3142_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12126),U_12127),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12131,U_12132,tc_fun(U_12126,tc_HOL_Obool)),U_12128),hAPP(hAPP(c_Product__Type_OPair(U_12131,U_12132),U_12129),U_12130))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12126),U_12127),hAPP(hAPP(U_12128,U_12129),U_12130))) ),
    inference(clausify,[status(thm)],[f_3142_2]) ).

fof(f_3143_1,plain,
    ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_3143_2,plain,
    ! [U_12137,U_12136,U_12135,U_12134,U_12133] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12136,U_12137,tc_HOL_Obool),U_12133),hAPP(hAPP(c_Product__Type_OPair(U_12136,U_12137),U_12134),U_12135)))
      | ~ hBOOL(hAPP(hAPP(U_12133,U_12134),U_12135)) ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

cnf(f_3143_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12136,U_12137,tc_HOL_Obool),U_12133),hAPP(hAPP(c_Product__Type_OPair(U_12136,U_12137),U_12134),U_12135)))
    | ~ hBOOL(hAPP(hAPP(U_12133,U_12134),U_12135)) ),
    inference(clausify,[status(thm)],[f_3143_2]) ).

fof(f_3144_1,plain,
    ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_3144_2,plain,
    ! [U_12142,U_12141,U_12140,U_12139,U_12138] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12141,U_12142,tc_HOL_Obool),U_12138),hAPP(hAPP(c_Product__Type_OPair(U_12141,U_12142),U_12139),U_12140)))
      | ~ hBOOL(hAPP(hAPP(U_12138,U_12139),U_12140)) ),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

cnf(f_3144_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12141,U_12142,tc_HOL_Obool),U_12138),hAPP(hAPP(c_Product__Type_OPair(U_12141,U_12142),U_12139),U_12140)))
    | ~ hBOOL(hAPP(hAPP(U_12138,U_12139),U_12140)) ),
    inference(clausify,[status(thm)],[f_3144_2]) ).

fof(f_3145_1,plain,
    ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_bot2E]) ).

fof(f_3145_2,plain,
    ! [U_12146,U_12145,U_12144,U_12143] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_12143,tc_fun(U_12144,tc_HOL_Obool))),U_12145),U_12146)),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

cnf(f_3145_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_12143,tc_fun(U_12144,tc_HOL_Obool))),U_12145),U_12146)),
    inference(clausify,[status(thm)],[f_3145_2]) ).

fof(f_3146_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
      ( 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_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).

fof(f_3146_2,plain,
    ! [U_12153,U_12152,U_12151,U_12150,U_12149,U_12148,U_12147] :
      ( hBOOL(hAPP(hAPP(hAPP(U_12150,U_12151),U_12152),U_12153))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12147,U_12148,tc_fun(U_12149,tc_HOL_Obool)),U_12150),hAPP(hAPP(c_Product__Type_OPair(U_12147,U_12148),U_12151),U_12152)),U_12153)) ),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

fof(f_3146_3,plain,
    ! [U_12153,U_12152,U_12151,U_12150] :
      ( ! [U_12149,U_12148,U_12147] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12147,U_12148,tc_fun(U_12149,tc_HOL_Obool)),U_12150),hAPP(hAPP(c_Product__Type_OPair(U_12147,U_12148),U_12151),U_12152)),U_12153))
      | hBOOL(hAPP(hAPP(hAPP(U_12150,U_12151),U_12152),U_12153)) ),
    inference(miniscope,[status(thm)],[f_3146_2]) ).

cnf(f_3146_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12147,U_12148,tc_fun(U_12149,tc_HOL_Obool)),U_12150),hAPP(hAPP(c_Product__Type_OPair(U_12147,U_12148),U_12151),U_12152)),U_12153))
    | hBOOL(hAPP(hAPP(hAPP(U_12150,U_12151),U_12152),U_12153)) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

fof(f_3147_1,plain,
    ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_swap__inj__on]) ).

fof(f_3147_2,plain,
    ! [U_12156,U_12155,U_12154] : c_Fun_Oinj__on(tc_prod(U_12154,U_12155),tc_prod(U_12155,U_12154),hAPP(c_Product__Type_Oprod_Oprod__case(U_12154,U_12155,tc_prod(U_12155,U_12154)),hAPP(c_COMBC(U_12155,U_12154,tc_prod(U_12155,U_12154)),c_Product__Type_OPair(U_12155,U_12154))),U_12156),
    inference(variable_rename,[status(thm)],[f_3147_1]) ).

cnf(f_3147_3,plain,
    c_Fun_Oinj__on(tc_prod(U_12154,U_12155),tc_prod(U_12155,U_12154),hAPP(c_Product__Type_Oprod_Oprod__case(U_12154,U_12155,tc_prod(U_12155,U_12154)),hAPP(c_COMBC(U_12155,U_12154,tc_prod(U_12155,U_12154)),c_Product__Type_OPair(U_12155,U_12154))),U_12156),
    inference(clausify,[status(thm)],[f_3147_2]) ).

fof(f_3148_1,plain,
    ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,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_3148_2,plain,
    ! [U_12162,U_12161,U_12160,U_12159,U_12158,U_12157] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12160,tc_fun(U_12161,tc_HOL_Obool))),U_12162),U_12157),U_12158),U_12159))
      | ~ hBOOL(hAPP(hAPP(U_12157,U_12158),U_12159)) ),
    inference(variable_rename,[status(thm)],[f_3148_1]) ).

cnf(f_3148_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12160,tc_fun(U_12161,tc_HOL_Obool))),U_12162),U_12157),U_12158),U_12159))
    | ~ hBOOL(hAPP(hAPP(U_12157,U_12158),U_12159)) ),
    inference(clausify,[status(thm)],[f_3148_2]) ).

fof(f_3149_1,plain,
    ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,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_3149_2,plain,
    ! [U_12168,U_12167,U_12166,U_12165,U_12164,U_12163] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12166,tc_fun(U_12167,tc_HOL_Obool))),U_12163),U_12168),U_12164),U_12165))
      | ~ hBOOL(hAPP(hAPP(U_12163,U_12164),U_12165)) ),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

cnf(f_3149_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12166,tc_fun(U_12167,tc_HOL_Obool))),U_12163),U_12168),U_12164),U_12165))
    | ~ hBOOL(hAPP(hAPP(U_12163,U_12164),U_12165)) ),
    inference(clausify,[status(thm)],[f_3149_2]) ).

fof(f_3150_1,plain,
    ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).

fof(f_3150_2,plain,
    ! [U_12174,U_12173,U_12172,U_12171,U_12170,U_12169] :
      ( hBOOL(hAPP(hAPP(U_12174,U_12170),U_12171))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12172,tc_fun(U_12173,tc_HOL_Obool))),U_12169),U_12174))
      | ~ hBOOL(hAPP(hAPP(U_12169,U_12170),U_12171)) ),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

cnf(f_3150_3,plain,
    ( hBOOL(hAPP(hAPP(U_12174,U_12170),U_12171))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12172,tc_fun(U_12173,tc_HOL_Obool))),U_12169),U_12174))
    | ~ hBOOL(hAPP(hAPP(U_12169,U_12170),U_12171)) ),
    inference(clausify,[status(thm)],[f_3150_2]) ).

fof(f_3151_1,plain,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).

fof(f_3151_2,plain,
    ! [U_12180,U_12179,U_12178,U_12177,U_12176,U_12175] :
      ( hBOOL(hAPP(hAPP(U_12178,U_12179),U_12180))
      | ~ hBOOL(hAPP(hAPP(U_12177,U_12179),U_12180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12175,tc_fun(U_12176,tc_HOL_Obool))),U_12177),U_12178)) ),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

fof(f_3151_3,plain,
    ! [U_12180,U_12179,U_12178,U_12177] :
      ( ! [U_12176,U_12175] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12175,tc_fun(U_12176,tc_HOL_Obool))),U_12177),U_12178))
      | hBOOL(hAPP(hAPP(U_12178,U_12179),U_12180))
      | ~ hBOOL(hAPP(hAPP(U_12177,U_12179),U_12180)) ),
    inference(miniscope,[status(thm)],[f_3151_2]) ).

cnf(f_3151_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12175,tc_fun(U_12176,tc_HOL_Obool))),U_12177),U_12178))
    | hBOOL(hAPP(hAPP(U_12178,U_12179),U_12180))
    | ~ hBOOL(hAPP(hAPP(U_12177,U_12179),U_12180)) ),
    inference(clausify,[status(thm)],[f_3151_3]) ).

fof(f_3152_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( 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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).

fof(f_3152_2,plain,
    ! [U_12186,U_12185,U_12184,U_12183,U_12182,U_12181] :
      ( hBOOL(hAPP(hAPP(U_12184,U_12185),U_12186))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12181,tc_fun(U_12182,tc_HOL_Obool))),U_12183),U_12184),U_12185),U_12186)) ),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

fof(f_3152_3,plain,
    ! [U_12186,U_12185,U_12184] :
      ( ! [U_12183,U_12182,U_12181] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12181,tc_fun(U_12182,tc_HOL_Obool))),U_12183),U_12184),U_12185),U_12186))
      | hBOOL(hAPP(hAPP(U_12184,U_12185),U_12186)) ),
    inference(miniscope,[status(thm)],[f_3152_2]) ).

cnf(f_3152_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12181,tc_fun(U_12182,tc_HOL_Obool))),U_12183),U_12184),U_12185),U_12186))
    | hBOOL(hAPP(hAPP(U_12184,U_12185),U_12186)) ),
    inference(clausify,[status(thm)],[f_3152_3]) ).

fof(f_3153_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
      ( 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_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).

fof(f_3153_2,plain,
    ! [U_12192,U_12191,U_12190,U_12189,U_12188,U_12187] :
      ( hBOOL(hAPP(hAPP(U_12189,U_12191),U_12192))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12187,tc_fun(U_12188,tc_HOL_Obool))),U_12189),U_12190),U_12191),U_12192)) ),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

fof(f_3153_3,plain,
    ! [U_12192,U_12191,U_12190,U_12189] :
      ( ! [U_12188,U_12187] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12187,tc_fun(U_12188,tc_HOL_Obool))),U_12189),U_12190),U_12191),U_12192))
      | hBOOL(hAPP(hAPP(U_12189,U_12191),U_12192)) ),
    inference(miniscope,[status(thm)],[f_3153_2]) ).

cnf(f_3153_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12187,tc_fun(U_12188,tc_HOL_Obool))),U_12189),U_12190),U_12191),U_12192))
    | hBOOL(hAPP(hAPP(U_12189,U_12191),U_12192)) ),
    inference(clausify,[status(thm)],[f_3153_3]) ).

fof(f_3154_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_3154_2,plain,
    ! [U_12198,U_12197,U_12196,U_12195,U_12194,U_12193] :
      ( ( U_12196 = U_12198
        & U_12195 = U_12197 )
      | hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12195),U_12196) != hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12197),U_12198) ),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

fof(f_3154_3,plain,
    ! [U_12198,U_12197,U_12196,U_12195] :
      ( ! [U_12194,U_12193] : hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12195),U_12196) != hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12197),U_12198)
      | ( U_12196 = U_12198
        & U_12195 = U_12197 ) ),
    inference(miniscope,[status(thm)],[f_3154_2]) ).

cnf(f_3154_4,plain,
    ( U_12195 = U_12197
    | hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12195),U_12196) != hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12197),U_12198) ),
    inference(clausify,[status(thm)],[f_3154_3]) ).

cnf(f_3154_5,plain,
    ( U_12196 = U_12198
    | hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12195),U_12196) != hAPP(hAPP(c_Product__Type_OPair(U_12193,U_12194),U_12197),U_12198) ),
    inference(clausify,[status(thm)],[f_3154_3]) ).

fof(f_3155_1,plain,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_a,T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).

fof(f_3155_2,plain,
    ! [U_12204,U_12203,U_12202,U_12201,U_12200,U_12199] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_12199,U_12200),U_12201),U_12202) = hAPP(hAPP(c_Product__Type_OPair(U_12199,U_12200),U_12203),U_12204)
        | U_12202 != U_12204
        | U_12201 != U_12203 )
      & ( ( U_12202 = U_12204
          & U_12201 = U_12203 )
        | hAPP(hAPP(c_Product__Type_OPair(U_12199,U_12200),U_12201),U_12202) != hAPP(hAPP(c_Product__Type_OPair(U_12199,U_12200),U_12203),U_12204) ) ),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

fof(f_3155_3,plain,
    ( ! [U_12216,U_12214,U_12212,U_12210] :
        ( ! [U_12208,U_12206] : hAPP(hAPP(c_Product__Type_OPair(U_12206,U_12208),U_12210),U_12212) = hAPP(hAPP(c_Product__Type_OPair(U_12206,U_12208),U_12214),U_12216)
        | U_12212 != U_12216
        | U_12210 != U_12214 )
    & ! [U_12215,U_12213,U_12211,U_12209] :
        ( ! [U_12207,U_12205] : hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12209),U_12211) != hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12213),U_12215)
        | ( U_12211 = U_12215
          & U_12209 = U_12213 ) ) ),
    inference(miniscope,[status(thm)],[f_3155_2]) ).

cnf(f_3155_4,plain,
    ( U_12209 = U_12213
    | hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12209),U_12211) != hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12213),U_12215) ),
    inference(clausify,[status(thm)],[f_3155_3]) ).

cnf(f_3155_5,plain,
    ( U_12211 = U_12215
    | hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12209),U_12211) != hAPP(hAPP(c_Product__Type_OPair(U_12205,U_12207),U_12213),U_12215) ),
    inference(clausify,[status(thm)],[f_3155_3]) ).

cnf(f_3155_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_12206,U_12208),U_12210),U_12212) = hAPP(hAPP(c_Product__Type_OPair(U_12206,U_12208),U_12214),U_12216)
    | U_12212 != U_12216
    | U_12210 != U_12214 ),
    inference(clausify,[status(thm)],[f_3155_3]) ).

fof(f_3156_1,plain,
    ! [T_b,T_a,V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_a,B_b] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) )
      & ( ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)))
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).

fof(f_3156_2,plain,
    ! [U_12225,U_12224,U_12223] :
      ( ( ! [U_12222] : hBOOL(hAPP(U_12223,U_12222))
        | ? [U_12221,U_12220] : ~ hBOOL(hAPP(U_12223,hAPP(hAPP(c_Product__Type_OPair(U_12224,U_12225),U_12221),U_12220))) )
      & ( ! [U_12219,U_12218] : hBOOL(hAPP(U_12223,hAPP(hAPP(c_Product__Type_OPair(U_12224,U_12225),U_12219),U_12218)))
        | ? [U_12217] : ~ hBOOL(hAPP(U_12223,U_12217)) ) ),
    inference(variable_rename,[status(thm)],[f_3156_1]) ).

fof(f_3156_3,plain,
    ( ! [U_12231,U_12229,U_12227] :
        ( ! [U_12222] : hBOOL(hAPP(U_12227,U_12222))
        | ? [U_12221,U_12220] : ~ hBOOL(hAPP(U_12227,hAPP(hAPP(c_Product__Type_OPair(U_12229,U_12231),U_12221),U_12220))) )
    & ! [U_12230,U_12228,U_12226] :
        ( ! [U_12219,U_12218] : hBOOL(hAPP(U_12226,hAPP(hAPP(c_Product__Type_OPair(U_12228,U_12230),U_12219),U_12218)))
        | ? [U_12217] : ~ hBOOL(hAPP(U_12226,U_12217)) ) ),
    inference(miniscope,[status(thm)],[f_3156_2]) ).

fof(f_3156_4,plain,
    ( ! [U_12231,U_12229,U_12227] :
        ( ! [U_12222] : hBOOL(hAPP(U_12227,U_12222))
        | ? [U_12221,U_12220] : ~ hBOOL(hAPP(U_12227,hAPP(hAPP(c_Product__Type_OPair(U_12229,U_12231),U_12221),U_12220))) )
    & ! [U_12230,U_12228,U_12226] :
        ( ! [U_12219,U_12218] : hBOOL(hAPP(U_12226,hAPP(hAPP(c_Product__Type_OPair(U_12228,U_12230),U_12219),U_12218)))
        | ~ hBOOL(hAPP(U_12226,sK285(U_12230,U_12228,U_12226))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_12217,sK285(U_12230,U_12228,U_12226))],[f_3156_3]) ).

fof(f_3156_5,plain,
    ( ! [U_12231,U_12229,U_12227] :
        ( ! [U_12222] : hBOOL(hAPP(U_12227,U_12222))
        | ? [U_12220] : ~ hBOOL(hAPP(U_12227,hAPP(hAPP(c_Product__Type_OPair(U_12229,U_12231),sK286(U_12231,U_12229,U_12227)),U_12220))) )
    & ! [U_12230,U_12228,U_12226] :
        ( ! [U_12219,U_12218] : hBOOL(hAPP(U_12226,hAPP(hAPP(c_Product__Type_OPair(U_12228,U_12230),U_12219),U_12218)))
        | ~ hBOOL(hAPP(U_12226,sK285(U_12230,U_12228,U_12226))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_12221,sK286(U_12231,U_12229,U_12227))],[f_3156_4]) ).

fof(f_3156_6,plain,
    ( ! [U_12231,U_12229,U_12227] :
        ( ! [U_12222] : hBOOL(hAPP(U_12227,U_12222))
        | ~ hBOOL(hAPP(U_12227,hAPP(hAPP(c_Product__Type_OPair(U_12229,U_12231),sK286(U_12231,U_12229,U_12227)),sK287(U_12231,U_12229,U_12227)))) )
    & ! [U_12230,U_12228,U_12226] :
        ( ! [U_12219,U_12218] : hBOOL(hAPP(U_12226,hAPP(hAPP(c_Product__Type_OPair(U_12228,U_12230),U_12219),U_12218)))
        | ~ hBOOL(hAPP(U_12226,sK285(U_12230,U_12228,U_12226))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_12220,sK287(U_12231,U_12229,U_12227))],[f_3156_5]) ).

cnf(f_3156_7,plain,
    ( hBOOL(hAPP(U_12226,hAPP(hAPP(c_Product__Type_OPair(U_12228,U_12230),U_12219),U_12218)))
    | ~ hBOOL(hAPP(U_12226,sK285(U_12230,U_12228,U_12226))) ),
    inference(clausify,[status(thm)],[f_3156_6]) ).

cnf(f_3156_8,plain,
    ( hBOOL(hAPP(U_12227,U_12222))
    | ~ hBOOL(hAPP(U_12227,hAPP(hAPP(c_Product__Type_OPair(U_12229,U_12231),sK286(U_12231,U_12229,U_12227)),sK287(U_12231,U_12229,U_12227)))) ),
    inference(clausify,[status(thm)],[f_3156_6]) ).

fof(f_3157_1,plain,
    ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2)
      | V_p_2 != V_q_2 ),
    inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).

fof(f_3157_2,plain,
    ! [U_12237,U_12236,U_12235,U_12234,U_12233,U_12232] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12234,U_12235,U_12236),U_12237),U_12232) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12234,U_12235,U_12236),U_12237),U_12233)
      | U_12232 != U_12233 ),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

cnf(f_3157_3,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12234,U_12235,U_12236),U_12237),U_12232) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12234,U_12235,U_12236),U_12237),U_12233)
    | U_12232 != U_12233 ),
    inference(clausify,[status(thm)],[f_3157_2]) ).

fof(f_3158_1,plain,
    ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_split__twice]) ).

fof(f_3158_2,plain,
    ! [U_12245,U_12244,U_12243,U_12242,U_12241,U_12240,U_12239,U_12238] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12238,U_12239,U_12240),U_12241),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12242,U_12243,tc_prod(U_12238,U_12239)),U_12244),U_12245)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12242,U_12243,U_12240),hAPP(hAPP(c_COMBB(tc_fun(U_12243,tc_prod(U_12238,U_12239)),tc_fun(U_12243,U_12240),U_12242),hAPP(c_COMBB(tc_prod(U_12238,U_12239),U_12240,U_12243),hAPP(c_Product__Type_Oprod_Oprod__case(U_12238,U_12239,U_12240),U_12241))),U_12244)),U_12245),
    inference(variable_rename,[status(thm)],[f_3158_1]) ).

cnf(f_3158_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12238,U_12239,U_12240),U_12241),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12242,U_12243,tc_prod(U_12238,U_12239)),U_12244),U_12245)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12242,U_12243,U_12240),hAPP(hAPP(c_COMBB(tc_fun(U_12243,tc_prod(U_12238,U_12239)),tc_fun(U_12243,U_12240),U_12242),hAPP(c_COMBB(tc_prod(U_12238,U_12239),U_12240,U_12243),hAPP(c_Product__Type_Oprod_Oprod__case(U_12238,U_12239,U_12240),U_12241))),U_12244)),U_12245),
    inference(clausify,[status(thm)],[f_3158_2]) ).

fof(f_3159_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_3159_2,plain,
    ! [U_12251,U_12250,U_12249,U_12248,U_12247,U_12246] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12246,U_12247,U_12248),U_12249),hAPP(hAPP(c_Product__Type_OPair(U_12246,U_12247),U_12250),U_12251)) = hAPP(hAPP(U_12249,U_12250),U_12251),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

cnf(f_3159_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12246,U_12247,U_12248),U_12249),hAPP(hAPP(c_Product__Type_OPair(U_12246,U_12247),U_12250),U_12251)) = hAPP(hAPP(U_12249,U_12250),U_12251),
    inference(clausify,[status(thm)],[f_3159_2]) ).

fof(f_3160_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_3160_2,plain,
    ! [U_12257,U_12256,U_12255,U_12254,U_12253,U_12252] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12252,U_12253,U_12254),U_12255),hAPP(hAPP(c_Product__Type_OPair(U_12252,U_12253),U_12256),U_12257)) = hAPP(hAPP(U_12255,U_12256),U_12257),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

cnf(f_3160_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12252,U_12253,U_12254),U_12255),hAPP(hAPP(c_Product__Type_OPair(U_12252,U_12253),U_12256),U_12257)) = hAPP(hAPP(U_12255,U_12256),U_12257),
    inference(clausify,[status(thm)],[f_3160_2]) ).

fof(f_3161_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_splitD]) ).

fof(f_3161_2,plain,
    ! [U_12262,U_12261,U_12260,U_12259,U_12258] :
      ( hBOOL(hAPP(hAPP(U_12260,U_12261),U_12262))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12258,U_12259,tc_HOL_Obool),U_12260),hAPP(hAPP(c_Product__Type_OPair(U_12258,U_12259),U_12261),U_12262))) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ! [U_12262,U_12261,U_12260] :
      ( ! [U_12259,U_12258] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12258,U_12259,tc_HOL_Obool),U_12260),hAPP(hAPP(c_Product__Type_OPair(U_12258,U_12259),U_12261),U_12262)))
      | hBOOL(hAPP(hAPP(U_12260,U_12261),U_12262)) ),
    inference(miniscope,[status(thm)],[f_3161_2]) ).

cnf(f_3161_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12258,U_12259,tc_HOL_Obool),U_12260),hAPP(hAPP(c_Product__Type_OPair(U_12258,U_12259),U_12261),U_12262)))
    | hBOOL(hAPP(hAPP(U_12260,U_12261),U_12262)) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

fof(f_3162_1,plain,
    ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_split__eta]) ).

fof(f_3162_2,plain,
    ! [U_12266,U_12265,U_12264,U_12263] : hAPP(c_Product__Type_Oprod_Oprod__case(U_12263,U_12264,U_12265),hAPP(hAPP(c_COMBB(tc_fun(U_12264,tc_prod(U_12263,U_12264)),tc_fun(U_12264,U_12265),U_12263),hAPP(c_COMBB(tc_prod(U_12263,U_12264),U_12265,U_12264),U_12266)),c_Product__Type_OPair(U_12263,U_12264))) = U_12266,
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

cnf(f_3162_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_12263,U_12264,U_12265),hAPP(hAPP(c_COMBB(tc_fun(U_12264,tc_prod(U_12263,U_12264)),tc_fun(U_12264,U_12265),U_12263),hAPP(c_COMBB(tc_prod(U_12263,U_12264),U_12265,U_12264),U_12266)),c_Product__Type_OPair(U_12263,U_12264))) = U_12266,
    inference(clausify,[status(thm)],[f_3162_2]) ).

fof(f_3163_1,plain,
    ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).

fof(f_3163_2,plain,
    ! [U_12269,U_12268,U_12267] : c_HOL_OThe(tc_prod(U_12267,U_12268),U_12269) = c_HOL_OThe(tc_prod(U_12267,U_12268),hAPP(c_Product__Type_Oprod_Oprod__case(U_12267,U_12268,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12268,tc_prod(U_12267,U_12268)),tc_fun(U_12268,tc_HOL_Obool),U_12267),hAPP(c_COMBB(tc_prod(U_12267,U_12268),tc_HOL_Obool,U_12268),U_12269)),c_Product__Type_OPair(U_12267,U_12268)))),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

cnf(f_3163_3,plain,
    c_HOL_OThe(tc_prod(U_12267,U_12268),U_12269) = c_HOL_OThe(tc_prod(U_12267,U_12268),hAPP(c_Product__Type_Oprod_Oprod__case(U_12267,U_12268,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12268,tc_prod(U_12267,U_12268)),tc_fun(U_12268,tc_HOL_Obool),U_12267),hAPP(c_COMBB(tc_prod(U_12267,U_12268),tc_HOL_Obool,U_12268),U_12269)),c_Product__Type_OPair(U_12267,U_12268)))),
    inference(clausify,[status(thm)],[f_3163_2]) ).

fof(f_3164_1,plain,
    ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_The__split__eq]) ).

fof(f_3164_2,plain,
    ! [U_12273,U_12272,U_12271,U_12270] : c_HOL_OThe(tc_prod(U_12270,U_12271),hAPP(c_Product__Type_Oprod_Oprod__case(U_12270,U_12271,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12270,tc_fun(U_12271,tc_HOL_Obool),tc_fun(U_12271,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12271,tc_HOL_Obool),tc_fun(U_12271,tc_HOL_Obool)),U_12270),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12271)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12270),c_fconj),hAPP(c_fequal,U_12272)))),hAPP(c_fequal,U_12273)))) = hAPP(hAPP(c_Product__Type_OPair(U_12270,U_12271),U_12272),U_12273),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

cnf(f_3164_3,plain,
    c_HOL_OThe(tc_prod(U_12270,U_12271),hAPP(c_Product__Type_Oprod_Oprod__case(U_12270,U_12271,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12270,tc_fun(U_12271,tc_HOL_Obool),tc_fun(U_12271,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12271,tc_HOL_Obool),tc_fun(U_12271,tc_HOL_Obool)),U_12270),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12271)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12270),c_fconj),hAPP(c_fequal,U_12272)))),hAPP(c_fequal,U_12273)))) = hAPP(hAPP(c_Product__Type_OPair(U_12270,U_12271),U_12272),U_12273),
    inference(clausify,[status(thm)],[f_3164_2]) ).

fof(f_3165_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_3165_2,plain,
    ! [U_12274] : c_Divides_Oadjust(U_12274) = 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_12274))))),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_12274))))),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_3165_1]) ).

cnf(f_3165_3,plain,
    c_Divides_Oadjust(U_12274) = 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_12274))))),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_12274))))),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_3165_2]) ).

fof(f_3166_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).

fof(f_3166_2,plain,
    ! [U_12279,U_12278,U_12277,U_12276,U_12275] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12275,U_12276,U_12277),U_12278),U_12279))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12275,U_12276)),hAPP(hAPP(c_Product__Type_OPair(U_12275,U_12276),U_12278),U_12279)),U_12277)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12275,U_12276)),hAPP(hAPP(c_Product__Type_OPair(U_12275,U_12276),U_12278),U_12279)),U_12277))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12275,U_12276,U_12277),U_12278),U_12279)) ) ),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

fof(f_3166_3,plain,
    ( ! [U_12289,U_12287,U_12285,U_12283,U_12281] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12281,U_12283,U_12285),U_12287),U_12289))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12281,U_12283)),hAPP(hAPP(c_Product__Type_OPair(U_12281,U_12283),U_12287),U_12289)),U_12285)) )
    & ! [U_12288,U_12286,U_12284,U_12282,U_12280] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12282)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12282),U_12286),U_12288)),U_12284))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12280,U_12282,U_12284),U_12286),U_12288)) ) ),
    inference(miniscope,[status(thm)],[f_3166_2]) ).

cnf(f_3166_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12282)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12282),U_12286),U_12288)),U_12284))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12280,U_12282,U_12284),U_12286),U_12288)) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

cnf(f_3166_5,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_12281,U_12283,U_12285),U_12287),U_12289))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12281,U_12283)),hAPP(hAPP(c_Product__Type_OPair(U_12281,U_12283),U_12287),U_12289)),U_12285)) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

fof(f_3167_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_3167_2,plain,
    ! [U_12291,U_12290] : c_Code__Numeral_Odiv__mod__code__numeral(U_12290,U_12291) = 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_12290),U_12291)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_12290,U_12291)),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

cnf(f_3167_3,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_12290,U_12291) = 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_12290),U_12291)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_12290,U_12291)),
    inference(clausify,[status(thm)],[f_3167_2]) ).

fof(f_3168_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_3168_2,plain,
    ! [U_12292] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)),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_12292))))
          | 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_12292)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)) = 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_12292)))
          | ~ 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_12292)))) ) )
      | ~ 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_12292))) ),
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

cnf(f_3168_3,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)) = 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_12292)))
    | ~ 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_12292))))
    | ~ 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_12292))) ),
    inference(clausify,[status(thm)],[f_3168_2]) ).

cnf(f_3168_4,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12292)),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_12292))))
    | 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_12292))))
    | ~ 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_12292))) ),
    inference(clausify,[status(thm)],[f_3168_2]) ).

fof(f_3169_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_3169_2,plain,
    ! [U_12294,U_12293] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12293,U_12294),c_Divides_OnegDivAlg(U_12293,U_12294)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12294))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12293),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

cnf(f_3169_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12293,U_12294),c_Divides_OnegDivAlg(U_12293,U_12294)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12294))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12293),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3169_2]) ).

fof(f_3170_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_3170_2,plain,
    ! [U_12296,U_12295] :
      ( c_Divides_OnegDivAlg(U_12295,U_12296) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12295),U_12296)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12295,U_12296))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12296))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12295),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

cnf(f_3170_3,plain,
    ( c_Divides_OnegDivAlg(U_12295,U_12296) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12295),U_12296)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12295,U_12296))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12296))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12295),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3170_2]) ).

fof(f_3171_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_3171_2,plain,
    ! [U_12297] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_12297) = 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_12297),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3171_1]) ).

cnf(f_3171_3,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_12297) = 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_12297),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3171_2]) ).

fof(f_3172_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_3172_2,plain,
    ! [U_12299,U_12298] :
      ( ( c_Divides_OnegDivAlg(U_12298,U_12299) = hAPP(c_Divides_Oadjust(U_12299),c_Divides_OnegDivAlg(U_12298,hAPP(hAPP(c_Groups_Otimes__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_12299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12299),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_12298),U_12299))) )
      & ( c_Divides_OnegDivAlg(U_12298,U_12299) = 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_12298),U_12299))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12299),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_12298),U_12299))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

fof(f_3172_3,plain,
    ( ! [U_12303,U_12301] :
        ( c_Divides_OnegDivAlg(U_12301,U_12303) = hAPP(c_Divides_Oadjust(U_12303),c_Divides_OnegDivAlg(U_12301,hAPP(hAPP(c_Groups_Otimes__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_12303)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12303),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_12301),U_12303))) )
    & ! [U_12302,U_12300] :
        ( c_Divides_OnegDivAlg(U_12300,U_12302) = 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_12300),U_12302))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12302),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_12300),U_12302))) ) ) ),
    inference(miniscope,[status(thm)],[f_3172_2]) ).

cnf(f_3172_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_12300),U_12302)))
    | c_Divides_OnegDivAlg(U_12300,U_12302) = 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_12300),U_12302)) ),
    inference(clausify,[status(thm)],[f_3172_3]) ).

cnf(f_3172_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12302),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_12300,U_12302) = 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_12300),U_12302)) ),
    inference(clausify,[status(thm)],[f_3172_3]) ).

cnf(f_3172_6,plain,
    ( c_Divides_OnegDivAlg(U_12301,U_12303) = hAPP(c_Divides_Oadjust(U_12303),c_Divides_OnegDivAlg(U_12301,hAPP(hAPP(c_Groups_Otimes__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_12303)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12303),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_12301),U_12303))) ),
    inference(clausify,[status(thm)],[f_3172_3]) ).

fof(f_3173_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_3173_2,plain,
    ! [U_12305,U_12304] :
      ( ( ( c_Divides_OnegDivAlg(U_12305,U_12304) = hAPP(c_Divides_Oadjust(U_12304),c_Divides_OnegDivAlg(U_12305,hAPP(hAPP(c_Groups_Otimes__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_12304)))
          | 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_12305),U_12304))) )
        & ( c_Divides_OnegDivAlg(U_12305,U_12304) = 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_12305),U_12304))
          | ~ 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_12305),U_12304))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12304)) ),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

cnf(f_3173_3,plain,
    ( c_Divides_OnegDivAlg(U_12305,U_12304) = 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_12305),U_12304))
    | ~ 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_12305),U_12304)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12304)) ),
    inference(clausify,[status(thm)],[f_3173_2]) ).

cnf(f_3173_4,plain,
    ( c_Divides_OnegDivAlg(U_12305,U_12304) = hAPP(c_Divides_Oadjust(U_12304),c_Divides_OnegDivAlg(U_12305,hAPP(hAPP(c_Groups_Otimes__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_12304)))
    | 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_12305),U_12304)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12304)) ),
    inference(clausify,[status(thm)],[f_3173_2]) ).

fof(f_3174_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_3174_2,plain,
    ! [U_12307,U_12306] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(hAPP(c_Groups_Otimes__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_12306))))
          | 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)) = 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)))
          | ~ 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)))) ) )
      | ~ 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_12306))) ),
    inference(variable_rename,[status(thm)],[f_3174_1]) ).

cnf(f_3174_3,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)) = 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)))
    | ~ 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306))))
    | ~ 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_12306))) ),
    inference(clausify,[status(thm)],[f_3174_2]) ).

cnf(f_3174_4,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12307),hAPP(hAPP(c_Groups_Otimes__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_12306))))
    | 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_12307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12306))))
    | ~ 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_12306))) ),
    inference(clausify,[status(thm)],[f_3174_2]) ).

fof(f_3175_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Nitpick_Orefl_H(T_a,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
        | ~ c_Nitpick_Orefl_H(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).

fof(f_3175_2,plain,
    ! [U_12311,U_12310] :
      ( ( c_Nitpick_Orefl_H(U_12310,U_12311)
        | ? [U_12309] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12310,U_12310)),hAPP(hAPP(c_Product__Type_OPair(U_12310,U_12310),U_12309),U_12309)),U_12311)) )
      & ( ! [U_12308] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12310,U_12310)),hAPP(hAPP(c_Product__Type_OPair(U_12310,U_12310),U_12308),U_12308)),U_12311))
        | ~ c_Nitpick_Orefl_H(U_12310,U_12311) ) ),
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

fof(f_3175_3,plain,
    ( ! [U_12315,U_12313] :
        ( c_Nitpick_Orefl_H(U_12313,U_12315)
        | ? [U_12309] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12313,U_12313)),hAPP(hAPP(c_Product__Type_OPair(U_12313,U_12313),U_12309),U_12309)),U_12315)) )
    & ! [U_12314,U_12312] :
        ( ! [U_12308] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12312,U_12312)),hAPP(hAPP(c_Product__Type_OPair(U_12312,U_12312),U_12308),U_12308)),U_12314))
        | ~ c_Nitpick_Orefl_H(U_12312,U_12314) ) ),
    inference(miniscope,[status(thm)],[f_3175_2]) ).

fof(f_3175_4,plain,
    ( ! [U_12315,U_12313] :
        ( c_Nitpick_Orefl_H(U_12313,U_12315)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12313,U_12313)),hAPP(hAPP(c_Product__Type_OPair(U_12313,U_12313),sK288(U_12315,U_12313)),sK288(U_12315,U_12313))),U_12315)) )
    & ! [U_12314,U_12312] :
        ( ! [U_12308] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12312,U_12312)),hAPP(hAPP(c_Product__Type_OPair(U_12312,U_12312),U_12308),U_12308)),U_12314))
        | ~ c_Nitpick_Orefl_H(U_12312,U_12314) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_12309,sK288(U_12315,U_12313))],[f_3175_3]) ).

cnf(f_3175_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12312,U_12312)),hAPP(hAPP(c_Product__Type_OPair(U_12312,U_12312),U_12308),U_12308)),U_12314))
    | ~ c_Nitpick_Orefl_H(U_12312,U_12314) ),
    inference(clausify,[status(thm)],[f_3175_4]) ).

cnf(f_3175_6,plain,
    ( c_Nitpick_Orefl_H(U_12313,U_12315)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12313,U_12313)),hAPP(hAPP(c_Product__Type_OPair(U_12313,U_12313),sK288(U_12315,U_12313)),sK288(U_12315,U_12313))),U_12315)) ),
    inference(clausify,[status(thm)],[f_3175_4]) ).

fof(f_3176_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_3176_2,plain,
    ! [U_12316] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)),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_12316))))
          | 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_12316))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)) = 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_12316))) ) )
      | ~ 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_12316))) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

cnf(f_3176_3,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)) = 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_12316)))
    | ~ 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_12316))) ),
    inference(clausify,[status(thm)],[f_3176_2]) ).

cnf(f_3176_4,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12316)),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_12316))))
    | 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_12316)))
    | ~ 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_12316))) ),
    inference(clausify,[status(thm)],[f_3176_2]) ).

fof(f_3177_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_3177_2,plain,
    ! [U_12318,U_12317] :
      ( ( c_Divides_OposDivAlg(U_12317,U_12318) = hAPP(c_Divides_Oadjust(U_12318),c_Divides_OposDivAlg(U_12317,hAPP(hAPP(c_Groups_Otimes__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_12318)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12318),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12317),U_12318)) )
      & ( c_Divides_OposDivAlg(U_12317,U_12318) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12317)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12318),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12317),U_12318)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

fof(f_3177_3,plain,
    ( ! [U_12322,U_12320] :
        ( c_Divides_OposDivAlg(U_12320,U_12322) = hAPP(c_Divides_Oadjust(U_12322),c_Divides_OposDivAlg(U_12320,hAPP(hAPP(c_Groups_Otimes__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_12322)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12322),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12320),U_12322)) )
    & ! [U_12321,U_12319] :
        ( c_Divides_OposDivAlg(U_12319,U_12321) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12319)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12321),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12319),U_12321)) ) ) ),
    inference(miniscope,[status(thm)],[f_3177_2]) ).

cnf(f_3177_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12319),U_12321))
    | c_Divides_OposDivAlg(U_12319,U_12321) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12319) ),
    inference(clausify,[status(thm)],[f_3177_3]) ).

cnf(f_3177_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12321),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_12319,U_12321) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12319) ),
    inference(clausify,[status(thm)],[f_3177_3]) ).

cnf(f_3177_6,plain,
    ( c_Divides_OposDivAlg(U_12320,U_12322) = hAPP(c_Divides_Oadjust(U_12322),c_Divides_OposDivAlg(U_12320,hAPP(hAPP(c_Groups_Otimes__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_12322)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12322),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12320),U_12322)) ),
    inference(clausify,[status(thm)],[f_3177_3]) ).

fof(f_3178_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_3178_2,plain,
    ! [U_12323] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_12323) = 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_3178_1]) ).

cnf(f_3178_3,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_12323) = 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_3178_2]) ).

fof(f_3179_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_3179_2,plain,
    ! [U_12325,U_12324] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12324,U_12325),c_Divides_OposDivAlg(U_12324,U_12325)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12324)) ),
    inference(variable_rename,[status(thm)],[f_3179_1]) ).

cnf(f_3179_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12324,U_12325),c_Divides_OposDivAlg(U_12324,U_12325)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12324)) ),
    inference(clausify,[status(thm)],[f_3179_2]) ).

fof(f_3180_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_3180_2,plain,
    ! [U_12327,U_12326] :
      ( c_Divides_OposDivAlg(U_12326,U_12327) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12326),U_12327)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12326,U_12327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12326)) ),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

cnf(f_3180_3,plain,
    ( c_Divides_OposDivAlg(U_12326,U_12327) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12326),U_12327)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12326,U_12327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12326)) ),
    inference(clausify,[status(thm)],[f_3180_2]) ).

fof(f_3181_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_3181_2,plain,
    ! [U_12329,U_12328] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(hAPP(c_Groups_Otimes__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_12328))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)) = 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_12329))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328))) ) )
      | ~ 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_12328))) ),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

cnf(f_3181_3,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)) = 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_12329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)))
    | ~ 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_12328))) ),
    inference(clausify,[status(thm)],[f_3181_2]) ).

cnf(f_3181_4,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329),hAPP(hAPP(c_Groups_Otimes__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_12328))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12329)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12328)))
    | ~ 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_12328))) ),
    inference(clausify,[status(thm)],[f_3181_2]) ).

fof(f_3182_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_3182_2,plain,
    ! [U_12331,U_12330] :
      ( ( ( c_Divides_OposDivAlg(U_12331,U_12330) = hAPP(c_Divides_Oadjust(U_12330),c_Divides_OposDivAlg(U_12331,hAPP(hAPP(c_Groups_Otimes__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_12330)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12331),U_12330)) )
        & ( c_Divides_OposDivAlg(U_12331,U_12330) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12331)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12331),U_12330)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12330)) ),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

cnf(f_3182_3,plain,
    ( c_Divides_OposDivAlg(U_12331,U_12330) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12331)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12331),U_12330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12330)) ),
    inference(clausify,[status(thm)],[f_3182_2]) ).

cnf(f_3182_4,plain,
    ( c_Divides_OposDivAlg(U_12331,U_12330) = hAPP(c_Divides_Oadjust(U_12330),c_Divides_OposDivAlg(U_12331,hAPP(hAPP(c_Groups_Otimes__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_12330)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12331),U_12330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12330)) ),
    inference(clausify,[status(thm)],[f_3182_2]) ).

fof(f_3183_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_3183_2,plain,
    ! [U_12333,U_12332] :
      ( ( ( ( c_Divides_Odivmod__int(U_12332,U_12333) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12332),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12333)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12333)) )
          & ( c_Divides_Odivmod__int(U_12332,U_12333) = c_Divides_OnegDivAlg(U_12332,U_12333)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12333)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12332)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_12332,U_12333) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12332),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12333)))
                | U_12332 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_12332,U_12333) = 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_12332 != 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_12333)) )
          & ( c_Divides_Odivmod__int(U_12332,U_12333) = c_Divides_OposDivAlg(U_12332,U_12333)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12333)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12332)) ) ),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

fof(f_3183_3,plain,
    ( ! [U_12337,U_12335] :
        ( ( ( c_Divides_Odivmod__int(U_12335,U_12337) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12335),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12337)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12337)) )
          & ( c_Divides_Odivmod__int(U_12335,U_12337) = c_Divides_OnegDivAlg(U_12335,U_12337)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12337)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12335)) )
    & ! [U_12336,U_12334] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_12334,U_12336) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12334),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12336)))
                | U_12334 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_12334,U_12336) = 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_12334 != 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_12336)) )
          & ( c_Divides_Odivmod__int(U_12334,U_12336) = c_Divides_OposDivAlg(U_12334,U_12336)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12336)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12334)) ) ),
    inference(miniscope,[status(thm)],[f_3183_2]) ).

cnf(f_3183_4,plain,
    ( c_Divides_Odivmod__int(U_12334,U_12336) = c_Divides_OposDivAlg(U_12334,U_12336)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12334)) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_5,plain,
    ( c_Divides_Odivmod__int(U_12334,U_12336) = 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_12334 != 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_12336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12334)) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_6,plain,
    ( c_Divides_Odivmod__int(U_12334,U_12336) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12334),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12336)))
    | U_12334 = 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_12336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12334)) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_7,plain,
    ( c_Divides_Odivmod__int(U_12335,U_12337) = c_Divides_OnegDivAlg(U_12335,U_12337)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12337))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12335)) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_8,plain,
    ( c_Divides_Odivmod__int(U_12335,U_12337) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12335),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12337)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12337))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12335)) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

fof(f_3184_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_3184_2,plain,
    ! [U_12339,U_12338] :
      ( c_Divides_Odivmod__nat(U_12339,U_12338) = 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_12339),U_12338)),U_12338))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12339),U_12338),U_12338))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12338),U_12339))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12338)) ),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

cnf(f_3184_3,plain,
    ( c_Divides_Odivmod__nat(U_12339,U_12338) = 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_12339),U_12338)),U_12338))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12339),U_12338),U_12338))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12338),U_12339))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12338)) ),
    inference(clausify,[status(thm)],[f_3184_2]) ).

fof(f_3185_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_3185_2,plain,
    ! [U_12341,U_12340] :
      ( ( ( ( c_Divides_Odivmod__int(U_12340,U_12341) = 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_12341))),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_12341)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12340))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12341),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12340),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_12340,U_12341)),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_12341))))),c_Divides_Opdivmod(U_12340,U_12341))))
            | U_12341 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_12340,U_12341) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12340)
            | U_12341 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_12340 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_12340,U_12341) = 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_12340 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

fof(f_3185_3,plain,
    ( ! [U_12345,U_12343] :
        ( ( ( c_Divides_Odivmod__int(U_12343,U_12345) = 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_12345))),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_12345)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12343))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12345),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12343),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_12343,U_12345)),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_12345))))),c_Divides_Opdivmod(U_12343,U_12345))))
            | U_12345 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_12343,U_12345) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12343)
            | U_12345 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_12343 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_12344,U_12342] :
        ( c_Divides_Odivmod__int(U_12342,U_12344) = 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_12342 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_3185_2]) ).

cnf(f_3185_4,plain,
    ( c_Divides_Odivmod__int(U_12342,U_12344) = 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_12342 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

cnf(f_3185_5,plain,
    ( c_Divides_Odivmod__int(U_12343,U_12345) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12343)
    | U_12345 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12343 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

cnf(f_3185_6,plain,
    ( c_Divides_Odivmod__int(U_12343,U_12345) = 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_12345))),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_12345)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12343))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12345),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12343),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_12343,U_12345)),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_12345))))),c_Divides_Opdivmod(U_12343,U_12345))))
    | U_12345 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12343 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

fof(f_3186_1,plain,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__compose]) ).

fof(f_3186_2,plain,
    ! [U_12352,U_12351,U_12350,U_12349,U_12348,U_12347,U_12346] : hAPP(c_Product__Type_Oapsnd(U_12346,U_12347,U_12348,U_12349),hAPP(c_Product__Type_Oapsnd(U_12350,U_12346,U_12348,U_12351),U_12352)) = hAPP(c_Product__Type_Oapsnd(U_12350,U_12347,U_12348,hAPP(c_Fun_Ocomp(U_12346,U_12347,U_12350,U_12349),U_12351)),U_12352),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

cnf(f_3186_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_12346,U_12347,U_12348,U_12349),hAPP(c_Product__Type_Oapsnd(U_12350,U_12346,U_12348,U_12351),U_12352)) = hAPP(c_Product__Type_Oapsnd(U_12350,U_12347,U_12348,hAPP(c_Fun_Ocomp(U_12346,U_12347,U_12350,U_12349),U_12351)),U_12352),
    inference(clausify,[status(thm)],[f_3186_2]) ).

fof(f_3187_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]) ).

cnf(f_3187_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(clausify,[status(thm)],[f_3187_1]) ).

fof(f_3188_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).

fof(f_3188_2,plain,
    ! [U_12358,U_12357,U_12356,U_12355,U_12354,U_12353] : hAPP(c_Product__Type_Oapsnd(U_12353,U_12354,U_12355,U_12356),hAPP(hAPP(c_Product__Type_OPair(U_12355,U_12353),U_12357),U_12358)) = hAPP(hAPP(c_Product__Type_OPair(U_12355,U_12354),U_12357),hAPP(U_12356,U_12358)),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

cnf(f_3188_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_12353,U_12354,U_12355,U_12356),hAPP(hAPP(c_Product__Type_OPair(U_12355,U_12353),U_12357),U_12358)) = hAPP(hAPP(c_Product__Type_OPair(U_12355,U_12354),U_12357),hAPP(U_12356,U_12358)),
    inference(clausify,[status(thm)],[f_3188_2]) ).

fof(f_3189_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_3189_2,plain,
    ! [U_12359] : c_Divides_Odivmod__nat(U_12359,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_12359),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

cnf(f_3189_3,plain,
    c_Divides_Odivmod__nat(U_12359,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_12359),
    inference(clausify,[status(thm)],[f_3189_2]) ).

fof(f_3190_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_3190_2,plain,
    ! [U_12361,U_12360] :
      ( c_Divides_Odivmod__nat(U_12360,U_12361) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12360)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12360),U_12361)) ),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

cnf(f_3190_3,plain,
    ( c_Divides_Odivmod__nat(U_12360,U_12361) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12360)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12360),U_12361)) ),
    inference(clausify,[status(thm)],[f_3190_2]) ).

fof(f_3191_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_3191_2,plain,
    ! [U_12363,U_12362] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12362),U_12363)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12362),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12363)),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

cnf(f_3191_3,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12362),U_12363)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12362),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12363)),
    inference(clausify,[status(thm)],[f_3191_2]) ).

fof(f_3192_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_3192_2,plain,
    ! [U_12365,U_12364] : c_Divides_Odivmod__nat(U_12364,U_12365) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12364),U_12365)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12364,U_12365)),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

cnf(f_3192_3,plain,
    c_Divides_Odivmod__nat(U_12364,U_12365) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12364),U_12365)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12364,U_12365)),
    inference(clausify,[status(thm)],[f_3192_2]) ).

fof(f_3193_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_3193_2,plain,
    ! [U_12368,U_12367,U_12366] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12366,U_12367),hAPP(c_Divides_OnegateSnd,U_12368)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12366),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12367)),U_12368)) ),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

cnf(f_3193_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_12366,U_12367),hAPP(c_Divides_OnegateSnd,U_12368)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12366),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12367)),U_12368)) ),
    inference(clausify,[status(thm)],[f_3193_2]) ).

fof(f_3194_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_3194_2,plain,
    ! [U_12370,U_12369] :
      ( ( c_Divides_Odivmod__nat(U_12370,U_12369) = 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_12370),U_12369),U_12369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12370),U_12369))
        | U_12369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_12370,U_12369) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12370)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12370),U_12369))
          & U_12369 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

fof(f_3194_3,plain,
    ( ! [U_12374,U_12372] :
        ( c_Divides_Odivmod__nat(U_12374,U_12372) = 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_12374),U_12372),U_12372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12374),U_12372))
        | U_12372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_12373,U_12371] :
        ( c_Divides_Odivmod__nat(U_12373,U_12371) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12373)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12373),U_12371))
          & U_12371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_3194_2]) ).

cnf(f_3194_4,plain,
    ( U_12371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Divides_Odivmod__nat(U_12373,U_12371) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12373) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

cnf(f_3194_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12373),U_12371))
    | c_Divides_Odivmod__nat(U_12373,U_12371) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12373) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

cnf(f_3194_6,plain,
    ( c_Divides_Odivmod__nat(U_12374,U_12372) = 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_12374),U_12372),U_12372))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12374),U_12372))
    | U_12372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

fof(f_3195_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_3195_2,plain,
    ! [U_12376,U_12375] : c_Divides_Opdivmod(U_12375,U_12376) = 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_12375)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12376))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12375),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12376))),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

cnf(f_3195_3,plain,
    c_Divides_Opdivmod(U_12375,U_12376) = 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_12375)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12376))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12375),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12376))),
    inference(clausify,[status(thm)],[f_3195_2]) ).

fof(f_3196_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_3196_2,plain,
    ! [U_12378,U_12377] :
      ( ( c_Divides_Opdivmod(U_12378,U_12377) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12378),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12377))
        | U_12377 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_12378,U_12377) = 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_12378))
        | U_12377 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

fof(f_3196_3,plain,
    ( ! [U_12382,U_12380] :
        ( c_Divides_Opdivmod(U_12382,U_12380) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12382),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12380))
        | U_12380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_12381,U_12379] :
        ( c_Divides_Opdivmod(U_12381,U_12379) = 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_12381))
        | U_12379 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_3196_2]) ).

cnf(f_3196_4,plain,
    ( c_Divides_Opdivmod(U_12381,U_12379) = 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_12381))
    | U_12379 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3196_3]) ).

cnf(f_3196_5,plain,
    ( c_Divides_Opdivmod(U_12382,U_12380) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12382),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_12380))
    | U_12380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3196_3]) ).

fof(f_3197_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_3197_2,plain,
    ! [U_12384,U_12383] :
      ( ( ( ( c_Divides_Odivmod__int(U_12383,U_12384) = 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_12384))),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_12383)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_12384))),c_Divides_Opdivmod(U_12383,U_12384)),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_12384))))),c_Divides_Opdivmod(U_12383,U_12384))))
            | U_12384 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_12383,U_12384) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12383)
            | U_12384 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_12383 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_12383,U_12384) = 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_12383 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

fof(f_3197_3,plain,
    ( ! [U_12388,U_12386] :
        ( ( ( c_Divides_Odivmod__int(U_12386,U_12388) = 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_12388))),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_12386)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_12388))),c_Divides_Opdivmod(U_12386,U_12388)),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_12388))))),c_Divides_Opdivmod(U_12386,U_12388))))
            | U_12388 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_12386,U_12388) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12386)
            | U_12388 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_12386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_12387,U_12385] :
        ( c_Divides_Odivmod__int(U_12385,U_12387) = 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_12385 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_3197_2]) ).

cnf(f_3197_4,plain,
    ( c_Divides_Odivmod__int(U_12385,U_12387) = 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_12385 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3197_3]) ).

cnf(f_3197_5,plain,
    ( c_Divides_Odivmod__int(U_12386,U_12388) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12386)
    | U_12388 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3197_3]) ).

cnf(f_3197_6,plain,
    ( c_Divides_Odivmod__int(U_12386,U_12388) = 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_12388))),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_12386)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_12388))),c_Divides_Opdivmod(U_12386,U_12388)),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_12388))))),c_Divides_Opdivmod(U_12386,U_12388))))
    | U_12388 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_3197_3]) ).

fof(f_3198_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_3198_2,plain,
    ! [U_12393,U_12392,U_12391,U_12390,U_12389] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12389,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12390),U_12393)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12391),U_12393)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12390),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12391,U_12393))),U_12392))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12390))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12389,U_12390),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12391),U_12392))) ),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

cnf(f_3198_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12389,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12390),U_12393)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12391),U_12393)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12390),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12391,U_12393))),U_12392))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12390))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12389,U_12390),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12391),U_12392))) ),
    inference(clausify,[status(thm)],[f_3198_2]) ).

fof(f_3199_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_3199_2,plain,
    ! [U_12398,U_12397,U_12396,U_12395,U_12394] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12394),U_12395),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_12398),U_12396)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12397)),U_12395))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12397),U_12395))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12395))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12394,U_12395),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12396),U_12397))) ),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

cnf(f_3199_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12394),U_12395),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_12398),U_12396)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12397)),U_12395))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12398),U_12397),U_12395))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12395))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12394,U_12395),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12396),U_12397))) ),
    inference(clausify,[status(thm)],[f_3199_2]) ).

fof(f_3200_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_3200_2,plain,
    ! [U_12400,U_12399] :
      ( ( ( c_Divides_OnegDivAlg(U_12399,U_12400) = hAPP(c_Divides_Oadjust(U_12400),c_Divides_OnegDivAlg(U_12399,hAPP(hAPP(c_Groups_Otimes__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_12400)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12400),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_12399),U_12400))) )
        & ( c_Divides_OnegDivAlg(U_12399,U_12400) = 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_12399),U_12400))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12400),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_12399),U_12400))) ) ) )
      | ~ 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_12399),U_12400))) ),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

cnf(f_3200_3,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_12399),U_12400)))
    | c_Divides_OnegDivAlg(U_12399,U_12400) = 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_12399),U_12400))
    | ~ 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_12399),U_12400))) ),
    inference(clausify,[status(thm)],[f_3200_2]) ).

cnf(f_3200_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12400),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_12399,U_12400) = 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_12399),U_12400))
    | ~ 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_12399),U_12400))) ),
    inference(clausify,[status(thm)],[f_3200_2]) ).

cnf(f_3200_5,plain,
    ( c_Divides_OnegDivAlg(U_12399,U_12400) = hAPP(c_Divides_Oadjust(U_12400),c_Divides_OnegDivAlg(U_12399,hAPP(hAPP(c_Groups_Otimes__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_12400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12400),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_12399),U_12400)))
    | ~ 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_12399),U_12400))) ),
    inference(clausify,[status(thm)],[f_3200_2]) ).

fof(f_3201_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_3201_2,plain,
    ! [U_12404,U_12403,U_12402,U_12401] :
      ( U_12403 = U_12404
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12401,U_12402),U_12404))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12401,U_12402),U_12403)) ),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

cnf(f_3201_3,plain,
    ( U_12403 = U_12404
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12401,U_12402),U_12404))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12401,U_12402),U_12403)) ),
    inference(clausify,[status(thm)],[f_3201_2]) ).

fof(f_3202_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_3202_2,plain,
    ! [U_12406,U_12405] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12405,U_12406),c_Divides_Odivmod__nat(U_12405,U_12406))),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

cnf(f_3202_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12405,U_12406),c_Divides_Odivmod__nat(U_12405,U_12406))),
    inference(clausify,[status(thm)],[f_3202_2]) ).

fof(f_3203_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_3203_2,plain,
    ! [U_12409,U_12408,U_12407] :
      ( c_Divides_Odivmod__nat(U_12407,U_12408) = U_12409
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12407,U_12408),U_12409)) ),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

cnf(f_3203_3,plain,
    ( c_Divides_Odivmod__nat(U_12407,U_12408) = U_12409
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12407,U_12408),U_12409)) ),
    inference(clausify,[status(thm)],[f_3203_2]) ).

fof(f_3204_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_3204_2,plain,
    ! [U_12411,U_12410] : c_Divides_Odivmod__nat(U_12410,U_12411) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_12410,U_12411)),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

cnf(f_3204_3,plain,
    c_Divides_Odivmod__nat(U_12410,U_12411) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_12410,U_12411)),
    inference(clausify,[status(thm)],[f_3204_2]) ).

fof(f_3205_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_3205_2,plain,
    ! [U_12415,U_12414,U_12413,U_12412] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12412,U_12413) = U_12415
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12412,U_12413),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12414),U_12415))) ),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

cnf(f_3205_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12412,U_12413) = U_12415
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12412,U_12413),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12414),U_12415))) ),
    inference(clausify,[status(thm)],[f_3205_2]) ).

fof(f_3206_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_3206_2,plain,
    ! [U_12419,U_12418,U_12417,U_12416] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12416),U_12417) = U_12418
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12416,U_12417),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12418),U_12419))) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

cnf(f_3206_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12416),U_12417) = U_12418
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12416,U_12417),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12418),U_12419))) ),
    inference(clausify,[status(thm)],[f_3206_2]) ).

fof(f_3207_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_3207_2,plain,
    ! [U_12421,U_12420] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12420,U_12421),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12420),U_12421)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12420,U_12421)))),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

cnf(f_3207_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12420,U_12421),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12420),U_12421)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12420,U_12421)))),
    inference(clausify,[status(thm)],[f_3207_2]) ).

fof(f_3208_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_3208_2,plain,
    ! [U_12428,U_12427,U_12426,U_12425,U_12424,U_12423,U_12422] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12422),U_12426),U_12423),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_12424),U_12427)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12425),U_12428)),U_12423))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12425),U_12428),U_12423))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12423))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12426,U_12423),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12427),U_12428)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12422,U_12423),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12424),U_12425))) ),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

cnf(f_3208_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12422),U_12426),U_12423),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_12424),U_12427)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12425),U_12428)),U_12423))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12425),U_12428),U_12423))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12423))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12426,U_12423),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12427),U_12428)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12422,U_12423),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_12424),U_12425))) ),
    inference(clausify,[status(thm)],[f_3208_2]) ).

fof(f_3209_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_3209_2,plain,
    ! [U_12430,U_12429] :
      ( ( ( c_Divides_OposDivAlg(U_12429,U_12430) = hAPP(c_Divides_Oadjust(U_12430),c_Divides_OposDivAlg(U_12429,hAPP(hAPP(c_Groups_Otimes__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_12430)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12430),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12429),U_12430)) )
        & ( c_Divides_OposDivAlg(U_12429,U_12430) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12429)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12430),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12429),U_12430)) ) ) )
      | ~ 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_12429),U_12430))) ),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

cnf(f_3209_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12429),U_12430))
    | c_Divides_OposDivAlg(U_12429,U_12430) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12429)
    | ~ 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_12429),U_12430))) ),
    inference(clausify,[status(thm)],[f_3209_2]) ).

cnf(f_3209_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12430),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_12429,U_12430) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12429)
    | ~ 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_12429),U_12430))) ),
    inference(clausify,[status(thm)],[f_3209_2]) ).

cnf(f_3209_5,plain,
    ( c_Divides_OposDivAlg(U_12429,U_12430) = hAPP(c_Divides_Oadjust(U_12430),c_Divides_OposDivAlg(U_12429,hAPP(hAPP(c_Groups_Otimes__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_12430)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12430),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12429),U_12430))
    | ~ 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_12429),U_12430))) ),
    inference(clausify,[status(thm)],[f_3209_2]) ).

fof(f_3210_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_3210_2,plain,
    ! [U_12432,U_12431] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_12431,U_12432) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_12431),U_12432)),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_12431))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12432)))
              | U_12432 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_12431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_12431,U_12432) = 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_12432 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_12431 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12432),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_12431,U_12432) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12431),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12432))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12432),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_12431),U_12432))) ),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

cnf(f_3210_3,plain,
    ( c_Nitpick_Onorm__frac(U_12431,U_12432) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12431),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12432),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_12431),U_12432))) ),
    inference(clausify,[status(thm)],[f_3210_2]) ).

cnf(f_3210_4,plain,
    ( U_12431 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_12431,U_12432) = 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),U_12432),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_12431),U_12432))) ),
    inference(clausify,[status(thm)],[f_3210_2]) ).

cnf(f_3210_5,plain,
    ( U_12432 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_12431,U_12432) = 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),U_12432),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_12431),U_12432))) ),
    inference(clausify,[status(thm)],[f_3210_2]) ).

cnf(f_3210_6,plain,
    ( c_Nitpick_Onorm__frac(U_12431,U_12432) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_12431),U_12432)),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_12431))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12432)))
    | U_12432 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_12431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12432),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_12431),U_12432))) ),
    inference(clausify,[status(thm)],[f_3210_2]) ).

fof(f_3211_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct]) ).

fof(f_3211_2,plain,
    ! [U_12437,U_12436,U_12435] :
      ( hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
      | ? [U_12434,U_12433] :
          ( ~ hBOOL(hAPP(hAPP(U_12437,U_12434),U_12433))
          & ( hBOOL(hAPP(hAPP(U_12437,U_12434),hAPP(hAPP(c_Groups_Otimes__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_12433)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12433),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_12434),U_12433))) )
          & 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_12434),U_12433))) )
      | ~ 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_12435),U_12436))) ),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

fof(f_3211_3,plain,
    ! [U_12437,U_12436,U_12435] :
      ( hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
      | ? [U_12433] :
          ( ~ hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),U_12433))
          & ( hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),hAPP(hAPP(c_Groups_Otimes__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_12433)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12433),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),sK289(U_12437,U_12436,U_12435)),U_12433))) )
          & 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),sK289(U_12437,U_12436,U_12435)),U_12433))) )
      | ~ 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_12435),U_12436))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_12434,sK289(U_12437,U_12436,U_12435))],[f_3211_2]) ).

fof(f_3211_4,plain,
    ! [U_12437,U_12436,U_12435] :
      ( hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
      | ( ~ hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435)))
        & ( hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK290(U_12437,U_12436,U_12435))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK290(U_12437,U_12436,U_12435)),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),sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435)))) )
        & 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),sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435)))) )
      | ~ 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_12435),U_12436))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_12433,sK290(U_12437,U_12436,U_12435))],[f_3211_3]) ).

cnf(f_3211_5,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),sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435))))
    | hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
    | ~ 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_12435),U_12436))) ),
    inference(clausify,[status(thm)],[f_3211_4]) ).

cnf(f_3211_6,plain,
    ( hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK290(U_12437,U_12436,U_12435))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK290(U_12437,U_12436,U_12435)),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),sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435))))
    | hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
    | ~ 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_12435),U_12436))) ),
    inference(clausify,[status(thm)],[f_3211_4]) ).

cnf(f_3211_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12437,sK289(U_12437,U_12436,U_12435)),sK290(U_12437,U_12436,U_12435)))
    | hBOOL(hAPP(hAPP(U_12437,U_12435),U_12436))
    | ~ 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_12435),U_12436))) ),
    inference(clausify,[status(thm)],[f_3211_4]) ).

fof(f_3212_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct]) ).

fof(f_3212_2,plain,
    ! [U_12442,U_12441,U_12440] :
      ( hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
      | ? [U_12439,U_12438] :
          ( ~ hBOOL(hAPP(hAPP(U_12442,U_12439),U_12438))
          & ( hBOOL(hAPP(hAPP(U_12442,U_12439),hAPP(hAPP(c_Groups_Otimes__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_12438)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12438),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12439),U_12438)) )
          & 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_12439),U_12438))) )
      | ~ 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_12440),U_12441))) ),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

fof(f_3212_3,plain,
    ! [U_12442,U_12441,U_12440] :
      ( hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
      | ? [U_12438] :
          ( ~ hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),U_12438))
          & ( hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),hAPP(hAPP(c_Groups_Otimes__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_12438)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12438),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK291(U_12442,U_12441,U_12440)),U_12438)) )
          & 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),sK291(U_12442,U_12441,U_12440)),U_12438))) )
      | ~ 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_12440),U_12441))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_12439,sK291(U_12442,U_12441,U_12440))],[f_3212_2]) ).

fof(f_3212_4,plain,
    ! [U_12442,U_12441,U_12440] :
      ( hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
      | ( ~ hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440)))
        & ( hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK292(U_12442,U_12441,U_12440))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK292(U_12442,U_12441,U_12440)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440))) )
        & 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),sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440)))) )
      | ~ 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_12440),U_12441))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_12438,sK292(U_12442,U_12441,U_12440))],[f_3212_3]) ).

cnf(f_3212_5,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),sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440))))
    | hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
    | ~ 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_12440),U_12441))) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

cnf(f_3212_6,plain,
    ( hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK292(U_12442,U_12441,U_12440))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK292(U_12442,U_12441,U_12440)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440)))
    | hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
    | ~ 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_12440),U_12441))) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

cnf(f_3212_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12442,sK291(U_12442,U_12441,U_12440)),sK292(U_12442,U_12441,U_12440)))
    | hBOOL(hAPP(hAPP(U_12442,U_12440),U_12441))
    | ~ 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_12440),U_12441))) ),
    inference(clausify,[status(thm)],[f_3212_4]) ).

fof(f_3213_1,plain,
    ! [V_R2_2,V_R1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).

fof(f_3213_2,plain,
    ! [U_12445,U_12444,U_12443] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12443,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_12443,U_12445)),c_Wellfounded_Oaccp(U_12443,U_12444)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12443,tc_fun(U_12443,tc_HOL_Obool))),U_12444),U_12445)) ),
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

cnf(f_3213_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12443,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_12443,U_12445)),c_Wellfounded_Oaccp(U_12443,U_12444)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12443,tc_fun(U_12443,tc_HOL_Obool))),U_12444),U_12445)) ),
    inference(clausify,[status(thm)],[f_3213_2]) ).

fof(f_3214_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_3214_2,plain,
    ! [U_12446] :
      ( 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_12446)) = 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_12446)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12446)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

cnf(f_3214_3,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_12446)) = 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_12446)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12446)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3214_2]) ).

fof(f_3215_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_3215_2,plain,
    ! [U_12451,U_12450,U_12449,U_12448,U_12447] :
      ( U_12450 = U_12451
      | hAPP(c_Product__Type_Osnd(U_12447,U_12448),hAPP(hAPP(c_Product__Type_OPair(U_12447,U_12448),U_12449),U_12450)) != U_12451 ),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

fof(f_3215_3,plain,
    ! [U_12451,U_12450] :
      ( ! [U_12449,U_12448,U_12447] : hAPP(c_Product__Type_Osnd(U_12447,U_12448),hAPP(hAPP(c_Product__Type_OPair(U_12447,U_12448),U_12449),U_12450)) != U_12451
      | U_12450 = U_12451 ),
    inference(miniscope,[status(thm)],[f_3215_2]) ).

cnf(f_3215_4,plain,
    ( hAPP(c_Product__Type_Osnd(U_12447,U_12448),hAPP(hAPP(c_Product__Type_OPair(U_12447,U_12448),U_12449),U_12450)) != U_12451
    | U_12450 = U_12451 ),
    inference(clausify,[status(thm)],[f_3215_3]) ).

fof(f_3216_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_3216_2,plain,
    ! [U_12455,U_12454,U_12453,U_12452] : hAPP(c_Product__Type_Osnd(U_12452,U_12453),hAPP(hAPP(c_Product__Type_OPair(U_12452,U_12453),U_12454),U_12455)) = U_12455,
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

cnf(f_3216_3,plain,
    hAPP(c_Product__Type_Osnd(U_12452,U_12453),hAPP(hAPP(c_Product__Type_OPair(U_12452,U_12453),U_12454),U_12455)) = U_12455,
    inference(clausify,[status(thm)],[f_3216_2]) ).

fof(f_3217_1,plain,
    ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_snd__def]) ).

fof(f_3217_2,plain,
    ! [U_12458,U_12457,U_12456] : hAPP(c_Product__Type_Osnd(U_12456,U_12457),U_12458) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12456,U_12457,U_12457),hAPP(c_COMBK(tc_fun(U_12457,U_12457),U_12456),c_COMBI(U_12457))),U_12458),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

cnf(f_3217_3,plain,
    hAPP(c_Product__Type_Osnd(U_12456,U_12457),U_12458) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12456,U_12457,U_12457),hAPP(c_COMBK(tc_fun(U_12457,U_12457),U_12456),c_COMBI(U_12457))),U_12458),
    inference(clausify,[status(thm)],[f_3217_2]) ).

fof(f_3218_1,plain,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).

fof(f_3218_2,plain,
    ! [U_12463,U_12462,U_12461,U_12460,U_12459] : hAPP(c_Product__Type_Osnd(U_12459,U_12460),hAPP(c_Product__Type_Oapsnd(U_12461,U_12460,U_12459,U_12462),U_12463)) = hAPP(U_12462,hAPP(c_Product__Type_Osnd(U_12459,U_12461),U_12463)),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

cnf(f_3218_3,plain,
    hAPP(c_Product__Type_Osnd(U_12459,U_12460),hAPP(c_Product__Type_Oapsnd(U_12461,U_12460,U_12459,U_12462),U_12463)) = hAPP(U_12462,hAPP(c_Product__Type_Osnd(U_12459,U_12461),U_12463)),
    inference(clausify,[status(thm)],[f_3218_2]) ).

fof(f_3219_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
      ( ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2))
        | hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).

fof(f_3219_2,plain,
    ! [U_12469,U_12468,U_12467,U_12466,U_12465,U_12464] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_12464,U_12465,U_12466,U_12467),U_12468) = hAPP(c_Product__Type_Oapsnd(U_12464,U_12465,U_12466,U_12469),U_12468)
        | hAPP(U_12467,hAPP(c_Product__Type_Osnd(U_12466,U_12464),U_12468)) != hAPP(U_12469,hAPP(c_Product__Type_Osnd(U_12466,U_12464),U_12468)) )
      & ( hAPP(U_12467,hAPP(c_Product__Type_Osnd(U_12466,U_12464),U_12468)) = hAPP(U_12469,hAPP(c_Product__Type_Osnd(U_12466,U_12464),U_12468))
        | hAPP(c_Product__Type_Oapsnd(U_12464,U_12465,U_12466,U_12467),U_12468) != hAPP(c_Product__Type_Oapsnd(U_12464,U_12465,U_12466,U_12469),U_12468) ) ),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

fof(f_3219_3,plain,
    ( ! [U_12481,U_12479,U_12477,U_12475,U_12473,U_12471] :
        ( hAPP(c_Product__Type_Oapsnd(U_12471,U_12473,U_12475,U_12477),U_12479) = hAPP(c_Product__Type_Oapsnd(U_12471,U_12473,U_12475,U_12481),U_12479)
        | hAPP(U_12477,hAPP(c_Product__Type_Osnd(U_12475,U_12471),U_12479)) != hAPP(U_12481,hAPP(c_Product__Type_Osnd(U_12475,U_12471),U_12479)) )
    & ! [U_12480,U_12478,U_12476,U_12474,U_12472,U_12470] :
        ( hAPP(U_12476,hAPP(c_Product__Type_Osnd(U_12474,U_12470),U_12478)) = hAPP(U_12480,hAPP(c_Product__Type_Osnd(U_12474,U_12470),U_12478))
        | hAPP(c_Product__Type_Oapsnd(U_12470,U_12472,U_12474,U_12476),U_12478) != hAPP(c_Product__Type_Oapsnd(U_12470,U_12472,U_12474,U_12480),U_12478) ) ),
    inference(miniscope,[status(thm)],[f_3219_2]) ).

cnf(f_3219_4,plain,
    ( hAPP(U_12476,hAPP(c_Product__Type_Osnd(U_12474,U_12470),U_12478)) = hAPP(U_12480,hAPP(c_Product__Type_Osnd(U_12474,U_12470),U_12478))
    | hAPP(c_Product__Type_Oapsnd(U_12470,U_12472,U_12474,U_12476),U_12478) != hAPP(c_Product__Type_Oapsnd(U_12470,U_12472,U_12474,U_12480),U_12478) ),
    inference(clausify,[status(thm)],[f_3219_3]) ).

cnf(f_3219_5,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_12471,U_12473,U_12475,U_12477),U_12479) = hAPP(c_Product__Type_Oapsnd(U_12471,U_12473,U_12475,U_12481),U_12479)
    | hAPP(U_12477,hAPP(c_Product__Type_Osnd(U_12475,U_12471),U_12479)) != hAPP(U_12481,hAPP(c_Product__Type_Osnd(U_12475,U_12471),U_12479)) ),
    inference(clausify,[status(thm)],[f_3219_3]) ).

fof(f_3220_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_3220_2,plain,
    ! [U_12483,U_12482] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12482,U_12483) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_12482,U_12483)),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

cnf(f_3220_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12482,U_12483) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_12482,U_12483)),
    inference(clausify,[status(thm)],[f_3220_2]) ).

fof(f_3221_1,plain,
    ! [V_a_2,V_b_2,V_r_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).

fof(f_3221_2,plain,
    ! [U_12487,U_12486,U_12485,U_12484] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12484,U_12485),U_12487))
      | ~ hBOOL(hAPP(hAPP(U_12485,U_12487),U_12486))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12484,U_12485),U_12486)) ),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

cnf(f_3221_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12484,U_12485),U_12487))
    | ~ hBOOL(hAPP(hAPP(U_12485,U_12487),U_12486))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12484,U_12485),U_12486)) ),
    inference(clausify,[status(thm)],[f_3221_2]) ).

fof(f_3222_1,plain,
    ! [V_a_2,V_r_2,T_a] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).

fof(f_3222_2,plain,
    ! [U_12492,U_12491,U_12490] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12490,U_12491),U_12492))
        | ? [U_12489] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12490,U_12491),U_12489))
            & hBOOL(hAPP(hAPP(U_12491,U_12489),U_12492)) ) )
      & ( ! [U_12488] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12490,U_12491),U_12488))
            | ~ hBOOL(hAPP(hAPP(U_12491,U_12488),U_12492)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12490,U_12491),U_12492)) ) ),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

fof(f_3222_3,plain,
    ( ! [U_12498,U_12496,U_12494] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),U_12498))
        | ? [U_12489] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),U_12489))
            & hBOOL(hAPP(hAPP(U_12496,U_12489),U_12498)) ) )
    & ! [U_12497,U_12495,U_12493] :
        ( ! [U_12488] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12488))
            | ~ hBOOL(hAPP(hAPP(U_12495,U_12488),U_12497)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12497)) ) ),
    inference(miniscope,[status(thm)],[f_3222_2]) ).

fof(f_3222_4,plain,
    ( ! [U_12498,U_12496,U_12494] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),U_12498))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),sK293(U_12498,U_12496,U_12494)))
          & hBOOL(hAPP(hAPP(U_12496,sK293(U_12498,U_12496,U_12494)),U_12498)) ) )
    & ! [U_12497,U_12495,U_12493] :
        ( ! [U_12488] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12488))
            | ~ hBOOL(hAPP(hAPP(U_12495,U_12488),U_12497)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12497)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_12489,sK293(U_12498,U_12496,U_12494))],[f_3222_3]) ).

cnf(f_3222_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12488))
    | ~ hBOOL(hAPP(hAPP(U_12495,U_12488),U_12497))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,U_12495),U_12497)) ),
    inference(clausify,[status(thm)],[f_3222_4]) ).

cnf(f_3222_6,plain,
    ( hBOOL(hAPP(hAPP(U_12496,sK293(U_12498,U_12496,U_12494)),U_12498))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),U_12498)) ),
    inference(clausify,[status(thm)],[f_3222_4]) ).

cnf(f_3222_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),sK293(U_12498,U_12496,U_12494)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_12494,U_12496),U_12498)) ),
    inference(clausify,[status(thm)],[f_3222_4]) ).

fof(f_3223_1,plain,
    ! [V_a_2,V_r_2,T_a] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).

fof(f_3223_2,plain,
    ! [U_12503,U_12502,U_12501] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12501,U_12502),U_12503))
        | ? [U_12500] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12501,U_12502),U_12500))
            & hBOOL(hAPP(hAPP(U_12502,U_12500),U_12503)) ) )
      & ( ! [U_12499] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12501,U_12502),U_12499))
            | ~ hBOOL(hAPP(hAPP(U_12502,U_12499),U_12503)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12501,U_12502),U_12503)) ) ),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

fof(f_3223_3,plain,
    ( ! [U_12509,U_12507,U_12505] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),U_12509))
        | ? [U_12500] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),U_12500))
            & hBOOL(hAPP(hAPP(U_12507,U_12500),U_12509)) ) )
    & ! [U_12508,U_12506,U_12504] :
        ( ! [U_12499] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12499))
            | ~ hBOOL(hAPP(hAPP(U_12506,U_12499),U_12508)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12508)) ) ),
    inference(miniscope,[status(thm)],[f_3223_2]) ).

fof(f_3223_4,plain,
    ( ! [U_12509,U_12507,U_12505] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),U_12509))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),sK294(U_12509,U_12507,U_12505)))
          & hBOOL(hAPP(hAPP(U_12507,sK294(U_12509,U_12507,U_12505)),U_12509)) ) )
    & ! [U_12508,U_12506,U_12504] :
        ( ! [U_12499] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12499))
            | ~ hBOOL(hAPP(hAPP(U_12506,U_12499),U_12508)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12508)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_12500,sK294(U_12509,U_12507,U_12505))],[f_3223_3]) ).

cnf(f_3223_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12499))
    | ~ hBOOL(hAPP(hAPP(U_12506,U_12499),U_12508))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12504,U_12506),U_12508)) ),
    inference(clausify,[status(thm)],[f_3223_4]) ).

cnf(f_3223_6,plain,
    ( hBOOL(hAPP(hAPP(U_12507,sK294(U_12509,U_12507,U_12505)),U_12509))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),U_12509)) ),
    inference(clausify,[status(thm)],[f_3223_4]) ).

cnf(f_3223_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),sK294(U_12509,U_12507,U_12505)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_12505,U_12507),U_12509)) ),
    inference(clausify,[status(thm)],[f_3223_4]) ).

fof(f_3224_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_3224_2,plain,
    ! [U_12511,U_12510] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12510,U_12511) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_12510,U_12511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12510),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

cnf(f_3224_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12510,U_12511) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_12510,U_12511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12510),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3224_2]) ).

fof(f_3225_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_3225_2,plain,
    ! [U_12513,U_12512] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12512,U_12513) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_12512,U_12513))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12513))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12512)) ),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

cnf(f_3225_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12512,U_12513) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_12512,U_12513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12512)) ),
    inference(clausify,[status(thm)],[f_3225_2]) ).

fof(f_3226_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_3226_2,plain,
    ! [U_12514] :
      ( 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_12514)) = 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_12514)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_12514))) ),
    inference(variable_rename,[status(thm)],[f_3226_1]) ).

cnf(f_3226_3,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_12514)) = 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_12514)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_12514))) ),
    inference(clausify,[status(thm)],[f_3226_2]) ).

fof(f_3227_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_3227_2,plain,
    ! [U_12516,U_12515] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12515,U_12516) = 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_12515),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12516))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12516),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_12515)) ),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

cnf(f_3227_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12515,U_12516) = 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_12515),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12516))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12516),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_12515)) ),
    inference(clausify,[status(thm)],[f_3227_2]) ).

fof(f_3228_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_3228_2,plain,
    ! [U_12518,U_12517] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12517,U_12518) = 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_12517),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12518))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12518),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

cnf(f_3228_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_12517,U_12518) = 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_12517),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12518))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12518),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3228_2]) ).

fof(f_3229_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_3229_2,plain,
    ! [U_12520,U_12519] :
      ( ( ( c_Nitpick_Onat__gcd(U_12519,U_12520) = c_Nitpick_Onat__gcd(U_12520,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12519,U_12520))
          | U_12520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_12519,U_12520) = U_12519
          | U_12520 != 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_12519),U_12520))) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

cnf(f_3229_3,plain,
    ( c_Nitpick_Onat__gcd(U_12519,U_12520) = U_12519
    | U_12520 != 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_12519),U_12520))) ),
    inference(clausify,[status(thm)],[f_3229_2]) ).

cnf(f_3229_4,plain,
    ( c_Nitpick_Onat__gcd(U_12519,U_12520) = c_Nitpick_Onat__gcd(U_12520,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12519,U_12520))
    | U_12520 = 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_12519),U_12520))) ),
    inference(clausify,[status(thm)],[f_3229_2]) ).

fof(f_3230_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_3230_2,plain,
    ! [U_12521] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_12521)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_12521)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

cnf(f_3230_3,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_12521)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_12521)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3230_2]) ).

fof(f_3231_1,plain,
    ! [V_f_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__measure]) ).

fof(f_3231_2,plain,
    ! [U_12525,U_12524,U_12523,U_12522] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12522,U_12522)),hAPP(hAPP(c_Product__Type_OPair(U_12522,U_12522),U_12523),U_12524)),hAPP(c_Wellfounded_Omeasure(U_12522),U_12525)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12525,U_12523)),hAPP(U_12525,U_12524))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12525,U_12523)),hAPP(U_12525,U_12524)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12522,U_12522)),hAPP(hAPP(c_Product__Type_OPair(U_12522,U_12522),U_12523),U_12524)),hAPP(c_Wellfounded_Omeasure(U_12522),U_12525))) ) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

fof(f_3231_3,plain,
    ( ! [U_12533,U_12531,U_12529] :
        ( ! [U_12527] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12527,U_12527)),hAPP(hAPP(c_Product__Type_OPair(U_12527,U_12527),U_12529),U_12531)),hAPP(c_Wellfounded_Omeasure(U_12527),U_12533)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12533,U_12529)),hAPP(U_12533,U_12531))) )
    & ! [U_12532,U_12530,U_12528] :
        ( ! [U_12526] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12526,U_12526)),hAPP(hAPP(c_Product__Type_OPair(U_12526,U_12526),U_12528),U_12530)),hAPP(c_Wellfounded_Omeasure(U_12526),U_12532)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12532,U_12528)),hAPP(U_12532,U_12530))) ) ),
    inference(miniscope,[status(thm)],[f_3231_2]) ).

cnf(f_3231_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12526,U_12526)),hAPP(hAPP(c_Product__Type_OPair(U_12526,U_12526),U_12528),U_12530)),hAPP(c_Wellfounded_Omeasure(U_12526),U_12532)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12532,U_12528)),hAPP(U_12532,U_12530))) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

cnf(f_3231_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12527,U_12527)),hAPP(hAPP(c_Product__Type_OPair(U_12527,U_12527),U_12529),U_12531)),hAPP(c_Wellfounded_Omeasure(U_12527),U_12533)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12533,U_12529)),hAPP(U_12533,U_12531))) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

fof(f_3232_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_3232_2,plain,
    ! [U_12535,U_12534] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12534,U_12535) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_12534,U_12535)),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

cnf(f_3232_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12534,U_12535) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_12534,U_12535)),
    inference(clausify,[status(thm)],[f_3232_2]) ).

fof(f_3233_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]) ).

cnf(f_3233_2,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_3233_1]) ).

fof(f_3234_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Relation_Oirrefl(T_a,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
        | ~ c_Relation_Oirrefl(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).

fof(f_3234_2,plain,
    ! [U_12539,U_12538] :
      ( ( c_Relation_Oirrefl(U_12538,U_12539)
        | ? [U_12537] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12538,U_12538)),hAPP(hAPP(c_Product__Type_OPair(U_12538,U_12538),U_12537),U_12537)),U_12539)) )
      & ( ! [U_12536] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12538,U_12538)),hAPP(hAPP(c_Product__Type_OPair(U_12538,U_12538),U_12536),U_12536)),U_12539))
        | ~ c_Relation_Oirrefl(U_12538,U_12539) ) ),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

fof(f_3234_3,plain,
    ( ! [U_12543,U_12541] :
        ( c_Relation_Oirrefl(U_12541,U_12543)
        | ? [U_12537] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12541,U_12541)),hAPP(hAPP(c_Product__Type_OPair(U_12541,U_12541),U_12537),U_12537)),U_12543)) )
    & ! [U_12542,U_12540] :
        ( ! [U_12536] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12540,U_12540)),hAPP(hAPP(c_Product__Type_OPair(U_12540,U_12540),U_12536),U_12536)),U_12542))
        | ~ c_Relation_Oirrefl(U_12540,U_12542) ) ),
    inference(miniscope,[status(thm)],[f_3234_2]) ).

fof(f_3234_4,plain,
    ( ! [U_12543,U_12541] :
        ( c_Relation_Oirrefl(U_12541,U_12543)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12541,U_12541)),hAPP(hAPP(c_Product__Type_OPair(U_12541,U_12541),sK295(U_12543,U_12541)),sK295(U_12543,U_12541))),U_12543)) )
    & ! [U_12542,U_12540] :
        ( ! [U_12536] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12540,U_12540)),hAPP(hAPP(c_Product__Type_OPair(U_12540,U_12540),U_12536),U_12536)),U_12542))
        | ~ c_Relation_Oirrefl(U_12540,U_12542) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_12537,sK295(U_12543,U_12541))],[f_3234_3]) ).

cnf(f_3234_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12540,U_12540)),hAPP(hAPP(c_Product__Type_OPair(U_12540,U_12540),U_12536),U_12536)),U_12542))
    | ~ c_Relation_Oirrefl(U_12540,U_12542) ),
    inference(clausify,[status(thm)],[f_3234_4]) ).

cnf(f_3234_6,plain,
    ( c_Relation_Oirrefl(U_12541,U_12543)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12541,U_12541)),hAPP(hAPP(c_Product__Type_OPair(U_12541,U_12541),sK295(U_12543,U_12541)),sK295(U_12543,U_12541))),U_12543)) ),
    inference(clausify,[status(thm)],[f_3234_4]) ).

fof(f_3235_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).

fof(f_3235_2,plain,
    ! [U_12548,U_12547,U_12546] :
      ( hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
      | ? [U_12545,U_12544] :
          ( ~ hBOOL(hAPP(hAPP(U_12548,U_12545),U_12544))
          & ( hBOOL(hAPP(hAPP(U_12548,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12545)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12544)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12544),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_12545),U_12544))) )
      | ~ 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_12546),U_12547))) ),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

fof(f_3235_3,plain,
    ! [U_12548,U_12547,U_12546] :
      ( hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
      | ? [U_12544] :
          ( ~ hBOOL(hAPP(hAPP(U_12548,sK296(U_12548,U_12547,U_12546)),U_12544))
          & ( hBOOL(hAPP(hAPP(U_12548,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK296(U_12548,U_12547,U_12546))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12544)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12544),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),sK296(U_12548,U_12547,U_12546)),U_12544))) )
      | ~ 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_12546),U_12547))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_12545,sK296(U_12548,U_12547,U_12546))],[f_3235_2]) ).

fof(f_3235_4,plain,
    ! [U_12548,U_12547,U_12546] :
      ( hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
      | ( ~ hBOOL(hAPP(hAPP(U_12548,sK296(U_12548,U_12547,U_12546)),sK297(U_12548,U_12547,U_12546)))
        & ( hBOOL(hAPP(hAPP(U_12548,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK296(U_12548,U_12547,U_12546))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK297(U_12548,U_12547,U_12546))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK297(U_12548,U_12547,U_12546)),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),sK296(U_12548,U_12547,U_12546)),sK297(U_12548,U_12547,U_12546)))) )
      | ~ 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_12546),U_12547))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_12544,sK297(U_12548,U_12547,U_12546))],[f_3235_3]) ).

cnf(f_3235_5,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),sK296(U_12548,U_12547,U_12546)),sK297(U_12548,U_12547,U_12546))))
    | hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
    | ~ 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_12546),U_12547))) ),
    inference(clausify,[status(thm)],[f_3235_4]) ).

cnf(f_3235_6,plain,
    ( hBOOL(hAPP(hAPP(U_12548,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK296(U_12548,U_12547,U_12546))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK297(U_12548,U_12547,U_12546))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK297(U_12548,U_12547,U_12546)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
    | ~ 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_12546),U_12547))) ),
    inference(clausify,[status(thm)],[f_3235_4]) ).

cnf(f_3235_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12548,sK296(U_12548,U_12547,U_12546)),sK297(U_12548,U_12547,U_12546)))
    | hBOOL(hAPP(hAPP(U_12548,U_12546),U_12547))
    | ~ 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_12546),U_12547))) ),
    inference(clausify,[status(thm)],[f_3235_4]) ).

fof(f_3236_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_3236_2,plain,
    ! [U_12549] :
      ( 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_12549)) = 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_12549)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12549)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

cnf(f_3236_3,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_12549)) = 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_12549)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_12549)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3236_2]) ).

fof(f_3237_1,plain,
    ! [T_b,T_a,V_t_2,V_s_2] :
      ( ( V_s_2 = V_t_2
        | hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) != hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2)
        | hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) != hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) )
      & ( ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2)
          & hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) )
        | V_s_2 != V_t_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq]) ).

fof(f_3237_2,plain,
    ! [U_12553,U_12552,U_12551,U_12550] :
      ( ( U_12550 = U_12551
        | hAPP(c_Product__Type_Osnd(U_12552,U_12553),U_12550) != hAPP(c_Product__Type_Osnd(U_12552,U_12553),U_12551)
        | hAPP(c_Product__Type_Ofst(U_12552,U_12553),U_12550) != hAPP(c_Product__Type_Ofst(U_12552,U_12553),U_12551) )
      & ( ( hAPP(c_Product__Type_Osnd(U_12552,U_12553),U_12550) = hAPP(c_Product__Type_Osnd(U_12552,U_12553),U_12551)
          & hAPP(c_Product__Type_Ofst(U_12552,U_12553),U_12550) = hAPP(c_Product__Type_Ofst(U_12552,U_12553),U_12551) )
        | U_12550 != U_12551 ) ),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

fof(f_3237_3,plain,
    ( ! [U_12561,U_12559,U_12557,U_12555] :
        ( U_12555 = U_12557
        | hAPP(c_Product__Type_Osnd(U_12559,U_12561),U_12555) != hAPP(c_Product__Type_Osnd(U_12559,U_12561),U_12557)
        | hAPP(c_Product__Type_Ofst(U_12559,U_12561),U_12555) != hAPP(c_Product__Type_Ofst(U_12559,U_12561),U_12557) )
    & ! [U_12560,U_12558,U_12556,U_12554] :
        ( ( hAPP(c_Product__Type_Osnd(U_12558,U_12560),U_12554) = hAPP(c_Product__Type_Osnd(U_12558,U_12560),U_12556)
          & hAPP(c_Product__Type_Ofst(U_12558,U_12560),U_12554) = hAPP(c_Product__Type_Ofst(U_12558,U_12560),U_12556) )
        | U_12554 != U_12556 ) ),
    inference(miniscope,[status(thm)],[f_3237_2]) ).

cnf(f_3237_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_12558,U_12560),U_12554) = hAPP(c_Product__Type_Ofst(U_12558,U_12560),U_12556)
    | U_12554 != U_12556 ),
    inference(clausify,[status(thm)],[f_3237_3]) ).

cnf(f_3237_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_12558,U_12560),U_12554) = hAPP(c_Product__Type_Osnd(U_12558,U_12560),U_12556)
    | U_12554 != U_12556 ),
    inference(clausify,[status(thm)],[f_3237_3]) ).

cnf(f_3237_6,plain,
    ( U_12555 = U_12557
    | hAPP(c_Product__Type_Osnd(U_12559,U_12561),U_12555) != hAPP(c_Product__Type_Osnd(U_12559,U_12561),U_12557)
    | hAPP(c_Product__Type_Ofst(U_12559,U_12561),U_12555) != hAPP(c_Product__Type_Ofst(U_12559,U_12561),U_12557) ),
    inference(clausify,[status(thm)],[f_3237_3]) ).

fof(f_3238_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_3238_2,plain,
    ! [U_12565,U_12564,U_12563,U_12562] :
      ( U_12564 = U_12565
      | hAPP(c_Product__Type_Osnd(U_12562,U_12563),U_12564) != hAPP(c_Product__Type_Osnd(U_12562,U_12563),U_12565)
      | hAPP(c_Product__Type_Ofst(U_12562,U_12563),U_12564) != hAPP(c_Product__Type_Ofst(U_12562,U_12563),U_12565) ),
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

cnf(f_3238_3,plain,
    ( U_12564 = U_12565
    | hAPP(c_Product__Type_Osnd(U_12562,U_12563),U_12564) != hAPP(c_Product__Type_Osnd(U_12562,U_12563),U_12565)
    | hAPP(c_Product__Type_Ofst(U_12562,U_12563),U_12564) != hAPP(c_Product__Type_Ofst(U_12562,U_12563),U_12565) ),
    inference(clausify,[status(thm)],[f_3238_2]) ).

fof(f_3239_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_3239_2,plain,
    ! [U_12570,U_12569,U_12568,U_12567,U_12566] :
      ( U_12568 = U_12570
      | hAPP(c_Product__Type_Ofst(U_12566,U_12567),hAPP(hAPP(c_Product__Type_OPair(U_12566,U_12567),U_12568),U_12569)) != U_12570 ),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12570,U_12569,U_12568] :
      ( ! [U_12567,U_12566] : hAPP(c_Product__Type_Ofst(U_12566,U_12567),hAPP(hAPP(c_Product__Type_OPair(U_12566,U_12567),U_12568),U_12569)) != U_12570
      | U_12568 = U_12570 ),
    inference(miniscope,[status(thm)],[f_3239_2]) ).

cnf(f_3239_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_12566,U_12567),hAPP(hAPP(c_Product__Type_OPair(U_12566,U_12567),U_12568),U_12569)) != U_12570
    | U_12568 = U_12570 ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_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_3240_2,plain,
    ! [U_12574,U_12573,U_12572,U_12571] : hAPP(c_Product__Type_Ofst(U_12571,U_12572),hAPP(hAPP(c_Product__Type_OPair(U_12571,U_12572),U_12573),U_12574)) = U_12573,
    inference(variable_rename,[status(thm)],[f_3240_1]) ).

cnf(f_3240_3,plain,
    hAPP(c_Product__Type_Ofst(U_12571,U_12572),hAPP(hAPP(c_Product__Type_OPair(U_12571,U_12572),U_12573),U_12574)) = U_12573,
    inference(clausify,[status(thm)],[f_3240_2]) ).

fof(f_3241_1,plain,
    ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_fst__def]) ).

fof(f_3241_2,plain,
    ! [U_12577,U_12576,U_12575] : hAPP(c_Product__Type_Ofst(U_12575,U_12576),U_12577) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12575,U_12576,U_12575),c_COMBK(U_12575,U_12576)),U_12577),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

cnf(f_3241_3,plain,
    hAPP(c_Product__Type_Ofst(U_12575,U_12576),U_12577) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12575,U_12576,U_12575),c_COMBK(U_12575,U_12576)),U_12577),
    inference(clausify,[status(thm)],[f_3241_2]) ).

fof(f_3242_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_fst__apsnd]) ).

fof(f_3242_2,plain,
    ! [U_12582,U_12581,U_12580,U_12579,U_12578] : hAPP(c_Product__Type_Ofst(U_12578,U_12579),hAPP(c_Product__Type_Oapsnd(U_12580,U_12579,U_12578,U_12581),U_12582)) = hAPP(c_Product__Type_Ofst(U_12578,U_12580),U_12582),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

cnf(f_3242_3,plain,
    hAPP(c_Product__Type_Ofst(U_12578,U_12579),hAPP(c_Product__Type_Oapsnd(U_12580,U_12579,U_12578,U_12581),U_12582)) = hAPP(c_Product__Type_Ofst(U_12578,U_12580),U_12582),
    inference(clausify,[status(thm)],[f_3242_2]) ).

fof(f_3243_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_3243_2,plain,
    ! [U_12585,U_12584,U_12583] : hAPP(hAPP(c_Product__Type_OPair(U_12583,U_12584),hAPP(c_Product__Type_Ofst(U_12583,U_12584),U_12585)),hAPP(c_Product__Type_Osnd(U_12583,U_12584),U_12585)) = U_12585,
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

cnf(f_3243_3,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_12583,U_12584),hAPP(c_Product__Type_Ofst(U_12583,U_12584),U_12585)),hAPP(c_Product__Type_Osnd(U_12583,U_12584),U_12585)) = U_12585,
    inference(clausify,[status(thm)],[f_3243_2]) ).

fof(f_3244_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_3244_2,plain,
    ! [U_12588,U_12587,U_12586] : U_12586 = hAPP(hAPP(c_Product__Type_OPair(U_12587,U_12588),hAPP(c_Product__Type_Ofst(U_12587,U_12588),U_12586)),hAPP(c_Product__Type_Osnd(U_12587,U_12588),U_12586)),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

cnf(f_3244_3,plain,
    U_12586 = hAPP(hAPP(c_Product__Type_OPair(U_12587,U_12588),hAPP(c_Product__Type_Ofst(U_12587,U_12588),U_12586)),hAPP(c_Product__Type_Osnd(U_12587,U_12588),U_12586)),
    inference(clausify,[status(thm)],[f_3244_2]) ).

fof(f_3245_1,plain,
    ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_prod__case__beta]) ).

fof(f_3245_2,plain,
    ! [U_12593,U_12592,U_12591,U_12590,U_12589] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12589,U_12590,U_12591),U_12592),U_12593) = hAPP(hAPP(U_12592,hAPP(c_Product__Type_Ofst(U_12589,U_12590),U_12593)),hAPP(c_Product__Type_Osnd(U_12589,U_12590),U_12593)),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

cnf(f_3245_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12589,U_12590,U_12591),U_12592),U_12593) = hAPP(hAPP(U_12592,hAPP(c_Product__Type_Ofst(U_12589,U_12590),U_12593)),hAPP(c_Product__Type_Osnd(U_12589,U_12590),U_12593)),
    inference(clausify,[status(thm)],[f_3245_2]) ).

fof(f_3246_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_3246_2,plain,
    ! [U_12595,U_12594] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12594),U_12595) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_12594,U_12595)),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

cnf(f_3246_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12594),U_12595) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_12594,U_12595)),
    inference(clausify,[status(thm)],[f_3246_2]) ).

fof(f_3247_1,plain,
    ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp__eq]) ).

fof(f_3247_2,plain,
    ! [U_12601,U_12600,U_12599,U_12598,U_12597,U_12596] : hAPP(hAPP(c_COMBS(tc_prod(U_12596,U_12597),U_12597,U_12598),hAPP(hAPP(c_COMBB(U_12599,tc_fun(U_12597,U_12598),tc_prod(U_12596,U_12597)),U_12600),hAPP(hAPP(c_COMBB(U_12596,U_12599,tc_prod(U_12596,U_12597)),U_12601),c_Product__Type_Ofst(U_12596,U_12597)))),c_Product__Type_Osnd(U_12596,U_12597)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12596,U_12597,U_12598),hAPP(hAPP(c_COMBB(U_12599,tc_fun(U_12597,U_12598),U_12596),U_12600),U_12601)),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

cnf(f_3247_3,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_12596,U_12597),U_12597,U_12598),hAPP(hAPP(c_COMBB(U_12599,tc_fun(U_12597,U_12598),tc_prod(U_12596,U_12597)),U_12600),hAPP(hAPP(c_COMBB(U_12596,U_12599,tc_prod(U_12596,U_12597)),U_12601),c_Product__Type_Ofst(U_12596,U_12597)))),c_Product__Type_Osnd(U_12596,U_12597)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12596,U_12597,U_12598),hAPP(hAPP(c_COMBB(U_12599,tc_fun(U_12597,U_12598),U_12596),U_12600),U_12601)),
    inference(clausify,[status(thm)],[f_3247_2]) ).

fof(f_3248_1,plain,
    ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_split__beta]) ).

fof(f_3248_2,plain,
    ! [U_12606,U_12605,U_12604,U_12603,U_12602] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12602,U_12603,U_12604),U_12605),U_12606) = hAPP(hAPP(U_12605,hAPP(c_Product__Type_Ofst(U_12602,U_12603),U_12606)),hAPP(c_Product__Type_Osnd(U_12602,U_12603),U_12606)),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

cnf(f_3248_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12602,U_12603,U_12604),U_12605),U_12606) = hAPP(hAPP(U_12605,hAPP(c_Product__Type_Ofst(U_12602,U_12603),U_12606)),hAPP(c_Product__Type_Osnd(U_12602,U_12603),U_12606)),
    inference(clausify,[status(thm)],[f_3248_2]) ).

fof(f_3249_1,plain,
    ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_split__def]) ).

fof(f_3249_2,plain,
    ! [U_12611,U_12610,U_12609,U_12608,U_12607] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12607,U_12608,U_12609),U_12610),U_12611) = hAPP(hAPP(U_12610,hAPP(c_Product__Type_Ofst(U_12607,U_12608),U_12611)),hAPP(c_Product__Type_Osnd(U_12607,U_12608),U_12611)),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

cnf(f_3249_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12607,U_12608,U_12609),U_12610),U_12611) = hAPP(hAPP(U_12610,hAPP(c_Product__Type_Ofst(U_12607,U_12608),U_12611)),hAPP(c_Product__Type_Osnd(U_12607,U_12608),U_12611)),
    inference(clausify,[status(thm)],[f_3249_2]) ).

fof(f_3250_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp]) ).

fof(f_3250_2,plain,
    ! [U_12618,U_12617,U_12616,U_12615,U_12614,U_12613,U_12612] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12612,U_12613,U_12614),hAPP(c_Fun_Ocomp(U_12615,tc_fun(U_12613,U_12614),U_12612,U_12616),U_12617)),U_12618) = hAPP(hAPP(U_12616,hAPP(U_12617,hAPP(c_Product__Type_Ofst(U_12612,U_12613),U_12618))),hAPP(c_Product__Type_Osnd(U_12612,U_12613),U_12618)),
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

cnf(f_3250_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12612,U_12613,U_12614),hAPP(c_Fun_Ocomp(U_12615,tc_fun(U_12613,U_12614),U_12612,U_12616),U_12617)),U_12618) = hAPP(hAPP(U_12616,hAPP(U_12617,hAPP(c_Product__Type_Ofst(U_12612,U_12613),U_12618))),hAPP(c_Product__Type_Osnd(U_12612,U_12613),U_12618)),
    inference(clausify,[status(thm)],[f_3250_2]) ).

fof(f_3251_1,plain,
    ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))),
    inference(fof_nnf,[status(thm)],[fact_The__split]) ).

fof(f_3251_2,plain,
    ! [U_12621,U_12620,U_12619] : c_HOL_OThe(tc_prod(U_12619,U_12620),hAPP(c_Product__Type_Oprod_Oprod__case(U_12619,U_12620,tc_HOL_Obool),U_12621)) = c_HOL_OThe(tc_prod(U_12619,U_12620),hAPP(hAPP(c_COMBS(tc_prod(U_12619,U_12620),U_12620,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12619,tc_fun(U_12620,tc_HOL_Obool),tc_prod(U_12619,U_12620)),U_12621),c_Product__Type_Ofst(U_12619,U_12620))),c_Product__Type_Osnd(U_12619,U_12620))),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

cnf(f_3251_3,plain,
    c_HOL_OThe(tc_prod(U_12619,U_12620),hAPP(c_Product__Type_Oprod_Oprod__case(U_12619,U_12620,tc_HOL_Obool),U_12621)) = c_HOL_OThe(tc_prod(U_12619,U_12620),hAPP(hAPP(c_COMBS(tc_prod(U_12619,U_12620),U_12620,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12619,tc_fun(U_12620,tc_HOL_Obool),tc_prod(U_12619,U_12620)),U_12621),c_Product__Type_Ofst(U_12619,U_12620))),c_Product__Type_Osnd(U_12619,U_12620))),
    inference(clausify,[status(thm)],[f_3251_2]) ).

fof(f_3252_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_3252_2,plain,
    ! [U_12623,U_12622] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12622),U_12623) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_12622,U_12623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12622),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

cnf(f_3252_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12622),U_12623) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_12622,U_12623))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12623))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12622),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3252_2]) ).

fof(f_3253_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_3253_2,plain,
    ! [U_12625,U_12624] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12624),U_12625) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_12624,U_12625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12624)) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

cnf(f_3253_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12624),U_12625) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_12624,U_12625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12624)) ),
    inference(clausify,[status(thm)],[f_3253_2]) ).

fof(f_3254_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_3254_2,plain,
    ! [U_12626] :
      ( 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_12626)) = 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_12626)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_12626))) ),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

cnf(f_3254_3,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_12626)) = 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_12626)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__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_12626))) ),
    inference(clausify,[status(thm)],[f_3254_2]) ).

fof(f_3255_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_3255_2,plain,
    ! [U_12628,U_12627] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12627),U_12628) = 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_12627),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12628))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12628),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_12627)) ),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

cnf(f_3255_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12627),U_12628) = 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_12627),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12628))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12628),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_12627)) ),
    inference(clausify,[status(thm)],[f_3255_2]) ).

fof(f_3256_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_3256_2,plain,
    ! [U_12630,U_12629] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12629),U_12630) = 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_12629),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12630))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12630),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12629),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

cnf(f_3256_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_12629),U_12630) = 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_12629),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12630))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_12630),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_12629),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3256_2]) ).

fof(f_3257_1,plain,
    ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,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_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),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_3257_2,plain,
    ! [U_12635,U_12634,U_12633,U_12632,U_12631] : c_Product__Type_Oprod_Oprod__size(U_12631,U_12632,U_12633,U_12634,U_12635) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_12633,hAPP(c_Product__Type_Ofst(U_12631,U_12632),U_12635))),hAPP(U_12634,hAPP(c_Product__Type_Osnd(U_12631,U_12632),U_12635)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

cnf(f_3257_3,plain,
    c_Product__Type_Oprod_Oprod__size(U_12631,U_12632,U_12633,U_12634,U_12635) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_12633,hAPP(c_Product__Type_Ofst(U_12631,U_12632),U_12635))),hAPP(U_12634,hAPP(c_Product__Type_Osnd(U_12631,U_12632),U_12635)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3257_2]) ).

fof(f_3258_1,plain,
    ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).

fof(f_3258_2,plain,
    ! [U_12640,U_12639,U_12638,U_12637,U_12636] :
      ( hBOOL(hAPP(hAPP(U_12636,hAPP(c_Product__Type_Osnd(U_12639,U_12640),hAPP(hAPP(c_Product__Type_OPair(U_12639,U_12640),U_12638),U_12637))),hAPP(c_Product__Type_Ofst(U_12639,U_12640),hAPP(hAPP(c_Product__Type_OPair(U_12639,U_12640),U_12638),U_12637))))
      | ~ hBOOL(hAPP(hAPP(U_12636,U_12637),U_12638)) ),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

cnf(f_3258_3,plain,
    ( hBOOL(hAPP(hAPP(U_12636,hAPP(c_Product__Type_Osnd(U_12639,U_12640),hAPP(hAPP(c_Product__Type_OPair(U_12639,U_12640),U_12638),U_12637))),hAPP(c_Product__Type_Ofst(U_12639,U_12640),hAPP(hAPP(c_Product__Type_OPair(U_12639,U_12640),U_12638),U_12637))))
    | ~ hBOOL(hAPP(hAPP(U_12636,U_12637),U_12638)) ),
    inference(clausify,[status(thm)],[f_3258_2]) ).

fof(f_3259_1,plain,
    ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2))))
        & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) )
      | ~ hBOOL(hAPP(V_Q_2,V_q_2))
      | ~ hBOOL(hAPP(V_P_2,V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).

fof(f_3259_2,plain,
    ! [U_12646,U_12645,U_12644,U_12643,U_12642,U_12641] :
      ( ( hBOOL(hAPP(U_12643,hAPP(c_Product__Type_Osnd(U_12645,U_12646),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12642),U_12644))))
        & hBOOL(hAPP(U_12641,hAPP(c_Product__Type_Ofst(U_12645,U_12646),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12642),U_12644)))) )
      | ~ hBOOL(hAPP(U_12643,U_12644))
      | ~ hBOOL(hAPP(U_12641,U_12642)) ),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

cnf(f_3259_3,plain,
    ( hBOOL(hAPP(U_12641,hAPP(c_Product__Type_Ofst(U_12645,U_12646),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12642),U_12644))))
    | ~ hBOOL(hAPP(U_12643,U_12644))
    | ~ hBOOL(hAPP(U_12641,U_12642)) ),
    inference(clausify,[status(thm)],[f_3259_2]) ).

cnf(f_3259_4,plain,
    ( hBOOL(hAPP(U_12643,hAPP(c_Product__Type_Osnd(U_12645,U_12646),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12642),U_12644))))
    | ~ hBOOL(hAPP(U_12643,U_12644))
    | ~ hBOOL(hAPP(U_12641,U_12642)) ),
    inference(clausify,[status(thm)],[f_3259_2]) ).

fof(f_3260_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_3260_2,plain,
    ! [U_12648,U_12647] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12647),U_12648) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_12647,U_12648)),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

cnf(f_3260_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_12647),U_12648) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_12647,U_12648)),
    inference(clausify,[status(thm)],[f_3260_2]) ).

fof(f_3261_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_3261_2,plain,
    ! [U_12651,U_12650,U_12649] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12649,U_12650),U_12651))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12650),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12650)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)),U_12650))
                | ~ 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_12651))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12650)) ) )
          & U_12650 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12651) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_12650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_12649 != 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_12651)),U_12650)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12650),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12650)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)),U_12650))
                  & 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_12651))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12650)) ) )
            | U_12650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_12650 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_12649 = 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_12651)),U_12650)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12651)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12649,U_12650),U_12651)) ) ),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

fof(f_3261_3,plain,
    ( ! [U_12657,U_12655,U_12653] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12655),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),U_12655))
                | ~ 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_12657))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655)) ) )
          & U_12655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)) )
    & ! [U_12656,U_12654,U_12652] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12654),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12654)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656)),U_12654))
                  & 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_12656))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12654)) ) )
            | U_12654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_12654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_12652 = 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_12656)),U_12654)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ) ),
    inference(miniscope,[status(thm)],[f_3261_2]) ).

cnf(f_3261_4,plain,
    ( U_12652 = 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_12656)),U_12654)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_5,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_6,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_12656)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12654))
    | U_12654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656)),U_12654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12654))
    | U_12654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12654),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12656)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12654))
    | U_12654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_9,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_12656)),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_12654))
    | U_12654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12652,U_12654),U_12656)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_10,plain,
    ( U_12655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_12,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_12657)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12655),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),U_12655))
    | ~ 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_12657)))
    | U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_14,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_12657)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12655),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),U_12655))
    | ~ 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_12657)))
    | U_12655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_15,plain,
    ( U_12655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_17,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_12657)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12655),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12655))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),U_12655))
    | ~ 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_12657)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

cnf(f_3261_19,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_12657)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12655),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657)),U_12655))
    | ~ 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_12657)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_12657) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_12653 != 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_12657)),U_12655)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_12657))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_12653,U_12655),U_12657)) ),
    inference(clausify,[status(thm)],[f_3261_3]) ).

fof(f_3262_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_3262_2,plain,
    ! [U_12658] : hAPP(c_Int_Onat,U_12658) = 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_12658)),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_3262_1]) ).

cnf(f_3262_3,plain,
    hAPP(c_Int_Onat,U_12658) = 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_12658)),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_3262_2]) ).

fof(f_3263_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_x),B_y))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
            | B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).

fof(f_3263_2,plain,
    ! [U_12663,U_12662,U_12661] :
      ( hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
      | ? [U_12660,U_12659] :
          ( ~ hBOOL(hAPP(hAPP(U_12663,U_12660),U_12659))
          & ( hBOOL(hAPP(hAPP(U_12663,U_12659),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_12660,U_12659)))
            | U_12659 = 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_12660),U_12659))) )
      | ~ 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_12661),U_12662))) ),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

fof(f_3263_3,plain,
    ! [U_12663,U_12662,U_12661] :
      ( hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
      | ? [U_12659] :
          ( ~ hBOOL(hAPP(hAPP(U_12663,sK298(U_12663,U_12662,U_12661)),U_12659))
          & ( hBOOL(hAPP(hAPP(U_12663,U_12659),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK298(U_12663,U_12662,U_12661),U_12659)))
            | U_12659 = 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),sK298(U_12663,U_12662,U_12661)),U_12659))) )
      | ~ 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_12661),U_12662))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_12660,sK298(U_12663,U_12662,U_12661))],[f_3263_2]) ).

fof(f_3263_4,plain,
    ! [U_12663,U_12662,U_12661] :
      ( hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
      | ( ~ hBOOL(hAPP(hAPP(U_12663,sK298(U_12663,U_12662,U_12661)),sK299(U_12663,U_12662,U_12661)))
        & ( hBOOL(hAPP(hAPP(U_12663,sK299(U_12663,U_12662,U_12661)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK298(U_12663,U_12662,U_12661),sK299(U_12663,U_12662,U_12661))))
          | sK299(U_12663,U_12662,U_12661) = 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),sK298(U_12663,U_12662,U_12661)),sK299(U_12663,U_12662,U_12661)))) )
      | ~ 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_12661),U_12662))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_12659,sK299(U_12663,U_12662,U_12661))],[f_3263_3]) ).

cnf(f_3263_5,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),sK298(U_12663,U_12662,U_12661)),sK299(U_12663,U_12662,U_12661))))
    | hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
    | ~ 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_12661),U_12662))) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

cnf(f_3263_6,plain,
    ( hBOOL(hAPP(hAPP(U_12663,sK299(U_12663,U_12662,U_12661)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK298(U_12663,U_12662,U_12661),sK299(U_12663,U_12662,U_12661))))
    | sK299(U_12663,U_12662,U_12661) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
    | ~ 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_12661),U_12662))) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

cnf(f_3263_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12663,sK298(U_12663,U_12662,U_12661)),sK299(U_12663,U_12662,U_12661)))
    | hBOOL(hAPP(hAPP(U_12663,U_12661),U_12662))
    | ~ 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_12661),U_12662))) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

fof(f_3264_1,plain,
    ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,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_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),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_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_inv__image__def]) ).

fof(f_3264_2,plain,
    ! [U_12667,U_12666,U_12665,U_12664] : hAPP(hAPP(c_Relation_Oinv__image(U_12664,U_12665),U_12666),U_12667) = hAPP(c_Set_OCollect(tc_prod(U_12665,U_12665)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12665,U_12665,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12665,tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_fun(U_12665,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12665,tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_fun(U_12665,tc_HOL_Obool)),U_12665),c_COMBC(U_12665,tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12665,tc_prod(U_12664,U_12664)),tc_fun(U_12665,tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),U_12665),hAPP(c_COMBB(tc_prod(U_12664,U_12664),tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool),U_12665),c_member(tc_prod(U_12664,U_12664)))),hAPP(hAPP(c_COMBC(U_12665,tc_fun(U_12665,U_12664),tc_fun(U_12665,tc_prod(U_12664,U_12664))),hAPP(hAPP(c_COMBB(tc_fun(U_12664,tc_prod(U_12664,U_12664)),tc_fun(tc_fun(U_12665,U_12664),tc_fun(U_12665,tc_prod(U_12664,U_12664))),U_12665),c_COMBB(U_12664,tc_prod(U_12664,U_12664),U_12665)),hAPP(hAPP(c_COMBB(U_12664,tc_fun(U_12664,tc_prod(U_12664,U_12664)),U_12665),c_Product__Type_OPair(U_12664,U_12664)),U_12667))),U_12667)))),U_12666))),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

cnf(f_3264_3,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_12664,U_12665),U_12666),U_12667) = hAPP(c_Set_OCollect(tc_prod(U_12665,U_12665)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12665,U_12665,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12665,tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_fun(U_12665,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12665,tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_fun(U_12665,tc_HOL_Obool)),U_12665),c_COMBC(U_12665,tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12665,tc_prod(U_12664,U_12664)),tc_fun(U_12665,tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool)),U_12665),hAPP(c_COMBB(tc_prod(U_12664,U_12664),tc_fun(tc_fun(tc_prod(U_12664,U_12664),tc_HOL_Obool),tc_HOL_Obool),U_12665),c_member(tc_prod(U_12664,U_12664)))),hAPP(hAPP(c_COMBC(U_12665,tc_fun(U_12665,U_12664),tc_fun(U_12665,tc_prod(U_12664,U_12664))),hAPP(hAPP(c_COMBB(tc_fun(U_12664,tc_prod(U_12664,U_12664)),tc_fun(tc_fun(U_12665,U_12664),tc_fun(U_12665,tc_prod(U_12664,U_12664))),U_12665),c_COMBB(U_12664,tc_prod(U_12664,U_12664),U_12665)),hAPP(hAPP(c_COMBB(U_12664,tc_fun(U_12664,tc_prod(U_12664,U_12664)),U_12665),c_Product__Type_OPair(U_12664,U_12664)),U_12667))),U_12667)))),U_12666))),
    inference(clausify,[status(thm)],[f_3264_2]) ).

fof(f_3265_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_3265_2,plain,
    ! [U_12669,U_12668] :
      ( ( hAPP(c_Int_ORep__Integ,U_12668) = hAPP(c_Int_ORep__Integ,U_12669)
        | U_12668 != U_12669 )
      & ( U_12668 = U_12669
        | hAPP(c_Int_ORep__Integ,U_12668) != hAPP(c_Int_ORep__Integ,U_12669) ) ),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

fof(f_3265_3,plain,
    ( ! [U_12673,U_12671] :
        ( hAPP(c_Int_ORep__Integ,U_12671) = hAPP(c_Int_ORep__Integ,U_12673)
        | U_12671 != U_12673 )
    & ! [U_12672,U_12670] :
        ( U_12670 = U_12672
        | hAPP(c_Int_ORep__Integ,U_12670) != hAPP(c_Int_ORep__Integ,U_12672) ) ),
    inference(miniscope,[status(thm)],[f_3265_2]) ).

cnf(f_3265_4,plain,
    ( U_12670 = U_12672
    | hAPP(c_Int_ORep__Integ,U_12670) != hAPP(c_Int_ORep__Integ,U_12672) ),
    inference(clausify,[status(thm)],[f_3265_3]) ).

cnf(f_3265_5,plain,
    ( hAPP(c_Int_ORep__Integ,U_12671) = hAPP(c_Int_ORep__Integ,U_12673)
    | U_12671 != U_12673 ),
    inference(clausify,[status(thm)],[f_3265_3]) ).

fof(f_3266_1,plain,
    ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),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),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),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).

fof(f_3266_2,plain,
    ! [U_12679,U_12678,U_12677,U_12676,U_12675,U_12674] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12674,U_12674)),hAPP(hAPP(c_Product__Type_OPair(U_12674,U_12674),U_12675),U_12676)),hAPP(hAPP(c_Relation_Oinv__image(U_12677,U_12674),U_12678),U_12679)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12677,U_12677)),hAPP(hAPP(c_Product__Type_OPair(U_12677,U_12677),hAPP(U_12679,U_12675)),hAPP(U_12679,U_12676))),U_12678)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12677,U_12677)),hAPP(hAPP(c_Product__Type_OPair(U_12677,U_12677),hAPP(U_12679,U_12675)),hAPP(U_12679,U_12676))),U_12678))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12674,U_12674)),hAPP(hAPP(c_Product__Type_OPair(U_12674,U_12674),U_12675),U_12676)),hAPP(hAPP(c_Relation_Oinv__image(U_12677,U_12674),U_12678),U_12679))) ) ),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

fof(f_3266_3,plain,
    ( ! [U_12691,U_12689,U_12687,U_12685,U_12683] :
        ( ! [U_12681] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12681,U_12681)),hAPP(hAPP(c_Product__Type_OPair(U_12681,U_12681),U_12683),U_12685)),hAPP(hAPP(c_Relation_Oinv__image(U_12687,U_12681),U_12689),U_12691)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12687,U_12687)),hAPP(hAPP(c_Product__Type_OPair(U_12687,U_12687),hAPP(U_12691,U_12683)),hAPP(U_12691,U_12685))),U_12689)) )
    & ! [U_12690,U_12688,U_12686,U_12684,U_12682] :
        ( ! [U_12680] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12680,U_12680)),hAPP(hAPP(c_Product__Type_OPair(U_12680,U_12680),U_12682),U_12684)),hAPP(hAPP(c_Relation_Oinv__image(U_12686,U_12680),U_12688),U_12690)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12686,U_12686)),hAPP(hAPP(c_Product__Type_OPair(U_12686,U_12686),hAPP(U_12690,U_12682)),hAPP(U_12690,U_12684))),U_12688)) ) ),
    inference(miniscope,[status(thm)],[f_3266_2]) ).

cnf(f_3266_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12680,U_12680)),hAPP(hAPP(c_Product__Type_OPair(U_12680,U_12680),U_12682),U_12684)),hAPP(hAPP(c_Relation_Oinv__image(U_12686,U_12680),U_12688),U_12690)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12686,U_12686)),hAPP(hAPP(c_Product__Type_OPair(U_12686,U_12686),hAPP(U_12690,U_12682)),hAPP(U_12690,U_12684))),U_12688)) ),
    inference(clausify,[status(thm)],[f_3266_3]) ).

cnf(f_3266_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12681,U_12681)),hAPP(hAPP(c_Product__Type_OPair(U_12681,U_12681),U_12683),U_12685)),hAPP(hAPP(c_Relation_Oinv__image(U_12687,U_12681),U_12689),U_12691)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12687,U_12687)),hAPP(hAPP(c_Product__Type_OPair(U_12687,U_12687),hAPP(U_12691,U_12683)),hAPP(U_12691,U_12685))),U_12689)) ),
    inference(clausify,[status(thm)],[f_3266_3]) ).

fof(f_3267_1,plain,
    ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).

fof(f_3267_2,plain,
    ! [U_12693,U_12692] : c_FunDef_Orp__inv__image(U_12692,U_12693) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),c_COMBS(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(U_12693,U_12692)),c_Product__Type_OPair(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),c_Relation_Oinv__image(U_12692,U_12693))))),c_Relation_Oinv__image(U_12692,U_12693))),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

cnf(f_3267_3,plain,
    c_FunDef_Orp__inv__image(U_12692,U_12693) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),c_COMBS(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)),tc_fun(tc_fun(U_12693,U_12692),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),tc_fun(tc_prod(U_12692,U_12692),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool))),tc_fun(U_12693,U_12692)),c_Product__Type_OPair(tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool),tc_fun(tc_prod(U_12693,U_12693),tc_HOL_Obool)))),c_Relation_Oinv__image(U_12692,U_12693))))),c_Relation_Oinv__image(U_12692,U_12693))),
    inference(clausify,[status(thm)],[f_3267_2]) ).

fof(f_3268_1,plain,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint]) ).

fof(f_3268_2,plain,
    ! [U_12699,U_12698,U_12697,U_12696,U_12695,U_12694] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12694,U_12694)),hAPP(hAPP(c_Product__Type_OPair(U_12694,U_12694),U_12698),U_12699)),U_12696))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12694),U_12697),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12694,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12694,U_12694,U_12696),hAPP(hAPP(c_Set_Oinsert(U_12694),U_12698),c_Orderings_Obot__class_Obot(tc_fun(U_12694,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12694,U_12694,U_12696),hAPP(hAPP(c_Set_Oinsert(U_12694),U_12699),c_Orderings_Obot__class_Obot(tc_fun(U_12694,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_12694,U_12695,U_12696) ),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

cnf(f_3268_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12694,U_12694)),hAPP(hAPP(c_Product__Type_OPair(U_12694,U_12694),U_12698),U_12699)),U_12696))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12694),U_12697),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12694,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12694,U_12694,U_12696),hAPP(hAPP(c_Set_Oinsert(U_12694),U_12698),c_Orderings_Obot__class_Obot(tc_fun(U_12694,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12694,U_12694,U_12696),hAPP(hAPP(c_Set_Oinsert(U_12694),U_12699),c_Orderings_Obot__class_Obot(tc_fun(U_12694,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_12694,U_12695,U_12696) ),
    inference(clausify,[status(thm)],[f_3268_2]) ).

fof(f_3269_1,plain,
    ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__equiv__class]) ).

fof(f_3269_2,plain,
    ! [U_12704,U_12703,U_12702,U_12701,U_12700] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12700,U_12700)),hAPP(hAPP(c_Product__Type_OPair(U_12700,U_12700),U_12704),U_12703)),U_12702))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12700),U_12703),U_12701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12700,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12700,U_12700,U_12702),hAPP(hAPP(c_Set_Oinsert(U_12700),U_12703),c_Orderings_Obot__class_Obot(tc_fun(U_12700,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12700,U_12700,U_12702),hAPP(hAPP(c_Set_Oinsert(U_12700),U_12704),c_Orderings_Obot__class_Obot(tc_fun(U_12700,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_12700,U_12701,U_12702) ),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

cnf(f_3269_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12700,U_12700)),hAPP(hAPP(c_Product__Type_OPair(U_12700,U_12700),U_12704),U_12703)),U_12702))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12700),U_12703),U_12701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12700,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12700,U_12700,U_12702),hAPP(hAPP(c_Set_Oinsert(U_12700),U_12703),c_Orderings_Obot__class_Obot(tc_fun(U_12700,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12700,U_12700,U_12702),hAPP(hAPP(c_Set_Oinsert(U_12700),U_12704),c_Orderings_Obot__class_Obot(tc_fun(U_12700,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_12700,U_12701,U_12702) ),
    inference(clausify,[status(thm)],[f_3269_2]) ).

fof(f_3270_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_Union__quotient]) ).

fof(f_3270_2,plain,
    ! [U_12707,U_12706,U_12705] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12705,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12705),U_12706),U_12707)) = U_12706
      | ~ c_Equiv__Relations_Oequiv(U_12705,U_12706,U_12707) ),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

cnf(f_3270_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12705,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12705),U_12706),U_12707)) = U_12706
    | ~ c_Equiv__Relations_Oequiv(U_12705,U_12706,U_12707) ),
    inference(clausify,[status(thm)],[f_3270_2]) ).

fof(f_3271_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__self]) ).

fof(f_3271_2,plain,
    ! [U_12711,U_12710,U_12709,U_12708] :
      ( hBOOL(hAPP(hAPP(c_member(U_12708),U_12711),hAPP(c_Relation_OImage(U_12708,U_12708,U_12710),hAPP(hAPP(c_Set_Oinsert(U_12708),U_12711),c_Orderings_Obot__class_Obot(tc_fun(U_12708,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12708),U_12711),U_12709))
      | ~ c_Equiv__Relations_Oequiv(U_12708,U_12709,U_12710) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

cnf(f_3271_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12708),U_12711),hAPP(c_Relation_OImage(U_12708,U_12708,U_12710),hAPP(hAPP(c_Set_Oinsert(U_12708),U_12711),c_Orderings_Obot__class_Obot(tc_fun(U_12708,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12708),U_12711),U_12709))
    | ~ c_Equiv__Relations_Oequiv(U_12708,U_12709,U_12710) ),
    inference(clausify,[status(thm)],[f_3271_2]) ).

fof(f_3272_1,plain,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__disj]) ).

fof(f_3272_2,plain,
    ! [U_12716,U_12715,U_12714,U_12713,U_12712] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12712,tc_HOL_Obool)),U_12715),U_12716) = c_Orderings_Obot__class_Obot(tc_fun(U_12712,tc_HOL_Obool))
      | U_12715 = U_12716
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12712,tc_HOL_Obool)),U_12716),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12712),U_12713),U_12714)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12712,tc_HOL_Obool)),U_12715),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12712),U_12713),U_12714)))
      | ~ c_Equiv__Relations_Oequiv(U_12712,U_12713,U_12714) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

cnf(f_3272_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12712,tc_HOL_Obool)),U_12715),U_12716) = c_Orderings_Obot__class_Obot(tc_fun(U_12712,tc_HOL_Obool))
    | U_12715 = U_12716
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12712,tc_HOL_Obool)),U_12716),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12712),U_12713),U_12714)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12712,tc_HOL_Obool)),U_12715),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12712),U_12713),U_12714)))
    | ~ c_Equiv__Relations_Oequiv(U_12712,U_12713,U_12714) ),
    inference(clausify,[status(thm)],[f_3272_2]) ).

fof(f_3273_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
      ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq]) ).

fof(f_3273_2,plain,
    ! [U_12721,U_12720,U_12719,U_12718,U_12717] :
      ( hAPP(c_Relation_OImage(U_12717,U_12717,U_12719),hAPP(hAPP(c_Set_Oinsert(U_12717),U_12720),c_Orderings_Obot__class_Obot(tc_fun(U_12717,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12717,U_12717,U_12719),hAPP(hAPP(c_Set_Oinsert(U_12717),U_12721),c_Orderings_Obot__class_Obot(tc_fun(U_12717,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12717,U_12717)),hAPP(hAPP(c_Product__Type_OPair(U_12717,U_12717),U_12720),U_12721)),U_12719))
      | ~ c_Equiv__Relations_Oequiv(U_12717,U_12718,U_12719) ),
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

cnf(f_3273_3,plain,
    ( hAPP(c_Relation_OImage(U_12717,U_12717,U_12719),hAPP(hAPP(c_Set_Oinsert(U_12717),U_12720),c_Orderings_Obot__class_Obot(tc_fun(U_12717,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12717,U_12717,U_12719),hAPP(hAPP(c_Set_Oinsert(U_12717),U_12721),c_Orderings_Obot__class_Obot(tc_fun(U_12717,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12717,U_12717)),hAPP(hAPP(c_Product__Type_OPair(U_12717,U_12717),U_12720),U_12721)),U_12719))
    | ~ c_Equiv__Relations_Oequiv(U_12717,U_12718,U_12719) ),
    inference(clausify,[status(thm)],[f_3273_2]) ).

fof(f_3274_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
      ( V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eqI]) ).

fof(f_3274_2,plain,
    ! [U_12728,U_12727,U_12726,U_12725,U_12724,U_12723,U_12722] :
      ( U_12725 = U_12726
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12722,U_12722)),hAPP(hAPP(c_Product__Type_OPair(U_12722,U_12722),U_12727),U_12728)),U_12724))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12722),U_12728),U_12726))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12722),U_12727),U_12725))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12722,tc_HOL_Obool)),U_12726),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12722),U_12723),U_12724)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12722,tc_HOL_Obool)),U_12725),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12722),U_12723),U_12724)))
      | ~ c_Equiv__Relations_Oequiv(U_12722,U_12723,U_12724) ),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

cnf(f_3274_3,plain,
    ( U_12725 = U_12726
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12722,U_12722)),hAPP(hAPP(c_Product__Type_OPair(U_12722,U_12722),U_12727),U_12728)),U_12724))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12722),U_12728),U_12726))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12722),U_12727),U_12725))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12722,tc_HOL_Obool)),U_12726),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12722),U_12723),U_12724)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12722,tc_HOL_Obool)),U_12725),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12722),U_12723),U_12724)))
    | ~ c_Equiv__Relations_Oequiv(U_12722,U_12723,U_12724) ),
    inference(clausify,[status(thm)],[f_3274_2]) ).

fof(f_3275_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
      ( ( ( V_X_2 = V_Y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
          | V_X_2 != V_Y_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff]) ).

fof(f_3275_2,plain,
    ! [U_12735,U_12734,U_12733,U_12732,U_12731,U_12730,U_12729] :
      ( ( ( U_12732 = U_12733
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12729,U_12729)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12729),U_12734),U_12735)),U_12731)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12729,U_12729)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12729),U_12734),U_12735)),U_12731))
          | U_12732 != U_12733 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12735),U_12733))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12734),U_12732))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12733),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12732),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
      | ~ c_Equiv__Relations_Oequiv(U_12729,U_12730,U_12731) ),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

cnf(f_3275_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12729,U_12729)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12729),U_12734),U_12735)),U_12731))
    | U_12732 != U_12733
    | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12735),U_12733))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12734),U_12732))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12733),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12732),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
    | ~ c_Equiv__Relations_Oequiv(U_12729,U_12730,U_12731) ),
    inference(clausify,[status(thm)],[f_3275_2]) ).

cnf(f_3275_4,plain,
    ( U_12732 = U_12733
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12729,U_12729)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12729),U_12734),U_12735)),U_12731))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12735),U_12733))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12729),U_12734),U_12732))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12733),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12729,tc_HOL_Obool)),U_12732),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12729),U_12730),U_12731)))
    | ~ c_Equiv__Relations_Oequiv(U_12729,U_12730,U_12731) ),
    inference(clausify,[status(thm)],[f_3275_2]) ).

fof(f_3276_1,plain,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
      | hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class]) ).

fof(f_3276_2,plain,
    ! [U_12740,U_12739,U_12738,U_12737,U_12736] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12736,U_12736)),hAPP(hAPP(c_Product__Type_OPair(U_12736,U_12736),U_12738),U_12739)),U_12737))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12736),U_12739),U_12740))
      | ~ c_Equiv__Relations_Oequiv(U_12736,U_12740,U_12737)
      | hAPP(c_Relation_OImage(U_12736,U_12736,U_12737),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12738),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12736,U_12736,U_12737),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12739),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

cnf(f_3276_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12736,U_12736)),hAPP(hAPP(c_Product__Type_OPair(U_12736,U_12736),U_12738),U_12739)),U_12737))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12736),U_12739),U_12740))
    | ~ c_Equiv__Relations_Oequiv(U_12736,U_12740,U_12737)
    | hAPP(c_Relation_OImage(U_12736,U_12736,U_12737),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12738),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12736,U_12736,U_12737),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12739),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3276_2]) ).

fof(f_3277_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( ( ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
          | hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff]) ).

fof(f_3277_2,plain,
    ! [U_12745,U_12744,U_12743,U_12742,U_12741] :
      ( ( ( hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12744),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12745),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12741,U_12741)),hAPP(hAPP(c_Product__Type_OPair(U_12741,U_12741),U_12744),U_12745)),U_12743)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12741,U_12741)),hAPP(hAPP(c_Product__Type_OPair(U_12741,U_12741),U_12744),U_12745)),U_12743))
          | hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12744),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12745),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12745),U_12742))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12744),U_12742))
      | ~ c_Equiv__Relations_Oequiv(U_12741,U_12742,U_12743) ),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

cnf(f_3277_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12741,U_12741)),hAPP(hAPP(c_Product__Type_OPair(U_12741,U_12741),U_12744),U_12745)),U_12743))
    | hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12744),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12745),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12745),U_12742))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12744),U_12742))
    | ~ c_Equiv__Relations_Oequiv(U_12741,U_12742,U_12743) ),
    inference(clausify,[status(thm)],[f_3277_2]) ).

cnf(f_3277_4,plain,
    ( hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12744),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12741,U_12741,U_12743),hAPP(hAPP(c_Set_Oinsert(U_12741),U_12745),c_Orderings_Obot__class_Obot(tc_fun(U_12741,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12741,U_12741)),hAPP(hAPP(c_Product__Type_OPair(U_12741,U_12741),U_12744),U_12745)),U_12743))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12745),U_12742))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12741),U_12744),U_12742))
    | ~ c_Equiv__Relations_Oequiv(U_12741,U_12742,U_12743) ),
    inference(clausify,[status(thm)],[f_3277_2]) ).

fof(f_3278_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
          | hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
            & hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) )
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff]) ).

fof(f_3278_2,plain,
    ! [U_12750,U_12749,U_12748,U_12747,U_12746] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12746),U_12750),U_12747))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12746),U_12749),U_12747))
          | hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12749),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12750),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_12746),U_12750),U_12747))
            & hBOOL(hAPP(hAPP(c_member(U_12746),U_12749),U_12747))
            & hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12749),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12750),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_12746,U_12747,U_12748) ),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

cnf(f_3278_3,plain,
    ( hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12749),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12750),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748))
    | ~ c_Equiv__Relations_Oequiv(U_12746,U_12747,U_12748) ),
    inference(clausify,[status(thm)],[f_3278_2]) ).

cnf(f_3278_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12746),U_12749),U_12747))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748))
    | ~ c_Equiv__Relations_Oequiv(U_12746,U_12747,U_12748) ),
    inference(clausify,[status(thm)],[f_3278_2]) ).

cnf(f_3278_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12746),U_12750),U_12747))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748))
    | ~ c_Equiv__Relations_Oequiv(U_12746,U_12747,U_12748) ),
    inference(clausify,[status(thm)],[f_3278_2]) ).

cnf(f_3278_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12746,U_12746)),hAPP(hAPP(c_Product__Type_OPair(U_12746,U_12746),U_12749),U_12750)),U_12748))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12746),U_12750),U_12747))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12746),U_12749),U_12747))
    | hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12749),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12746,U_12746,U_12748),hAPP(hAPP(c_Set_Oinsert(U_12746),U_12750),c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool))))
    | ~ c_Equiv__Relations_Oequiv(U_12746,U_12747,U_12748) ),
    inference(clausify,[status(thm)],[f_3278_2]) ).

fof(f_3279_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__subset]) ).

fof(f_3279_2,plain,
    ! [U_12755,U_12754,U_12753,U_12752,U_12751] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12751,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12751,U_12751,U_12753),hAPP(hAPP(c_Set_Oinsert(U_12751),U_12754),c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12751,U_12751,U_12753),hAPP(hAPP(c_Set_Oinsert(U_12751),U_12755),c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12751,U_12751)),hAPP(hAPP(c_Product__Type_OPair(U_12751,U_12751),U_12754),U_12755)),U_12753))
      | ~ c_Equiv__Relations_Oequiv(U_12751,U_12752,U_12753) ),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

cnf(f_3279_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12751,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12751,U_12751,U_12753),hAPP(hAPP(c_Set_Oinsert(U_12751),U_12754),c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12751,U_12751,U_12753),hAPP(hAPP(c_Set_Oinsert(U_12751),U_12755),c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12751,U_12751)),hAPP(hAPP(c_Product__Type_OPair(U_12751,U_12751),U_12754),U_12755)),U_12753))
    | ~ c_Equiv__Relations_Oequiv(U_12751,U_12752,U_12753) ),
    inference(clausify,[status(thm)],[f_3279_2]) ).

fof(f_3280_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2]) ).

fof(f_3280_2,plain,
    ! [U_12760,U_12759,U_12758,U_12757,U_12756] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12759),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12760),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12756,U_12756)),hAPP(hAPP(c_Product__Type_OPair(U_12756,U_12756),U_12759),U_12760)),U_12758)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12756,U_12756)),hAPP(hAPP(c_Product__Type_OPair(U_12756,U_12756),U_12759),U_12760)),U_12758))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12759),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12760),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12760),U_12757))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12759),U_12757))
      | ~ c_Equiv__Relations_Oequiv(U_12756,U_12757,U_12758) ),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

cnf(f_3280_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12756,U_12756)),hAPP(hAPP(c_Product__Type_OPair(U_12756,U_12756),U_12759),U_12760)),U_12758))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12759),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12760),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12760),U_12757))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12759),U_12757))
    | ~ c_Equiv__Relations_Oequiv(U_12756,U_12757,U_12758) ),
    inference(clausify,[status(thm)],[f_3280_2]) ).

cnf(f_3280_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12759),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12756),hAPP(hAPP(c_Set_Oinsert(U_12756),U_12760),c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)))),U_12758)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12756,U_12756)),hAPP(hAPP(c_Product__Type_OPair(U_12756,U_12756),U_12759),U_12760)),U_12758))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12760),U_12757))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12756),U_12759),U_12757))
    | ~ c_Equiv__Relations_Oequiv(U_12756,U_12757,U_12758) ),
    inference(clausify,[status(thm)],[f_3280_2]) ).

fof(f_3281_1,plain,
    ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class]) ).

fof(f_3281_2,plain,
    ! [U_12766,U_12765,U_12764,U_12763,U_12762,U_12761] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12761,tc_fun(U_12764,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12761,U_12761,U_12763),hAPP(hAPP(c_Set_Oinsert(U_12761),U_12766),c_Orderings_Obot__class_Obot(tc_fun(U_12761,tc_HOL_Obool))))),U_12765) = hAPP(U_12765,U_12766)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12766),U_12762))
      | ~ c_Equiv__Relations_Ocongruent(U_12761,tc_fun(U_12764,tc_HOL_Obool),U_12763,U_12765)
      | ~ c_Equiv__Relations_Oequiv(U_12761,U_12762,U_12763) ),
    inference(variable_rename,[status(thm)],[f_3281_1]) ).

cnf(f_3281_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12761,tc_fun(U_12764,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12761,U_12761,U_12763),hAPP(hAPP(c_Set_Oinsert(U_12761),U_12766),c_Orderings_Obot__class_Obot(tc_fun(U_12761,tc_HOL_Obool))))),U_12765) = hAPP(U_12765,U_12766)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12766),U_12762))
    | ~ c_Equiv__Relations_Ocongruent(U_12761,tc_fun(U_12764,tc_HOL_Obool),U_12763,U_12765)
    | ~ c_Equiv__Relations_Oequiv(U_12761,U_12762,U_12763) ),
    inference(clausify,[status(thm)],[f_3281_2]) ).

fof(f_3282_1,plain,
    ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2]) ).

fof(f_3282_2,plain,
    ! [U_12776,U_12775,U_12774,U_12773,U_12772,U_12771,U_12770,U_12769,U_12768,U_12767] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12773,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12767,U_12767,U_12769),hAPP(hAPP(c_Set_Oinsert(U_12767),U_12775),c_Orderings_Obot__class_Obot(tc_fun(U_12767,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12770,tc_fun(U_12773,tc_HOL_Obool)),tc_fun(U_12773,tc_HOL_Obool),U_12767),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12770,tc_fun(U_12773,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12770,U_12770,U_12772),hAPP(hAPP(c_Set_Oinsert(U_12770),U_12776),c_Orderings_Obot__class_Obot(tc_fun(U_12770,tc_HOL_Obool)))))),U_12774)) = hAPP(hAPP(U_12774,U_12775),U_12776)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12770),U_12776),U_12771))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12767),U_12775),U_12768))
      | ~ c_Equiv__Relations_Ocongruent2(U_12767,U_12770,tc_fun(U_12773,tc_HOL_Obool),U_12769,U_12772,U_12774)
      | ~ c_Equiv__Relations_Oequiv(U_12770,U_12771,U_12772)
      | ~ c_Equiv__Relations_Oequiv(U_12767,U_12768,U_12769) ),
    inference(variable_rename,[status(thm)],[f_3282_1]) ).

cnf(f_3282_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12767,tc_fun(U_12773,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12767,U_12767,U_12769),hAPP(hAPP(c_Set_Oinsert(U_12767),U_12775),c_Orderings_Obot__class_Obot(tc_fun(U_12767,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12770,tc_fun(U_12773,tc_HOL_Obool)),tc_fun(U_12773,tc_HOL_Obool),U_12767),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12770,tc_fun(U_12773,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12770,U_12770,U_12772),hAPP(hAPP(c_Set_Oinsert(U_12770),U_12776),c_Orderings_Obot__class_Obot(tc_fun(U_12770,tc_HOL_Obool)))))),U_12774)) = hAPP(hAPP(U_12774,U_12775),U_12776)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12770),U_12776),U_12771))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12767),U_12775),U_12768))
    | ~ c_Equiv__Relations_Ocongruent2(U_12767,U_12770,tc_fun(U_12773,tc_HOL_Obool),U_12769,U_12772,U_12774)
    | ~ c_Equiv__Relations_Oequiv(U_12770,U_12771,U_12772)
    | ~ c_Equiv__Relations_Oequiv(U_12767,U_12768,U_12769) ),
    inference(clausify,[status(thm)],[f_3282_2]) ).

fof(f_3283_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__finite__psubset]) ).

fof(f_3283_2,plain,
    ! [U_12779,U_12778,U_12777] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12777,tc_HOL_Obool),tc_fun(U_12777,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12777,tc_HOL_Obool),tc_fun(U_12777,tc_HOL_Obool)),U_12778),U_12779)),c_Wellfounded_Ofinite__psubset(U_12777)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12777),U_12779))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12777,tc_HOL_Obool)),U_12778),U_12779)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12777),U_12779))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12777,tc_HOL_Obool)),U_12778),U_12779)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12777,tc_HOL_Obool),tc_fun(U_12777,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12777,tc_HOL_Obool),tc_fun(U_12777,tc_HOL_Obool)),U_12778),U_12779)),c_Wellfounded_Ofinite__psubset(U_12777))) ) ),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

fof(f_3283_3,plain,
    ( ! [U_12785,U_12783,U_12781] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12781,tc_HOL_Obool),tc_fun(U_12781,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12781,tc_HOL_Obool),tc_fun(U_12781,tc_HOL_Obool)),U_12783),U_12785)),c_Wellfounded_Ofinite__psubset(U_12781)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12781),U_12785))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12781,tc_HOL_Obool)),U_12783),U_12785)) )
    & ! [U_12784,U_12782,U_12780] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12784))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12780,tc_HOL_Obool)),U_12782),U_12784)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool)),U_12782),U_12784)),c_Wellfounded_Ofinite__psubset(U_12780))) ) ),
    inference(miniscope,[status(thm)],[f_3283_2]) ).

cnf(f_3283_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12780,tc_HOL_Obool)),U_12782),U_12784))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool)),U_12782),U_12784)),c_Wellfounded_Ofinite__psubset(U_12780))) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

cnf(f_3283_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12784))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12780,tc_HOL_Obool),tc_fun(U_12780,tc_HOL_Obool)),U_12782),U_12784)),c_Wellfounded_Ofinite__psubset(U_12780))) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

cnf(f_3283_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12781,tc_HOL_Obool),tc_fun(U_12781,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12781,tc_HOL_Obool),tc_fun(U_12781,tc_HOL_Obool)),U_12783),U_12785)),c_Wellfounded_Ofinite__psubset(U_12781)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12781),U_12785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12781,tc_HOL_Obool)),U_12783),U_12785)) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

fof(f_3284_1,plain,
    ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent]) ).

fof(f_3284_2,plain,
    ! [U_12793,U_12792,U_12791,U_12790,U_12789,U_12788,U_12787,U_12786] :
      ( c_Equiv__Relations_Ocongruent(U_12789,U_12790,U_12791,hAPP(U_12792,U_12793))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12786),U_12793),U_12787))
      | ~ c_Equiv__Relations_Ocongruent2(U_12786,U_12789,U_12790,U_12788,U_12791,U_12792)
      | ~ c_Equiv__Relations_Oequiv(U_12786,U_12787,U_12788) ),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

cnf(f_3284_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_12789,U_12790,U_12791,hAPP(U_12792,U_12793))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12786),U_12793),U_12787))
    | ~ c_Equiv__Relations_Ocongruent2(U_12786,U_12789,U_12790,U_12788,U_12791,U_12792)
    | ~ c_Equiv__Relations_Oequiv(U_12786,U_12787,U_12788) ),
    inference(clausify,[status(thm)],[f_3284_2]) ).

fof(f_3285_1,plain,
    ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] :
      ( 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_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2D]) ).

fof(f_3285_2,plain,
    ! [U_12803,U_12802,U_12801,U_12800,U_12799,U_12798,U_12797,U_12796,U_12795,U_12794] :
      ( hAPP(hAPP(U_12799,U_12800),U_12802) = hAPP(hAPP(U_12799,U_12801),U_12803)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12795,U_12795)),hAPP(hAPP(c_Product__Type_OPair(U_12795,U_12795),U_12802),U_12803)),U_12798))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12794,U_12794)),hAPP(hAPP(c_Product__Type_OPair(U_12794,U_12794),U_12800),U_12801)),U_12797))
      | ~ c_Equiv__Relations_Ocongruent2(U_12794,U_12795,U_12796,U_12797,U_12798,U_12799) ),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

cnf(f_3285_3,plain,
    ( hAPP(hAPP(U_12799,U_12800),U_12802) = hAPP(hAPP(U_12799,U_12801),U_12803)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12795,U_12795)),hAPP(hAPP(c_Product__Type_OPair(U_12795,U_12795),U_12802),U_12803)),U_12798))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12794,U_12794)),hAPP(hAPP(c_Product__Type_OPair(U_12794,U_12794),U_12800),U_12801)),U_12797))
    | ~ c_Equiv__Relations_Ocongruent2(U_12794,U_12795,U_12796,U_12797,U_12798,U_12799) ),
    inference(clausify,[status(thm)],[f_3285_2]) ).

fof(f_3286_1,plain,
    ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
      ( hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2))
      | ~ c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruentD]) ).

fof(f_3286_2,plain,
    ! [U_12809,U_12808,U_12807,U_12806,U_12805,U_12804] :
      ( hAPP(U_12807,U_12808) = hAPP(U_12807,U_12809)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12804,U_12804)),hAPP(hAPP(c_Product__Type_OPair(U_12804,U_12804),U_12808),U_12809)),U_12806))
      | ~ c_Equiv__Relations_Ocongruent(U_12804,U_12805,U_12806,U_12807) ),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

cnf(f_3286_3,plain,
    ( hAPP(U_12807,U_12808) = hAPP(U_12807,U_12809)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12804,U_12804)),hAPP(hAPP(c_Product__Type_OPair(U_12804,U_12804),U_12808),U_12809)),U_12806))
    | ~ c_Equiv__Relations_Ocongruent(U_12804,U_12805,U_12806,U_12807) ),
    inference(clausify,[status(thm)],[f_3286_2]) ).

fof(f_3287_1,plain,
    ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_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))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN]) ).

fof(f_3287_2,plain,
    ! [U_12818,U_12817,U_12816,U_12815,U_12814,U_12813,U_12812,U_12811,U_12810] :
      ( c_Equiv__Relations_Ocongruent(U_12810,tc_fun(U_12816,tc_HOL_Obool),U_12812,hAPP(hAPP(c_COMBB(tc_fun(U_12813,tc_fun(U_12816,tc_HOL_Obool)),tc_fun(U_12816,tc_HOL_Obool),U_12810),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12813,tc_fun(U_12816,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12813,U_12813,U_12815),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12818),c_Orderings_Obot__class_Obot(tc_fun(U_12813,tc_HOL_Obool)))))),U_12817))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12813),U_12818),U_12814))
      | ~ c_Equiv__Relations_Ocongruent2(U_12810,U_12813,tc_fun(U_12816,tc_HOL_Obool),U_12812,U_12815,U_12817)
      | ~ c_Equiv__Relations_Oequiv(U_12813,U_12814,U_12815)
      | ~ c_Equiv__Relations_Oequiv(U_12810,U_12811,U_12812) ),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

cnf(f_3287_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_12810,tc_fun(U_12816,tc_HOL_Obool),U_12812,hAPP(hAPP(c_COMBB(tc_fun(U_12813,tc_fun(U_12816,tc_HOL_Obool)),tc_fun(U_12816,tc_HOL_Obool),U_12810),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12813,tc_fun(U_12816,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12813,U_12813,U_12815),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12818),c_Orderings_Obot__class_Obot(tc_fun(U_12813,tc_HOL_Obool)))))),U_12817))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12813),U_12818),U_12814))
    | ~ c_Equiv__Relations_Ocongruent2(U_12810,U_12813,tc_fun(U_12816,tc_HOL_Obool),U_12812,U_12815,U_12817)
    | ~ c_Equiv__Relations_Oequiv(U_12813,U_12814,U_12815)
    | ~ c_Equiv__Relations_Oequiv(U_12810,U_12811,U_12812) ),
    inference(clausify,[status(thm)],[f_3287_2]) ).

fof(f_3288_1,plain,
    ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))),
    inference(fof_nnf,[status(thm)],[fact_finite__psubset__def]) ).

fof(f_3288_2,plain,
    ! [U_12819] : c_Wellfounded_Ofinite__psubset(U_12819) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_12819,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_12819,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12819,tc_HOL_Obool)),c_COMBS(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_12819,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_12819)))),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

cnf(f_3288_3,plain,
    c_Wellfounded_Ofinite__psubset(U_12819) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_12819,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_12819,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12819,tc_HOL_Obool)),c_COMBS(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12819,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12819,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12819,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_12819,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_12819)))),
    inference(clausify,[status(thm)],[f_3288_2]) ).

fof(f_3289_1,plain,
    ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
      ( V_X_2 = V_Y_2
      | ? [B_x] :
          ( ? [B_y] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a),B_y),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2)
      | ~ c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject]) ).

fof(f_3289_2,plain,
    ! [U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822] :
      ( U_12827 = U_12828
      | ? [U_12821] :
          ( ? [U_12820] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12822)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12822),U_12821),U_12820)),U_12824))
              & hAPP(U_12826,U_12821) = hAPP(U_12826,U_12820)
              & hBOOL(hAPP(hAPP(c_member(U_12822),U_12820),U_12823)) )
          & hBOOL(hAPP(hAPP(c_member(U_12822),U_12821),U_12823)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
      | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
      | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

fof(f_3289_3,plain,
    ! [U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822] :
      ( U_12827 = U_12828
      | ( ? [U_12820] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12822)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12820)),U_12824))
            & hAPP(U_12826,sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)) = hAPP(U_12826,U_12820)
            & hBOOL(hAPP(hAPP(c_member(U_12822),U_12820),U_12823)) )
        & hBOOL(hAPP(hAPP(c_member(U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12823)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
      | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
      | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_12821,sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))],[f_3289_2]) ).

fof(f_3289_4,plain,
    ! [U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822] :
      ( U_12827 = U_12828
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12822)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))),U_12824))
        & hAPP(U_12826,sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)) = hAPP(U_12826,sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))
        & hBOOL(hAPP(hAPP(c_member(U_12822),sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12823))
        & hBOOL(hAPP(hAPP(c_member(U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12823)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
      | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
      | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_12820,sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))],[f_3289_3]) ).

cnf(f_3289_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12823))
    | U_12827 = U_12828
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
    | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
    | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3289_4]) ).

cnf(f_3289_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12822),sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),U_12823))
    | U_12827 = U_12828
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
    | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
    | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3289_4]) ).

cnf(f_3289_7,plain,
    ( hAPP(U_12826,sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)) = hAPP(U_12826,sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))
    | U_12827 = U_12828
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
    | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
    | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3289_4]) ).

cnf(f_3289_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12822)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12822),sK300(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822)),sK301(U_12828,U_12827,U_12826,U_12825,U_12824,U_12823,U_12822))),U_12824))
    | U_12827 = U_12828
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12828),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12822,tc_HOL_Obool)),U_12827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12822),U_12823),U_12824)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12827),U_12826) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12822,tc_fun(U_12825,tc_HOL_Obool)),U_12828),U_12826)
    | ~ c_Equiv__Relations_Ocongruent(U_12822,tc_fun(U_12825,tc_HOL_Obool),U_12824,U_12826)
    | ~ c_Equiv__Relations_Oequiv(U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3289_4]) ).

fof(f_3290_1,plain,
    ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))
      | ? [B_x1] :
          ( ? [B_x2] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2)))
      | ~ c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2]) ).

fof(f_3290_2,plain,
    ! [U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
      | ? [U_12830] :
          ( ? [U_12829] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(U_12838,U_12830),U_12829)),U_12841))
              & hBOOL(hAPP(hAPP(c_member(U_12834),U_12829),U_12835)) )
          & hBOOL(hAPP(hAPP(c_member(U_12831),U_12830),U_12832)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
      | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
      | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

fof(f_3290_3,plain,
    ! [U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
      | ( ? [U_12829] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(U_12838,sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12829)),U_12841))
            & hBOOL(hAPP(hAPP(c_member(U_12834),U_12829),U_12835)) )
        & hBOOL(hAPP(hAPP(c_member(U_12831),sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12832)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
      | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
      | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_12830,sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831))],[f_3290_2]) ).

fof(f_3290_4,plain,
    ! [U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(U_12838,sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),sK303(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831))),U_12841))
        & hBOOL(hAPP(hAPP(c_member(U_12834),sK303(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12835))
        & hBOOL(hAPP(hAPP(c_member(U_12831),sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12832)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
      | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
      | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_12829,sK303(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831))],[f_3290_3]) ).

cnf(f_3290_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12831),sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12832))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
    | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
    | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

cnf(f_3290_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12834),sK303(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),U_12835))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
    | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
    | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

cnf(f_3290_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(U_12838,sK302(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831)),sK303(U_12841,U_12840,U_12839,U_12838,U_12837,U_12836,U_12835,U_12834,U_12833,U_12832,U_12831))),U_12841))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12831,tc_fun(U_12837,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(U_12837,tc_HOL_Obool)),tc_fun(U_12837,tc_HOL_Obool),U_12831),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12834,tc_fun(U_12837,tc_HOL_Obool)),U_12840)),U_12838))),U_12841))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12834,tc_HOL_Obool)),U_12840),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12834),U_12835),U_12836)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12831,tc_HOL_Obool)),U_12839),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12831),U_12832),U_12833)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12831,U_12834,tc_fun(U_12837,tc_HOL_Obool),U_12833,U_12836,U_12838)
    | ~ c_Equiv__Relations_Oequiv(U_12834,U_12835,U_12836)
    | ~ c_Equiv__Relations_Oequiv(U_12831,U_12832,U_12833) ),
    inference(clausify,[status(thm)],[f_3290_4]) ).

fof(f_3291_1,plain,
    ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type]) ).

fof(f_3291_2,plain,
    ! [U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12843,tc_fun(U_12846,tc_HOL_Obool)),U_12848),U_12847)),U_12849))
      | ? [U_12842] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(U_12847,U_12842)),U_12849))
          & hBOOL(hAPP(hAPP(c_member(U_12843),U_12842),U_12844)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12843,tc_HOL_Obool)),U_12848),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12843),U_12844),U_12845)))
      | ~ c_Equiv__Relations_Ocongruent(U_12843,tc_fun(U_12846,tc_HOL_Obool),U_12845,U_12847)
      | ~ c_Equiv__Relations_Oequiv(U_12843,U_12844,U_12845) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

fof(f_3291_3,plain,
    ! [U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12843,tc_fun(U_12846,tc_HOL_Obool)),U_12848),U_12847)),U_12849))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(U_12847,sK304(U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843))),U_12849))
        & hBOOL(hAPP(hAPP(c_member(U_12843),sK304(U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843)),U_12844)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12843,tc_HOL_Obool)),U_12848),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12843),U_12844),U_12845)))
      | ~ c_Equiv__Relations_Ocongruent(U_12843,tc_fun(U_12846,tc_HOL_Obool),U_12845,U_12847)
      | ~ c_Equiv__Relations_Oequiv(U_12843,U_12844,U_12845) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_12842,sK304(U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843))],[f_3291_2]) ).

cnf(f_3291_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12843),sK304(U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843)),U_12844))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12843,tc_fun(U_12846,tc_HOL_Obool)),U_12848),U_12847)),U_12849))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12843,tc_HOL_Obool)),U_12848),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12843),U_12844),U_12845)))
    | ~ c_Equiv__Relations_Ocongruent(U_12843,tc_fun(U_12846,tc_HOL_Obool),U_12845,U_12847)
    | ~ c_Equiv__Relations_Oequiv(U_12843,U_12844,U_12845) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

cnf(f_3291_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(U_12847,sK304(U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843))),U_12849))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12846,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12843,tc_fun(U_12846,tc_HOL_Obool)),U_12848),U_12847)),U_12849))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12843,tc_HOL_Obool)),U_12848),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12843),U_12844),U_12845)))
    | ~ c_Equiv__Relations_Ocongruent(U_12843,tc_fun(U_12846,tc_HOL_Obool),U_12845,U_12847)
    | ~ c_Equiv__Relations_Oequiv(U_12843,U_12844,U_12845) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

fof(f_3292_1,plain,
    ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_3292_2,plain,
    ! [U_12854,U_12853,U_12852,U_12851,U_12850] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12853,U_12853)),hAPP(hAPP(c_Product__Type_OPair(U_12853,U_12853),U_12851),U_12852)),c_Wellfounded_Omlex__prod(U_12853,U_12850,U_12854)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12853,U_12853)),hAPP(hAPP(c_Product__Type_OPair(U_12853,U_12853),U_12851),U_12852)),U_12854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12850,U_12851)),hAPP(U_12850,U_12852))) ),
    inference(variable_rename,[status(thm)],[f_3292_1]) ).

cnf(f_3292_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12853,U_12853)),hAPP(hAPP(c_Product__Type_OPair(U_12853,U_12853),U_12851),U_12852)),c_Wellfounded_Omlex__prod(U_12853,U_12850,U_12854)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12853,U_12853)),hAPP(hAPP(c_Product__Type_OPair(U_12853,U_12853),U_12851),U_12852)),U_12854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12850,U_12851)),hAPP(U_12850,U_12852))) ),
    inference(clausify,[status(thm)],[f_3292_2]) ).

fof(f_3293_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_3293_2,plain,
    ! [U_12855] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_12855)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_12855)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

cnf(f_3293_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_12855)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_12855)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3293_2]) ).

fof(f_3294_1,plain,
    ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,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_3294_2,plain,
    ! [U_12860,U_12859,U_12858,U_12857,U_12856] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12859,U_12859)),hAPP(hAPP(c_Product__Type_OPair(U_12859,U_12859),U_12857),U_12858)),c_Wellfounded_Omlex__prod(U_12859,U_12856,U_12860)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12856,U_12857)),hAPP(U_12856,U_12858))) ),
    inference(variable_rename,[status(thm)],[f_3294_1]) ).

cnf(f_3294_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12859,U_12859)),hAPP(hAPP(c_Product__Type_OPair(U_12859,U_12859),U_12857),U_12858)),c_Wellfounded_Omlex__prod(U_12859,U_12856,U_12860)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_12856,U_12857)),hAPP(U_12856,U_12858))) ),
    inference(clausify,[status(thm)],[f_3294_2]) ).

fof(f_3295_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_3295_2,plain,
    ! [U_12862,U_12861] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_12861) = c_Code__Numeral_OSuc__code__numeral(U_12862)
        | U_12861 != U_12862 )
      & ( U_12861 = U_12862
        | c_Code__Numeral_OSuc__code__numeral(U_12861) != c_Code__Numeral_OSuc__code__numeral(U_12862) ) ),
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

fof(f_3295_3,plain,
    ( ! [U_12866,U_12864] :
        ( c_Code__Numeral_OSuc__code__numeral(U_12864) = c_Code__Numeral_OSuc__code__numeral(U_12866)
        | U_12864 != U_12866 )
    & ! [U_12865,U_12863] :
        ( U_12863 = U_12865
        | c_Code__Numeral_OSuc__code__numeral(U_12863) != c_Code__Numeral_OSuc__code__numeral(U_12865) ) ),
    inference(miniscope,[status(thm)],[f_3295_2]) ).

cnf(f_3295_4,plain,
    ( U_12863 = U_12865
    | c_Code__Numeral_OSuc__code__numeral(U_12863) != c_Code__Numeral_OSuc__code__numeral(U_12865) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

cnf(f_3295_5,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_12864) = c_Code__Numeral_OSuc__code__numeral(U_12866)
    | U_12864 != U_12866 ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

fof(f_3296_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_3296_2,plain,
    ! [U_12867] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_12867),
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

cnf(f_3296_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_12867),
    inference(clausify,[status(thm)],[f_3296_2]) ).

fof(f_3297_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_3297_2,plain,
    ! [U_12868] : c_Code__Numeral_OSuc__code__numeral(U_12868) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

cnf(f_3297_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_12868) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_3297_2]) ).

fof(f_3298_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_3298_2,plain,
    ! [U_12869] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_12869)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_12869,
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

cnf(f_3298_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_12869)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_12869,
    inference(clausify,[status(thm)],[f_3298_2]) ).

fof(f_3299_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_3299_2,plain,
    ! [U_12870] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_12870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_12870)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

cnf(f_3299_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_12870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_12870)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3299_2]) ).

fof(f_3300_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_3300_2,plain,
    ! [U_12871] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_12871)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

cnf(f_3300_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_12871)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3300_2]) ).

fof(f_3301_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_3301_2,plain,
    ! [U_12877,U_12876,U_12875,U_12874,U_12873,U_12872] : c_Product__Type_Oprod_Oprod__rec(U_12872,U_12873,U_12874,U_12875,hAPP(hAPP(c_Product__Type_OPair(U_12872,U_12873),U_12876),U_12877)) = hAPP(hAPP(U_12875,U_12876),U_12877),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

cnf(f_3301_3,plain,
    c_Product__Type_Oprod_Oprod__rec(U_12872,U_12873,U_12874,U_12875,hAPP(hAPP(c_Product__Type_OPair(U_12872,U_12873),U_12876),U_12877)) = hAPP(hAPP(U_12875,U_12876),U_12877),
    inference(clausify,[status(thm)],[f_3301_2]) ).

fof(f_3302_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_3302_2,plain,
    ! [U_12878] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_12878) = U_12878,
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

cnf(f_3302_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_12878) = U_12878,
    inference(clausify,[status(thm)],[f_3302_2]) ).

fof(f_3303_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]) ).

cnf(f_3303_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(clausify,[status(thm)],[f_3303_1]) ).

fof(f_3304_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]) ).

cnf(f_3304_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(clausify,[status(thm)],[f_3304_1]) ).

fof(f_3305_1,plain,
    ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_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_b_H_2)),V_s_2))
            | V_a_2 != V_a_H_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_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_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).

fof(f_3305_2,plain,
    ! [U_12886,U_12885,U_12884,U_12883,U_12882,U_12881,U_12880,U_12879] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12879,U_12880),tc_prod(U_12879,U_12880))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12879,U_12880),tc_prod(U_12879,U_12880)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12880),U_12881),U_12882)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12880),U_12883),U_12884))),c_Wellfounded_Olex__prod(U_12879,U_12880,U_12885,U_12886)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12880,U_12880)),hAPP(hAPP(c_Product__Type_OPair(U_12880,U_12880),U_12882),U_12884)),U_12886))
            | U_12881 != U_12883 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12879,U_12879)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12879),U_12881),U_12883)),U_12885)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12880,U_12880)),hAPP(hAPP(c_Product__Type_OPair(U_12880,U_12880),U_12882),U_12884)),U_12886))
          & U_12881 = U_12883 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12879,U_12879)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12879),U_12881),U_12883)),U_12885))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12879,U_12880),tc_prod(U_12879,U_12880))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12879,U_12880),tc_prod(U_12879,U_12880)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12880),U_12881),U_12882)),hAPP(hAPP(c_Product__Type_OPair(U_12879,U_12880),U_12883),U_12884))),c_Wellfounded_Olex__prod(U_12879,U_12880,U_12885,U_12886))) ) ),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

fof(f_3305_3,plain,
    ( ! [U_12902,U_12900,U_12898,U_12896,U_12894,U_12892,U_12890,U_12888] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12892),U_12894)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12896),U_12898))),c_Wellfounded_Olex__prod(U_12888,U_12890,U_12900,U_12902)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12890,U_12890)),hAPP(hAPP(c_Product__Type_OPair(U_12890,U_12890),U_12894),U_12898)),U_12902))
            | U_12892 != U_12896 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12888,U_12888)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12888),U_12892),U_12896)),U_12900)) ) )
    & ! [U_12901,U_12899,U_12897,U_12895,U_12893,U_12891,U_12889,U_12887] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12889,U_12889)),hAPP(hAPP(c_Product__Type_OPair(U_12889,U_12889),U_12893),U_12897)),U_12901))
          & U_12891 = U_12895 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12887,U_12887)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12887),U_12891),U_12895)),U_12899))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12891),U_12893)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12895),U_12897))),c_Wellfounded_Olex__prod(U_12887,U_12889,U_12899,U_12901))) ) ),
    inference(miniscope,[status(thm)],[f_3305_2]) ).

cnf(f_3305_4,plain,
    ( U_12891 = U_12895
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12887,U_12887)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12887),U_12891),U_12895)),U_12899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12891),U_12893)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12895),U_12897))),c_Wellfounded_Olex__prod(U_12887,U_12889,U_12899,U_12901))) ),
    inference(clausify,[status(thm)],[f_3305_3]) ).

cnf(f_3305_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12889,U_12889)),hAPP(hAPP(c_Product__Type_OPair(U_12889,U_12889),U_12893),U_12897)),U_12901))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_12887,U_12887)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12887),U_12891),U_12895)),U_12899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12887,U_12889),tc_prod(U_12887,U_12889)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12891),U_12893)),hAPP(hAPP(c_Product__Type_OPair(U_12887,U_12889),U_12895),U_12897))),c_Wellfounded_Olex__prod(U_12887,U_12889,U_12899,U_12901))) ),
    inference(clausify,[status(thm)],[f_3305_3]) ).

cnf(f_3305_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12888,U_12888)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12888),U_12892),U_12896)),U_12900))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12892),U_12894)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12896),U_12898))),c_Wellfounded_Olex__prod(U_12888,U_12890,U_12900,U_12902))) ),
    inference(clausify,[status(thm)],[f_3305_3]) ).

cnf(f_3305_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12890,U_12890)),hAPP(hAPP(c_Product__Type_OPair(U_12890,U_12890),U_12894),U_12898)),U_12902))
    | U_12892 != U_12896
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_12888,U_12890),tc_prod(U_12888,U_12890)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12892),U_12894)),hAPP(hAPP(c_Product__Type_OPair(U_12888,U_12890),U_12896),U_12898))),c_Wellfounded_Olex__prod(U_12888,U_12890,U_12900,U_12902))) ),
    inference(clausify,[status(thm)],[f_3305_3]) ).

fof(f_3306_1,plain,
    ! [V_A_2,T_a] :
      ( ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
        | ~ c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) )
      & ( c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2))
        | ~ c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__equiv]) ).

fof(f_3306_2,plain,
    ! [U_12904,U_12903] :
      ( ( c_Equiv__Relations_Oequiv(U_12903,c_Orderings_Otop__class_Otop(tc_fun(U_12903,tc_HOL_Obool)),U_12904)
        | ~ c_Equiv__Relations_Oequivp(U_12903,hAPP(hAPP(c_COMBC(U_12903,tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_fun(U_12903,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12903,tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_fun(U_12903,tc_HOL_Obool)),U_12903),c_COMBC(U_12903,tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12903,tc_prod(U_12903,U_12903)),tc_fun(U_12903,tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),U_12903),hAPP(c_COMBB(tc_prod(U_12903,U_12903),tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool),U_12903),c_member(tc_prod(U_12903,U_12903)))),c_Product__Type_OPair(U_12903,U_12903)))),U_12904)) )
      & ( c_Equiv__Relations_Oequivp(U_12903,hAPP(hAPP(c_COMBC(U_12903,tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_fun(U_12903,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12903,tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_fun(U_12903,tc_HOL_Obool)),U_12903),c_COMBC(U_12903,tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12903,tc_prod(U_12903,U_12903)),tc_fun(U_12903,tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool)),U_12903),hAPP(c_COMBB(tc_prod(U_12903,U_12903),tc_fun(tc_fun(tc_prod(U_12903,U_12903),tc_HOL_Obool),tc_HOL_Obool),U_12903),c_member(tc_prod(U_12903,U_12903)))),c_Product__Type_OPair(U_12903,U_12903)))),U_12904))
        | ~ c_Equiv__Relations_Oequiv(U_12903,c_Orderings_Otop__class_Otop(tc_fun(U_12903,tc_HOL_Obool)),U_12904) ) ),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

fof(f_3306_3,plain,
    ( ! [U_12908,U_12906] :
        ( c_Equiv__Relations_Oequiv(U_12906,c_Orderings_Otop__class_Otop(tc_fun(U_12906,tc_HOL_Obool)),U_12908)
        | ~ c_Equiv__Relations_Oequivp(U_12906,hAPP(hAPP(c_COMBC(U_12906,tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_fun(U_12906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12906,tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_fun(U_12906,tc_HOL_Obool)),U_12906),c_COMBC(U_12906,tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12906,tc_prod(U_12906,U_12906)),tc_fun(U_12906,tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),U_12906),hAPP(c_COMBB(tc_prod(U_12906,U_12906),tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool),U_12906),c_member(tc_prod(U_12906,U_12906)))),c_Product__Type_OPair(U_12906,U_12906)))),U_12908)) )
    & ! [U_12907,U_12905] :
        ( c_Equiv__Relations_Oequivp(U_12905,hAPP(hAPP(c_COMBC(U_12905,tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_fun(U_12905,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12905,tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_fun(U_12905,tc_HOL_Obool)),U_12905),c_COMBC(U_12905,tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12905,tc_prod(U_12905,U_12905)),tc_fun(U_12905,tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),U_12905),hAPP(c_COMBB(tc_prod(U_12905,U_12905),tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool),U_12905),c_member(tc_prod(U_12905,U_12905)))),c_Product__Type_OPair(U_12905,U_12905)))),U_12907))
        | ~ c_Equiv__Relations_Oequiv(U_12905,c_Orderings_Otop__class_Otop(tc_fun(U_12905,tc_HOL_Obool)),U_12907) ) ),
    inference(miniscope,[status(thm)],[f_3306_2]) ).

cnf(f_3306_4,plain,
    ( c_Equiv__Relations_Oequivp(U_12905,hAPP(hAPP(c_COMBC(U_12905,tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_fun(U_12905,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12905,tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_fun(U_12905,tc_HOL_Obool)),U_12905),c_COMBC(U_12905,tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12905,tc_prod(U_12905,U_12905)),tc_fun(U_12905,tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool)),U_12905),hAPP(c_COMBB(tc_prod(U_12905,U_12905),tc_fun(tc_fun(tc_prod(U_12905,U_12905),tc_HOL_Obool),tc_HOL_Obool),U_12905),c_member(tc_prod(U_12905,U_12905)))),c_Product__Type_OPair(U_12905,U_12905)))),U_12907))
    | ~ c_Equiv__Relations_Oequiv(U_12905,c_Orderings_Otop__class_Otop(tc_fun(U_12905,tc_HOL_Obool)),U_12907) ),
    inference(clausify,[status(thm)],[f_3306_3]) ).

cnf(f_3306_5,plain,
    ( c_Equiv__Relations_Oequiv(U_12906,c_Orderings_Otop__class_Otop(tc_fun(U_12906,tc_HOL_Obool)),U_12908)
    | ~ c_Equiv__Relations_Oequivp(U_12906,hAPP(hAPP(c_COMBC(U_12906,tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_fun(U_12906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12906,tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_fun(U_12906,tc_HOL_Obool)),U_12906),c_COMBC(U_12906,tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12906,tc_prod(U_12906,U_12906)),tc_fun(U_12906,tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool)),U_12906),hAPP(c_COMBB(tc_prod(U_12906,U_12906),tc_fun(tc_fun(tc_prod(U_12906,U_12906),tc_HOL_Obool),tc_HOL_Obool),U_12906),c_member(tc_prod(U_12906,U_12906)))),c_Product__Type_OPair(U_12906,U_12906)))),U_12908)) ),
    inference(clausify,[status(thm)],[f_3306_3]) ).

fof(f_3307_1,plain,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apfst__apsnd]) ).

fof(f_3307_2,plain,
    ! [U_12915,U_12914,U_12913,U_12912,U_12911,U_12910,U_12909] : hAPP(c_Product__Type_Oapfst(U_12909,U_12910,U_12911,U_12912),hAPP(c_Product__Type_Oapsnd(U_12913,U_12911,U_12909,U_12914),U_12915)) = hAPP(hAPP(c_Product__Type_OPair(U_12910,U_12911),hAPP(U_12912,hAPP(c_Product__Type_Ofst(U_12909,U_12913),U_12915))),hAPP(U_12914,hAPP(c_Product__Type_Osnd(U_12909,U_12913),U_12915))),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

cnf(f_3307_3,plain,
    hAPP(c_Product__Type_Oapfst(U_12909,U_12910,U_12911,U_12912),hAPP(c_Product__Type_Oapsnd(U_12913,U_12911,U_12909,U_12914),U_12915)) = hAPP(hAPP(c_Product__Type_OPair(U_12910,U_12911),hAPP(U_12912,hAPP(c_Product__Type_Ofst(U_12909,U_12913),U_12915))),hAPP(U_12914,hAPP(c_Product__Type_Osnd(U_12909,U_12913),U_12915))),
    inference(clausify,[status(thm)],[f_3307_2]) ).

fof(f_3308_1,plain,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__compose]) ).

fof(f_3308_2,plain,
    ! [U_12922,U_12921,U_12920,U_12919,U_12918,U_12917,U_12916] : hAPP(c_Product__Type_Oapfst(U_12916,U_12917,U_12918,U_12919),hAPP(c_Product__Type_Oapfst(U_12920,U_12916,U_12918,U_12921),U_12922)) = hAPP(c_Product__Type_Oapfst(U_12920,U_12917,U_12918,hAPP(c_Fun_Ocomp(U_12916,U_12917,U_12920,U_12919),U_12921)),U_12922),
    inference(variable_rename,[status(thm)],[f_3308_1]) ).

cnf(f_3308_3,plain,
    hAPP(c_Product__Type_Oapfst(U_12916,U_12917,U_12918,U_12919),hAPP(c_Product__Type_Oapfst(U_12920,U_12916,U_12918,U_12921),U_12922)) = hAPP(c_Product__Type_Oapfst(U_12920,U_12917,U_12918,hAPP(c_Fun_Ocomp(U_12916,U_12917,U_12920,U_12919),U_12921)),U_12922),
    inference(clausify,[status(thm)],[f_3308_2]) ).

fof(f_3309_1,plain,
    ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3309_2,plain,
    ! [U_12923] : c_Equiv__Relations_Oequivp(U_12923,c_fequal),
    inference(variable_rename,[status(thm)],[f_3309_1]) ).

cnf(f_3309_3,plain,
    c_Equiv__Relations_Oequivp(U_12923,c_fequal),
    inference(clausify,[status(thm)],[f_3309_2]) ).

fof(f_3310_1,plain,
    ! [V_R_2,T_a] :
      ( ( c_Equiv__Relations_Oequivp(T_a,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_a,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__def]) ).

fof(f_3310_2,plain,
    ! [U_12929,U_12928] :
      ( ( c_Equiv__Relations_Oequivp(U_12928,U_12929)
        | ? [U_12927,U_12926] :
            ( ( ~ hBOOL(hAPP(hAPP(U_12929,U_12927),U_12926))
              & hAPP(U_12929,U_12927) = hAPP(U_12929,U_12926) )
            | ( hAPP(U_12929,U_12927) != hAPP(U_12929,U_12926)
              & hBOOL(hAPP(hAPP(U_12929,U_12927),U_12926)) ) ) )
      & ( ! [U_12925,U_12924] :
            ( ( hBOOL(hAPP(hAPP(U_12929,U_12925),U_12924))
              | hAPP(U_12929,U_12925) != hAPP(U_12929,U_12924) )
            & ( hAPP(U_12929,U_12925) = hAPP(U_12929,U_12924)
              | ~ hBOOL(hAPP(hAPP(U_12929,U_12925),U_12924)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_12928,U_12929) ) ),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

fof(f_3310_3,plain,
    ( ! [U_12941] :
        ( ! [U_12939] : c_Equiv__Relations_Oequivp(U_12939,U_12941)
        | ? [U_12937,U_12935] :
            ( ~ hBOOL(hAPP(hAPP(U_12941,U_12937),U_12935))
            & hAPP(U_12941,U_12937) = hAPP(U_12941,U_12935) )
        | ? [U_12936,U_12934] :
            ( hAPP(U_12941,U_12936) != hAPP(U_12941,U_12934)
            & hBOOL(hAPP(hAPP(U_12941,U_12936),U_12934)) ) )
    & ! [U_12940] :
        ( ! [U_12938] : ~ c_Equiv__Relations_Oequivp(U_12938,U_12940)
        | ( ! [U_12933,U_12931] :
              ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
              | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931) )
          & ! [U_12932,U_12930] :
              ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
              | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3310_2]) ).

fof(f_3310_4,plain,
    ( ! [U_12941] :
        ( ! [U_12939] : c_Equiv__Relations_Oequivp(U_12939,U_12941)
        | ? [U_12937,U_12935] :
            ( ~ hBOOL(hAPP(hAPP(U_12941,U_12937),U_12935))
            & hAPP(U_12941,U_12937) = hAPP(U_12941,U_12935) )
        | ? [U_12934] :
            ( hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,U_12934)
            & hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),U_12934)) ) )
    & ! [U_12940] :
        ( ! [U_12938] : ~ c_Equiv__Relations_Oequivp(U_12938,U_12940)
        | ( ! [U_12933,U_12931] :
              ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
              | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931) )
          & ! [U_12932,U_12930] :
              ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
              | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_12936,sK305(U_12941))],[f_3310_3]) ).

fof(f_3310_5,plain,
    ( ! [U_12941] :
        ( ! [U_12939] : c_Equiv__Relations_Oequivp(U_12939,U_12941)
        | ? [U_12937,U_12935] :
            ( ~ hBOOL(hAPP(hAPP(U_12941,U_12937),U_12935))
            & hAPP(U_12941,U_12937) = hAPP(U_12941,U_12935) )
        | ( hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,sK306(U_12941))
          & hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),sK306(U_12941))) ) )
    & ! [U_12940] :
        ( ! [U_12938] : ~ c_Equiv__Relations_Oequivp(U_12938,U_12940)
        | ( ! [U_12933,U_12931] :
              ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
              | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931) )
          & ! [U_12932,U_12930] :
              ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
              | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_12934,sK306(U_12941))],[f_3310_4]) ).

fof(f_3310_6,plain,
    ( ! [U_12941] :
        ( ! [U_12939] : c_Equiv__Relations_Oequivp(U_12939,U_12941)
        | ? [U_12935] :
            ( ~ hBOOL(hAPP(hAPP(U_12941,sK307(U_12941)),U_12935))
            & hAPP(U_12941,sK307(U_12941)) = hAPP(U_12941,U_12935) )
        | ( hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,sK306(U_12941))
          & hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),sK306(U_12941))) ) )
    & ! [U_12940] :
        ( ! [U_12938] : ~ c_Equiv__Relations_Oequivp(U_12938,U_12940)
        | ( ! [U_12933,U_12931] :
              ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
              | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931) )
          & ! [U_12932,U_12930] :
              ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
              | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_12937,sK307(U_12941))],[f_3310_5]) ).

fof(f_3310_7,plain,
    ( ! [U_12941] :
        ( ! [U_12939] : c_Equiv__Relations_Oequivp(U_12939,U_12941)
        | ( ~ hBOOL(hAPP(hAPP(U_12941,sK307(U_12941)),sK308(U_12941)))
          & hAPP(U_12941,sK307(U_12941)) = hAPP(U_12941,sK308(U_12941)) )
        | ( hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,sK306(U_12941))
          & hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),sK306(U_12941))) ) )
    & ! [U_12940] :
        ( ! [U_12938] : ~ c_Equiv__Relations_Oequivp(U_12938,U_12940)
        | ( ! [U_12933,U_12931] :
              ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
              | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931) )
          & ! [U_12932,U_12930] :
              ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
              | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_12935,sK308(U_12941))],[f_3310_6]) ).

cnf(f_3310_8,plain,
    ( hAPP(U_12940,U_12932) = hAPP(U_12940,U_12930)
    | ~ hBOOL(hAPP(hAPP(U_12940,U_12932),U_12930))
    | ~ c_Equiv__Relations_Oequivp(U_12938,U_12940) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

cnf(f_3310_9,plain,
    ( hBOOL(hAPP(hAPP(U_12940,U_12933),U_12931))
    | hAPP(U_12940,U_12933) != hAPP(U_12940,U_12931)
    | ~ c_Equiv__Relations_Oequivp(U_12938,U_12940) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

cnf(f_3310_10,plain,
    ( hAPP(U_12941,sK307(U_12941)) = hAPP(U_12941,sK308(U_12941))
    | hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),sK306(U_12941)))
    | c_Equiv__Relations_Oequivp(U_12939,U_12941) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

cnf(f_3310_11,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12941,sK307(U_12941)),sK308(U_12941)))
    | hBOOL(hAPP(hAPP(U_12941,sK305(U_12941)),sK306(U_12941)))
    | c_Equiv__Relations_Oequivp(U_12939,U_12941) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

cnf(f_3310_12,plain,
    ( hAPP(U_12941,sK307(U_12941)) = hAPP(U_12941,sK308(U_12941))
    | hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,sK306(U_12941))
    | c_Equiv__Relations_Oequivp(U_12939,U_12941) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

cnf(f_3310_13,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12941,sK307(U_12941)),sK308(U_12941)))
    | hAPP(U_12941,sK305(U_12941)) != hAPP(U_12941,sK306(U_12941))
    | c_Equiv__Relations_Oequivp(U_12939,U_12941) ),
    inference(clausify,[status(thm)],[f_3310_7]) ).

fof(f_3311_1,plain,
    ! [V_x_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
      | ~ c_Equiv__Relations_Oequivp(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__reflp]) ).

fof(f_3311_2,plain,
    ! [U_12944,U_12943,U_12942] :
      ( hBOOL(hAPP(hAPP(U_12943,U_12944),U_12944))
      | ~ c_Equiv__Relations_Oequivp(U_12942,U_12943) ),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

fof(f_3311_3,plain,
    ! [U_12944,U_12943] :
      ( ! [U_12942] : ~ c_Equiv__Relations_Oequivp(U_12942,U_12943)
      | hBOOL(hAPP(hAPP(U_12943,U_12944),U_12944)) ),
    inference(miniscope,[status(thm)],[f_3311_2]) ).

cnf(f_3311_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12942,U_12943)
    | hBOOL(hAPP(hAPP(U_12943,U_12944),U_12944)) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

fof(f_3312_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_a] :
      ( 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_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__symp]) ).

fof(f_3312_2,plain,
    ! [U_12948,U_12947,U_12946,U_12945] :
      ( hBOOL(hAPP(hAPP(U_12946,U_12948),U_12947))
      | ~ hBOOL(hAPP(hAPP(U_12946,U_12947),U_12948))
      | ~ c_Equiv__Relations_Oequivp(U_12945,U_12946) ),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

fof(f_3312_3,plain,
    ! [U_12948,U_12947,U_12946] :
      ( ! [U_12945] : ~ c_Equiv__Relations_Oequivp(U_12945,U_12946)
      | hBOOL(hAPP(hAPP(U_12946,U_12948),U_12947))
      | ~ hBOOL(hAPP(hAPP(U_12946,U_12947),U_12948)) ),
    inference(miniscope,[status(thm)],[f_3312_2]) ).

cnf(f_3312_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12945,U_12946)
    | hBOOL(hAPP(hAPP(U_12946,U_12948),U_12947))
    | ~ hBOOL(hAPP(hAPP(U_12946,U_12947),U_12948)) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

fof(f_3313_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
      ( 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_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__transp]) ).

fof(f_3313_2,plain,
    ! [U_12953,U_12952,U_12951,U_12950,U_12949] :
      ( hBOOL(hAPP(hAPP(U_12950,U_12951),U_12953))
      | ~ hBOOL(hAPP(hAPP(U_12950,U_12952),U_12953))
      | ~ hBOOL(hAPP(hAPP(U_12950,U_12951),U_12952))
      | ~ c_Equiv__Relations_Oequivp(U_12949,U_12950) ),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

fof(f_3313_3,plain,
    ! [U_12953,U_12952,U_12951,U_12950] :
      ( ! [U_12949] : ~ c_Equiv__Relations_Oequivp(U_12949,U_12950)
      | hBOOL(hAPP(hAPP(U_12950,U_12951),U_12953))
      | ~ hBOOL(hAPP(hAPP(U_12950,U_12952),U_12953))
      | ~ hBOOL(hAPP(hAPP(U_12950,U_12951),U_12952)) ),
    inference(miniscope,[status(thm)],[f_3313_2]) ).

cnf(f_3313_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12949,U_12950)
    | hBOOL(hAPP(hAPP(U_12950,U_12951),U_12953))
    | ~ hBOOL(hAPP(hAPP(U_12950,U_12952),U_12953))
    | ~ hBOOL(hAPP(hAPP(U_12950,U_12951),U_12952)) ),
    inference(clausify,[status(thm)],[f_3313_3]) ).

fof(f_3314_1,plain,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_snd__apfst]) ).

fof(f_3314_2,plain,
    ! [U_12958,U_12957,U_12956,U_12955,U_12954] : hAPP(c_Product__Type_Osnd(U_12954,U_12955),hAPP(c_Product__Type_Oapfst(U_12956,U_12954,U_12955,U_12957),U_12958)) = hAPP(c_Product__Type_Osnd(U_12956,U_12955),U_12958),
    inference(variable_rename,[status(thm)],[f_3314_1]) ).

cnf(f_3314_3,plain,
    hAPP(c_Product__Type_Osnd(U_12954,U_12955),hAPP(c_Product__Type_Oapfst(U_12956,U_12954,U_12955,U_12957),U_12958)) = hAPP(c_Product__Type_Osnd(U_12956,U_12955),U_12958),
    inference(clausify,[status(thm)],[f_3314_2]) ).

fof(f_3315_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
      ( ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2))
        | hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv]) ).

fof(f_3315_2,plain,
    ! [U_12964,U_12963,U_12962,U_12961,U_12960,U_12959] :
      ( ( hAPP(c_Product__Type_Oapfst(U_12959,U_12960,U_12961,U_12962),U_12963) = hAPP(c_Product__Type_Oapfst(U_12959,U_12960,U_12961,U_12964),U_12963)
        | hAPP(U_12962,hAPP(c_Product__Type_Ofst(U_12959,U_12961),U_12963)) != hAPP(U_12964,hAPP(c_Product__Type_Ofst(U_12959,U_12961),U_12963)) )
      & ( hAPP(U_12962,hAPP(c_Product__Type_Ofst(U_12959,U_12961),U_12963)) = hAPP(U_12964,hAPP(c_Product__Type_Ofst(U_12959,U_12961),U_12963))
        | hAPP(c_Product__Type_Oapfst(U_12959,U_12960,U_12961,U_12962),U_12963) != hAPP(c_Product__Type_Oapfst(U_12959,U_12960,U_12961,U_12964),U_12963) ) ),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

fof(f_3315_3,plain,
    ( ! [U_12976,U_12974,U_12972,U_12970,U_12968,U_12966] :
        ( hAPP(c_Product__Type_Oapfst(U_12966,U_12968,U_12970,U_12972),U_12974) = hAPP(c_Product__Type_Oapfst(U_12966,U_12968,U_12970,U_12976),U_12974)
        | hAPP(U_12972,hAPP(c_Product__Type_Ofst(U_12966,U_12970),U_12974)) != hAPP(U_12976,hAPP(c_Product__Type_Ofst(U_12966,U_12970),U_12974)) )
    & ! [U_12975,U_12973,U_12971,U_12969,U_12967,U_12965] :
        ( hAPP(U_12971,hAPP(c_Product__Type_Ofst(U_12965,U_12969),U_12973)) = hAPP(U_12975,hAPP(c_Product__Type_Ofst(U_12965,U_12969),U_12973))
        | hAPP(c_Product__Type_Oapfst(U_12965,U_12967,U_12969,U_12971),U_12973) != hAPP(c_Product__Type_Oapfst(U_12965,U_12967,U_12969,U_12975),U_12973) ) ),
    inference(miniscope,[status(thm)],[f_3315_2]) ).

cnf(f_3315_4,plain,
    ( hAPP(U_12971,hAPP(c_Product__Type_Ofst(U_12965,U_12969),U_12973)) = hAPP(U_12975,hAPP(c_Product__Type_Ofst(U_12965,U_12969),U_12973))
    | hAPP(c_Product__Type_Oapfst(U_12965,U_12967,U_12969,U_12971),U_12973) != hAPP(c_Product__Type_Oapfst(U_12965,U_12967,U_12969,U_12975),U_12973) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

cnf(f_3315_5,plain,
    ( hAPP(c_Product__Type_Oapfst(U_12966,U_12968,U_12970,U_12972),U_12974) = hAPP(c_Product__Type_Oapfst(U_12966,U_12968,U_12970,U_12976),U_12974)
    | hAPP(U_12972,hAPP(c_Product__Type_Ofst(U_12966,U_12970),U_12974)) != hAPP(U_12976,hAPP(c_Product__Type_Ofst(U_12966,U_12970),U_12974)) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

fof(f_3316_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__apfst]) ).

fof(f_3316_2,plain,
    ! [U_12981,U_12980,U_12979,U_12978,U_12977] : hAPP(c_Product__Type_Ofst(U_12977,U_12978),hAPP(c_Product__Type_Oapfst(U_12979,U_12977,U_12978,U_12980),U_12981)) = hAPP(U_12980,hAPP(c_Product__Type_Ofst(U_12979,U_12978),U_12981)),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

cnf(f_3316_3,plain,
    hAPP(c_Product__Type_Ofst(U_12977,U_12978),hAPP(c_Product__Type_Oapfst(U_12979,U_12977,U_12978,U_12980),U_12981)) = hAPP(U_12980,hAPP(c_Product__Type_Ofst(U_12979,U_12978),U_12981)),
    inference(clausify,[status(thm)],[f_3316_2]) ).

fof(f_3317_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__conv]) ).

fof(f_3317_2,plain,
    ! [U_12987,U_12986,U_12985,U_12984,U_12983,U_12982] : hAPP(c_Product__Type_Oapfst(U_12982,U_12983,U_12984,U_12985),hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12984),U_12986),U_12987)) = hAPP(hAPP(c_Product__Type_OPair(U_12983,U_12984),hAPP(U_12985,U_12986)),U_12987),
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

cnf(f_3317_3,plain,
    hAPP(c_Product__Type_Oapfst(U_12982,U_12983,U_12984,U_12985),hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12984),U_12986),U_12987)) = hAPP(hAPP(c_Product__Type_OPair(U_12983,U_12984),hAPP(U_12985,U_12986)),U_12987),
    inference(clausify,[status(thm)],[f_3317_2]) ).

fof(f_3318_1,plain,
    ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(f_3318_2,plain,
    ! [U_12994,U_12993,U_12992,U_12991,U_12990,U_12989,U_12988] : hAPP(c_Product__Type_Oapsnd(U_12988,U_12989,U_12990,U_12991),hAPP(c_Product__Type_Oapfst(U_12992,U_12990,U_12988,U_12993),U_12994)) = hAPP(c_Product__Type_Oapfst(U_12992,U_12990,U_12989,U_12993),hAPP(c_Product__Type_Oapsnd(U_12988,U_12989,U_12992,U_12991),U_12994)),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

cnf(f_3318_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_12988,U_12989,U_12990,U_12991),hAPP(c_Product__Type_Oapfst(U_12992,U_12990,U_12988,U_12993),U_12994)) = hAPP(c_Product__Type_Oapfst(U_12992,U_12990,U_12989,U_12993),hAPP(c_Product__Type_Oapsnd(U_12988,U_12989,U_12992,U_12991),U_12994)),
    inference(clausify,[status(thm)],[f_3318_2]) ).

fof(f_3319_1,plain,
    ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst]) ).

fof(f_3319_2,plain,
    ! [U_13001,U_13000,U_12999,U_12998,U_12997,U_12996,U_12995] : hAPP(c_Product__Type_Oapsnd(U_12995,U_12996,U_12997,U_12998),hAPP(c_Product__Type_Oapfst(U_12999,U_12997,U_12995,U_13000),U_13001)) = hAPP(hAPP(c_Product__Type_OPair(U_12997,U_12996),hAPP(U_13000,hAPP(c_Product__Type_Ofst(U_12999,U_12995),U_13001))),hAPP(U_12998,hAPP(c_Product__Type_Osnd(U_12999,U_12995),U_13001))),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

cnf(f_3319_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_12995,U_12996,U_12997,U_12998),hAPP(c_Product__Type_Oapfst(U_12999,U_12997,U_12995,U_13000),U_13001)) = hAPP(hAPP(c_Product__Type_OPair(U_12997,U_12996),hAPP(U_13000,hAPP(c_Product__Type_Ofst(U_12999,U_12995),U_13001))),hAPP(U_12998,hAPP(c_Product__Type_Osnd(U_12999,U_12995),U_13001))),
    inference(clausify,[status(thm)],[f_3319_2]) ).

fof(f_3320_1,plain,
    ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_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_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).

fof(f_3320_2,plain,
    ! [U_13008,U_13007,U_13006,U_13005,U_13004,U_13003,U_13002] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_13008,U_13004),tc_prod(U_13008,U_13004))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_13008,U_13004),tc_prod(U_13008,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13008,U_13004),U_13003),U_13005)),hAPP(hAPP(c_Product__Type_OPair(U_13008,U_13004),U_13003),U_13006))),c_Recdef_Osame__fst(U_13008,U_13004,U_13002,U_13007)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13004,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13004,U_13004),U_13005),U_13006)),hAPP(U_13007,U_13003)))
      | ~ hBOOL(hAPP(U_13002,U_13003)) ),
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

cnf(f_3320_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_13008,U_13004),tc_prod(U_13008,U_13004))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_13008,U_13004),tc_prod(U_13008,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13008,U_13004),U_13003),U_13005)),hAPP(hAPP(c_Product__Type_OPair(U_13008,U_13004),U_13003),U_13006))),c_Recdef_Osame__fst(U_13008,U_13004,U_13002,U_13007)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13004,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13004,U_13004),U_13005),U_13006)),hAPP(U_13007,U_13003)))
    | ~ hBOOL(hAPP(U_13002,U_13003)) ),
    inference(clausify,[status(thm)],[f_3320_2]) ).

fof(f_3321_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_3321_2,plain,
    ! [U_13012,U_13011,U_13010,U_13009] :
      ( 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_13009),U_13011)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13010),U_13012))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13011),U_13012))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13009),U_13010)) ),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

cnf(f_3321_3,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_13009),U_13011)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13010),U_13012))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13011),U_13012))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13009),U_13010)) ),
    inference(clausify,[status(thm)],[f_3321_2]) ).

fof(f_3322_1,plain,
    ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ImageE]) ).

fof(f_3322_2,plain,
    ! [U_13018,U_13017,U_13016,U_13015,U_13014] :
      ( ? [U_13013] :
          ( hBOOL(hAPP(hAPP(c_member(U_13016),U_13013),U_13018))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13016,U_13014)),hAPP(hAPP(c_Product__Type_OPair(U_13016,U_13014),U_13013),U_13015)),U_13017)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13014),U_13015),hAPP(c_Relation_OImage(U_13016,U_13014,U_13017),U_13018))) ),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

fof(f_3322_3,plain,
    ! [U_13018,U_13017,U_13016,U_13015,U_13014] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13016),sK309(U_13018,U_13017,U_13016,U_13015,U_13014)),U_13018))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13016,U_13014)),hAPP(hAPP(c_Product__Type_OPair(U_13016,U_13014),sK309(U_13018,U_13017,U_13016,U_13015,U_13014)),U_13015)),U_13017)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13014),U_13015),hAPP(c_Relation_OImage(U_13016,U_13014,U_13017),U_13018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_13013,sK309(U_13018,U_13017,U_13016,U_13015,U_13014))],[f_3322_2]) ).

cnf(f_3322_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13016,U_13014)),hAPP(hAPP(c_Product__Type_OPair(U_13016,U_13014),sK309(U_13018,U_13017,U_13016,U_13015,U_13014)),U_13015)),U_13017))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13014),U_13015),hAPP(c_Relation_OImage(U_13016,U_13014,U_13017),U_13018))) ),
    inference(clausify,[status(thm)],[f_3322_3]) ).

cnf(f_3322_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13016),sK309(U_13018,U_13017,U_13016,U_13015,U_13014)),U_13018))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13014),U_13015),hAPP(c_Relation_OImage(U_13016,U_13014,U_13017),U_13018))) ),
    inference(clausify,[status(thm)],[f_3322_3]) ).

fof(f_3323_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_3323_2,plain,
    ! [U_13022,U_13021,U_13020,U_13019] :
      ( 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_13019),U_13021)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13020),U_13022))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13019),U_13020)) ),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

cnf(f_3323_3,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_13019),U_13021)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13020),U_13022))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13019),U_13020)) ),
    inference(clausify,[status(thm)],[f_3323_2]) ).

fof(f_3324_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_3324_2,plain,
    ! [U_13026,U_13025,U_13024,U_13023] :
      ( 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_13023),U_13025)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13024),U_13026))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13025),U_13026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13023),U_13024)) ),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

cnf(f_3324_3,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_13023),U_13025)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13024),U_13026))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13025),U_13026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13023),U_13024)) ),
    inference(clausify,[status(thm)],[f_3324_2]) ).

fof(f_3325_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_3325_2,plain,
    ! [U_13030,U_13029,U_13028,U_13027] :
      ( 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_13029),U_13030)),U_13028)),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_13030),U_13028)),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_13029),U_13027)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13027),U_13028)) ),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

cnf(f_3325_3,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_13029),U_13030)),U_13028)),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_13030),U_13028)),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_13029),U_13027)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13027),U_13028)) ),
    inference(clausify,[status(thm)],[f_3325_2]) ).

fof(f_3326_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_3326_2,plain,
    ! [U_13034,U_13033,U_13032,U_13031] :
      ( 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_13032),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13033),U_13034))),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_13032),U_13034)),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_13031),U_13033)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13031),U_13032)) ),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

cnf(f_3326_3,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_13032),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13033),U_13034))),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_13032),U_13034)),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_13031),U_13033)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13031),U_13032)) ),
    inference(clausify,[status(thm)],[f_3326_2]) ).

fof(f_3327_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_3327_2,plain,
    ! [U_13035] :
      ( 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_13035),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_13035 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

cnf(f_3327_3,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_13035),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_13035 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3327_2]) ).

fof(f_3328_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_3328_2,plain,
    ! [U_13036] :
      ( 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_13036)),c_FunDef_Omax__strict))
      | U_13036 = 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_13036)) ),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

cnf(f_3328_3,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_13036)),c_FunDef_Omax__strict))
    | U_13036 = 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_13036)) ),
    inference(clausify,[status(thm)],[f_3328_2]) ).

fof(f_3329_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_3329_2,plain,
    ! [U_13040,U_13039,U_13038,U_13037] :
      ( 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_13037),U_13039)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13038),U_13040))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13037),U_13038)) ),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

cnf(f_3329_3,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_13037),U_13039)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13038),U_13040))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13037),U_13038)) ),
    inference(clausify,[status(thm)],[f_3329_2]) ).

fof(f_3330_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_3330_2,plain,
    ! [U_13044,U_13043,U_13042,U_13041] :
      ( 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_13042),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13043),U_13044))),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_13042),U_13044)),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_13041),U_13043)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13041),U_13042)) ),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

cnf(f_3330_3,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_13042),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13043),U_13044))),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_13042),U_13044)),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_13041),U_13043)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13041),U_13042)) ),
    inference(clausify,[status(thm)],[f_3330_2]) ).

fof(f_3331_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_3331_2,plain,
    ! [U_13048,U_13047,U_13046,U_13045] :
      ( 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_13047),U_13048)),U_13046)),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_13048),U_13046)),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_13047),U_13045)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13045),U_13046)) ),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

cnf(f_3331_3,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_13047),U_13048)),U_13046)),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_13048),U_13046)),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_13047),U_13045)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13045),U_13046)) ),
    inference(clausify,[status(thm)],[f_3331_2]) ).

fof(f_3332_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__insert]) ).

fof(f_3332_2,plain,
    ! [U_13052,U_13051,U_13050,U_13049] : hAPP(c_Relation_OField(U_13049),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13049,U_13049)),hAPP(hAPP(c_Product__Type_OPair(U_13049,U_13049),U_13050),U_13051)),U_13052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13049,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13050),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13051),c_Orderings_Obot__class_Obot(tc_fun(U_13049,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_13049),U_13052)),
    inference(variable_rename,[status(thm)],[f_3332_1]) ).

cnf(f_3332_3,plain,
    hAPP(c_Relation_OField(U_13049),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13049,U_13049)),hAPP(hAPP(c_Product__Type_OPair(U_13049,U_13049),U_13050),U_13051)),U_13052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13049,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13050),hAPP(hAPP(c_Set_Oinsert(U_13049),U_13051),c_Orderings_Obot__class_Obot(tc_fun(U_13049,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_13049),U_13052)),
    inference(clausify,[status(thm)],[f_3332_2]) ).

fof(f_3333_1,plain,
    ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Union]) ).

fof(f_3333_2,plain,
    ! [U_13054,U_13053] : hAPP(c_Relation_OField(U_13053),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13053,U_13053),tc_HOL_Obool),U_13054)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_13053,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_13053,U_13053),tc_HOL_Obool),tc_fun(U_13053,tc_HOL_Obool),c_Relation_OField(U_13053)),U_13054)),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

cnf(f_3333_3,plain,
    hAPP(c_Relation_OField(U_13053),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13053,U_13053),tc_HOL_Obool),U_13054)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_13053,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_13053,U_13053),tc_HOL_Obool),tc_fun(U_13053,tc_HOL_Obool),c_Relation_OField(U_13053)),U_13054)),
    inference(clausify,[status(thm)],[f_3333_2]) ).

fof(f_3334_1,plain,
    ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Field__empty]) ).

fof(f_3334_2,plain,
    ! [U_13055] : hAPP(c_Relation_OField(U_13055),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13055,U_13055),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13055,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

cnf(f_3334_3,plain,
    hAPP(c_Relation_OField(U_13055),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13055,U_13055),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13055,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3334_2]) ).

fof(f_3335_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_mono__Field]) ).

fof(f_3335_2,plain,
    ! [U_13058,U_13057,U_13056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13056,tc_HOL_Obool)),hAPP(c_Relation_OField(U_13056),U_13057)),hAPP(c_Relation_OField(U_13056),U_13058)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13056,U_13056),tc_HOL_Obool)),U_13057),U_13058)) ),
    inference(variable_rename,[status(thm)],[f_3335_1]) ).

cnf(f_3335_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13056,tc_HOL_Obool)),hAPP(c_Relation_OField(U_13056),U_13057)),hAPP(c_Relation_OField(U_13056),U_13058)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13056,U_13056),tc_HOL_Obool)),U_13057),U_13058)) ),
    inference(clausify,[status(thm)],[f_3335_2]) ).

fof(f_3336_1,plain,
    ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Un]) ).

fof(f_3336_2,plain,
    ! [U_13061,U_13060,U_13059] : hAPP(c_Relation_OField(U_13059),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13059,U_13059),tc_HOL_Obool)),U_13060),U_13061)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13059,tc_HOL_Obool)),hAPP(c_Relation_OField(U_13059),U_13060)),hAPP(c_Relation_OField(U_13059),U_13061)),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

cnf(f_3336_3,plain,
    hAPP(c_Relation_OField(U_13059),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13059,U_13059),tc_HOL_Obool)),U_13060),U_13061)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13059,tc_HOL_Obool)),hAPP(c_Relation_OField(U_13059),U_13060)),hAPP(c_Relation_OField(U_13059),U_13061)),
    inference(clausify,[status(thm)],[f_3336_2]) ).

fof(f_3337_1,plain,
    ! [V_r_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Field]) ).

fof(f_3337_2,plain,
    ! [U_13063,U_13062] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13062),hAPP(c_Relation_OField(U_13062),U_13063)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13062,U_13062)),U_13063)) ),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

cnf(f_3337_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13062),hAPP(c_Relation_OField(U_13062),U_13063)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13062,U_13062)),U_13063)) ),
    inference(clausify,[status(thm)],[f_3337_2]) ).

fof(f_3338_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_3338_2,plain,
    ! [U_13064] :
      ( 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_13064)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13064)) ),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

cnf(f_3338_3,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_13064)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_13064)) ),
    inference(clausify,[status(thm)],[f_3338_2]) ).

fof(f_3339_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_3339_2,plain,
    ! [U_13065] : 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_13065),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_3339_1]) ).

cnf(f_3339_3,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_13065),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_3339_2]) ).

fof(f_3340_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]) ).

cnf(f_3340_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(clausify,[status(thm)],[f_3340_1]) ).

fof(f_3341_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]) ).

cnf(f_3341_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(clausify,[status(thm)],[f_3341_1]) ).

fof(f_3342_1,plain,
    ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def]) ).

fof(f_3342_2,plain,
    ! [U_13067,U_13066] : c_Relation_OId__on(U_13066,U_13067) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13066,tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),U_13067),hAPP(hAPP(c_COMBC(U_13066,tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool),tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_13066,U_13066),tc_fun(tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool),tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),U_13066),c_Set_Oinsert(tc_prod(U_13066,U_13066))),hAPP(hAPP(c_COMBS(U_13066,U_13066,tc_prod(U_13066,U_13066)),c_Product__Type_OPair(U_13066,U_13066)),c_COMBI(U_13066)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

cnf(f_3342_3,plain,
    c_Relation_OId__on(U_13066,U_13067) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13066,tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),U_13067),hAPP(hAPP(c_COMBC(U_13066,tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool),tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_13066,U_13066),tc_fun(tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool),tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)),U_13066),c_Set_Oinsert(tc_prod(U_13066,U_13066))),hAPP(hAPP(c_COMBS(U_13066,U_13066,tc_prod(U_13066,U_13066)),c_Product__Type_OPair(U_13066,U_13066)),c_COMBI(U_13066)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13066,U_13066),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3342_2]) ).

fof(f_3343_1,plain,
    ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def_H]) ).

fof(f_3343_2,plain,
    ! [U_13069,U_13068] : c_Relation_OId__on(U_13068,U_13069) = hAPP(c_Product__Type_Oprod_Oprod__case(U_13068,U_13068,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13068,tc_HOL_Obool,tc_fun(U_13068,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13068,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_13068,tc_HOL_Obool)),U_13068),c_COMBC(U_13068,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13068,tc_HOL_Obool),tc_fun(U_13068,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13068),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13068),c_fconj)),c_fequal))),U_13069)),
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

cnf(f_3343_3,plain,
    c_Relation_OId__on(U_13068,U_13069) = hAPP(c_Product__Type_Oprod_Oprod__case(U_13068,U_13068,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13068,tc_HOL_Obool,tc_fun(U_13068,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13068,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_13068,tc_HOL_Obool)),U_13068),c_COMBC(U_13068,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13068,tc_HOL_Obool),tc_fun(U_13068,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13068),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13068),c_fconj)),c_fequal))),U_13069)),
    inference(clausify,[status(thm)],[f_3343_2]) ).

fof(f_3344_1,plain,
    ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__empty]) ).

fof(f_3344_2,plain,
    ! [U_13070] : c_Relation_OId__on(U_13070,c_Orderings_Obot__class_Obot(tc_fun(U_13070,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13070,U_13070),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

cnf(f_3344_3,plain,
    c_Relation_OId__on(U_13070,c_Orderings_Obot__class_Obot(tc_fun(U_13070,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13070,U_13070),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3344_2]) ).

fof(f_3345_1,plain,
    ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Image__Id__on]) ).

fof(f_3345_2,plain,
    ! [U_13073,U_13072,U_13071] : hAPP(c_Relation_OImage(U_13071,U_13071,c_Relation_OId__on(U_13071,U_13072)),U_13073) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13071,tc_HOL_Obool)),U_13072),U_13073),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

cnf(f_3345_3,plain,
    hAPP(c_Relation_OImage(U_13071,U_13071,c_Relation_OId__on(U_13071,U_13072)),U_13073) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13071,tc_HOL_Obool)),U_13072),U_13073),
    inference(clausify,[status(thm)],[f_3345_2]) ).

fof(f_3346_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
        | V_x_2 != V_y_2 )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
          & V_x_2 = V_y_2 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__iff]) ).

fof(f_3346_2,plain,
    ! [U_13077,U_13076,U_13075,U_13074] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13074,U_13074)),hAPP(hAPP(c_Product__Type_OPair(U_13074,U_13074),U_13075),U_13076)),c_Relation_OId__on(U_13074,U_13077)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13074),U_13075),U_13077))
        | U_13075 != U_13076 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_13074),U_13075),U_13077))
          & U_13075 = U_13076 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13074,U_13074)),hAPP(hAPP(c_Product__Type_OPair(U_13074,U_13074),U_13075),U_13076)),c_Relation_OId__on(U_13074,U_13077))) ) ),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

fof(f_3346_3,plain,
    ( ! [U_13085,U_13083,U_13081,U_13079] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13079,U_13079)),hAPP(hAPP(c_Product__Type_OPair(U_13079,U_13079),U_13081),U_13083)),c_Relation_OId__on(U_13079,U_13085)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13079),U_13081),U_13085))
        | U_13081 != U_13083 )
    & ! [U_13084,U_13082,U_13080,U_13078] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_13078),U_13080),U_13084))
          & U_13080 = U_13082 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13078,U_13078)),hAPP(hAPP(c_Product__Type_OPair(U_13078,U_13078),U_13080),U_13082)),c_Relation_OId__on(U_13078,U_13084))) ) ),
    inference(miniscope,[status(thm)],[f_3346_2]) ).

cnf(f_3346_4,plain,
    ( U_13080 = U_13082
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13078,U_13078)),hAPP(hAPP(c_Product__Type_OPair(U_13078,U_13078),U_13080),U_13082)),c_Relation_OId__on(U_13078,U_13084))) ),
    inference(clausify,[status(thm)],[f_3346_3]) ).

cnf(f_3346_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13078),U_13080),U_13084))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13078,U_13078)),hAPP(hAPP(c_Product__Type_OPair(U_13078,U_13078),U_13080),U_13082)),c_Relation_OId__on(U_13078,U_13084))) ),
    inference(clausify,[status(thm)],[f_3346_3]) ).

cnf(f_3346_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13079,U_13079)),hAPP(hAPP(c_Product__Type_OPair(U_13079,U_13079),U_13081),U_13083)),c_Relation_OId__on(U_13079,U_13085)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13079),U_13081),U_13085))
    | U_13081 != U_13083 ),
    inference(clausify,[status(thm)],[f_3346_3]) ).

fof(f_3347_1,plain,
    ! [V_A_2,T_a,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__eqI]) ).

fof(f_3347_2,plain,
    ! [U_13089,U_13088,U_13087,U_13086] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13088,U_13088)),hAPP(hAPP(c_Product__Type_OPair(U_13088,U_13088),U_13086),U_13087)),c_Relation_OId__on(U_13088,U_13089)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13086),U_13089))
      | U_13086 != U_13087 ),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

cnf(f_3347_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13088,U_13088)),hAPP(hAPP(c_Product__Type_OPair(U_13088,U_13088),U_13086),U_13087)),c_Relation_OId__on(U_13088,U_13089)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13086),U_13089))
    | U_13086 != U_13087 ),
    inference(clausify,[status(thm)],[f_3347_2]) ).

fof(f_3348_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]) ).

cnf(f_3348_2,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_3348_1]) ).

fof(f_3349_1,plain,
    ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__additive]) ).

fof(f_3349_2,plain,
    ! [U_13095,U_13094,U_13093,U_13092,U_13091,U_13090] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13090,tc_HOL_Obool)),U_13091),U_13094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13090,tc_HOL_Obool)),U_13092),U_13095))),c_Wellfounded_Omax__ext(U_13090,U_13093)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13094),U_13095)),c_Wellfounded_Omax__ext(U_13090,U_13093)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13091),U_13092)),c_Wellfounded_Omax__ext(U_13090,U_13093))) ),
    inference(variable_rename,[status(thm)],[f_3349_1]) ).

cnf(f_3349_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13090,tc_HOL_Obool)),U_13091),U_13094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13090,tc_HOL_Obool)),U_13092),U_13095))),c_Wellfounded_Omax__ext(U_13090,U_13093)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13094),U_13095)),c_Wellfounded_Omax__ext(U_13090,U_13093)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13090,tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13091),U_13092)),c_Wellfounded_Omax__ext(U_13090,U_13093))) ),
    inference(clausify,[status(thm)],[f_3349_2]) ).

fof(f_3350_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]) ).

cnf(f_3350_2,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_3350_1]) ).

fof(f_3351_1,plain,
    ! [V_xa_2,V_x_2,V_R_2,T_a] :
      ( ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
        | ~ c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq]) ).

fof(f_3351_2,plain,
    ! [U_13099,U_13098,U_13097,U_13096] :
      ( ( c_Wellfounded_Omax__extp(U_13096,hAPP(hAPP(c_COMBC(U_13096,tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13096,tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),U_13096),c_COMBC(U_13096,tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13096,tc_prod(U_13096,U_13096)),tc_fun(U_13096,tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),U_13096),hAPP(c_COMBB(tc_prod(U_13096,U_13096),tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool),U_13096),c_member(tc_prod(U_13096,U_13096)))),c_Product__Type_OPair(U_13096,U_13096)))),U_13097),U_13098,U_13099)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13096,tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13096,tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),U_13098),U_13099)),c_Wellfounded_Omax__ext(U_13096,U_13097))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13096,tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13096,tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),U_13098),U_13099)),c_Wellfounded_Omax__ext(U_13096,U_13097)))
        | ~ c_Wellfounded_Omax__extp(U_13096,hAPP(hAPP(c_COMBC(U_13096,tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13096,tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_fun(U_13096,tc_HOL_Obool)),U_13096),c_COMBC(U_13096,tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13096,tc_prod(U_13096,U_13096)),tc_fun(U_13096,tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool)),U_13096),hAPP(c_COMBB(tc_prod(U_13096,U_13096),tc_fun(tc_fun(tc_prod(U_13096,U_13096),tc_HOL_Obool),tc_HOL_Obool),U_13096),c_member(tc_prod(U_13096,U_13096)))),c_Product__Type_OPair(U_13096,U_13096)))),U_13097),U_13098,U_13099) ) ),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

fof(f_3351_3,plain,
    ( ! [U_13107,U_13105,U_13103,U_13101] :
        ( c_Wellfounded_Omax__extp(U_13101,hAPP(hAPP(c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13101),c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_prod(U_13101,U_13101)),tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),U_13101),hAPP(c_COMBB(tc_prod(U_13101,U_13101),tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool),U_13101),c_member(tc_prod(U_13101,U_13101)))),c_Product__Type_OPair(U_13101,U_13101)))),U_13103),U_13105,U_13107)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13101,tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13101,tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13105),U_13107)),c_Wellfounded_Omax__ext(U_13101,U_13103))) )
    & ! [U_13106,U_13104,U_13102,U_13100] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13100,tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13100,tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),U_13104),U_13106)),c_Wellfounded_Omax__ext(U_13100,U_13102)))
        | ~ c_Wellfounded_Omax__extp(U_13100,hAPP(hAPP(c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13100,tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),U_13100),c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13100,tc_prod(U_13100,U_13100)),tc_fun(U_13100,tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),U_13100),hAPP(c_COMBB(tc_prod(U_13100,U_13100),tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool),U_13100),c_member(tc_prod(U_13100,U_13100)))),c_Product__Type_OPair(U_13100,U_13100)))),U_13102),U_13104,U_13106) ) ),
    inference(miniscope,[status(thm)],[f_3351_2]) ).

cnf(f_3351_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13100,tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13100,tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),U_13104),U_13106)),c_Wellfounded_Omax__ext(U_13100,U_13102)))
    | ~ c_Wellfounded_Omax__extp(U_13100,hAPP(hAPP(c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13100,tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_fun(U_13100,tc_HOL_Obool)),U_13100),c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13100,tc_prod(U_13100,U_13100)),tc_fun(U_13100,tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool)),U_13100),hAPP(c_COMBB(tc_prod(U_13100,U_13100),tc_fun(tc_fun(tc_prod(U_13100,U_13100),tc_HOL_Obool),tc_HOL_Obool),U_13100),c_member(tc_prod(U_13100,U_13100)))),c_Product__Type_OPair(U_13100,U_13100)))),U_13102),U_13104,U_13106) ),
    inference(clausify,[status(thm)],[f_3351_3]) ).

cnf(f_3351_5,plain,
    ( c_Wellfounded_Omax__extp(U_13101,hAPP(hAPP(c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13101),c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_prod(U_13101,U_13101)),tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool)),U_13101),hAPP(c_COMBB(tc_prod(U_13101,U_13101),tc_fun(tc_fun(tc_prod(U_13101,U_13101),tc_HOL_Obool),tc_HOL_Obool),U_13101),c_member(tc_prod(U_13101,U_13101)))),c_Product__Type_OPair(U_13101,U_13101)))),U_13103),U_13105,U_13107)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13101,tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13101,tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13105),U_13107)),c_Wellfounded_Omax__ext(U_13101,U_13103))) ),
    inference(clausify,[status(thm)],[f_3351_3]) ).

fof(f_3352_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]) ).

cnf(f_3352_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(clausify,[status(thm)],[f_3352_1]) ).

fof(f_3353_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]) ).

cnf(f_3353_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(clausify,[status(thm)],[f_3353_1]) ).

fof(f_3354_1,plain,
    ! [V_f_2,T_b,V_P_2,T_a] :
      ( c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2))
      | ~ c_FunDef_Oreduction__pair(T_a,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).

fof(f_3354_2,plain,
    ! [U_13111,U_13110,U_13109,U_13108] :
      ( c_FunDef_Oreduction__pair(U_13110,hAPP(hAPP(c_FunDef_Orp__inv__image(U_13108,U_13110),U_13109),U_13111))
      | ~ c_FunDef_Oreduction__pair(U_13108,U_13109) ),
    inference(variable_rename,[status(thm)],[f_3354_1]) ).

cnf(f_3354_3,plain,
    ( c_FunDef_Oreduction__pair(U_13110,hAPP(hAPP(c_FunDef_Orp__inv__image(U_13108,U_13110),U_13109),U_13111))
    | ~ c_FunDef_Oreduction__pair(U_13108,U_13109) ),
    inference(clausify,[status(thm)],[f_3354_2]) ).

fof(f_3355_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_3355_2,plain,
    ! [U_13113,U_13112] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),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_13112),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_13113),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_13112),U_13113)),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_13112),U_13113)),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_13112),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_13113),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

fof(f_3355_3,plain,
    ( ! [U_13117,U_13115] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),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_13115),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_13117),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_13115),U_13117)),c_Int_Ointrel)) )
    & ! [U_13116,U_13114] :
        ( 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_13114),U_13116)),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_13114),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_13116),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3355_2]) ).

cnf(f_3355_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)),U_13114),U_13116)),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_13114),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_13116),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3355_3]) ).

cnf(f_3355_5,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_13115),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_13117),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_13115),U_13117)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3355_3]) ).

fof(f_3356_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_3356_2,plain,
    ! [U_13119,U_13118] :
      ( ( 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_13118),U_13119)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13118),U_13119)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13118),U_13119))
        | ~ 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_13118),U_13119)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

fof(f_3356_3,plain,
    ( ! [U_13123,U_13121] :
        ( 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_13121),U_13123)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13121),U_13123)) )
    & ! [U_13122,U_13120] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13120),U_13122))
        | ~ 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_13120),U_13122)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_3356_2]) ).

cnf(f_3356_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13120),U_13122))
    | ~ 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_13120),U_13122)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

cnf(f_3356_5,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_13121),U_13123)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_13121),U_13123)) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

fof(f_3357_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_3357_2,plain,
    ! [U_13127,U_13126,U_13125,U_13124] :
      ( ( 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_13124),U_13125)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13126),U_13127))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13124),U_13127) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13126),U_13125) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13124),U_13127) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13126),U_13125)
        | ~ 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_13124),U_13125)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13126),U_13127))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

fof(f_3357_3,plain,
    ( ! [U_13135,U_13133,U_13131,U_13129] :
        ( 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_13129),U_13131)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13133),U_13135))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13129),U_13135) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13133),U_13131) )
    & ! [U_13134,U_13132,U_13130,U_13128] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13128),U_13134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13132),U_13130)
        | ~ 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_13128),U_13130)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13132),U_13134))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_3357_2]) ).

cnf(f_3357_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13128),U_13134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13132),U_13130)
    | ~ 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_13128),U_13130)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13132),U_13134))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3357_3]) ).

cnf(f_3357_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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13129),U_13131)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_13133),U_13135))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13129),U_13135) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13133),U_13131) ),
    inference(clausify,[status(thm)],[f_3357_3]) ).

fof(f_3358_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]) ).

cnf(f_3358_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(clausify,[status(thm)],[f_3358_1]) ).

fof(f_3359_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]) ).

cnf(f_3359_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(clausify,[status(thm)],[f_3359_1]) ).

fof(f_3360_1,plain,
    ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_measure__def]) ).

fof(f_3360_2,plain,
    ! [U_13136] : c_Wellfounded_Omeasure(U_13136) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_13136),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_3360_1]) ).

cnf(f_3360_3,plain,
    c_Wellfounded_Omeasure(U_13136) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_13136),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3360_2]) ).

fof(f_3361_1,plain,
    ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))),
    inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).

fof(f_3361_2,plain,
    ! [U_13139,U_13138,U_13137] : c_Wellfounded_Omlex__prod(U_13137,U_13138,U_13139) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_13137),U_13137),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_13137,c_Wellfounded_Oless__than,U_13139)),hAPP(hAPP(c_COMBS(U_13137,U_13137,tc_prod(tc_Nat_Onat,U_13137)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_13137,tc_prod(tc_Nat_Onat,U_13137)),U_13137),c_Product__Type_OPair(tc_Nat_Onat,U_13137)),U_13138)),c_COMBI(U_13137))),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

cnf(f_3361_3,plain,
    c_Wellfounded_Omlex__prod(U_13137,U_13138,U_13139) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_13137),U_13137),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_13137,c_Wellfounded_Oless__than,U_13139)),hAPP(hAPP(c_COMBS(U_13137,U_13137,tc_prod(tc_Nat_Onat,U_13137)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_13137,tc_prod(tc_Nat_Onat,U_13137)),U_13137),c_Product__Type_OPair(tc_Nat_Onat,U_13137)),U_13138)),c_COMBI(U_13137))),
    inference(clausify,[status(thm)],[f_3361_2]) ).

fof(f_3362_1,plain,
    ! [V_j_2,V_i_2,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int]) ).

fof(f_3362_2,plain,
    ! [U_13142,U_13141,U_13140] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_13140),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_13141),U_13142)),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_13140),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_13140),U_13141)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_13140),U_13142))
      | ~ class_Rings_Oring__1(U_13140) ),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

cnf(f_3362_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_13140),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_13141),U_13142)),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_13140),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_13140),U_13141)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_13140),U_13142))
    | ~ class_Rings_Oring__1(U_13140) ),
    inference(clausify,[status(thm)],[f_3362_2]) ).

fof(f_3363_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]) ).

cnf(f_3363_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(clausify,[status(thm)],[f_3363_1]) ).

fof(f_3364_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_3364_2,plain,
    ! [U_13146,U_13145,U_13144,U_13143] : 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_13143),U_13144)),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_13145),U_13146)),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_13143),U_13145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13144),U_13146))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13143),U_13146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13144),U_13145)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

cnf(f_3364_3,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_13143),U_13144)),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_13145),U_13146)),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_13143),U_13145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13144),U_13146))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13143),U_13146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13144),U_13145)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3364_2]) ).

fof(f_3365_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_3365_2,plain,
    ! [U_13147] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_13147)) = U_13147,
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

cnf(f_3365_3,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_13147)) = U_13147,
    inference(clausify,[status(thm)],[f_3365_2]) ).

fof(f_3366_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_3366_2,plain,
    ! [U_13149,U_13148] : 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_13148),U_13149)),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_13149),U_13148)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

cnf(f_3366_3,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_13148),U_13149)),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_13149),U_13148)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3366_2]) ).

fof(f_3367_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]) ).

cnf(f_3367_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(clausify,[status(thm)],[f_3367_1]) ).

fof(f_3368_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_3368_2,plain,
    ! [U_13150] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_13150) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_13150),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_3368_1]) ).

cnf(f_3368_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_13150) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_13150),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_3368_2]) ).

fof(f_3369_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_3369_2,plain,
    ! [U_13154,U_13153,U_13152,U_13151] : 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_13151),U_13152)),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_13153),U_13154)),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_13151),U_13153)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13152),U_13154))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3369_1]) ).

cnf(f_3369_3,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_13151),U_13152)),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_13153),U_13154)),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_13151),U_13153)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13152),U_13154))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3369_2]) ).

fof(f_3370_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_3370_2,plain,
    ! [U_13156,U_13155] : 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_13155),U_13156)),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_13155),U_13156),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

cnf(f_3370_3,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_13155),U_13156)),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_13155),U_13156),
    inference(clausify,[status(thm)],[f_3370_2]) ).

fof(f_3371_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_3371_2,plain,
    ! [U_13157] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_13157) = 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_13157)),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_3371_1]) ).

cnf(f_3371_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_13157) = 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_13157)),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_3371_2]) ).

fof(f_3372_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_3372_2,plain,
    ! [U_13161,U_13160,U_13159,U_13158] :
      ( ( 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_13158),U_13159)),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_13160),U_13161)),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_13158),U_13161)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13160),U_13159))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13158),U_13161)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13160),U_13159)))
        | ~ 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_13158),U_13159)),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_13160),U_13161)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

fof(f_3372_3,plain,
    ( ! [U_13169,U_13167,U_13165,U_13163] :
        ( 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_13163),U_13165)),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_13167),U_13169)),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_13163),U_13169)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13167),U_13165))) )
    & ! [U_13168,U_13166,U_13164,U_13162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13162),U_13168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13166),U_13164)))
        | ~ 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_13162),U_13164)),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_13166),U_13168)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3372_2]) ).

cnf(f_3372_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13162),U_13168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13166),U_13164)))
    | ~ 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_13162),U_13164)),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_13166),U_13168)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3372_3]) ).

cnf(f_3372_5,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_13163),U_13165)),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_13167),U_13169)),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_13163),U_13169)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13167),U_13165))) ),
    inference(clausify,[status(thm)],[f_3372_3]) ).

fof(f_3373_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_3373_2,plain,
    ! [U_13173,U_13172,U_13171,U_13170] :
      ( ( 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_13170),U_13171)),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_13172),U_13173)),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_13170),U_13173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13172),U_13171))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13170),U_13173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13172),U_13171)))
        | ~ 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_13170),U_13171)),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_13172),U_13173)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

fof(f_3373_3,plain,
    ( ! [U_13181,U_13179,U_13177,U_13175] :
        ( 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_13175),U_13177)),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_13179),U_13181)),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_13175),U_13181)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13179),U_13177))) )
    & ! [U_13180,U_13178,U_13176,U_13174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13174),U_13180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13178),U_13176)))
        | ~ 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_13174),U_13176)),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_13178),U_13180)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3373_2]) ).

cnf(f_3373_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_13174),U_13180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13178),U_13176)))
    | ~ 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_13174),U_13176)),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_13178),U_13180)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3373_3]) ).

cnf(f_3373_5,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_13175),U_13177)),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_13179),U_13181)),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_13175),U_13181)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13179),U_13177))) ),
    inference(clausify,[status(thm)],[f_3373_3]) ).

fof(f_3374_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_3374_2,plain,
    ! [U_13184] :
    ? [U_13183,U_13182] : U_13184 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(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_13183),U_13182)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

fof(f_3374_3,plain,
    ! [U_13184] :
    ? [U_13182] : U_13184 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK310(U_13184)),U_13182)),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,[sK310]),skolemize(U_13183,sK310(U_13184))],[f_3374_2]) ).

fof(f_3374_4,plain,
    ! [U_13184] : U_13184 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK310(U_13184)),sK311(U_13184))),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,[sK311]),skolemize(U_13182,sK311(U_13184))],[f_3374_3]) ).

cnf(f_3374_5,plain,
    U_13184 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK310(U_13184)),sK311(U_13184))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3374_4]) ).

fof(f_3375_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]) ).

cnf(f_3375_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(clausify,[status(thm)],[f_3375_1]) ).

fof(f_3376_1,plain,
    ! [V_A_2,V_c_2,T_a] :
      ( ? [B_x] :
          ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).

fof(f_3376_2,plain,
    ! [U_13188,U_13187,U_13186] :
      ( ? [U_13185] :
          ( U_13187 = hAPP(hAPP(c_Product__Type_OPair(U_13186,U_13186),U_13185),U_13185)
          & hBOOL(hAPP(hAPP(c_member(U_13186),U_13185),U_13188)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13186,U_13186)),U_13187),c_Relation_OId__on(U_13186,U_13188))) ),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

fof(f_3376_3,plain,
    ! [U_13188,U_13187,U_13186] :
      ( ( U_13187 = hAPP(hAPP(c_Product__Type_OPair(U_13186,U_13186),sK312(U_13188,U_13187,U_13186)),sK312(U_13188,U_13187,U_13186))
        & hBOOL(hAPP(hAPP(c_member(U_13186),sK312(U_13188,U_13187,U_13186)),U_13188)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13186,U_13186)),U_13187),c_Relation_OId__on(U_13186,U_13188))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_13185,sK312(U_13188,U_13187,U_13186))],[f_3376_2]) ).

cnf(f_3376_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13186),sK312(U_13188,U_13187,U_13186)),U_13188))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13186,U_13186)),U_13187),c_Relation_OId__on(U_13186,U_13188))) ),
    inference(clausify,[status(thm)],[f_3376_3]) ).

cnf(f_3376_5,plain,
    ( U_13187 = hAPP(hAPP(c_Product__Type_OPair(U_13186,U_13186),sK312(U_13188,U_13187,U_13186)),sK312(U_13188,U_13187,U_13186))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13186,U_13186)),U_13187),c_Relation_OId__on(U_13186,U_13188))) ),
    inference(clausify,[status(thm)],[f_3376_3]) ).

fof(f_3377_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_3377_2,plain,
    ! [U_13189] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_13189)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

cnf(f_3377_3,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_13189)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3377_2]) ).

fof(f_3378_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]) ).

cnf(f_3378_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(clausify,[status(thm)],[f_3378_1]) ).

fof(f_3379_1,plain,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,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_3379_2,plain,
    ! [U_13193,U_13192,U_13191,U_13190] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_13190,U_13191,U_13192,c_Code__Numeral_OSuc__code__numeral(U_13193)) = hAPP(U_13192,U_13193),
    inference(variable_rename,[status(thm)],[f_3379_1]) ).

cnf(f_3379_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_13190,U_13191,U_13192,c_Code__Numeral_OSuc__code__numeral(U_13193)) = hAPP(U_13192,U_13193),
    inference(clausify,[status(thm)],[f_3379_2]) ).

fof(f_3380_1,plain,
    ! [V_x_2,V_r_2,T_a] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp__acc__eq]) ).

fof(f_3380_2,plain,
    ! [U_13196,U_13195,U_13194] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13194,hAPP(hAPP(c_COMBC(U_13194,tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool)),U_13194),c_COMBC(U_13194,tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_prod(U_13194,U_13194)),tc_fun(U_13194,tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),U_13194),hAPP(c_COMBB(tc_prod(U_13194,U_13194),tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool),U_13194),c_member(tc_prod(U_13194,U_13194)))),c_Product__Type_OPair(U_13194,U_13194)))),U_13195)),U_13196))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13194),U_13196),c_Wellfounded_Oacc(U_13194,U_13195))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13194),U_13196),c_Wellfounded_Oacc(U_13194,U_13195)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13194,hAPP(hAPP(c_COMBC(U_13194,tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool)),U_13194),c_COMBC(U_13194,tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_prod(U_13194,U_13194)),tc_fun(U_13194,tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool)),U_13194),hAPP(c_COMBB(tc_prod(U_13194,U_13194),tc_fun(tc_fun(tc_prod(U_13194,U_13194),tc_HOL_Obool),tc_HOL_Obool),U_13194),c_member(tc_prod(U_13194,U_13194)))),c_Product__Type_OPair(U_13194,U_13194)))),U_13195)),U_13196)) ) ),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

fof(f_3380_3,plain,
    ( ! [U_13202,U_13200,U_13198] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13198,hAPP(hAPP(c_COMBC(U_13198,tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_fun(U_13198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13198,tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_fun(U_13198,tc_HOL_Obool)),U_13198),c_COMBC(U_13198,tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13198,tc_prod(U_13198,U_13198)),tc_fun(U_13198,tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),U_13198),hAPP(c_COMBB(tc_prod(U_13198,U_13198),tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool),U_13198),c_member(tc_prod(U_13198,U_13198)))),c_Product__Type_OPair(U_13198,U_13198)))),U_13200)),U_13202))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13198),U_13202),c_Wellfounded_Oacc(U_13198,U_13200))) )
    & ! [U_13201,U_13199,U_13197] :
        ( hBOOL(hAPP(hAPP(c_member(U_13197),U_13201),c_Wellfounded_Oacc(U_13197,U_13199)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13197,hAPP(hAPP(c_COMBC(U_13197,tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool)),U_13197),c_COMBC(U_13197,tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_prod(U_13197,U_13197)),tc_fun(U_13197,tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),U_13197),hAPP(c_COMBB(tc_prod(U_13197,U_13197),tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool),U_13197),c_member(tc_prod(U_13197,U_13197)))),c_Product__Type_OPair(U_13197,U_13197)))),U_13199)),U_13201)) ) ),
    inference(miniscope,[status(thm)],[f_3380_2]) ).

cnf(f_3380_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13197),U_13201),c_Wellfounded_Oacc(U_13197,U_13199)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13197,hAPP(hAPP(c_COMBC(U_13197,tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool)),U_13197),c_COMBC(U_13197,tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_prod(U_13197,U_13197)),tc_fun(U_13197,tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool)),U_13197),hAPP(c_COMBB(tc_prod(U_13197,U_13197),tc_fun(tc_fun(tc_prod(U_13197,U_13197),tc_HOL_Obool),tc_HOL_Obool),U_13197),c_member(tc_prod(U_13197,U_13197)))),c_Product__Type_OPair(U_13197,U_13197)))),U_13199)),U_13201)) ),
    inference(clausify,[status(thm)],[f_3380_3]) ).

cnf(f_3380_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13198,hAPP(hAPP(c_COMBC(U_13198,tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_fun(U_13198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13198,tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_fun(U_13198,tc_HOL_Obool)),U_13198),c_COMBC(U_13198,tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13198,tc_prod(U_13198,U_13198)),tc_fun(U_13198,tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool)),U_13198),hAPP(c_COMBB(tc_prod(U_13198,U_13198),tc_fun(tc_fun(tc_prod(U_13198,U_13198),tc_HOL_Obool),tc_HOL_Obool),U_13198),c_member(tc_prod(U_13198,U_13198)))),c_Product__Type_OPair(U_13198,U_13198)))),U_13200)),U_13202))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13198),U_13202),c_Wellfounded_Oacc(U_13198,U_13200))) ),
    inference(clausify,[status(thm)],[f_3380_3]) ).

fof(f_3381_1,plain,
    ! [V_R2_2,V_R1_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_acc__subset]) ).

fof(f_3381_2,plain,
    ! [U_13205,U_13204,U_13203] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13203,tc_HOL_Obool)),c_Wellfounded_Oacc(U_13203,U_13205)),c_Wellfounded_Oacc(U_13203,U_13204)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13203,U_13203),tc_HOL_Obool)),U_13204),U_13205)) ),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

cnf(f_3381_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13203,tc_HOL_Obool)),c_Wellfounded_Oacc(U_13203,U_13205)),c_Wellfounded_Oacc(U_13203,U_13204)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13203,U_13203),tc_HOL_Obool)),U_13204),U_13205)) ),
    inference(clausify,[status(thm)],[f_3381_2]) ).

fof(f_3382_1,plain,
    ! [V_a_2,V_r_2,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downward]) ).

fof(f_3382_2,plain,
    ! [U_13209,U_13208,U_13207,U_13206] :
      ( hBOOL(hAPP(hAPP(c_member(U_13206),U_13209),c_Wellfounded_Oacc(U_13206,U_13208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13206,U_13206)),hAPP(hAPP(c_Product__Type_OPair(U_13206,U_13206),U_13209),U_13207)),U_13208))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13206),U_13207),c_Wellfounded_Oacc(U_13206,U_13208))) ),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

cnf(f_3382_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13206),U_13209),c_Wellfounded_Oacc(U_13206,U_13208)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13206,U_13206)),hAPP(hAPP(c_Product__Type_OPair(U_13206,U_13206),U_13209),U_13207)),U_13208))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13206),U_13207),c_Wellfounded_Oacc(U_13206,U_13208))) ),
    inference(clausify,[status(thm)],[f_3382_2]) ).

fof(f_3383_1,plain,
    ! [V_r_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_Osimps]) ).

fof(f_3383_2,plain,
    ! [U_13214,U_13213,U_13212] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13212),U_13213),c_Wellfounded_Oacc(U_13212,U_13214)))
        | ? [U_13211] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13212),U_13211),c_Wellfounded_Oacc(U_13212,U_13214)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13212,U_13212)),hAPP(hAPP(c_Product__Type_OPair(U_13212,U_13212),U_13211),U_13213)),U_13214)) ) )
      & ( ! [U_13210] :
            ( hBOOL(hAPP(hAPP(c_member(U_13212),U_13210),c_Wellfounded_Oacc(U_13212,U_13214)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13212,U_13212)),hAPP(hAPP(c_Product__Type_OPair(U_13212,U_13212),U_13210),U_13213)),U_13214)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13212),U_13213),c_Wellfounded_Oacc(U_13212,U_13214))) ) ),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

fof(f_3383_3,plain,
    ( ! [U_13220,U_13218,U_13216] :
        ( hBOOL(hAPP(hAPP(c_member(U_13216),U_13218),c_Wellfounded_Oacc(U_13216,U_13220)))
        | ? [U_13211] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13216),U_13211),c_Wellfounded_Oacc(U_13216,U_13220)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13216,U_13216)),hAPP(hAPP(c_Product__Type_OPair(U_13216,U_13216),U_13211),U_13218)),U_13220)) ) )
    & ! [U_13219,U_13217,U_13215] :
        ( ! [U_13210] :
            ( hBOOL(hAPP(hAPP(c_member(U_13215),U_13210),c_Wellfounded_Oacc(U_13215,U_13219)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13215,U_13215)),hAPP(hAPP(c_Product__Type_OPair(U_13215,U_13215),U_13210),U_13217)),U_13219)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13215),U_13217),c_Wellfounded_Oacc(U_13215,U_13219))) ) ),
    inference(miniscope,[status(thm)],[f_3383_2]) ).

fof(f_3383_4,plain,
    ( ! [U_13220,U_13218,U_13216] :
        ( hBOOL(hAPP(hAPP(c_member(U_13216),U_13218),c_Wellfounded_Oacc(U_13216,U_13220)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_13216),sK313(U_13220,U_13218,U_13216)),c_Wellfounded_Oacc(U_13216,U_13220)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13216,U_13216)),hAPP(hAPP(c_Product__Type_OPair(U_13216,U_13216),sK313(U_13220,U_13218,U_13216)),U_13218)),U_13220)) ) )
    & ! [U_13219,U_13217,U_13215] :
        ( ! [U_13210] :
            ( hBOOL(hAPP(hAPP(c_member(U_13215),U_13210),c_Wellfounded_Oacc(U_13215,U_13219)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13215,U_13215)),hAPP(hAPP(c_Product__Type_OPair(U_13215,U_13215),U_13210),U_13217)),U_13219)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13215),U_13217),c_Wellfounded_Oacc(U_13215,U_13219))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_13211,sK313(U_13220,U_13218,U_13216))],[f_3383_3]) ).

cnf(f_3383_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13215),U_13210),c_Wellfounded_Oacc(U_13215,U_13219)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13215,U_13215)),hAPP(hAPP(c_Product__Type_OPair(U_13215,U_13215),U_13210),U_13217)),U_13219))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13215),U_13217),c_Wellfounded_Oacc(U_13215,U_13219))) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

cnf(f_3383_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13216,U_13216)),hAPP(hAPP(c_Product__Type_OPair(U_13216,U_13216),sK313(U_13220,U_13218,U_13216)),U_13218)),U_13220))
    | hBOOL(hAPP(hAPP(c_member(U_13216),U_13218),c_Wellfounded_Oacc(U_13216,U_13220))) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

cnf(f_3383_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13216),sK313(U_13220,U_13218,U_13216)),c_Wellfounded_Oacc(U_13216,U_13220)))
    | hBOOL(hAPP(hAPP(c_member(U_13216),U_13218),c_Wellfounded_Oacc(U_13216,U_13220))) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

fof(f_3384_1,plain,
    ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,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_3384_2,plain,
    ! [U_13223,U_13222,U_13221] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_13221,U_13222,U_13223,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_13222,
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

cnf(f_3384_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_13221,U_13222,U_13223,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_13222,
    inference(clausify,[status(thm)],[f_3384_2]) ).

fof(f_3385_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range]) ).

fof(f_3385_2,plain,
    ! [U_13228,U_13227,U_13226,U_13225,U_13224] :
      ( hAPP(c_Set_Oimage(U_13224,U_13225,U_13226),c_Orderings_Otop__class_Otop(tc_fun(U_13224,tc_HOL_Obool))) = U_13228
      | ~ c_Typedef_Otype__definition(U_13224,U_13225,U_13226,U_13227,U_13228) ),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

cnf(f_3385_3,plain,
    ( hAPP(c_Set_Oimage(U_13224,U_13225,U_13226),c_Orderings_Otop__class_Otop(tc_fun(U_13224,tc_HOL_Obool))) = U_13228
    | ~ c_Typedef_Otype__definition(U_13224,U_13225,U_13226,U_13227,U_13228) ),
    inference(clausify,[status(thm)],[f_3385_2]) ).

fof(f_3386_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image]) ).

fof(f_3386_2,plain,
    ! [U_13233,U_13232,U_13231,U_13230,U_13229] :
      ( hAPP(c_Set_Oimage(U_13230,U_13229,U_13232),U_13233) = c_Orderings_Otop__class_Otop(tc_fun(U_13229,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_13229,U_13230,U_13231,U_13232,U_13233) ),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

cnf(f_3386_3,plain,
    ( hAPP(c_Set_Oimage(U_13230,U_13229,U_13232),U_13233) = c_Orderings_Otop__class_Otop(tc_fun(U_13229,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_13229,U_13230,U_13231,U_13232,U_13233) ),
    inference(clausify,[status(thm)],[f_3386_2]) ).

fof(f_3387_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( ( ( 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_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject]) ).

fof(f_3387_2,plain,
    ! [U_13240,U_13239,U_13238,U_13237,U_13236,U_13235,U_13234] :
      ( ( ( hAPP(U_13237,U_13239) = hAPP(U_13237,U_13240)
          | U_13239 != U_13240 )
        & ( U_13239 = U_13240
          | hAPP(U_13237,U_13239) != hAPP(U_13237,U_13240) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13240),U_13238))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13239),U_13238))
      | ~ c_Typedef_Otype__definition(U_13234,U_13235,U_13236,U_13237,U_13238) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ! [U_13240,U_13239,U_13238,U_13237,U_13236,U_13235] :
      ( ! [U_13234] : ~ c_Typedef_Otype__definition(U_13234,U_13235,U_13236,U_13237,U_13238)
      | ( ( hAPP(U_13237,U_13239) = hAPP(U_13237,U_13240)
          | U_13239 != U_13240 )
        & ( U_13239 = U_13240
          | hAPP(U_13237,U_13239) != hAPP(U_13237,U_13240) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13240),U_13238))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13239),U_13238)) ),
    inference(miniscope,[status(thm)],[f_3387_2]) ).

cnf(f_3387_4,plain,
    ( U_13239 = U_13240
    | hAPP(U_13237,U_13239) != hAPP(U_13237,U_13240)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13240),U_13238))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13239),U_13238))
    | ~ c_Typedef_Otype__definition(U_13234,U_13235,U_13236,U_13237,U_13238) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

cnf(f_3387_5,plain,
    ( hAPP(U_13237,U_13239) = hAPP(U_13237,U_13240)
    | U_13239 != U_13240
    | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13240),U_13238))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13235),U_13239),U_13238))
    | ~ c_Typedef_Otype__definition(U_13234,U_13235,U_13236,U_13237,U_13238) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

fof(f_3388_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( ( ( 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_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject]) ).

fof(f_3388_2,plain,
    ! [U_13247,U_13246,U_13245,U_13244,U_13243,U_13242,U_13241] :
      ( ( ( hAPP(U_13243,U_13246) = hAPP(U_13243,U_13247)
          | U_13246 != U_13247 )
        & ( U_13246 = U_13247
          | hAPP(U_13243,U_13246) != hAPP(U_13243,U_13247) ) )
      | ~ c_Typedef_Otype__definition(U_13241,U_13242,U_13243,U_13244,U_13245) ),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

fof(f_3388_3,plain,
    ! [U_13247,U_13246,U_13245,U_13244,U_13243] :
      ( ! [U_13242,U_13241] : ~ c_Typedef_Otype__definition(U_13241,U_13242,U_13243,U_13244,U_13245)
      | ( ( hAPP(U_13243,U_13246) = hAPP(U_13243,U_13247)
          | U_13246 != U_13247 )
        & ( U_13246 = U_13247
          | hAPP(U_13243,U_13246) != hAPP(U_13243,U_13247) ) ) ),
    inference(miniscope,[status(thm)],[f_3388_2]) ).

cnf(f_3388_4,plain,
    ( U_13246 = U_13247
    | hAPP(U_13243,U_13246) != hAPP(U_13243,U_13247)
    | ~ c_Typedef_Otype__definition(U_13241,U_13242,U_13243,U_13244,U_13245) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

cnf(f_3388_5,plain,
    ( hAPP(U_13243,U_13246) = hAPP(U_13243,U_13247)
    | U_13246 != U_13247
    | ~ c_Typedef_Otype__definition(U_13241,U_13242,U_13243,U_13244,U_13245) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

fof(f_3389_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse]) ).

fof(f_3389_2,plain,
    ! [U_13253,U_13252,U_13251,U_13250,U_13249,U_13248] :
      ( hAPP(U_13251,hAPP(U_13250,U_13253)) = U_13253
      | ~ c_Typedef_Otype__definition(U_13248,U_13249,U_13250,U_13251,U_13252) ),
    inference(variable_rename,[status(thm)],[f_3389_1]) ).

fof(f_3389_3,plain,
    ! [U_13253,U_13252,U_13251,U_13250] :
      ( ! [U_13249,U_13248] : ~ c_Typedef_Otype__definition(U_13248,U_13249,U_13250,U_13251,U_13252)
      | hAPP(U_13251,hAPP(U_13250,U_13253)) = U_13253 ),
    inference(miniscope,[status(thm)],[f_3389_2]) ).

cnf(f_3389_4,plain,
    ( ~ c_Typedef_Otype__definition(U_13248,U_13249,U_13250,U_13251,U_13252)
    | hAPP(U_13251,hAPP(U_13250,U_13253)) = U_13253 ),
    inference(clausify,[status(thm)],[f_3389_3]) ).

fof(f_3390_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2))
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep]) ).

fof(f_3390_2,plain,
    ! [U_13259,U_13258,U_13257,U_13256,U_13255,U_13254] :
      ( hBOOL(hAPP(hAPP(c_member(U_13255),hAPP(U_13256,U_13259)),U_13258))
      | ~ c_Typedef_Otype__definition(U_13254,U_13255,U_13256,U_13257,U_13258) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ! [U_13259,U_13258,U_13257,U_13256,U_13255] :
      ( ! [U_13254] : ~ c_Typedef_Otype__definition(U_13254,U_13255,U_13256,U_13257,U_13258)
      | hBOOL(hAPP(hAPP(c_member(U_13255),hAPP(U_13256,U_13259)),U_13258)) ),
    inference(miniscope,[status(thm)],[f_3390_2]) ).

cnf(f_3390_4,plain,
    ( ~ c_Typedef_Otype__definition(U_13254,U_13255,U_13256,U_13257,U_13258)
    | hBOOL(hAPP(hAPP(c_member(U_13255),hAPP(U_13256,U_13259)),U_13258)) ),
    inference(clausify,[status(thm)],[f_3390_3]) ).

fof(f_3391_1,plain,
    ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
      ( hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse]) ).

fof(f_3391_2,plain,
    ! [U_13265,U_13264,U_13263,U_13262,U_13261,U_13260] :
      ( hAPP(U_13262,hAPP(U_13263,U_13265)) = U_13265
      | ~ hBOOL(hAPP(hAPP(c_member(U_13261),U_13265),U_13264))
      | ~ c_Typedef_Otype__definition(U_13260,U_13261,U_13262,U_13263,U_13264) ),
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

fof(f_3391_3,plain,
    ! [U_13265,U_13264,U_13263,U_13262,U_13261] :
      ( ! [U_13260] : ~ c_Typedef_Otype__definition(U_13260,U_13261,U_13262,U_13263,U_13264)
      | hAPP(U_13262,hAPP(U_13263,U_13265)) = U_13265
      | ~ hBOOL(hAPP(hAPP(c_member(U_13261),U_13265),U_13264)) ),
    inference(miniscope,[status(thm)],[f_3391_2]) ).

cnf(f_3391_4,plain,
    ( ~ c_Typedef_Otype__definition(U_13260,U_13261,U_13262,U_13263,U_13264)
    | hAPP(U_13262,hAPP(U_13263,U_13265)) = U_13265
    | ~ hBOOL(hAPP(hAPP(c_member(U_13261),U_13265),U_13264)) ),
    inference(clausify,[status(thm)],[f_3391_3]) ).

fof(f_3392_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),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_a,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(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_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(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_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),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_s_2))))),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__def]) ).

fof(f_3392_2,plain,
    ! [U_13270,U_13269,U_13268,U_13267,U_13266] : hAPP(hAPP(c_Relation_Orel__comp(U_13266,U_13267,U_13268),U_13269),U_13270) = hAPP(c_Set_OCollect(tc_prod(U_13266,U_13268)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13266,U_13268,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_HOL_Obool),U_13266),hAPP(c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_HOL_Obool,U_13268),c_HOL_OEx(U_13267))),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),tc_fun(tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool))),U_13266),c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool),U_13268)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13266),c_COMBS(U_13267,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13267),c_fconj)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13266),c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13266,U_13267)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_prod(U_13266,U_13267),tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13266,U_13267)))),c_Product__Type_OPair(U_13266,U_13267)))),U_13269))))),hAPP(hAPP(c_COMBC(U_13268,tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13268),c_COMBC(U_13267,tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13267,U_13268)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),U_13268),hAPP(c_COMBB(tc_prod(U_13267,U_13268),tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13267,U_13268)))),hAPP(c_COMBC(U_13267,U_13268,tc_prod(U_13267,U_13268)),c_Product__Type_OPair(U_13267,U_13268))))),U_13270))))),
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

cnf(f_3392_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13266,U_13267,U_13268),U_13269),U_13270) = hAPP(c_Set_OCollect(tc_prod(U_13266,U_13268)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13266,U_13268,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_HOL_Obool),U_13266),hAPP(c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_HOL_Obool,U_13268),c_HOL_OEx(U_13267))),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),tc_fun(tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool)),tc_fun(U_13268,tc_fun(U_13267,tc_HOL_Obool))),U_13266),c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool),U_13268)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13266),c_COMBS(U_13267,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_HOL_Obool),tc_fun(U_13267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13267),c_fconj)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13266),c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13266,U_13267)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_prod(U_13266,U_13267),tc_fun(tc_fun(tc_prod(U_13266,U_13267),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13266,U_13267)))),c_Product__Type_OPair(U_13266,U_13267)))),U_13269))))),hAPP(hAPP(c_COMBC(U_13268,tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13268),c_COMBC(U_13267,tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13267,U_13268)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool)),U_13268),hAPP(c_COMBB(tc_prod(U_13267,U_13268),tc_fun(tc_fun(tc_prod(U_13267,U_13268),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13267,U_13268)))),hAPP(c_COMBC(U_13267,U_13268,tc_prod(U_13267,U_13268)),c_Product__Type_OPair(U_13267,U_13268))))),U_13270))))),
    inference(clausify,[status(thm)],[f_3392_2]) ).

fof(f_3393_1,plain,
    ! [V_a2_2,V_a1_2,V_R_2,T_a] :
      ( ( c_Wellfounded_Omax__extp(T_a,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_a),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) )
        | ~ c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp_Oequations]) ).

fof(f_3393_2,plain,
    ! [U_13278,U_13277,U_13276,U_13275] :
      ( ( c_Wellfounded_Omax__extp(U_13275,U_13276,U_13277,U_13278)
        | ? [U_13274] :
            ( ! [U_13273] :
                ( ~ hBOOL(hAPP(hAPP(U_13276,U_13274),U_13273))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13275),U_13273),U_13278)) )
            & hBOOL(hAPP(hAPP(c_member(U_13275),U_13274),U_13277)) )
        | U_13278 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13278))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13277)) )
      & ( ( ! [U_13272] :
              ( ? [U_13271] :
                  ( hBOOL(hAPP(hAPP(U_13276,U_13272),U_13271))
                  & hBOOL(hAPP(hAPP(c_member(U_13275),U_13271),U_13278)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13275),U_13272),U_13277)) )
          & U_13278 != c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13278))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13277)) )
        | ~ c_Wellfounded_Omax__extp(U_13275,U_13276,U_13277,U_13278) ) ),
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

fof(f_3393_3,plain,
    ( ! [U_13286,U_13284,U_13282,U_13280] :
        ( c_Wellfounded_Omax__extp(U_13280,U_13282,U_13284,U_13286)
        | ? [U_13274] :
            ( ! [U_13273] :
                ( ~ hBOOL(hAPP(hAPP(U_13282,U_13274),U_13273))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13280),U_13273),U_13286)) )
            & hBOOL(hAPP(hAPP(c_member(U_13280),U_13274),U_13284)) )
        | U_13286 = c_Orderings_Obot__class_Obot(tc_fun(U_13280,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13286))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13284)) )
    & ! [U_13285,U_13283,U_13281,U_13279] :
        ( ( ! [U_13272] :
              ( ? [U_13271] :
                  ( hBOOL(hAPP(hAPP(U_13281,U_13272),U_13271))
                  & hBOOL(hAPP(hAPP(c_member(U_13279),U_13271),U_13285)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13279),U_13272),U_13283)) )
          & U_13285 != c_Orderings_Obot__class_Obot(tc_fun(U_13279,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13285))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13283)) )
        | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ) ),
    inference(miniscope,[status(thm)],[f_3393_2]) ).

fof(f_3393_4,plain,
    ( ! [U_13286,U_13284,U_13282,U_13280] :
        ( c_Wellfounded_Omax__extp(U_13280,U_13282,U_13284,U_13286)
        | ? [U_13274] :
            ( ! [U_13273] :
                ( ~ hBOOL(hAPP(hAPP(U_13282,U_13274),U_13273))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13280),U_13273),U_13286)) )
            & hBOOL(hAPP(hAPP(c_member(U_13280),U_13274),U_13284)) )
        | U_13286 = c_Orderings_Obot__class_Obot(tc_fun(U_13280,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13286))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13284)) )
    & ! [U_13285,U_13283,U_13281,U_13279] :
        ( ( ! [U_13272] :
              ( ( hBOOL(hAPP(hAPP(U_13281,U_13272),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)))
                & hBOOL(hAPP(hAPP(c_member(U_13279),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)),U_13285)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13279),U_13272),U_13283)) )
          & U_13285 != c_Orderings_Obot__class_Obot(tc_fun(U_13279,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13285))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13283)) )
        | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_13271,sK314(U_13285,U_13283,U_13281,U_13279,U_13272))],[f_3393_3]) ).

fof(f_3393_5,plain,
    ( ! [U_13286,U_13284,U_13282,U_13280] :
        ( c_Wellfounded_Omax__extp(U_13280,U_13282,U_13284,U_13286)
        | ( ! [U_13273] :
              ( ~ hBOOL(hAPP(hAPP(U_13282,sK315(U_13286,U_13284,U_13282,U_13280)),U_13273))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13280),U_13273),U_13286)) )
          & hBOOL(hAPP(hAPP(c_member(U_13280),sK315(U_13286,U_13284,U_13282,U_13280)),U_13284)) )
        | U_13286 = c_Orderings_Obot__class_Obot(tc_fun(U_13280,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13286))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13284)) )
    & ! [U_13285,U_13283,U_13281,U_13279] :
        ( ( ! [U_13272] :
              ( ( hBOOL(hAPP(hAPP(U_13281,U_13272),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)))
                & hBOOL(hAPP(hAPP(c_member(U_13279),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)),U_13285)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13279),U_13272),U_13283)) )
          & U_13285 != c_Orderings_Obot__class_Obot(tc_fun(U_13279,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13285))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13283)) )
        | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_13274,sK315(U_13286,U_13284,U_13282,U_13280))],[f_3393_4]) ).

cnf(f_3393_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13283))
    | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13279),U_13285))
    | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_8,plain,
    ( U_13285 != c_Orderings_Obot__class_Obot(tc_fun(U_13279,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13279),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)),U_13285))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13279),U_13272),U_13283))
    | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_10,plain,
    ( hBOOL(hAPP(hAPP(U_13281,U_13272),sK314(U_13285,U_13283,U_13281,U_13279,U_13272)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13279),U_13272),U_13283))
    | ~ c_Wellfounded_Omax__extp(U_13279,U_13281,U_13283,U_13285) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13280),sK315(U_13286,U_13284,U_13282,U_13280)),U_13284))
    | U_13286 = c_Orderings_Obot__class_Obot(tc_fun(U_13280,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13286))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13284))
    | c_Wellfounded_Omax__extp(U_13280,U_13282,U_13284,U_13286) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

cnf(f_3393_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_13282,sK315(U_13286,U_13284,U_13282,U_13280)),U_13273))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13280),U_13273),U_13286))
    | U_13286 = c_Orderings_Obot__class_Obot(tc_fun(U_13280,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13286))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),U_13284))
    | c_Wellfounded_Omax__extp(U_13280,U_13282,U_13284,U_13286) ),
    inference(clausify,[status(thm)],[f_3393_5]) ).

fof(f_3394_1,plain,
    ! [V_R_2,V_Y_2,V_X_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
      | ? [B_x] :
          ( ! [B_xa] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) )
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros]) ).

fof(f_3394_2,plain,
    ! [U_13292,U_13291,U_13290,U_13289] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool)),U_13290),U_13291)),c_Wellfounded_Omax__ext(U_13289,U_13292)))
      | ? [U_13288] :
          ( ! [U_13287] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13289,U_13289)),hAPP(hAPP(c_Product__Type_OPair(U_13289,U_13289),U_13288),U_13287)),U_13292))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13289),U_13287),U_13291)) )
          & hBOOL(hAPP(hAPP(c_member(U_13289),U_13288),U_13290)) )
      | U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13289,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13291))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13290)) ),
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

fof(f_3394_3,plain,
    ! [U_13292,U_13291,U_13290,U_13289] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool)),U_13290),U_13291)),c_Wellfounded_Omax__ext(U_13289,U_13292)))
      | ( ! [U_13287] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13289,U_13289)),hAPP(hAPP(c_Product__Type_OPair(U_13289,U_13289),sK316(U_13292,U_13291,U_13290,U_13289)),U_13287)),U_13292))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13289),U_13287),U_13291)) )
        & hBOOL(hAPP(hAPP(c_member(U_13289),sK316(U_13292,U_13291,U_13290,U_13289)),U_13290)) )
      | U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13289,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13291))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13290)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_13288,sK316(U_13292,U_13291,U_13290,U_13289))],[f_3394_2]) ).

cnf(f_3394_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13289),sK316(U_13292,U_13291,U_13290,U_13289)),U_13290))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool)),U_13290),U_13291)),c_Wellfounded_Omax__ext(U_13289,U_13292)))
    | U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13289,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13291))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13290)) ),
    inference(clausify,[status(thm)],[f_3394_3]) ).

cnf(f_3394_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13289,U_13289)),hAPP(hAPP(c_Product__Type_OPair(U_13289,U_13289),sK316(U_13292,U_13291,U_13290,U_13289)),U_13287)),U_13292))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13289),U_13287),U_13291))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13289,tc_HOL_Obool),tc_fun(U_13289,tc_HOL_Obool)),U_13290),U_13291)),c_Wellfounded_Omax__ext(U_13289,U_13292)))
    | U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13289,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13291))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13289),U_13290)) ),
    inference(clausify,[status(thm)],[f_3394_3]) ).

fof(f_3395_1,plain,
    ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),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_b_2),V_c_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).

fof(f_3395_2,plain,
    ! [U_13300,U_13299,U_13298,U_13297,U_13296,U_13295,U_13294,U_13293] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13298)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13298),U_13295),U_13299)),hAPP(hAPP(c_Relation_Orel__comp(U_13293,U_13294,U_13298),U_13297),U_13300)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13294,U_13298)),hAPP(hAPP(c_Product__Type_OPair(U_13294,U_13298),U_13296),U_13299)),U_13300))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13294)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13294),U_13295),U_13296)),U_13297)) ),
    inference(variable_rename,[status(thm)],[f_3395_1]) ).

cnf(f_3395_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13298)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13298),U_13295),U_13299)),hAPP(hAPP(c_Relation_Orel__comp(U_13293,U_13294,U_13298),U_13297),U_13300)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13294,U_13298)),hAPP(hAPP(c_Product__Type_OPair(U_13294,U_13298),U_13296),U_13299)),U_13300))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13294)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13294),U_13295),U_13296)),U_13297)) ),
    inference(clausify,[status(thm)],[f_3395_2]) ).

fof(f_3396_1,plain,
    ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(f_3396_2,plain,
    ! [U_13307,U_13306,U_13305,U_13304,U_13303,U_13302,U_13301] : hAPP(hAPP(c_Relation_Orel__comp(U_13301,U_13302,U_13303),U_13304),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13305,tc_fun(tc_prod(U_13302,U_13303),tc_HOL_Obool)),U_13306),U_13307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13305,tc_fun(tc_prod(U_13301,U_13303),tc_HOL_Obool)),U_13306),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13302,U_13303),tc_HOL_Obool),tc_fun(tc_prod(U_13301,U_13303),tc_HOL_Obool),U_13305),hAPP(c_Relation_Orel__comp(U_13301,U_13302,U_13303),U_13304)),U_13307)),
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

cnf(f_3396_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13301,U_13302,U_13303),U_13304),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13305,tc_fun(tc_prod(U_13302,U_13303),tc_HOL_Obool)),U_13306),U_13307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13305,tc_fun(tc_prod(U_13301,U_13303),tc_HOL_Obool)),U_13306),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13302,U_13303),tc_HOL_Obool),tc_fun(tc_prod(U_13301,U_13303),tc_HOL_Obool),U_13305),hAPP(c_Relation_Orel__comp(U_13301,U_13302,U_13303),U_13304)),U_13307)),
    inference(clausify,[status(thm)],[f_3396_2]) ).

fof(f_3397_1,plain,
    ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(f_3397_2,plain,
    ! [U_13314,U_13313,U_13312,U_13311,U_13310,U_13309,U_13308] : hAPP(hAPP(c_Relation_Orel__comp(U_13308,U_13309,U_13310),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13311,tc_fun(tc_prod(U_13308,U_13309),tc_HOL_Obool)),U_13312),U_13313)),U_13314) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13311,tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),U_13312),hAPP(hAPP(c_COMBC(U_13311,tc_fun(tc_prod(U_13309,U_13310),tc_HOL_Obool),tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13308,U_13309),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13309,U_13310),tc_HOL_Obool),tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),U_13311),c_Relation_Orel__comp(U_13308,U_13309,U_13310)),U_13313)),U_13314)),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

cnf(f_3397_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13308,U_13309,U_13310),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13311,tc_fun(tc_prod(U_13308,U_13309),tc_HOL_Obool)),U_13312),U_13313)),U_13314) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13311,tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),U_13312),hAPP(hAPP(c_COMBC(U_13311,tc_fun(tc_prod(U_13309,U_13310),tc_HOL_Obool),tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13308,U_13309),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13309,U_13310),tc_HOL_Obool),tc_fun(tc_prod(U_13308,U_13310),tc_HOL_Obool)),U_13311),c_Relation_Orel__comp(U_13308,U_13309,U_13310)),U_13313)),U_13314)),
    inference(clausify,[status(thm)],[f_3397_2]) ).

fof(f_3398_1,plain,
    ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty2]) ).

fof(f_3398_2,plain,
    ! [U_13318,U_13317,U_13316,U_13315] : hAPP(hAPP(c_Relation_Orel__comp(U_13315,U_13316,U_13317),U_13318),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13316,U_13317),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13315,U_13317),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

cnf(f_3398_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13315,U_13316,U_13317),U_13318),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13316,U_13317),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13315,U_13317),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3398_2]) ).

fof(f_3399_1,plain,
    ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty1]) ).

fof(f_3399_2,plain,
    ! [U_13322,U_13321,U_13320,U_13319] : hAPP(hAPP(c_Relation_Orel__comp(U_13319,U_13320,U_13321),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13319,U_13320),tc_HOL_Obool))),U_13322) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13319,U_13321),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

cnf(f_3399_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13319,U_13320,U_13321),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13319,U_13320),tc_HOL_Obool))),U_13322) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13319,U_13321),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3399_2]) ).

fof(f_3400_1,plain,
    ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(f_3400_2,plain,
    ! [U_13328,U_13327,U_13326,U_13325,U_13324,U_13323] : hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13323,U_13324),tc_HOL_Obool)),U_13326),U_13327)),U_13328) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13323,U_13325),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),U_13326),U_13328)),hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),U_13327),U_13328)),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

cnf(f_3400_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13323,U_13324),tc_HOL_Obool)),U_13326),U_13327)),U_13328) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13323,U_13325),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),U_13326),U_13328)),hAPP(hAPP(c_Relation_Orel__comp(U_13323,U_13324,U_13325),U_13327),U_13328)),
    inference(clausify,[status(thm)],[f_3400_2]) ).

fof(f_3401_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib]) ).

fof(f_3401_2,plain,
    ! [U_13334,U_13333,U_13332,U_13331,U_13330,U_13329] : hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13330,U_13331),tc_HOL_Obool)),U_13333),U_13334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13329,U_13331),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),U_13333)),hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),U_13334)),
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

cnf(f_3401_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13330,U_13331),tc_HOL_Obool)),U_13333),U_13334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13329,U_13331),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),U_13333)),hAPP(hAPP(c_Relation_Orel__comp(U_13329,U_13330,U_13331),U_13332),U_13334)),
    inference(clausify,[status(thm)],[f_3401_2]) ).

fof(f_3402_1,plain,
    ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),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_s_H_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__mono]) ).

fof(f_3402_2,plain,
    ! [U_13341,U_13340,U_13339,U_13338,U_13337,U_13336,U_13335] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13335,U_13339),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13335,U_13336,U_13339),U_13337),U_13340)),hAPP(hAPP(c_Relation_Orel__comp(U_13335,U_13336,U_13339),U_13338),U_13341)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13336,U_13339),tc_HOL_Obool)),U_13340),U_13341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13335,U_13336),tc_HOL_Obool)),U_13337),U_13338)) ),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

cnf(f_3402_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13335,U_13339),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13335,U_13336,U_13339),U_13337),U_13340)),hAPP(hAPP(c_Relation_Orel__comp(U_13335,U_13336,U_13339),U_13338),U_13341)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13336,U_13339),tc_HOL_Obool)),U_13340),U_13341))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13335,U_13336),tc_HOL_Obool)),U_13337),U_13338)) ),
    inference(clausify,[status(thm)],[f_3402_2]) ).

fof(f_3403_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_O__assoc]) ).

fof(f_3403_2,plain,
    ! [U_13348,U_13347,U_13346,U_13345,U_13344,U_13343,U_13342] : hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13343,U_13344),hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13345,U_13343),U_13346),U_13347)),U_13348) = hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13345,U_13344),U_13346),hAPP(hAPP(c_Relation_Orel__comp(U_13345,U_13343,U_13344),U_13347),U_13348)),
    inference(variable_rename,[status(thm)],[f_3403_1]) ).

cnf(f_3403_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13343,U_13344),hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13345,U_13343),U_13346),U_13347)),U_13348) = hAPP(hAPP(c_Relation_Orel__comp(U_13342,U_13345,U_13344),U_13346),hAPP(hAPP(c_Relation_Orel__comp(U_13345,U_13343,U_13344),U_13347),U_13348)),
    inference(clausify,[status(thm)],[f_3403_2]) ).

fof(f_3404_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR]) ).

fof(f_3404_2,plain,
    ! [U_13352,U_13351,U_13350,U_13349] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool)),U_13351),U_13352)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),U_13352) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),U_13351) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3404_1]) ).

cnf(f_3404_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool)),U_13351),U_13352)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),U_13352) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13349,U_13349,U_13349),U_13350),U_13351) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13349,U_13349),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3404_2]) ).

fof(f_3405_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL]) ).

fof(f_3405_2,plain,
    ! [U_13356,U_13355,U_13354,U_13353] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool)),U_13354),U_13356)),U_13355) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),U_13356),U_13355) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),U_13354),U_13355) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

cnf(f_3405_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool)),U_13354),U_13356)),U_13355) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),U_13356),U_13355) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13353,U_13353),U_13354),U_13355) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13353,U_13353),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3405_2]) ).

fof(f_3406_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__compat]) ).

fof(f_3406_2,plain,
    ! [U_13359,U_13358,U_13357] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13357,U_13358)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13357,U_13359)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13357,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13357,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13357,U_13358)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13357,U_13357),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13357,U_13357,U_13357),U_13358),U_13359)),U_13358)) ),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

cnf(f_3406_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13357,U_13358)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13357,U_13359)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13357,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13357,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13357,tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13357,U_13358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13357,U_13357),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13357,U_13357,U_13357),U_13358),U_13359)),U_13358)) ),
    inference(clausify,[status(thm)],[f_3406_2]) ).

fof(f_3407_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__compat]) ).

fof(f_3407_2,plain,
    ! [U_13362,U_13361,U_13360] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13360,U_13361)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13360,U_13362)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13360,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13360,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13360,U_13361)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13360,U_13360),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13360,U_13360,U_13360),U_13361),U_13362)),U_13361)) ),
    inference(variable_rename,[status(thm)],[f_3407_1]) ).

cnf(f_3407_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13360,U_13361)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13360,U_13362)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13360,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13360,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13360,tc_HOL_Obool),tc_fun(U_13360,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13360,U_13361)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13360,U_13360),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13360,U_13360,U_13360),U_13361),U_13362)),U_13361)) ),
    inference(clausify,[status(thm)],[f_3407_2]) ).

fof(f_3408_1,plain,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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_pred__comp__rel__comp__eq]) ).

fof(f_3408_2,plain,
    ! [U_13369,U_13368,U_13367,U_13366,U_13365,U_13364,U_13363] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13363,U_13364,U_13365,hAPP(hAPP(c_COMBC(U_13363,tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_fun(U_13364,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13364,tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_fun(U_13364,tc_HOL_Obool)),U_13363),c_COMBC(U_13364,tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13364,tc_prod(U_13363,U_13364)),tc_fun(U_13364,tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),U_13363),hAPP(c_COMBB(tc_prod(U_13363,U_13364),tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool),U_13364),c_member(tc_prod(U_13363,U_13364)))),c_Product__Type_OPair(U_13363,U_13364)))),U_13366),hAPP(hAPP(c_COMBC(U_13364,tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_fun(U_13365,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13365,tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_fun(U_13365,tc_HOL_Obool)),U_13364),c_COMBC(U_13365,tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13365,tc_prod(U_13364,U_13365)),tc_fun(U_13365,tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),U_13364),hAPP(c_COMBB(tc_prod(U_13364,U_13365),tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool),U_13365),c_member(tc_prod(U_13364,U_13365)))),c_Product__Type_OPair(U_13364,U_13365)))),U_13367)),U_13368),U_13369))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13363,U_13365)),hAPP(hAPP(c_Product__Type_OPair(U_13363,U_13365),U_13368),U_13369)),hAPP(hAPP(c_Relation_Orel__comp(U_13363,U_13364,U_13365),U_13366),U_13367))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13363,U_13365)),hAPP(hAPP(c_Product__Type_OPair(U_13363,U_13365),U_13368),U_13369)),hAPP(hAPP(c_Relation_Orel__comp(U_13363,U_13364,U_13365),U_13366),U_13367)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13363,U_13364,U_13365,hAPP(hAPP(c_COMBC(U_13363,tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_fun(U_13364,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13364,tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_fun(U_13364,tc_HOL_Obool)),U_13363),c_COMBC(U_13364,tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13364,tc_prod(U_13363,U_13364)),tc_fun(U_13364,tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool)),U_13363),hAPP(c_COMBB(tc_prod(U_13363,U_13364),tc_fun(tc_fun(tc_prod(U_13363,U_13364),tc_HOL_Obool),tc_HOL_Obool),U_13364),c_member(tc_prod(U_13363,U_13364)))),c_Product__Type_OPair(U_13363,U_13364)))),U_13366),hAPP(hAPP(c_COMBC(U_13364,tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_fun(U_13365,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13365,tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_fun(U_13365,tc_HOL_Obool)),U_13364),c_COMBC(U_13365,tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13365,tc_prod(U_13364,U_13365)),tc_fun(U_13365,tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool)),U_13364),hAPP(c_COMBB(tc_prod(U_13364,U_13365),tc_fun(tc_fun(tc_prod(U_13364,U_13365),tc_HOL_Obool),tc_HOL_Obool),U_13365),c_member(tc_prod(U_13364,U_13365)))),c_Product__Type_OPair(U_13364,U_13365)))),U_13367)),U_13368),U_13369)) ) ),
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

fof(f_3408_3,plain,
    ( ! [U_13383,U_13381,U_13379,U_13377,U_13375,U_13373,U_13371] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13371,U_13373,U_13375,hAPP(hAPP(c_COMBC(U_13371,tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_fun(U_13373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_fun(U_13373,tc_HOL_Obool)),U_13371),c_COMBC(U_13373,tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_prod(U_13371,U_13373)),tc_fun(U_13373,tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_prod(U_13371,U_13373),tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool),U_13373),c_member(tc_prod(U_13371,U_13373)))),c_Product__Type_OPair(U_13371,U_13373)))),U_13377),hAPP(hAPP(c_COMBC(U_13373,tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_fun(U_13375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13375,tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_fun(U_13375,tc_HOL_Obool)),U_13373),c_COMBC(U_13375,tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13375,tc_prod(U_13373,U_13375)),tc_fun(U_13375,tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),U_13373),hAPP(c_COMBB(tc_prod(U_13373,U_13375),tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool),U_13375),c_member(tc_prod(U_13373,U_13375)))),c_Product__Type_OPair(U_13373,U_13375)))),U_13379)),U_13381),U_13383))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13371,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13371,U_13375),U_13381),U_13383)),hAPP(hAPP(c_Relation_Orel__comp(U_13371,U_13373,U_13375),U_13377),U_13379))) )
    & ! [U_13382,U_13380,U_13378,U_13376,U_13374,U_13372,U_13370] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13370,U_13374)),hAPP(hAPP(c_Product__Type_OPair(U_13370,U_13374),U_13380),U_13382)),hAPP(hAPP(c_Relation_Orel__comp(U_13370,U_13372,U_13374),U_13376),U_13378)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13370,U_13372,U_13374,hAPP(hAPP(c_COMBC(U_13370,tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13370),c_COMBC(U_13372,tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13370,U_13372)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),U_13370),hAPP(c_COMBB(tc_prod(U_13370,U_13372),tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13370,U_13372)))),c_Product__Type_OPair(U_13370,U_13372)))),U_13376),hAPP(hAPP(c_COMBC(U_13372,tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_fun(U_13374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13374,tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_fun(U_13374,tc_HOL_Obool)),U_13372),c_COMBC(U_13374,tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13374,tc_prod(U_13372,U_13374)),tc_fun(U_13374,tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),U_13372),hAPP(c_COMBB(tc_prod(U_13372,U_13374),tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool),U_13374),c_member(tc_prod(U_13372,U_13374)))),c_Product__Type_OPair(U_13372,U_13374)))),U_13378)),U_13380),U_13382)) ) ),
    inference(miniscope,[status(thm)],[f_3408_2]) ).

cnf(f_3408_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13370,U_13374)),hAPP(hAPP(c_Product__Type_OPair(U_13370,U_13374),U_13380),U_13382)),hAPP(hAPP(c_Relation_Orel__comp(U_13370,U_13372,U_13374),U_13376),U_13378)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13370,U_13372,U_13374,hAPP(hAPP(c_COMBC(U_13370,tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13370),c_COMBC(U_13372,tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13370,U_13372)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool)),U_13370),hAPP(c_COMBB(tc_prod(U_13370,U_13372),tc_fun(tc_fun(tc_prod(U_13370,U_13372),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13370,U_13372)))),c_Product__Type_OPair(U_13370,U_13372)))),U_13376),hAPP(hAPP(c_COMBC(U_13372,tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_fun(U_13374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13374,tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_fun(U_13374,tc_HOL_Obool)),U_13372),c_COMBC(U_13374,tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13374,tc_prod(U_13372,U_13374)),tc_fun(U_13374,tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool)),U_13372),hAPP(c_COMBB(tc_prod(U_13372,U_13374),tc_fun(tc_fun(tc_prod(U_13372,U_13374),tc_HOL_Obool),tc_HOL_Obool),U_13374),c_member(tc_prod(U_13372,U_13374)))),c_Product__Type_OPair(U_13372,U_13374)))),U_13378)),U_13380),U_13382)) ),
    inference(clausify,[status(thm)],[f_3408_3]) ).

cnf(f_3408_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13371,U_13373,U_13375,hAPP(hAPP(c_COMBC(U_13371,tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_fun(U_13373,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_fun(U_13373,tc_HOL_Obool)),U_13371),c_COMBC(U_13373,tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_prod(U_13371,U_13373)),tc_fun(U_13373,tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_prod(U_13371,U_13373),tc_fun(tc_fun(tc_prod(U_13371,U_13373),tc_HOL_Obool),tc_HOL_Obool),U_13373),c_member(tc_prod(U_13371,U_13373)))),c_Product__Type_OPair(U_13371,U_13373)))),U_13377),hAPP(hAPP(c_COMBC(U_13373,tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_fun(U_13375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13375,tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_fun(U_13375,tc_HOL_Obool)),U_13373),c_COMBC(U_13375,tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13375,tc_prod(U_13373,U_13375)),tc_fun(U_13375,tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool)),U_13373),hAPP(c_COMBB(tc_prod(U_13373,U_13375),tc_fun(tc_fun(tc_prod(U_13373,U_13375),tc_HOL_Obool),tc_HOL_Obool),U_13375),c_member(tc_prod(U_13373,U_13375)))),c_Product__Type_OPair(U_13373,U_13375)))),U_13379)),U_13381),U_13383))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13371,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13371,U_13375),U_13381),U_13383)),hAPP(hAPP(c_Relation_Orel__comp(U_13371,U_13373,U_13375),U_13377),U_13379))) ),
    inference(clausify,[status(thm)],[f_3408_3]) ).

fof(f_3409_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pairI]) ).

fof(f_3409_2,plain,
    ! [U_13386,U_13385,U_13384] :
      ( c_FunDef_Oreduction__pair(U_13384,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool),tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool)),U_13385),U_13386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13384,U_13384,U_13384),U_13385),U_13386)),U_13385))
      | ~ c_Wellfounded_Owf(U_13384,U_13385) ),
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

cnf(f_3409_3,plain,
    ( c_FunDef_Oreduction__pair(U_13384,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool),tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool)),U_13385),U_13386))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13384,U_13384),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13384,U_13384,U_13384),U_13385),U_13386)),U_13385))
    | ~ c_Wellfounded_Owf(U_13384,U_13385) ),
    inference(clausify,[status(thm)],[f_3409_2]) ).

fof(f_3410_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_3410_2,plain,
    ! [U_13387] : c_Nitpick_Ozero__frac(U_13387) = c_Nitpick_OAbs__Frac(U_13387,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_3410_1]) ).

cnf(f_3410_3,plain,
    c_Nitpick_Ozero__frac(U_13387) = c_Nitpick_OAbs__Frac(U_13387,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_3410_2]) ).

fof(f_3411_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

cnf(f_3411_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3411_1]) ).

fof(f_3412_1,plain,
    ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,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_3412_2,plain,
    ! [U_13395,U_13394,U_13393,U_13392,U_13391,U_13390,U_13389,U_13388] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13393,U_13394,U_13395,U_13388,U_13391),U_13389),U_13392))
      | ~ hBOOL(hAPP(hAPP(U_13391,U_13390),U_13392))
      | ~ hBOOL(hAPP(hAPP(U_13388,U_13389),U_13390)) ),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

cnf(f_3412_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13393,U_13394,U_13395,U_13388,U_13391),U_13389),U_13392))
    | ~ hBOOL(hAPP(hAPP(U_13391,U_13390),U_13392))
    | ~ hBOOL(hAPP(hAPP(U_13388,U_13389),U_13390)) ),
    inference(clausify,[status(thm)],[f_3412_2]) ).

fof(f_3413_1,plain,
    ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_wf__empty]) ).

fof(f_3413_2,plain,
    ! [U_13396] : c_Wellfounded_Owf(U_13396,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13396,U_13396),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

cnf(f_3413_3,plain,
    c_Wellfounded_Owf(U_13396,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13396,U_13396),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3413_2]) ).

fof(f_3414_1,plain,
    ! [V_f_2,T_b,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__inv__image]) ).

fof(f_3414_2,plain,
    ! [U_13400,U_13399,U_13398,U_13397] :
      ( c_Wellfounded_Owf(U_13399,hAPP(hAPP(c_Relation_Oinv__image(U_13397,U_13399),U_13398),U_13400))
      | ~ c_Wellfounded_Owf(U_13397,U_13398) ),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

cnf(f_3414_3,plain,
    ( c_Wellfounded_Owf(U_13399,hAPP(hAPP(c_Relation_Oinv__image(U_13397,U_13399),U_13398),U_13400))
    | ~ c_Wellfounded_Owf(U_13397,U_13398) ),
    inference(clausify,[status(thm)],[f_3414_2]) ).

fof(f_3415_1,plain,
    ! [V_rb_2,T_b,V_ra_2,T_a] :
      ( c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2))
      | ~ c_Wellfounded_Owf(T_b,V_rb_2)
      | ~ c_Wellfounded_Owf(T_a,V_ra_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex__prod]) ).

fof(f_3415_2,plain,
    ! [U_13404,U_13403,U_13402,U_13401] :
      ( c_Wellfounded_Owf(tc_prod(U_13401,U_13403),c_Wellfounded_Olex__prod(U_13401,U_13403,U_13402,U_13404))
      | ~ c_Wellfounded_Owf(U_13403,U_13404)
      | ~ c_Wellfounded_Owf(U_13401,U_13402) ),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

cnf(f_3415_3,plain,
    ( c_Wellfounded_Owf(tc_prod(U_13401,U_13403),c_Wellfounded_Olex__prod(U_13401,U_13403,U_13402,U_13404))
    | ~ c_Wellfounded_Owf(U_13403,U_13404)
    | ~ c_Wellfounded_Owf(U_13401,U_13402) ),
    inference(clausify,[status(thm)],[f_3415_2]) ).

fof(f_3416_1,plain,
    ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__measure]) ).

fof(f_3416_2,plain,
    ! [U_13406,U_13405] : c_Wellfounded_Owf(U_13405,hAPP(c_Wellfounded_Omeasure(U_13405),U_13406)),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

cnf(f_3416_3,plain,
    c_Wellfounded_Owf(U_13405,hAPP(c_Wellfounded_Omeasure(U_13405),U_13406)),
    inference(clausify,[status(thm)],[f_3416_2]) ).

fof(f_3417_1,plain,
    ! [V_R_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,V_R_2)
        | ~ c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) )
      & ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2))
        | ~ c_Wellfounded_Owf(T_a,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__comp__self]) ).

fof(f_3417_2,plain,
    ! [U_13408,U_13407] :
      ( ( c_Wellfounded_Owf(U_13407,U_13408)
        | ~ c_Wellfounded_Owf(U_13407,hAPP(hAPP(c_Relation_Orel__comp(U_13407,U_13407,U_13407),U_13408),U_13408)) )
      & ( c_Wellfounded_Owf(U_13407,hAPP(hAPP(c_Relation_Orel__comp(U_13407,U_13407,U_13407),U_13408),U_13408))
        | ~ c_Wellfounded_Owf(U_13407,U_13408) ) ),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

fof(f_3417_3,plain,
    ( ! [U_13412,U_13410] :
        ( c_Wellfounded_Owf(U_13410,U_13412)
        | ~ c_Wellfounded_Owf(U_13410,hAPP(hAPP(c_Relation_Orel__comp(U_13410,U_13410,U_13410),U_13412),U_13412)) )
    & ! [U_13411,U_13409] :
        ( c_Wellfounded_Owf(U_13409,hAPP(hAPP(c_Relation_Orel__comp(U_13409,U_13409,U_13409),U_13411),U_13411))
        | ~ c_Wellfounded_Owf(U_13409,U_13411) ) ),
    inference(miniscope,[status(thm)],[f_3417_2]) ).

cnf(f_3417_4,plain,
    ( c_Wellfounded_Owf(U_13409,hAPP(hAPP(c_Relation_Orel__comp(U_13409,U_13409,U_13409),U_13411),U_13411))
    | ~ c_Wellfounded_Owf(U_13409,U_13411) ),
    inference(clausify,[status(thm)],[f_3417_3]) ).

cnf(f_3417_5,plain,
    ( c_Wellfounded_Owf(U_13410,U_13412)
    | ~ c_Wellfounded_Owf(U_13410,hAPP(hAPP(c_Relation_Orel__comp(U_13410,U_13410,U_13410),U_13412),U_13412)) ),
    inference(clausify,[status(thm)],[f_3417_3]) ).

fof(f_3418_1,plain,
    ! [V_a_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__refl]) ).

fof(f_3418_2,plain,
    ! [U_13415,U_13414,U_13413] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13413,U_13413)),hAPP(hAPP(c_Product__Type_OPair(U_13413,U_13413),U_13415),U_13415)),U_13414))
      | ~ c_Wellfounded_Owf(U_13413,U_13414) ),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

cnf(f_3418_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13413,U_13413)),hAPP(hAPP(c_Product__Type_OPair(U_13413,U_13413),U_13415),U_13415)),U_13414))
    | ~ c_Wellfounded_Owf(U_13413,U_13414) ),
    inference(clausify,[status(thm)],[f_3418_2]) ).

fof(f_3419_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__sym]) ).

fof(f_3419_2,plain,
    ! [U_13419,U_13418,U_13417,U_13416] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13416,U_13416)),hAPP(hAPP(c_Product__Type_OPair(U_13416,U_13416),U_13419),U_13418)),U_13417))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13416,U_13416)),hAPP(hAPP(c_Product__Type_OPair(U_13416,U_13416),U_13418),U_13419)),U_13417))
      | ~ c_Wellfounded_Owf(U_13416,U_13417) ),
    inference(variable_rename,[status(thm)],[f_3419_1]) ).

cnf(f_3419_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13416,U_13416)),hAPP(hAPP(c_Product__Type_OPair(U_13416,U_13416),U_13419),U_13418)),U_13417))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13416,U_13416)),hAPP(hAPP(c_Product__Type_OPair(U_13416,U_13416),U_13418),U_13419)),U_13417))
    | ~ c_Wellfounded_Owf(U_13416,U_13417) ),
    inference(clausify,[status(thm)],[f_3419_2]) ).

fof(f_3420_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__asym]) ).

fof(f_3420_2,plain,
    ! [U_13423,U_13422,U_13421,U_13420] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13420,U_13420)),hAPP(hAPP(c_Product__Type_OPair(U_13420,U_13420),U_13423),U_13422)),U_13421))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13420,U_13420)),hAPP(hAPP(c_Product__Type_OPair(U_13420,U_13420),U_13422),U_13423)),U_13421))
      | ~ c_Wellfounded_Owf(U_13420,U_13421) ),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

cnf(f_3420_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13420,U_13420)),hAPP(hAPP(c_Product__Type_OPair(U_13420,U_13420),U_13423),U_13422)),U_13421))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13420,U_13420)),hAPP(hAPP(c_Product__Type_OPair(U_13420,U_13420),U_13422),U_13423)),U_13421))
    | ~ c_Wellfounded_Owf(U_13420,U_13421) ),
    inference(clausify,[status(thm)],[f_3420_2]) ).

fof(f_3421_1,plain,
    ! [V_a_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__irrefl]) ).

fof(f_3421_2,plain,
    ! [U_13426,U_13425,U_13424] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13424,U_13424)),hAPP(hAPP(c_Product__Type_OPair(U_13424,U_13424),U_13426),U_13426)),U_13425))
      | ~ c_Wellfounded_Owf(U_13424,U_13425) ),
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

cnf(f_3421_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13424,U_13424)),hAPP(hAPP(c_Product__Type_OPair(U_13424,U_13424),U_13426),U_13426)),U_13425))
    | ~ c_Wellfounded_Owf(U_13424,U_13425) ),
    inference(clausify,[status(thm)],[f_3421_2]) ).

fof(f_3422_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__wf]) ).

fof(f_3422_2,plain,
    ! [U_13428,U_13427] :
      ( c_Wellfounded_Owf(tc_fun(U_13427,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13427,U_13428))
      | ~ c_Wellfounded_Owf(U_13427,U_13428) ),
    inference(variable_rename,[status(thm)],[f_3422_1]) ).

cnf(f_3422_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13427,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13427,U_13428))
    | ~ c_Wellfounded_Owf(U_13427,U_13428) ),
    inference(clausify,[status(thm)],[f_3422_2]) ).

fof(f_3423_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]) ).

cnf(f_3423_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3423_1]) ).

fof(f_3424_1,plain,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,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_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations]) ).

fof(f_3424_2,plain,
    ! [U_13437,U_13436,U_13435,U_13434,U_13433,U_13432,U_13431] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13431,U_13432,U_13433,U_13434,U_13435),U_13436),U_13437))
        | ! [U_13430] :
            ( ~ hBOOL(hAPP(hAPP(U_13435,U_13430),U_13437))
            | ~ hBOOL(hAPP(hAPP(U_13434,U_13436),U_13430)) ) )
      & ( ? [U_13429] :
            ( hBOOL(hAPP(hAPP(U_13435,U_13429),U_13437))
            & hBOOL(hAPP(hAPP(U_13434,U_13436),U_13429)) )
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13431,U_13432,U_13433,U_13434,U_13435),U_13436),U_13437)) ) ),
    inference(variable_rename,[status(thm)],[f_3424_1]) ).

fof(f_3424_3,plain,
    ( ! [U_13451,U_13449,U_13447,U_13445] :
        ( ! [U_13443,U_13441,U_13439] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13439,U_13441,U_13443,U_13445,U_13447),U_13449),U_13451))
        | ! [U_13430] :
            ( ~ hBOOL(hAPP(hAPP(U_13447,U_13430),U_13451))
            | ~ hBOOL(hAPP(hAPP(U_13445,U_13449),U_13430)) ) )
    & ! [U_13450,U_13448,U_13446,U_13444] :
        ( ! [U_13442,U_13440,U_13438] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13438,U_13440,U_13442,U_13444,U_13446),U_13448),U_13450))
        | ? [U_13429] :
            ( hBOOL(hAPP(hAPP(U_13446,U_13429),U_13450))
            & hBOOL(hAPP(hAPP(U_13444,U_13448),U_13429)) ) ) ),
    inference(miniscope,[status(thm)],[f_3424_2]) ).

fof(f_3424_4,plain,
    ( ! [U_13451,U_13449,U_13447,U_13445] :
        ( ! [U_13443,U_13441,U_13439] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13439,U_13441,U_13443,U_13445,U_13447),U_13449),U_13451))
        | ! [U_13430] :
            ( ~ hBOOL(hAPP(hAPP(U_13447,U_13430),U_13451))
            | ~ hBOOL(hAPP(hAPP(U_13445,U_13449),U_13430)) ) )
    & ! [U_13450,U_13448,U_13446,U_13444] :
        ( ! [U_13442,U_13440,U_13438] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13438,U_13440,U_13442,U_13444,U_13446),U_13448),U_13450))
        | ( hBOOL(hAPP(hAPP(U_13446,sK317(U_13450,U_13448,U_13446,U_13444)),U_13450))
          & hBOOL(hAPP(hAPP(U_13444,U_13448),sK317(U_13450,U_13448,U_13446,U_13444))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_13429,sK317(U_13450,U_13448,U_13446,U_13444))],[f_3424_3]) ).

cnf(f_3424_5,plain,
    ( hBOOL(hAPP(hAPP(U_13444,U_13448),sK317(U_13450,U_13448,U_13446,U_13444)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13438,U_13440,U_13442,U_13444,U_13446),U_13448),U_13450)) ),
    inference(clausify,[status(thm)],[f_3424_4]) ).

cnf(f_3424_6,plain,
    ( hBOOL(hAPP(hAPP(U_13446,sK317(U_13450,U_13448,U_13446,U_13444)),U_13450))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13438,U_13440,U_13442,U_13444,U_13446),U_13448),U_13450)) ),
    inference(clausify,[status(thm)],[f_3424_4]) ).

cnf(f_3424_7,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13439,U_13441,U_13443,U_13445,U_13447),U_13449),U_13451))
    | ~ hBOOL(hAPP(hAPP(U_13447,U_13430),U_13451))
    | ~ hBOOL(hAPP(hAPP(U_13445,U_13449),U_13430)) ),
    inference(clausify,[status(thm)],[f_3424_4]) ).

fof(f_3425_1,plain,
    ! [V_p_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__subset]) ).

fof(f_3425_2,plain,
    ! [U_13454,U_13453,U_13452] :
      ( c_Wellfounded_Owf(U_13452,U_13454)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13452,U_13452),tc_HOL_Obool)),U_13454),U_13453))
      | ~ c_Wellfounded_Owf(U_13452,U_13453) ),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

cnf(f_3425_3,plain,
    ( c_Wellfounded_Owf(U_13452,U_13454)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13452,U_13452),tc_HOL_Obool)),U_13454),U_13453))
    | ~ c_Wellfounded_Owf(U_13452,U_13453) ),
    inference(clausify,[status(thm)],[f_3425_2]) ).

fof(f_3426_1,plain,
    ! [V_r_H_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int1]) ).

fof(f_3426_2,plain,
    ! [U_13457,U_13456,U_13455] :
      ( c_Wellfounded_Owf(U_13455,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13455,U_13455),tc_HOL_Obool)),U_13456),U_13457))
      | ~ c_Wellfounded_Owf(U_13455,U_13456) ),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

cnf(f_3426_3,plain,
    ( c_Wellfounded_Owf(U_13455,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13455,U_13455),tc_HOL_Obool)),U_13456),U_13457))
    | ~ c_Wellfounded_Owf(U_13455,U_13456) ),
    inference(clausify,[status(thm)],[f_3426_2]) ).

fof(f_3427_1,plain,
    ! [V_r_H_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int2]) ).

fof(f_3427_2,plain,
    ! [U_13460,U_13459,U_13458] :
      ( c_Wellfounded_Owf(U_13458,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)),U_13460),U_13459))
      | ~ c_Wellfounded_Owf(U_13458,U_13459) ),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

cnf(f_3427_3,plain,
    ( c_Wellfounded_Owf(U_13458,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)),U_13460),U_13459))
    | ~ c_Wellfounded_Owf(U_13458,U_13459) ),
    inference(clausify,[status(thm)],[f_3427_2]) ).

fof(f_3428_1,plain,
    ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)),
    inference(fof_nnf,[status(thm)],[fact_wf__finite__psubset]) ).

fof(f_3428_2,plain,
    ! [U_13461] : c_Wellfounded_Owf(tc_fun(U_13461,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13461)),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

cnf(f_3428_3,plain,
    c_Wellfounded_Owf(tc_fun(U_13461,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13461)),
    inference(clausify,[status(thm)],[f_3428_2]) ).

fof(f_3429_1,plain,
    ! [V_f_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))
      | ~ c_Wellfounded_Owf(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__mlex]) ).

fof(f_3429_2,plain,
    ! [U_13464,U_13463,U_13462] :
      ( c_Wellfounded_Owf(U_13462,c_Wellfounded_Omlex__prod(U_13462,U_13464,U_13463))
      | ~ c_Wellfounded_Owf(U_13462,U_13463) ),
    inference(variable_rename,[status(thm)],[f_3429_1]) ).

cnf(f_3429_3,plain,
    ( c_Wellfounded_Owf(U_13462,c_Wellfounded_Omlex__prod(U_13462,U_13464,U_13463))
    | ~ c_Wellfounded_Owf(U_13462,U_13463) ),
    inference(clausify,[status(thm)],[f_3429_2]) ).

fof(f_3430_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__wf]) ).

fof(f_3430_2,plain,
    ! [U_13466,U_13465] :
      ( c_Wellfounded_Owf(tc_fun(U_13465,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13465,U_13466))
      | ~ c_Wellfounded_Owf(U_13465,U_13466) ),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

cnf(f_3430_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13465,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13465,U_13466))
    | ~ c_Wellfounded_Owf(U_13465,U_13466) ),
    inference(clausify,[status(thm)],[f_3430_2]) ).

fof(f_3431_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]) ).

cnf(f_3431_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(clausify,[status(thm)],[f_3431_1]) ).

fof(f_3432_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_3432_2,plain,
    ! [U_13467] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13467)),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

cnf(f_3432_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13467)),
    inference(clausify,[status(thm)],[f_3432_2]) ).

fof(f_3433_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_3433_2,plain,
    ! [U_13468] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13468)),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

cnf(f_3433_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13468)),
    inference(clausify,[status(thm)],[f_3433_2]) ).

fof(f_3434_1,plain,
    ! [V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_acc__wfD]) ).

fof(f_3434_2,plain,
    ! [U_13471,U_13470,U_13469] :
      ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),c_Wellfounded_Oacc(U_13469,U_13470)))
      | ~ c_Wellfounded_Owf(U_13469,U_13470) ),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

cnf(f_3434_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),c_Wellfounded_Oacc(U_13469,U_13470)))
    | ~ c_Wellfounded_Owf(U_13469,U_13470) ),
    inference(clausify,[status(thm)],[f_3434_2]) ).

fof(f_3435_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2)))
        | ~ c_Wellfounded_Owf(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acc__iff]) ).

fof(f_3435_2,plain,
    ! [U_13475,U_13474] :
      ( ( c_Wellfounded_Owf(U_13474,U_13475)
        | ? [U_13473] : ~ hBOOL(hAPP(hAPP(c_member(U_13474),U_13473),c_Wellfounded_Oacc(U_13474,U_13475))) )
      & ( ! [U_13472] : hBOOL(hAPP(hAPP(c_member(U_13474),U_13472),c_Wellfounded_Oacc(U_13474,U_13475)))
        | ~ c_Wellfounded_Owf(U_13474,U_13475) ) ),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

fof(f_3435_3,plain,
    ( ! [U_13479,U_13477] :
        ( c_Wellfounded_Owf(U_13477,U_13479)
        | ? [U_13473] : ~ hBOOL(hAPP(hAPP(c_member(U_13477),U_13473),c_Wellfounded_Oacc(U_13477,U_13479))) )
    & ! [U_13478,U_13476] :
        ( ! [U_13472] : hBOOL(hAPP(hAPP(c_member(U_13476),U_13472),c_Wellfounded_Oacc(U_13476,U_13478)))
        | ~ c_Wellfounded_Owf(U_13476,U_13478) ) ),
    inference(miniscope,[status(thm)],[f_3435_2]) ).

fof(f_3435_4,plain,
    ( ! [U_13479,U_13477] :
        ( c_Wellfounded_Owf(U_13477,U_13479)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13477),sK318(U_13479,U_13477)),c_Wellfounded_Oacc(U_13477,U_13479))) )
    & ! [U_13478,U_13476] :
        ( ! [U_13472] : hBOOL(hAPP(hAPP(c_member(U_13476),U_13472),c_Wellfounded_Oacc(U_13476,U_13478)))
        | ~ c_Wellfounded_Owf(U_13476,U_13478) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_13473,sK318(U_13479,U_13477))],[f_3435_3]) ).

cnf(f_3435_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13476),U_13472),c_Wellfounded_Oacc(U_13476,U_13478)))
    | ~ c_Wellfounded_Owf(U_13476,U_13478) ),
    inference(clausify,[status(thm)],[f_3435_4]) ).

cnf(f_3435_6,plain,
    ( c_Wellfounded_Owf(U_13477,U_13479)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13477),sK318(U_13479,U_13477)),c_Wellfounded_Oacc(U_13477,U_13479))) ),
    inference(clausify,[status(thm)],[f_3435_4]) ).

fof(f_3436_1,plain,
    ! [V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__loop]) ).

fof(f_3436_2,plain,
    ! [U_13481,U_13480] :
      ( c_Wellfounded_Owf(U_13480,U_13481)
      | hAPP(hAPP(c_Relation_Orel__comp(U_13480,U_13480,U_13480),U_13481),U_13481) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13480,U_13480),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3436_1]) ).

cnf(f_3436_3,plain,
    ( c_Wellfounded_Owf(U_13480,U_13481)
    | hAPP(hAPP(c_Relation_Orel__comp(U_13480,U_13480,U_13480),U_13481),U_13481) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13480,U_13480),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3436_2]) ).

fof(f_3437_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) )
      & ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2))
        | ~ c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__merge]) ).

fof(f_3437_2,plain,
    ! [U_13484,U_13483,U_13482] :
      ( ( c_Wellfounded_Owf(U_13482,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),U_13483),U_13484))
        | ~ c_Wellfounded_Owf(U_13482,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13482,U_13482,U_13482),U_13483),U_13483)),hAPP(hAPP(c_Relation_Orel__comp(U_13482,U_13482,U_13482),U_13484),U_13483))),U_13484)) )
      & ( c_Wellfounded_Owf(U_13482,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13482,U_13482,U_13482),U_13483),U_13483)),hAPP(hAPP(c_Relation_Orel__comp(U_13482,U_13482,U_13482),U_13484),U_13483))),U_13484))
        | ~ c_Wellfounded_Owf(U_13482,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13482,U_13482),tc_HOL_Obool)),U_13483),U_13484)) ) ),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

fof(f_3437_3,plain,
    ( ! [U_13490,U_13488,U_13486] :
        ( c_Wellfounded_Owf(U_13486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),U_13488),U_13490))
        | ~ c_Wellfounded_Owf(U_13486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13486,U_13486,U_13486),U_13488),U_13488)),hAPP(hAPP(c_Relation_Orel__comp(U_13486,U_13486,U_13486),U_13490),U_13488))),U_13490)) )
    & ! [U_13489,U_13487,U_13485] :
        ( c_Wellfounded_Owf(U_13485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13485,U_13485,U_13485),U_13487),U_13487)),hAPP(hAPP(c_Relation_Orel__comp(U_13485,U_13485,U_13485),U_13489),U_13487))),U_13489))
        | ~ c_Wellfounded_Owf(U_13485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),U_13487),U_13489)) ) ),
    inference(miniscope,[status(thm)],[f_3437_2]) ).

cnf(f_3437_4,plain,
    ( c_Wellfounded_Owf(U_13485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13485,U_13485,U_13485),U_13487),U_13487)),hAPP(hAPP(c_Relation_Orel__comp(U_13485,U_13485,U_13485),U_13489),U_13487))),U_13489))
    | ~ c_Wellfounded_Owf(U_13485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13485,U_13485),tc_HOL_Obool)),U_13487),U_13489)) ),
    inference(clausify,[status(thm)],[f_3437_3]) ).

cnf(f_3437_5,plain,
    ( c_Wellfounded_Owf(U_13486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),U_13488),U_13490))
    | ~ c_Wellfounded_Owf(U_13486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13486,U_13486),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13486,U_13486,U_13486),U_13488),U_13488)),hAPP(hAPP(c_Relation_Orel__comp(U_13486,U_13486,U_13486),U_13490),U_13488))),U_13490)) ),
    inference(clausify,[status(thm)],[f_3437_3]) ).

fof(f_3438_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,V_r_2)
        | ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2))
        | ~ c_Wellfounded_Owf(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain]) ).

fof(f_3438_2,plain,
    ! [U_13496,U_13495] :
      ( ( c_Wellfounded_Owf(U_13495,U_13496)
        | ? [U_13494] :
          ! [U_13493] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13495,U_13495)),hAPP(hAPP(c_Product__Type_OPair(U_13495,U_13495),hAPP(U_13494,hAPP(c_Nat_OSuc,U_13493))),hAPP(U_13494,U_13493))),U_13496)) )
      & ( ! [U_13492] :
          ? [U_13491] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13495,U_13495)),hAPP(hAPP(c_Product__Type_OPair(U_13495,U_13495),hAPP(U_13492,hAPP(c_Nat_OSuc,U_13491))),hAPP(U_13492,U_13491))),U_13496))
        | ~ c_Wellfounded_Owf(U_13495,U_13496) ) ),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

fof(f_3438_3,plain,
    ( ! [U_13500,U_13498] :
        ( c_Wellfounded_Owf(U_13498,U_13500)
        | ? [U_13494] :
          ! [U_13493] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13498,U_13498)),hAPP(hAPP(c_Product__Type_OPair(U_13498,U_13498),hAPP(U_13494,hAPP(c_Nat_OSuc,U_13493))),hAPP(U_13494,U_13493))),U_13500)) )
    & ! [U_13499,U_13497] :
        ( ! [U_13492] :
          ? [U_13491] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13497,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13497,U_13497),hAPP(U_13492,hAPP(c_Nat_OSuc,U_13491))),hAPP(U_13492,U_13491))),U_13499))
        | ~ c_Wellfounded_Owf(U_13497,U_13499) ) ),
    inference(miniscope,[status(thm)],[f_3438_2]) ).

fof(f_3438_4,plain,
    ( ! [U_13500,U_13498] :
        ( c_Wellfounded_Owf(U_13498,U_13500)
        | ? [U_13494] :
          ! [U_13493] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13498,U_13498)),hAPP(hAPP(c_Product__Type_OPair(U_13498,U_13498),hAPP(U_13494,hAPP(c_Nat_OSuc,U_13493))),hAPP(U_13494,U_13493))),U_13500)) )
    & ! [U_13499,U_13497] :
        ( ! [U_13492] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13497,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13497,U_13497),hAPP(U_13492,hAPP(c_Nat_OSuc,sK319(U_13499,U_13497,U_13492)))),hAPP(U_13492,sK319(U_13499,U_13497,U_13492)))),U_13499))
        | ~ c_Wellfounded_Owf(U_13497,U_13499) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13491,sK319(U_13499,U_13497,U_13492))],[f_3438_3]) ).

fof(f_3438_5,plain,
    ( ! [U_13500,U_13498] :
        ( c_Wellfounded_Owf(U_13498,U_13500)
        | ! [U_13493] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13498,U_13498)),hAPP(hAPP(c_Product__Type_OPair(U_13498,U_13498),hAPP(sK320(U_13500,U_13498),hAPP(c_Nat_OSuc,U_13493))),hAPP(sK320(U_13500,U_13498),U_13493))),U_13500)) )
    & ! [U_13499,U_13497] :
        ( ! [U_13492] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13497,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13497,U_13497),hAPP(U_13492,hAPP(c_Nat_OSuc,sK319(U_13499,U_13497,U_13492)))),hAPP(U_13492,sK319(U_13499,U_13497,U_13492)))),U_13499))
        | ~ c_Wellfounded_Owf(U_13497,U_13499) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13494,sK320(U_13500,U_13498))],[f_3438_4]) ).

cnf(f_3438_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13497,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13497,U_13497),hAPP(U_13492,hAPP(c_Nat_OSuc,sK319(U_13499,U_13497,U_13492)))),hAPP(U_13492,sK319(U_13499,U_13497,U_13492)))),U_13499))
    | ~ c_Wellfounded_Owf(U_13497,U_13499) ),
    inference(clausify,[status(thm)],[f_3438_5]) ).

cnf(f_3438_7,plain,
    ( c_Wellfounded_Owf(U_13498,U_13500)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13498,U_13498)),hAPP(hAPP(c_Product__Type_OPair(U_13498,U_13498),hAPP(sK320(U_13500,U_13498),hAPP(c_Nat_OSuc,U_13493))),hAPP(sK320(U_13500,U_13498),U_13493))),U_13500)) ),
    inference(clausify,[status(thm)],[f_3438_5]) ).

fof(f_3439_1,plain,
    ! [V_A_2,V_R_2,T_a] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2)))
      | ~ c_Wellfounded_Owf(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfE__pf]) ).

fof(f_3439_2,plain,
    ! [U_13503,U_13502,U_13501] :
      ( U_13503 = c_Orderings_Obot__class_Obot(tc_fun(U_13501,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13501,tc_HOL_Obool)),U_13503),hAPP(c_Relation_OImage(U_13501,U_13501,U_13502),U_13503)))
      | ~ c_Wellfounded_Owf(U_13501,U_13502) ),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

cnf(f_3439_3,plain,
    ( U_13503 = c_Orderings_Obot__class_Obot(tc_fun(U_13501,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13501,tc_HOL_Obool)),U_13503),hAPP(c_Relation_OImage(U_13501,U_13501,U_13502),U_13503)))
    | ~ c_Wellfounded_Owf(U_13501,U_13502) ),
    inference(clausify,[status(thm)],[f_3439_2]) ).

fof(f_3440_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_a,V_S_2)
      | ~ c_Wellfounded_Owf(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__compatible]) ).

fof(f_3440_2,plain,
    ! [U_13506,U_13505,U_13504] :
      ( c_Wellfounded_Owf(U_13504,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13504,U_13504),tc_HOL_Obool)),U_13505),U_13506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13504,U_13504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13504,U_13504,U_13504),U_13505),U_13506)),U_13505))
      | ~ c_Wellfounded_Owf(U_13504,U_13506)
      | ~ c_Wellfounded_Owf(U_13504,U_13505) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

cnf(f_3440_3,plain,
    ( c_Wellfounded_Owf(U_13504,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13504,U_13504),tc_HOL_Obool)),U_13505),U_13506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13504,U_13504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13504,U_13504,U_13504),U_13505),U_13506)),U_13505))
    | ~ c_Wellfounded_Owf(U_13504,U_13506)
    | ~ c_Wellfounded_Owf(U_13504,U_13505) ),
    inference(clausify,[status(thm)],[f_3440_2]) ).

fof(f_3441_1,plain,
    ! [T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a))))
      | ~ class_Orderings_Owellorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_wf]) ).

fof(f_3441_2,plain,
    ! [U_13507] :
      ( c_Wellfounded_Owf(U_13507,hAPP(c_Set_OCollect(tc_prod(U_13507,U_13507)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13507,U_13507,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13507))))
      | ~ class_Orderings_Owellorder(U_13507) ),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

cnf(f_3441_3,plain,
    ( c_Wellfounded_Owf(U_13507,hAPP(c_Set_OCollect(tc_prod(U_13507,U_13507)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13507,U_13507,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13507))))
    | ~ class_Orderings_Owellorder(U_13507) ),
    inference(clausify,[status(thm)],[f_3441_2]) ).

fof(f_3442_1,plain,
    ! [V_P_2,T_a] :
      ( ( c_FunDef_Oreduction__pair(T_a,V_P_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
        | ~ c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
          & c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) )
        | ~ c_FunDef_Oreduction__pair(T_a,V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).

fof(f_3442_2,plain,
    ! [U_13509,U_13508] :
      ( ( c_FunDef_Oreduction__pair(U_13508,U_13509)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13508,U_13508,U_13508),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)))
        | ~ c_Wellfounded_Owf(U_13508,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13508,U_13508,U_13508),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)))
          & c_Wellfounded_Owf(U_13508,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool),tc_fun(tc_prod(U_13508,U_13508),tc_HOL_Obool)),U_13509)) )
        | ~ c_FunDef_Oreduction__pair(U_13508,U_13509) ) ),
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

fof(f_3442_3,plain,
    ( ! [U_13513,U_13511] :
        ( c_FunDef_Oreduction__pair(U_13511,U_13513)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13511,U_13511,U_13511),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)))
        | ~ c_Wellfounded_Owf(U_13511,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)) )
    & ! [U_13512,U_13510] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13510,U_13510,U_13510),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512)))
          & c_Wellfounded_Owf(U_13510,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512)) )
        | ~ c_FunDef_Oreduction__pair(U_13510,U_13512) ) ),
    inference(miniscope,[status(thm)],[f_3442_2]) ).

cnf(f_3442_4,plain,
    ( c_Wellfounded_Owf(U_13510,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512))
    | ~ c_FunDef_Oreduction__pair(U_13510,U_13512) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

cnf(f_3442_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13510,U_13510,U_13510),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool),tc_fun(tc_prod(U_13510,U_13510),tc_HOL_Obool)),U_13512)))
    | ~ c_FunDef_Oreduction__pair(U_13510,U_13512) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

cnf(f_3442_6,plain,
    ( c_FunDef_Oreduction__pair(U_13511,U_13513)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13511,U_13511,U_13511),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)))
    | ~ c_Wellfounded_Owf(U_13511,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool),tc_fun(tc_prod(U_13511,U_13511),tc_HOL_Obool)),U_13513)) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

fof(f_3443_1,plain,
    ! [V_S_2,V_R_2,V_P_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ c_Wellfounded_Owf(T_a,V_S_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
      | ~ c_FunDef_Oreduction__pair(T_a,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).

fof(f_3443_2,plain,
    ! [U_13517,U_13516,U_13515,U_13514] :
      ( c_Wellfounded_Owf(U_13514,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13516),U_13517))
      | ~ c_Wellfounded_Owf(U_13514,U_13517)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13517),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool),tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13515)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13516),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool),tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13515)))
      | ~ c_FunDef_Oreduction__pair(U_13514,U_13515) ),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

cnf(f_3443_3,plain,
    ( c_Wellfounded_Owf(U_13514,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13516),U_13517))
    | ~ c_Wellfounded_Owf(U_13514,U_13517)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13517),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool),tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13516),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool),tc_fun(tc_prod(U_13514,U_13514),tc_HOL_Obool)),U_13515)))
    | ~ c_FunDef_Oreduction__pair(U_13514,U_13515) ),
    inference(clausify,[status(thm)],[f_3443_2]) ).

fof(f_3444_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_3444_2,plain,
    ! [U_13518] : c_Nitpick_Oone__frac(U_13518) = c_Nitpick_OAbs__Frac(U_13518,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_3444_1]) ).

cnf(f_3444_3,plain,
    c_Nitpick_Oone__frac(U_13518) = c_Nitpick_OAbs__Frac(U_13518,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_3444_2]) ).

fof(f_3445_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_3445_2,plain,
    ! [U_13520,U_13519] : c_Nitpick_Onumber__of__frac(U_13519,U_13520) = c_Nitpick_OAbs__Frac(U_13519,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_13520),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

cnf(f_3445_3,plain,
    c_Nitpick_Onumber__of__frac(U_13519,U_13520) = c_Nitpick_OAbs__Frac(U_13519,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_13520),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3445_2]) ).

fof(f_3446_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_3446_2,plain,
    ! [U_13523,U_13522,U_13521] : hAPP(hAPP(c_Nitpick_Ofrac(U_13521),U_13522),U_13523) = c_Nitpick_OAbs__Frac(U_13521,c_Nitpick_Onorm__frac(U_13522,U_13523)),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

cnf(f_3446_3,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_13521),U_13522),U_13523) = c_Nitpick_OAbs__Frac(U_13521,c_Nitpick_Onorm__frac(U_13522,U_13523)),
    inference(clausify,[status(thm)],[f_3446_2]) ).

fof(f_3447_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]) ).

cnf(f_3447_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(clausify,[status(thm)],[f_3447_1]) ).

fof(f_3448_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lenlex]) ).

fof(f_3448_2,plain,
    ! [U_13525,U_13524] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13524),c_List_Olenlex(U_13524,U_13525))
      | ~ c_Wellfounded_Owf(U_13524,U_13525) ),
    inference(variable_rename,[status(thm)],[f_3448_1]) ).

cnf(f_3448_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13524),c_List_Olenlex(U_13524,U_13525))
    | ~ c_Wellfounded_Owf(U_13524,U_13525) ),
    inference(clausify,[status(thm)],[f_3448_2]) ).

fof(f_3449_1,plain,
    ! [T_a,V_R_2,T_b,V_P_2] :
      ( c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))
      | ? [B_x] :
          ( ~ c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).

fof(f_3449_2,plain,
    ! [U_13530,U_13529,U_13528,U_13527] :
      ( c_Wellfounded_Owf(tc_prod(U_13530,U_13528),c_Recdef_Osame__fst(U_13530,U_13528,U_13527,U_13529))
      | ? [U_13526] :
          ( ~ c_Wellfounded_Owf(U_13528,hAPP(U_13529,U_13526))
          & hBOOL(hAPP(U_13527,U_13526)) ) ),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

fof(f_3449_3,plain,
    ! [U_13530,U_13529,U_13528,U_13527] :
      ( c_Wellfounded_Owf(tc_prod(U_13530,U_13528),c_Recdef_Osame__fst(U_13530,U_13528,U_13527,U_13529))
      | ( ~ c_Wellfounded_Owf(U_13528,hAPP(U_13529,sK321(U_13530,U_13529,U_13528,U_13527)))
        & hBOOL(hAPP(U_13527,sK321(U_13530,U_13529,U_13528,U_13527))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_13526,sK321(U_13530,U_13529,U_13528,U_13527))],[f_3449_2]) ).

cnf(f_3449_4,plain,
    ( hBOOL(hAPP(U_13527,sK321(U_13530,U_13529,U_13528,U_13527)))
    | c_Wellfounded_Owf(tc_prod(U_13530,U_13528),c_Recdef_Osame__fst(U_13530,U_13528,U_13527,U_13529)) ),
    inference(clausify,[status(thm)],[f_3449_3]) ).

cnf(f_3449_5,plain,
    ( ~ c_Wellfounded_Owf(U_13528,hAPP(U_13529,sK321(U_13530,U_13529,U_13528,U_13527)))
    | c_Wellfounded_Owf(tc_prod(U_13530,U_13528),c_Recdef_Osame__fst(U_13530,U_13528,U_13527,U_13529)) ),
    inference(clausify,[status(thm)],[f_3449_3]) ).

fof(f_3450_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

cnf(f_3450_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3450_1]) ).

fof(f_3451_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex]) ).

fof(f_3451_2,plain,
    ! [U_13532,U_13531] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13531),c_List_Olex(U_13531,U_13532))
      | ~ c_Wellfounded_Owf(U_13531,U_13532) ),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

cnf(f_3451_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13531),c_List_Olex(U_13531,U_13532))
    | ~ c_Wellfounded_Owf(U_13531,U_13532) ),
    inference(clausify,[status(thm)],[f_3451_2]) ).

fof(f_3452_1,plain,
    ! [V_n_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lexn]) ).

fof(f_3452_2,plain,
    ! [U_13535,U_13534,U_13533] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13533),hAPP(c_List_Olexn(U_13533,U_13534),U_13535))
      | ~ c_Wellfounded_Owf(U_13533,U_13534) ),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

cnf(f_3452_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13533),hAPP(c_List_Olexn(U_13533,U_13534),U_13535))
    | ~ c_Wellfounded_Owf(U_13533,U_13534) ),
    inference(clausify,[status(thm)],[f_3452_2]) ).

fof(f_3453_1,plain,
    ! [T_a,V_g_2,V_f_2,V_P_2] :
      ( c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2)))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).

fof(f_3453_2,plain,
    ! [U_13540,U_13539,U_13538,U_13537] :
      ( c_Wellfounded_Owf(U_13540,hAPP(c_Set_OCollect(tc_prod(U_13540,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13540,U_13540,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(U_13540,tc_HOL_Obool),U_13540),hAPP(c_COMBS(U_13540,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13540),c_fconj),U_13537))),hAPP(hAPP(c_COMBC(U_13540,tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),U_13540),c_COMBB(U_13540,tc_HOL_Obool,U_13540)),c_fequal)),U_13539)))))
      | ? [U_13536] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13538,hAPP(U_13539,U_13536))),hAPP(U_13538,U_13536)))
          & hBOOL(hAPP(U_13537,U_13536)) ) ),
    inference(variable_rename,[status(thm)],[f_3453_1]) ).

fof(f_3453_3,plain,
    ! [U_13540,U_13539,U_13538,U_13537] :
      ( c_Wellfounded_Owf(U_13540,hAPP(c_Set_OCollect(tc_prod(U_13540,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13540,U_13540,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(U_13540,tc_HOL_Obool),U_13540),hAPP(c_COMBS(U_13540,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13540),c_fconj),U_13537))),hAPP(hAPP(c_COMBC(U_13540,tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),U_13540),c_COMBB(U_13540,tc_HOL_Obool,U_13540)),c_fequal)),U_13539)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13538,hAPP(U_13539,sK322(U_13540,U_13539,U_13538,U_13537)))),hAPP(U_13538,sK322(U_13540,U_13539,U_13538,U_13537))))
        & hBOOL(hAPP(U_13537,sK322(U_13540,U_13539,U_13538,U_13537))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_13536,sK322(U_13540,U_13539,U_13538,U_13537))],[f_3453_2]) ).

cnf(f_3453_4,plain,
    ( hBOOL(hAPP(U_13537,sK322(U_13540,U_13539,U_13538,U_13537)))
    | c_Wellfounded_Owf(U_13540,hAPP(c_Set_OCollect(tc_prod(U_13540,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13540,U_13540,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(U_13540,tc_HOL_Obool),U_13540),hAPP(c_COMBS(U_13540,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13540),c_fconj),U_13537))),hAPP(hAPP(c_COMBC(U_13540,tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),U_13540),c_COMBB(U_13540,tc_HOL_Obool,U_13540)),c_fequal)),U_13539))))) ),
    inference(clausify,[status(thm)],[f_3453_3]) ).

cnf(f_3453_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13538,hAPP(U_13539,sK322(U_13540,U_13539,U_13538,U_13537)))),hAPP(U_13538,sK322(U_13540,U_13539,U_13538,U_13537))))
    | c_Wellfounded_Owf(U_13540,hAPP(c_Set_OCollect(tc_prod(U_13540,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13540,U_13540,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(U_13540,tc_HOL_Obool),U_13540),hAPP(c_COMBS(U_13540,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13540),c_fconj),U_13537))),hAPP(hAPP(c_COMBC(U_13540,tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_fun(tc_fun(U_13540,U_13540),tc_fun(U_13540,tc_HOL_Obool)),U_13540),c_COMBB(U_13540,tc_HOL_Obool,U_13540)),c_fequal)),U_13539))))) ),
    inference(clausify,[status(thm)],[f_3453_3]) ).

fof(f_3454_1,plain,
    ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_lex__def]) ).

fof(f_3454_2,plain,
    ! [U_13542,U_13541] : c_List_Olex(U_13541,U_13542) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13541),tc_List_Olist(U_13541)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13541,U_13542)),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

cnf(f_3454_3,plain,
    c_List_Olex(U_13541,U_13542) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13541),tc_List_Olist(U_13541)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13541,U_13542)),
    inference(clausify,[status(thm)],[f_3454_2]) ).

fof(f_3455_1,plain,
    ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(f_3455_2,plain,
    ! [U_13544,U_13543] : hAPP(c_List_Olexn(U_13543,U_13544),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13543),tc_List_Olist(U_13543)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

cnf(f_3455_3,plain,
    hAPP(c_List_Olexn(U_13543,U_13544),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13543),tc_List_Olist(U_13543)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3455_2]) ).

fof(f_3456_1,plain,
    ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).

fof(f_3456_2,plain,
    ! [U_13547,U_13546,U_13545] : hAPP(c_Relation_ORange(U_13545,U_13546),hAPP(c_Set_OCollect(tc_prod(U_13545,U_13546)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13545,U_13546,tc_HOL_Obool),U_13547))) = hAPP(c_Set_OCollect(U_13546),hAPP(hAPP(c_COMBB(tc_fun(U_13545,tc_HOL_Obool),tc_HOL_Obool,U_13546),c_HOL_OEx(U_13545)),hAPP(c_COMBC(U_13545,U_13546,tc_HOL_Obool),U_13547))),
    inference(variable_rename,[status(thm)],[f_3456_1]) ).

cnf(f_3456_3,plain,
    hAPP(c_Relation_ORange(U_13545,U_13546),hAPP(c_Set_OCollect(tc_prod(U_13545,U_13546)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13545,U_13546,tc_HOL_Obool),U_13547))) = hAPP(c_Set_OCollect(U_13546),hAPP(hAPP(c_COMBB(tc_fun(U_13545,tc_HOL_Obool),tc_HOL_Obool,U_13546),c_HOL_OEx(U_13545)),hAPP(c_COMBC(U_13545,U_13546,tc_HOL_Obool),U_13547))),
    inference(clausify,[status(thm)],[f_3456_2]) ).

fof(f_3457_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_image__split__eq__Sigma]) ).

fof(f_3457_2,plain,
    ! [U_13553,U_13552,U_13551,U_13550,U_13549,U_13548] : hAPP(c_Set_Oimage(U_13548,tc_prod(U_13549,U_13550),hAPP(hAPP(c_COMBS(U_13548,U_13550,tc_prod(U_13549,U_13550)),hAPP(hAPP(c_COMBB(U_13549,tc_fun(U_13550,tc_prod(U_13549,U_13550)),U_13548),c_Product__Type_OPair(U_13549,U_13550)),U_13551)),U_13552)),U_13553) = hAPP(hAPP(c_Product__Type_OSigma(U_13549,U_13550),hAPP(c_Set_Oimage(U_13548,U_13549,U_13551),U_13553)),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13550,tc_HOL_Obool),U_13549),c_Set_Oimage(U_13548,U_13550,U_13552)),hAPP(hAPP(c_COMBC(U_13549,tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool)),U_13549),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13548,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13549,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool),U_13549),c_Set_Ovimage(U_13548,U_13549,U_13551)),hAPP(hAPP(c_COMBC(U_13549,tc_fun(U_13549,tc_HOL_Obool),tc_fun(U_13549,tc_HOL_Obool)),c_Set_Oinsert(U_13549)),c_Orderings_Obot__class_Obot(tc_fun(U_13549,tc_HOL_Obool)))))),U_13553))),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

cnf(f_3457_3,plain,
    hAPP(c_Set_Oimage(U_13548,tc_prod(U_13549,U_13550),hAPP(hAPP(c_COMBS(U_13548,U_13550,tc_prod(U_13549,U_13550)),hAPP(hAPP(c_COMBB(U_13549,tc_fun(U_13550,tc_prod(U_13549,U_13550)),U_13548),c_Product__Type_OPair(U_13549,U_13550)),U_13551)),U_13552)),U_13553) = hAPP(hAPP(c_Product__Type_OSigma(U_13549,U_13550),hAPP(c_Set_Oimage(U_13548,U_13549,U_13551),U_13553)),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13550,tc_HOL_Obool),U_13549),c_Set_Oimage(U_13548,U_13550,U_13552)),hAPP(hAPP(c_COMBC(U_13549,tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool)),U_13549),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13548,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13549,tc_HOL_Obool),tc_fun(U_13548,tc_HOL_Obool),U_13549),c_Set_Ovimage(U_13548,U_13549,U_13551)),hAPP(hAPP(c_COMBC(U_13549,tc_fun(U_13549,tc_HOL_Obool),tc_fun(U_13549,tc_HOL_Obool)),c_Set_Oinsert(U_13549)),c_Orderings_Obot__class_Obot(tc_fun(U_13549,tc_HOL_Obool)))))),U_13553))),
    inference(clausify,[status(thm)],[f_3457_2]) ).

fof(f_3458_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_OwfP(T_a,V_r_2)
        | ~ c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) )
      & ( c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2)))
        | ~ c_Wellfounded_OwfP(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__def]) ).

fof(f_3458_2,plain,
    ! [U_13555,U_13554] :
      ( ( c_Wellfounded_OwfP(U_13554,U_13555)
        | ~ c_Wellfounded_Owf(U_13554,hAPP(c_Set_OCollect(tc_prod(U_13554,U_13554)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13554,U_13554,tc_HOL_Obool),U_13555))) )
      & ( c_Wellfounded_Owf(U_13554,hAPP(c_Set_OCollect(tc_prod(U_13554,U_13554)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13554,U_13554,tc_HOL_Obool),U_13555)))
        | ~ c_Wellfounded_OwfP(U_13554,U_13555) ) ),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

fof(f_3458_3,plain,
    ( ! [U_13559,U_13557] :
        ( c_Wellfounded_OwfP(U_13557,U_13559)
        | ~ c_Wellfounded_Owf(U_13557,hAPP(c_Set_OCollect(tc_prod(U_13557,U_13557)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13557,U_13557,tc_HOL_Obool),U_13559))) )
    & ! [U_13558,U_13556] :
        ( c_Wellfounded_Owf(U_13556,hAPP(c_Set_OCollect(tc_prod(U_13556,U_13556)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13556,U_13556,tc_HOL_Obool),U_13558)))
        | ~ c_Wellfounded_OwfP(U_13556,U_13558) ) ),
    inference(miniscope,[status(thm)],[f_3458_2]) ).

cnf(f_3458_4,plain,
    ( c_Wellfounded_Owf(U_13556,hAPP(c_Set_OCollect(tc_prod(U_13556,U_13556)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13556,U_13556,tc_HOL_Obool),U_13558)))
    | ~ c_Wellfounded_OwfP(U_13556,U_13558) ),
    inference(clausify,[status(thm)],[f_3458_3]) ).

cnf(f_3458_5,plain,
    ( c_Wellfounded_OwfP(U_13557,U_13559)
    | ~ c_Wellfounded_Owf(U_13557,hAPP(c_Set_OCollect(tc_prod(U_13557,U_13557)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13557,U_13557,tc_HOL_Obool),U_13559))) ),
    inference(clausify,[status(thm)],[f_3458_3]) ).

fof(f_3459_1,plain,
    ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))),
    inference(fof_nnf,[status(thm)],[fact_wfP__empty]) ).

fof(f_3459_2,plain,
    ! [U_13560] : c_Wellfounded_OwfP(U_13560,hAPP(c_COMBK(tc_fun(U_13560,tc_HOL_Obool),U_13560),hAPP(c_COMBK(tc_HOL_Obool,U_13560),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

cnf(f_3459_3,plain,
    c_Wellfounded_OwfP(U_13560,hAPP(c_COMBK(tc_fun(U_13560,tc_HOL_Obool),U_13560),hAPP(c_COMBK(tc_HOL_Obool,U_13560),c_fFalse))),
    inference(clausify,[status(thm)],[f_3459_2]) ).

fof(f_3460_1,plain,
    ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),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_a),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaI]) ).

fof(f_3460_2,plain,
    ! [U_13566,U_13565,U_13564,U_13563,U_13562,U_13561] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13561,U_13564)),hAPP(hAPP(c_Product__Type_OPair(U_13561,U_13564),U_13562),U_13565)),hAPP(hAPP(c_Product__Type_OSigma(U_13561,U_13564),U_13563),U_13566)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13564),U_13565),hAPP(U_13566,U_13562)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13561),U_13562),U_13563)) ),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

cnf(f_3460_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13561,U_13564)),hAPP(hAPP(c_Product__Type_OPair(U_13561,U_13564),U_13562),U_13565)),hAPP(hAPP(c_Product__Type_OSigma(U_13561,U_13564),U_13563),U_13566)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13564),U_13565),hAPP(U_13566,U_13562)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13561),U_13562),U_13563)) ),
    inference(clausify,[status(thm)],[f_3460_2]) ).

fof(f_3461_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_RangeI]) ).

fof(f_3461_2,plain,
    ! [U_13571,U_13570,U_13569,U_13568,U_13567] :
      ( hBOOL(hAPP(hAPP(c_member(U_13568),U_13570),hAPP(c_Relation_ORange(U_13567,U_13568),U_13571)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13567,U_13568)),hAPP(hAPP(c_Product__Type_OPair(U_13567,U_13568),U_13569),U_13570)),U_13571)) ),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

cnf(f_3461_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13568),U_13570),hAPP(c_Relation_ORange(U_13567,U_13568),U_13571)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13567,U_13568)),hAPP(hAPP(c_Product__Type_OPair(U_13567,U_13568),U_13569),U_13570)),U_13571)) ),
    inference(clausify,[status(thm)],[f_3461_2]) ).

fof(f_3462_1,plain,
    ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) != hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2]) ).

fof(f_3462_2,plain,
    ! [U_13577,U_13576,U_13575,U_13574,U_13573,U_13572] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13576),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574)) = hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13577),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574))
          | U_13576 != U_13577 )
        & ( U_13576 = U_13577
          | hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13576),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574)) != hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13577),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13572),U_13573),U_13574)) ),
    inference(variable_rename,[status(thm)],[f_3462_1]) ).

cnf(f_3462_3,plain,
    ( U_13576 = U_13577
    | hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13576),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574)) != hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13577),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13572),U_13573),U_13574)) ),
    inference(clausify,[status(thm)],[f_3462_2]) ).

cnf(f_3462_4,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13576),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574)) = hAPP(hAPP(c_Product__Type_OSigma(U_13575,U_13572),U_13577),hAPP(c_COMBK(tc_fun(U_13572,tc_HOL_Obool),U_13575),U_13574))
    | U_13576 != U_13577
    | ~ hBOOL(hAPP(hAPP(c_member(U_13572),U_13573),U_13574)) ),
    inference(clausify,[status(thm)],[f_3462_2]) ).

fof(f_3463_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_OwfP(T_a,V_r_2)
        | ? [B_x1] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) )
      & ( ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1))
        | ~ c_Wellfounded_OwfP(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff]) ).

fof(f_3463_2,plain,
    ! [U_13581,U_13580] :
      ( ( c_Wellfounded_OwfP(U_13580,U_13581)
        | ? [U_13579] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13580,U_13581),U_13579)) )
      & ( ! [U_13578] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13580,U_13581),U_13578))
        | ~ c_Wellfounded_OwfP(U_13580,U_13581) ) ),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

fof(f_3463_3,plain,
    ( ! [U_13585,U_13583] :
        ( c_Wellfounded_OwfP(U_13583,U_13585)
        | ? [U_13579] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13583,U_13585),U_13579)) )
    & ! [U_13584,U_13582] :
        ( ! [U_13578] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13582,U_13584),U_13578))
        | ~ c_Wellfounded_OwfP(U_13582,U_13584) ) ),
    inference(miniscope,[status(thm)],[f_3463_2]) ).

fof(f_3463_4,plain,
    ( ! [U_13585,U_13583] :
        ( c_Wellfounded_OwfP(U_13583,U_13585)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13583,U_13585),sK323(U_13585,U_13583))) )
    & ! [U_13584,U_13582] :
        ( ! [U_13578] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13582,U_13584),U_13578))
        | ~ c_Wellfounded_OwfP(U_13582,U_13584) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_13579,sK323(U_13585,U_13583))],[f_3463_3]) ).

cnf(f_3463_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13582,U_13584),U_13578))
    | ~ c_Wellfounded_OwfP(U_13582,U_13584) ),
    inference(clausify,[status(thm)],[f_3463_4]) ).

cnf(f_3463_6,plain,
    ( c_Wellfounded_OwfP(U_13583,U_13585)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13583,U_13585),sK323(U_13585,U_13583))) ),
    inference(clausify,[status(thm)],[f_3463_4]) ).

fof(f_3464_1,plain,
    ! [V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2))
      | ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_accp__wfPD]) ).

fof(f_3464_2,plain,
    ! [U_13588,U_13587,U_13586] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13586,U_13587),U_13588))
      | ~ c_Wellfounded_OwfP(U_13586,U_13587) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

cnf(f_3464_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13586,U_13587),U_13588))
    | ~ c_Wellfounded_OwfP(U_13586,U_13587) ),
    inference(clausify,[status(thm)],[f_3464_2]) ).

fof(f_3465_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

fof(f_3465_2,plain,
    ! [U_13593,U_13592,U_13591,U_13590,U_13589] : hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13589,tc_HOL_Obool)),U_13591),U_13592)),U_13593) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13589,U_13590),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),U_13591),U_13593)),hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),U_13592),U_13593)),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

cnf(f_3465_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13589,tc_HOL_Obool)),U_13591),U_13592)),U_13593) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13589,U_13590),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),U_13591),U_13593)),hAPP(hAPP(c_Product__Type_OSigma(U_13589,U_13590),U_13592),U_13593)),
    inference(clausify,[status(thm)],[f_3465_2]) ).

fof(f_3466_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(f_3466_2,plain,
    ! [U_13598,U_13597,U_13596,U_13595,U_13594] : hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13594,tc_HOL_Obool)),U_13596),U_13597)),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13594,U_13595),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),U_13596),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598))),hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),U_13597),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598))),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

cnf(f_3466_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13594,tc_HOL_Obool)),U_13596),U_13597)),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13594,U_13595),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),U_13596),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598))),hAPP(hAPP(c_Product__Type_OSigma(U_13594,U_13595),U_13597),hAPP(c_COMBK(tc_fun(U_13595,tc_HOL_Obool),U_13594),U_13598))),
    inference(clausify,[status(thm)],[f_3466_2]) ).

fof(f_3467_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(f_3467_2,plain,
    ! [U_13603,U_13602,U_13601,U_13600,U_13599] : hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),hAPP(hAPP(c_COMBS(U_13599,tc_fun(U_13600,tc_HOL_Obool),tc_fun(U_13600,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13600,tc_HOL_Obool),tc_fun(tc_fun(U_13600,tc_HOL_Obool),tc_fun(U_13600,tc_HOL_Obool)),U_13599),c_Groups_Ominus__class_Ominus(tc_fun(U_13600,tc_HOL_Obool))),U_13602)),U_13603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13599,U_13600),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),U_13602)),hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),U_13603)),
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

cnf(f_3467_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),hAPP(hAPP(c_COMBS(U_13599,tc_fun(U_13600,tc_HOL_Obool),tc_fun(U_13600,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13600,tc_HOL_Obool),tc_fun(tc_fun(U_13600,tc_HOL_Obool),tc_fun(U_13600,tc_HOL_Obool)),U_13599),c_Groups_Ominus__class_Ominus(tc_fun(U_13600,tc_HOL_Obool))),U_13602)),U_13603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13599,U_13600),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),U_13602)),hAPP(hAPP(c_Product__Type_OSigma(U_13599,U_13600),U_13601),U_13603)),
    inference(clausify,[status(thm)],[f_3467_2]) ).

fof(f_3468_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Range__Id__on]) ).

fof(f_3468_2,plain,
    ! [U_13605,U_13604] : hAPP(c_Relation_ORange(U_13604,U_13604),c_Relation_OId__on(U_13604,U_13605)) = U_13605,
    inference(variable_rename,[status(thm)],[f_3468_1]) ).

cnf(f_3468_3,plain,
    hAPP(c_Relation_ORange(U_13604,U_13604),c_Relation_OId__on(U_13604,U_13605)) = U_13605,
    inference(clausify,[status(thm)],[f_3468_2]) ).

fof(f_3469_1,plain,
    ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Union]) ).

fof(f_3469_2,plain,
    ! [U_13609,U_13608,U_13607,U_13606] : hAPP(hAPP(c_Product__Type_OSigma(U_13606,U_13607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_13606,tc_HOL_Obool),U_13608)),U_13609) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_13606,tc_HOL_Obool),tc_fun(tc_prod(U_13606,U_13607),tc_HOL_Obool)),U_13608),hAPP(hAPP(c_COMBC(tc_fun(U_13606,tc_HOL_Obool),tc_fun(U_13606,tc_fun(U_13607,tc_HOL_Obool)),tc_fun(tc_prod(U_13606,U_13607),tc_HOL_Obool)),c_Product__Type_OSigma(U_13606,U_13607)),U_13609)),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

cnf(f_3469_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13606,U_13607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_13606,tc_HOL_Obool),U_13608)),U_13609) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_13606,tc_HOL_Obool),tc_fun(tc_prod(U_13606,U_13607),tc_HOL_Obool)),U_13608),hAPP(hAPP(c_COMBC(tc_fun(U_13606,tc_HOL_Obool),tc_fun(U_13606,tc_fun(U_13607,tc_HOL_Obool)),tc_fun(tc_prod(U_13606,U_13607),tc_HOL_Obool)),c_Product__Type_OSigma(U_13606,U_13607)),U_13609)),
    inference(clausify,[status(thm)],[f_3469_2]) ).

fof(f_3470_1,plain,
    ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty1]) ).

fof(f_3470_2,plain,
    ! [U_13612,U_13611,U_13610] : hAPP(hAPP(c_Product__Type_OSigma(U_13610,U_13611),c_Orderings_Obot__class_Obot(tc_fun(U_13610,tc_HOL_Obool))),U_13612) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13610,U_13611),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

cnf(f_3470_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13610,U_13611),c_Orderings_Obot__class_Obot(tc_fun(U_13610,tc_HOL_Obool))),U_13612) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13610,U_13611),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3470_2]) ).

fof(f_3471_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product]) ).

fof(f_3471_2,plain,
    ! [U_13616,U_13615,U_13614,U_13613] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13613,U_13614)),hAPP(hAPP(c_Product__Type_OSigma(U_13613,U_13614),U_13615),hAPP(c_COMBK(tc_fun(U_13614,tc_HOL_Obool),U_13613),U_13616))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13613),U_13615)),hAPP(c_Finite__Set_Ocard(U_13614),U_13616)),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

cnf(f_3471_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_13613,U_13614)),hAPP(hAPP(c_Product__Type_OSigma(U_13613,U_13614),U_13615),hAPP(c_COMBK(tc_fun(U_13614,tc_HOL_Obool),U_13613),U_13616))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13613),U_13615)),hAPP(c_Finite__Set_Ocard(U_13614),U_13616)),
    inference(clausify,[status(thm)],[f_3471_2]) ).

fof(f_3472_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product]) ).

fof(f_3472_2,plain,
    ! [U_13622,U_13621,U_13620,U_13619,U_13618,U_13617] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13618,U_13617),hAPP(hAPP(c_COMBC(U_13618,tc_fun(U_13619,tc_HOL_Obool),U_13617),hAPP(hAPP(c_COMBB(tc_fun(U_13619,U_13617),tc_fun(tc_fun(U_13619,tc_HOL_Obool),U_13617),U_13618),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13619,U_13617)),U_13620)),U_13621)),U_13622) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13618,U_13619),U_13617),hAPP(c_Product__Type_Oprod_Oprod__case(U_13618,U_13619,U_13617),U_13620)),hAPP(hAPP(c_Product__Type_OSigma(U_13618,U_13619),U_13622),hAPP(c_COMBK(tc_fun(U_13619,tc_HOL_Obool),U_13618),U_13621)))
      | ~ class_Groups_Ocomm__monoid__add(U_13617) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

cnf(f_3472_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13618,U_13617),hAPP(hAPP(c_COMBC(U_13618,tc_fun(U_13619,tc_HOL_Obool),U_13617),hAPP(hAPP(c_COMBB(tc_fun(U_13619,U_13617),tc_fun(tc_fun(U_13619,tc_HOL_Obool),U_13617),U_13618),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13619,U_13617)),U_13620)),U_13621)),U_13622) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13618,U_13619),U_13617),hAPP(c_Product__Type_Oprod_Oprod__case(U_13618,U_13619,U_13617),U_13620)),hAPP(hAPP(c_Product__Type_OSigma(U_13618,U_13619),U_13622),hAPP(c_COMBK(tc_fun(U_13619,tc_HOL_Obool),U_13618),U_13621)))
    | ~ class_Groups_Ocomm__monoid__add(U_13617) ),
    inference(clausify,[status(thm)],[f_3472_2]) ).

fof(f_3473_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,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_a,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_a,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Times__empty]) ).

fof(f_3473_2,plain,
    ! [U_13626,U_13625,U_13624,U_13623] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_13623,U_13624),U_13625),hAPP(c_COMBK(tc_fun(U_13624,tc_HOL_Obool),U_13623),U_13626)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13623,U_13624),tc_HOL_Obool))
        | ( U_13626 != c_Orderings_Obot__class_Obot(tc_fun(U_13624,tc_HOL_Obool))
          & U_13625 != c_Orderings_Obot__class_Obot(tc_fun(U_13623,tc_HOL_Obool)) ) )
      & ( U_13626 = c_Orderings_Obot__class_Obot(tc_fun(U_13624,tc_HOL_Obool))
        | U_13625 = c_Orderings_Obot__class_Obot(tc_fun(U_13623,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_13623,U_13624),U_13625),hAPP(c_COMBK(tc_fun(U_13624,tc_HOL_Obool),U_13623),U_13626)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13623,U_13624),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

fof(f_3473_3,plain,
    ( ! [U_13634,U_13632,U_13630,U_13628] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_13628,U_13630),U_13632),hAPP(c_COMBK(tc_fun(U_13630,tc_HOL_Obool),U_13628),U_13634)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13628,U_13630),tc_HOL_Obool))
        | ( U_13634 != c_Orderings_Obot__class_Obot(tc_fun(U_13630,tc_HOL_Obool))
          & U_13632 != c_Orderings_Obot__class_Obot(tc_fun(U_13628,tc_HOL_Obool)) ) )
    & ! [U_13633,U_13631,U_13629,U_13627] :
        ( U_13633 = c_Orderings_Obot__class_Obot(tc_fun(U_13629,tc_HOL_Obool))
        | U_13631 = c_Orderings_Obot__class_Obot(tc_fun(U_13627,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_13627,U_13629),U_13631),hAPP(c_COMBK(tc_fun(U_13629,tc_HOL_Obool),U_13627),U_13633)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13627,U_13629),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3473_2]) ).

cnf(f_3473_4,plain,
    ( U_13633 = c_Orderings_Obot__class_Obot(tc_fun(U_13629,tc_HOL_Obool))
    | U_13631 = c_Orderings_Obot__class_Obot(tc_fun(U_13627,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_13627,U_13629),U_13631),hAPP(c_COMBK(tc_fun(U_13629,tc_HOL_Obool),U_13627),U_13633)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13627,U_13629),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3473_3]) ).

cnf(f_3473_5,plain,
    ( U_13632 != c_Orderings_Obot__class_Obot(tc_fun(U_13628,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_13628,U_13630),U_13632),hAPP(c_COMBK(tc_fun(U_13630,tc_HOL_Obool),U_13628),U_13634)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13628,U_13630),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3473_3]) ).

cnf(f_3473_6,plain,
    ( U_13634 != c_Orderings_Obot__class_Obot(tc_fun(U_13630,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_13628,U_13630),U_13632),hAPP(c_COMBK(tc_fun(U_13630,tc_HOL_Obool),U_13628),U_13634)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13628,U_13630),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3473_3]) ).

fof(f_3474_1,plain,
    ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty2]) ).

fof(f_3474_2,plain,
    ! [U_13637,U_13636,U_13635] : hAPP(hAPP(c_Product__Type_OSigma(U_13635,U_13636),U_13637),hAPP(c_COMBK(tc_fun(U_13636,tc_HOL_Obool),U_13635),c_Orderings_Obot__class_Obot(tc_fun(U_13636,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13635,U_13636),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

cnf(f_3474_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13635,U_13636),U_13637),hAPP(c_COMBK(tc_fun(U_13636,tc_HOL_Obool),U_13635),c_Orderings_Obot__class_Obot(tc_fun(U_13636,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13635,U_13636),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3474_2]) ).

fof(f_3475_1,plain,
    ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(f_3475_2,plain,
    ! [U_13640,U_13639,U_13638] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13638,U_13639),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13638,U_13639),c_Orderings_Otop__class_Otop(tc_fun(U_13638,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13639,tc_HOL_Obool),U_13638),U_13640))) = hAPP(hAPP(c_Product__Type_OSigma(U_13638,U_13639),c_Orderings_Otop__class_Otop(tc_fun(U_13638,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13639,tc_HOL_Obool),U_13638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13639,tc_HOL_Obool)),U_13640))),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

cnf(f_3475_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13638,U_13639),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13638,U_13639),c_Orderings_Otop__class_Otop(tc_fun(U_13638,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13639,tc_HOL_Obool),U_13638),U_13640))) = hAPP(hAPP(c_Product__Type_OSigma(U_13638,U_13639),c_Orderings_Otop__class_Otop(tc_fun(U_13638,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13639,tc_HOL_Obool),U_13638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13639,tc_HOL_Obool)),U_13640))),
    inference(clausify,[status(thm)],[f_3475_2]) ).

fof(f_3476_1,plain,
    ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(f_3476_2,plain,
    ! [U_13643,U_13642,U_13641] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13641,U_13642),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13641,U_13642),U_13643),hAPP(c_COMBK(tc_fun(U_13642,tc_HOL_Obool),U_13641),c_Orderings_Otop__class_Otop(tc_fun(U_13642,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_13641,U_13642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13641,tc_HOL_Obool)),U_13643)),hAPP(c_COMBK(tc_fun(U_13642,tc_HOL_Obool),U_13641),c_Orderings_Otop__class_Otop(tc_fun(U_13642,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3476_1]) ).

cnf(f_3476_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_13641,U_13642),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13641,U_13642),U_13643),hAPP(c_COMBK(tc_fun(U_13642,tc_HOL_Obool),U_13641),c_Orderings_Otop__class_Otop(tc_fun(U_13642,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_13641,U_13642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13641,tc_HOL_Obool)),U_13643)),hAPP(c_COMBK(tc_fun(U_13642,tc_HOL_Obool),U_13641),c_Orderings_Otop__class_Otop(tc_fun(U_13642,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3476_2]) ).

fof(f_3477_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product]) ).

fof(f_3477_2,plain,
    ! [U_13649,U_13648,U_13647,U_13646,U_13645,U_13644] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13645,U_13644),hAPP(hAPP(c_COMBC(U_13645,tc_fun(U_13646,tc_HOL_Obool),U_13644),hAPP(hAPP(c_COMBB(tc_fun(U_13646,U_13644),tc_fun(tc_fun(U_13646,tc_HOL_Obool),U_13644),U_13645),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13646,U_13644)),U_13647)),U_13648)),U_13649) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13645,U_13646),U_13644),hAPP(c_Product__Type_Oprod_Oprod__case(U_13645,U_13646,U_13644),U_13647)),hAPP(hAPP(c_Product__Type_OSigma(U_13645,U_13646),U_13649),hAPP(c_COMBK(tc_fun(U_13646,tc_HOL_Obool),U_13645),U_13648)))
      | ~ class_Groups_Ocomm__monoid__mult(U_13644) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

cnf(f_3477_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13645,U_13644),hAPP(hAPP(c_COMBC(U_13645,tc_fun(U_13646,tc_HOL_Obool),U_13644),hAPP(hAPP(c_COMBB(tc_fun(U_13646,U_13644),tc_fun(tc_fun(U_13646,tc_HOL_Obool),U_13644),U_13645),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13646,U_13644)),U_13647)),U_13648)),U_13649) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13645,U_13646),U_13644),hAPP(c_Product__Type_Oprod_Oprod__case(U_13645,U_13646,U_13644),U_13647)),hAPP(hAPP(c_Product__Type_OSigma(U_13645,U_13646),U_13649),hAPP(c_COMBK(tc_fun(U_13646,tc_HOL_Obool),U_13645),U_13648)))
    | ~ class_Groups_Ocomm__monoid__mult(U_13644) ),
    inference(clausify,[status(thm)],[f_3477_2]) ).

fof(f_3478_1,plain,
    ! [V_p_2,V_r_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2))
      | ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__subset]) ).

fof(f_3478_2,plain,
    ! [U_13652,U_13651,U_13650] :
      ( c_Wellfounded_OwfP(U_13650,U_13652)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13650,tc_fun(U_13650,tc_HOL_Obool))),U_13652),U_13651))
      | ~ c_Wellfounded_OwfP(U_13650,U_13651) ),
    inference(variable_rename,[status(thm)],[f_3478_1]) ).

cnf(f_3478_3,plain,
    ( c_Wellfounded_OwfP(U_13650,U_13652)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13650,tc_fun(U_13650,tc_HOL_Obool))),U_13652),U_13651))
    | ~ c_Wellfounded_OwfP(U_13650,U_13651) ),
    inference(clausify,[status(thm)],[f_3478_2]) ).

fof(f_3479_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(f_3479_2,plain,
    ! [U_13657,U_13656,U_13655,U_13654,U_13653] : hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13653,tc_HOL_Obool)),U_13655),U_13656)),U_13657) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13653,U_13654),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),U_13655),U_13657)),hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),U_13656),U_13657)),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

cnf(f_3479_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13653,tc_HOL_Obool)),U_13655),U_13656)),U_13657) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13653,U_13654),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),U_13655),U_13657)),hAPP(hAPP(c_Product__Type_OSigma(U_13653,U_13654),U_13656),U_13657)),
    inference(clausify,[status(thm)],[f_3479_2]) ).

fof(f_3480_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(f_3480_2,plain,
    ! [U_13662,U_13661,U_13660,U_13659,U_13658] : hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13658,tc_HOL_Obool)),U_13660),U_13661)),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13658,U_13659),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),U_13660),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662))),hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),U_13661),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662))),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

cnf(f_3480_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13658,tc_HOL_Obool)),U_13660),U_13661)),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13658,U_13659),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),U_13660),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662))),hAPP(hAPP(c_Product__Type_OSigma(U_13658,U_13659),U_13661),hAPP(c_COMBK(tc_fun(U_13659,tc_HOL_Obool),U_13658),U_13662))),
    inference(clausify,[status(thm)],[f_3480_2]) ).

fof(f_3481_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(f_3481_2,plain,
    ! [U_13667,U_13666,U_13665,U_13664,U_13663] : hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),hAPP(hAPP(c_COMBS(U_13663,tc_fun(U_13664,tc_HOL_Obool),tc_fun(U_13664,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13664,tc_HOL_Obool),tc_fun(tc_fun(U_13664,tc_HOL_Obool),tc_fun(U_13664,tc_HOL_Obool)),U_13663),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13664,tc_HOL_Obool))),U_13666)),U_13667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13663,U_13664),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),U_13666)),hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),U_13667)),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

cnf(f_3481_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),hAPP(hAPP(c_COMBS(U_13663,tc_fun(U_13664,tc_HOL_Obool),tc_fun(U_13664,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13664,tc_HOL_Obool),tc_fun(tc_fun(U_13664,tc_HOL_Obool),tc_fun(U_13664,tc_HOL_Obool)),U_13663),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13664,tc_HOL_Obool))),U_13666)),U_13667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13663,U_13664),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),U_13666)),hAPP(hAPP(c_Product__Type_OSigma(U_13663,U_13664),U_13665),U_13667)),
    inference(clausify,[status(thm)],[f_3481_2]) ).

fof(f_3482_1,plain,
    ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_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))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma]) ).

fof(f_3482_2,plain,
    ! [U_13675,U_13674,U_13673,U_13672,U_13671,U_13670,U_13669,U_13668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13668,U_13673),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13668,U_13669,U_13673),U_13670),U_13674)),hAPP(hAPP(c_Product__Type_OSigma(U_13668,U_13673),U_13671),hAPP(c_COMBK(tc_fun(U_13673,tc_HOL_Obool),U_13668),U_13675))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13669,U_13673),tc_HOL_Obool)),U_13674),hAPP(hAPP(c_Product__Type_OSigma(U_13669,U_13673),U_13672),hAPP(c_COMBK(tc_fun(U_13673,tc_HOL_Obool),U_13669),U_13675))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13668,U_13669),tc_HOL_Obool)),U_13670),hAPP(hAPP(c_Product__Type_OSigma(U_13668,U_13669),U_13671),hAPP(c_COMBK(tc_fun(U_13669,tc_HOL_Obool),U_13668),U_13672)))) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

cnf(f_3482_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13668,U_13673),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13668,U_13669,U_13673),U_13670),U_13674)),hAPP(hAPP(c_Product__Type_OSigma(U_13668,U_13673),U_13671),hAPP(c_COMBK(tc_fun(U_13673,tc_HOL_Obool),U_13668),U_13675))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13669,U_13673),tc_HOL_Obool)),U_13674),hAPP(hAPP(c_Product__Type_OSigma(U_13669,U_13673),U_13672),hAPP(c_COMBK(tc_fun(U_13673,tc_HOL_Obool),U_13669),U_13675))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13668,U_13669),tc_HOL_Obool)),U_13670),hAPP(hAPP(c_Product__Type_OSigma(U_13668,U_13669),U_13671),hAPP(c_COMBK(tc_fun(U_13669,tc_HOL_Obool),U_13668),U_13672)))) ),
    inference(clausify,[status(thm)],[f_3482_2]) ).

fof(f_3483_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_swap__product]) ).

fof(f_3483_2,plain,
    ! [U_13679,U_13678,U_13677,U_13676] : hAPP(c_Set_Oimage(tc_prod(U_13676,U_13677),tc_prod(U_13677,U_13676),hAPP(c_Product__Type_Oprod_Oprod__case(U_13676,U_13677,tc_prod(U_13677,U_13676)),hAPP(c_COMBC(U_13677,U_13676,tc_prod(U_13677,U_13676)),c_Product__Type_OPair(U_13677,U_13676)))),hAPP(hAPP(c_Product__Type_OSigma(U_13676,U_13677),U_13678),hAPP(c_COMBK(tc_fun(U_13677,tc_HOL_Obool),U_13676),U_13679))) = hAPP(hAPP(c_Product__Type_OSigma(U_13677,U_13676),U_13679),hAPP(c_COMBK(tc_fun(U_13676,tc_HOL_Obool),U_13677),U_13678)),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

cnf(f_3483_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13676,U_13677),tc_prod(U_13677,U_13676),hAPP(c_Product__Type_Oprod_Oprod__case(U_13676,U_13677,tc_prod(U_13677,U_13676)),hAPP(c_COMBC(U_13677,U_13676,tc_prod(U_13677,U_13676)),c_Product__Type_OPair(U_13677,U_13676)))),hAPP(hAPP(c_Product__Type_OSigma(U_13676,U_13677),U_13678),hAPP(c_COMBK(tc_fun(U_13677,tc_HOL_Obool),U_13676),U_13679))) = hAPP(hAPP(c_Product__Type_OSigma(U_13677,U_13676),U_13679),hAPP(c_COMBK(tc_fun(U_13676,tc_HOL_Obool),U_13677),U_13678)),
    inference(clausify,[status(thm)],[f_3483_2]) ).

fof(f_3484_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product]) ).

fof(f_3484_2,plain,
    ! [U_13683,U_13682,U_13681,U_13680] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13680,U_13682)),hAPP(hAPP(c_Product__Type_OSigma(U_13680,U_13682),U_13681),hAPP(c_COMBK(tc_fun(U_13682,tc_HOL_Obool),U_13680),U_13683))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13682),U_13683))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13680),U_13681)) ),
    inference(variable_rename,[status(thm)],[f_3484_1]) ).

cnf(f_3484_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13680,U_13682)),hAPP(hAPP(c_Product__Type_OSigma(U_13680,U_13682),U_13681),hAPP(c_COMBK(tc_fun(U_13682,tc_HOL_Obool),U_13680),U_13683))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13682),U_13683))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13680),U_13681)) ),
    inference(clausify,[status(thm)],[f_3484_2]) ).

fof(f_3485_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__type]) ).

fof(f_3485_2,plain,
    ! [U_13686,U_13685,U_13684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),U_13686),hAPP(hAPP(c_Product__Type_OSigma(U_13684,U_13684),U_13685),hAPP(c_COMBK(tc_fun(U_13684,tc_HOL_Obool),U_13684),U_13685))))
      | ~ c_Equiv__Relations_Oequiv(U_13684,U_13685,U_13686) ),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

cnf(f_3485_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),U_13686),hAPP(hAPP(c_Product__Type_OSigma(U_13684,U_13684),U_13685),hAPP(c_COMBK(tc_fun(U_13684,tc_HOL_Obool),U_13684),U_13685))))
    | ~ c_Equiv__Relations_Oequiv(U_13684,U_13685,U_13686) ),
    inference(clausify,[status(thm)],[f_3485_2]) ).

fof(f_3486_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(f_3486_2,plain,
    ! [U_13691,U_13690,U_13689,U_13688,U_13687] : hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),hAPP(hAPP(c_COMBS(U_13687,tc_fun(U_13688,tc_HOL_Obool),tc_fun(U_13688,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13688,tc_HOL_Obool),tc_fun(tc_fun(U_13688,tc_HOL_Obool),tc_fun(U_13688,tc_HOL_Obool)),U_13687),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13688,tc_HOL_Obool))),U_13690)),U_13691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13687,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),U_13690)),hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),U_13691)),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

cnf(f_3486_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),hAPP(hAPP(c_COMBS(U_13687,tc_fun(U_13688,tc_HOL_Obool),tc_fun(U_13688,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13688,tc_HOL_Obool),tc_fun(tc_fun(U_13688,tc_HOL_Obool),tc_fun(U_13688,tc_HOL_Obool)),U_13687),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13688,tc_HOL_Obool))),U_13690)),U_13691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13687,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),U_13690)),hAPP(hAPP(c_Product__Type_OSigma(U_13687,U_13688),U_13689),U_13691)),
    inference(clausify,[status(thm)],[f_3486_2]) ).

fof(f_3487_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(f_3487_2,plain,
    ! [U_13696,U_13695,U_13694,U_13693,U_13692] : hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13692,tc_HOL_Obool)),U_13694),U_13695)),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13692,U_13693),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),U_13694),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696))),hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),U_13695),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696))),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

cnf(f_3487_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13692,tc_HOL_Obool)),U_13694),U_13695)),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13692,U_13693),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),U_13694),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696))),hAPP(hAPP(c_Product__Type_OSigma(U_13692,U_13693),U_13695),hAPP(c_COMBK(tc_fun(U_13693,tc_HOL_Obool),U_13692),U_13696))),
    inference(clausify,[status(thm)],[f_3487_2]) ).

fof(f_3488_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(f_3488_2,plain,
    ! [U_13701,U_13700,U_13699,U_13698,U_13697] : hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13697,tc_HOL_Obool)),U_13699),U_13700)),U_13701) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13697,U_13698),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),U_13699),U_13701)),hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),U_13700),U_13701)),
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

cnf(f_3488_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13697,tc_HOL_Obool)),U_13699),U_13700)),U_13701) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13697,U_13698),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),U_13699),U_13701)),hAPP(hAPP(c_Product__Type_OSigma(U_13697,U_13698),U_13700),U_13701)),
    inference(clausify,[status(thm)],[f_3488_2]) ).

fof(f_3489_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(f_3489_2,plain,
    ! [U_13703,U_13702] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13702,U_13702),tc_HOL_Obool)),c_Relation_OId__on(U_13702,U_13703)),hAPP(hAPP(c_Product__Type_OSigma(U_13702,U_13702),U_13703),hAPP(c_COMBK(tc_fun(U_13702,tc_HOL_Obool),U_13702),U_13703)))),
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

cnf(f_3489_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13702,U_13702),tc_HOL_Obool)),c_Relation_OId__on(U_13702,U_13703)),hAPP(hAPP(c_Product__Type_OSigma(U_13702,U_13702),U_13703),hAPP(c_COMBK(tc_fun(U_13702,tc_HOL_Obool),U_13702),U_13703)))),
    inference(clausify,[status(thm)],[f_3489_2]) ).

fof(f_3490_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Diff__subset]) ).

fof(f_3490_2,plain,
    ! [U_13707,U_13706,U_13705,U_13704] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13704,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13704,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13705,U_13704),U_13706)),hAPP(c_Relation_ORange(U_13705,U_13704),U_13707))),hAPP(c_Relation_ORange(U_13705,U_13704),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13705,U_13704),tc_HOL_Obool)),U_13706),U_13707)))),
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

cnf(f_3490_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13704,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13704,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13705,U_13704),U_13706)),hAPP(c_Relation_ORange(U_13705,U_13704),U_13707))),hAPP(c_Relation_ORange(U_13705,U_13704),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13705,U_13704),tc_HOL_Obool)),U_13706),U_13707)))),
    inference(clausify,[status(thm)],[f_3490_2]) ).

fof(f_3491_1,plain,
    ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(f_3491_2,plain,
    ! [U_13709,U_13708] : hAPP(hAPP(c_Product__Type_OSigma(U_13708,U_13709),c_Orderings_Otop__class_Otop(tc_fun(U_13708,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13709,tc_HOL_Obool),U_13708),c_Orderings_Otop__class_Otop(tc_fun(U_13709,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13708,U_13709),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

cnf(f_3491_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13708,U_13709),c_Orderings_Otop__class_Otop(tc_fun(U_13708,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_13709,tc_HOL_Obool),U_13708),c_Orderings_Otop__class_Otop(tc_fun(U_13709,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13708,U_13709),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3491_2]) ).

fof(f_3492_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),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_a),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_a),V_a_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff]) ).

fof(f_3492_2,plain,
    ! [U_13715,U_13714,U_13713,U_13712,U_13711,U_13710] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13710,U_13711)),hAPP(hAPP(c_Product__Type_OPair(U_13710,U_13711),U_13712),U_13713)),hAPP(hAPP(c_Product__Type_OSigma(U_13710,U_13711),U_13714),U_13715)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13711),U_13713),hAPP(U_13715,U_13712)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13710),U_13712),U_13714)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_13711),U_13713),hAPP(U_13715,U_13712)))
          & hBOOL(hAPP(hAPP(c_member(U_13710),U_13712),U_13714)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13710,U_13711)),hAPP(hAPP(c_Product__Type_OPair(U_13710,U_13711),U_13712),U_13713)),hAPP(hAPP(c_Product__Type_OSigma(U_13710,U_13711),U_13714),U_13715))) ) ),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

fof(f_3492_3,plain,
    ( ! [U_13727,U_13725,U_13723,U_13721,U_13719,U_13717] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13717,U_13719)),hAPP(hAPP(c_Product__Type_OPair(U_13717,U_13719),U_13721),U_13723)),hAPP(hAPP(c_Product__Type_OSigma(U_13717,U_13719),U_13725),U_13727)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13719),U_13723),hAPP(U_13727,U_13721)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13717),U_13721),U_13725)) )
    & ! [U_13726,U_13724,U_13722,U_13720,U_13718,U_13716] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_13718),U_13722),hAPP(U_13726,U_13720)))
          & hBOOL(hAPP(hAPP(c_member(U_13716),U_13720),U_13724)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13716,U_13718)),hAPP(hAPP(c_Product__Type_OPair(U_13716,U_13718),U_13720),U_13722)),hAPP(hAPP(c_Product__Type_OSigma(U_13716,U_13718),U_13724),U_13726))) ) ),
    inference(miniscope,[status(thm)],[f_3492_2]) ).

cnf(f_3492_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13716),U_13720),U_13724))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13716,U_13718)),hAPP(hAPP(c_Product__Type_OPair(U_13716,U_13718),U_13720),U_13722)),hAPP(hAPP(c_Product__Type_OSigma(U_13716,U_13718),U_13724),U_13726))) ),
    inference(clausify,[status(thm)],[f_3492_3]) ).

cnf(f_3492_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13718),U_13722),hAPP(U_13726,U_13720)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13716,U_13718)),hAPP(hAPP(c_Product__Type_OPair(U_13716,U_13718),U_13720),U_13722)),hAPP(hAPP(c_Product__Type_OSigma(U_13716,U_13718),U_13724),U_13726))) ),
    inference(clausify,[status(thm)],[f_3492_3]) ).

cnf(f_3492_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13717,U_13719)),hAPP(hAPP(c_Product__Type_OPair(U_13717,U_13719),U_13721),U_13723)),hAPP(hAPP(c_Product__Type_OSigma(U_13717,U_13719),U_13725),U_13727)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13719),U_13723),hAPP(U_13727,U_13721)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13717),U_13721),U_13725)) ),
    inference(clausify,[status(thm)],[f_3492_3]) ).

fof(f_3493_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD1]) ).

fof(f_3493_2,plain,
    ! [U_13733,U_13732,U_13731,U_13730,U_13729,U_13728] :
      ( hBOOL(hAPP(hAPP(c_member(U_13728),U_13730),U_13732))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13728,U_13729)),hAPP(hAPP(c_Product__Type_OPair(U_13728,U_13729),U_13730),U_13731)),hAPP(hAPP(c_Product__Type_OSigma(U_13728,U_13729),U_13732),U_13733))) ),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

cnf(f_3493_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13728),U_13730),U_13732))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13728,U_13729)),hAPP(hAPP(c_Product__Type_OPair(U_13728,U_13729),U_13730),U_13731)),hAPP(hAPP(c_Product__Type_OSigma(U_13728,U_13729),U_13732),U_13733))) ),
    inference(clausify,[status(thm)],[f_3493_2]) ).

fof(f_3494_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD2]) ).

fof(f_3494_2,plain,
    ! [U_13739,U_13738,U_13737,U_13736,U_13735,U_13734] :
      ( hBOOL(hAPP(hAPP(c_member(U_13735),U_13737),hAPP(U_13739,U_13736)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13734,U_13735)),hAPP(hAPP(c_Product__Type_OPair(U_13734,U_13735),U_13736),U_13737)),hAPP(hAPP(c_Product__Type_OSigma(U_13734,U_13735),U_13738),U_13739))) ),
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

fof(f_3494_3,plain,
    ! [U_13739,U_13738,U_13737,U_13736,U_13735] :
      ( ! [U_13734] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13734,U_13735)),hAPP(hAPP(c_Product__Type_OPair(U_13734,U_13735),U_13736),U_13737)),hAPP(hAPP(c_Product__Type_OSigma(U_13734,U_13735),U_13738),U_13739)))
      | hBOOL(hAPP(hAPP(c_member(U_13735),U_13737),hAPP(U_13739,U_13736))) ),
    inference(miniscope,[status(thm)],[f_3494_2]) ).

cnf(f_3494_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13734,U_13735)),hAPP(hAPP(c_Product__Type_OPair(U_13734,U_13735),U_13736),U_13737)),hAPP(hAPP(c_Product__Type_OSigma(U_13734,U_13735),U_13738),U_13739)))
    | hBOOL(hAPP(hAPP(c_member(U_13735),U_13737),hAPP(U_13739,U_13736))) ),
    inference(clausify,[status(thm)],[f_3494_3]) ).

fof(f_3495_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE2]) ).

fof(f_3495_2,plain,
    ! [U_13745,U_13744,U_13743,U_13742,U_13741,U_13740] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13741),U_13743),hAPP(U_13745,U_13742)))
        & hBOOL(hAPP(hAPP(c_member(U_13740),U_13742),U_13744)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13741)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13741),U_13742),U_13743)),hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),U_13744),U_13745))) ),
    inference(variable_rename,[status(thm)],[f_3495_1]) ).

cnf(f_3495_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13740),U_13742),U_13744))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13741)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13741),U_13742),U_13743)),hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),U_13744),U_13745))) ),
    inference(clausify,[status(thm)],[f_3495_2]) ).

cnf(f_3495_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13741),U_13743),hAPP(U_13745,U_13742)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13741)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13741),U_13742),U_13743)),hAPP(hAPP(c_Product__Type_OSigma(U_13740,U_13741),U_13744),U_13745))) ),
    inference(clausify,[status(thm)],[f_3495_2]) ).

fof(f_3496_1,plain,
    ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)),
    inference(fof_nnf,[status(thm)],[fact_Range__Union]) ).

fof(f_3496_2,plain,
    ! [U_13748,U_13747,U_13746] : hAPP(c_Relation_ORange(U_13746,U_13747),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13746,U_13747),tc_HOL_Obool),U_13748)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13746,U_13747),tc_HOL_Obool),tc_fun(U_13747,tc_HOL_Obool)),U_13748),c_Relation_ORange(U_13746,U_13747)),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

cnf(f_3496_3,plain,
    hAPP(c_Relation_ORange(U_13746,U_13747),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13746,U_13747),tc_HOL_Obool),U_13748)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13746,U_13747),tc_HOL_Obool),tc_fun(U_13747,tc_HOL_Obool)),U_13748),c_Relation_ORange(U_13746,U_13747)),
    inference(clausify,[status(thm)],[f_3496_2]) ).

fof(f_3497_1,plain,
    ! [V_r_2,T_a,T_b] :
      ( ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(T_b,T_a),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__empty__iff]) ).

fof(f_3497_2,plain,
    ! [U_13751,U_13750,U_13749] :
      ( ( hAPP(c_Relation_ORange(U_13749,U_13750),U_13751) = c_Orderings_Obot__class_Obot(tc_fun(U_13750,tc_HOL_Obool))
        | U_13751 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13749,U_13750),tc_HOL_Obool)) )
      & ( U_13751 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13749,U_13750),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13749,U_13750),U_13751) != c_Orderings_Obot__class_Obot(tc_fun(U_13750,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3497_1]) ).

fof(f_3497_3,plain,
    ( ! [U_13757,U_13755,U_13753] :
        ( hAPP(c_Relation_ORange(U_13753,U_13755),U_13757) = c_Orderings_Obot__class_Obot(tc_fun(U_13755,tc_HOL_Obool))
        | U_13757 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13753,U_13755),tc_HOL_Obool)) )
    & ! [U_13756,U_13754,U_13752] :
        ( U_13756 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13752,U_13754),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13752,U_13754),U_13756) != c_Orderings_Obot__class_Obot(tc_fun(U_13754,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3497_2]) ).

cnf(f_3497_4,plain,
    ( U_13756 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13752,U_13754),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_13752,U_13754),U_13756) != c_Orderings_Obot__class_Obot(tc_fun(U_13754,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3497_3]) ).

cnf(f_3497_5,plain,
    ( hAPP(c_Relation_ORange(U_13753,U_13755),U_13757) = c_Orderings_Obot__class_Obot(tc_fun(U_13755,tc_HOL_Obool))
    | U_13757 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13753,U_13755),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3497_3]) ).

fof(f_3498_1,plain,
    ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__empty]) ).

fof(f_3498_2,plain,
    ! [U_13759,U_13758] : hAPP(c_Relation_ORange(U_13758,U_13759),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13758,U_13759),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13759,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

cnf(f_3498_3,plain,
    hAPP(c_Relation_ORange(U_13758,U_13759),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13758,U_13759),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13759,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3498_2]) ).

fof(f_3499_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__Un__eq]) ).

fof(f_3499_2,plain,
    ! [U_13763,U_13762,U_13761,U_13760] : hAPP(c_Relation_ORange(U_13760,U_13761),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13760,U_13761),tc_HOL_Obool)),U_13762),U_13763)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13761,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13760,U_13761),U_13762)),hAPP(c_Relation_ORange(U_13760,U_13761),U_13763)),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

cnf(f_3499_3,plain,
    hAPP(c_Relation_ORange(U_13760,U_13761),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13760,U_13761),tc_HOL_Obool)),U_13762),U_13763)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13761,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13760,U_13761),U_13762)),hAPP(c_Relation_ORange(U_13760,U_13761),U_13763)),
    inference(clausify,[status(thm)],[f_3499_2]) ).

fof(f_3500_1,plain,
    ! [V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Range]) ).

fof(f_3500_2,plain,
    ! [U_13766,U_13765,U_13764] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13765),hAPP(c_Relation_ORange(U_13764,U_13765),U_13766)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13764,U_13765)),U_13766)) ),
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

cnf(f_3500_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13765),hAPP(c_Relation_ORange(U_13764,U_13765),U_13766)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13764,U_13765)),U_13766)) ),
    inference(clausify,[status(thm)],[f_3500_2]) ).

fof(f_3501_1,plain,
    ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_snd__eq__Range]) ).

fof(f_3501_2,plain,
    ! [U_13769,U_13768,U_13767] : hAPP(c_Set_Oimage(tc_prod(U_13767,U_13768),U_13768,c_Product__Type_Osnd(U_13767,U_13768)),U_13769) = hAPP(c_Relation_ORange(U_13767,U_13768),U_13769),
    inference(variable_rename,[status(thm)],[f_3501_1]) ).

cnf(f_3501_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13767,U_13768),U_13768,c_Product__Type_Osnd(U_13767,U_13768)),U_13769) = hAPP(c_Relation_ORange(U_13767,U_13768),U_13769),
    inference(clausify,[status(thm)],[f_3501_2]) ).

fof(f_3502_1,plain,
    ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product__singleton]) ).

fof(f_3502_2,plain,
    ! [U_13773,U_13772,U_13771,U_13770] : hAPP(c_Finite__Set_Ocard(tc_prod(U_13770,U_13771)),hAPP(hAPP(c_Product__Type_OSigma(U_13770,U_13771),hAPP(hAPP(c_Set_Oinsert(U_13770),U_13772),c_Orderings_Obot__class_Obot(tc_fun(U_13770,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_13771,tc_HOL_Obool),U_13770),U_13773))) = hAPP(c_Finite__Set_Ocard(U_13771),U_13773),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

cnf(f_3502_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_13770,U_13771)),hAPP(hAPP(c_Product__Type_OSigma(U_13770,U_13771),hAPP(hAPP(c_Set_Oinsert(U_13770),U_13772),c_Orderings_Obot__class_Obot(tc_fun(U_13770,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_13771,tc_HOL_Obool),U_13770),U_13773))) = hAPP(c_Finite__Set_Ocard(U_13771),U_13773),
    inference(clausify,[status(thm)],[f_3502_2]) ).

fof(f_3503_1,plain,
    ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),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)) )
        & ( 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_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2]) ).

fof(f_3503_2,plain,
    ! [U_13779,U_13778,U_13777,U_13776,U_13775,U_13774] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13777,U_13774),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13778),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13779),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13777,tc_HOL_Obool)),U_13778),U_13779)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13777,tc_HOL_Obool)),U_13778),U_13779))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13777,U_13774),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13778),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13779),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13774),U_13775),U_13776)) ),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

cnf(f_3503_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13777,tc_HOL_Obool)),U_13778),U_13779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13777,U_13774),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13778),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13779),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13774),U_13775),U_13776)) ),
    inference(clausify,[status(thm)],[f_3503_2]) ).

cnf(f_3503_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13777,U_13774),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13778),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))),hAPP(hAPP(c_Product__Type_OSigma(U_13777,U_13774),U_13779),hAPP(c_COMBK(tc_fun(U_13774,tc_HOL_Obool),U_13777),U_13776))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13777,tc_HOL_Obool)),U_13778),U_13779))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13774),U_13775),U_13776)) ),
    inference(clausify,[status(thm)],[f_3503_2]) ).

fof(f_3504_1,plain,
    ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset]) ).

fof(f_3504_2,plain,
    ! [U_13785,U_13784,U_13783,U_13782,U_13781,U_13780] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13781,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13780,U_13781,U_13782),U_13785)),U_13784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13780,U_13781),tc_HOL_Obool)),U_13782),hAPP(hAPP(c_Product__Type_OSigma(U_13780,U_13781),U_13783),hAPP(c_COMBK(tc_fun(U_13781,tc_HOL_Obool),U_13780),U_13784)))) ),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

cnf(f_3504_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13781,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13780,U_13781,U_13782),U_13785)),U_13784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13780,U_13781),tc_HOL_Obool)),U_13782),hAPP(hAPP(c_Product__Type_OSigma(U_13780,U_13781),U_13783),hAPP(c_COMBK(tc_fun(U_13781,tc_HOL_Obool),U_13780),U_13784)))) ),
    inference(clausify,[status(thm)],[f_3504_2]) ).

fof(f_3505_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2]) ).

fof(f_3505_2,plain,
    ! [U_13789,U_13788,U_13787,U_13786] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13787),U_13789))
      | U_13788 = c_Orderings_Obot__class_Obot(tc_fun(U_13786,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13786,U_13787)),hAPP(hAPP(c_Product__Type_OSigma(U_13786,U_13787),U_13788),hAPP(c_COMBK(tc_fun(U_13787,tc_HOL_Obool),U_13786),U_13789)))) ),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

cnf(f_3505_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13787),U_13789))
    | U_13788 = c_Orderings_Obot__class_Obot(tc_fun(U_13786,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13786,U_13787)),hAPP(hAPP(c_Product__Type_OSigma(U_13786,U_13787),U_13788),hAPP(c_COMBK(tc_fun(U_13787,tc_HOL_Obool),U_13786),U_13789)))) ),
    inference(clausify,[status(thm)],[f_3505_2]) ).

fof(f_3506_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1]) ).

fof(f_3506_2,plain,
    ! [U_13793,U_13792,U_13791,U_13790] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13790),U_13792))
      | U_13793 = c_Orderings_Obot__class_Obot(tc_fun(U_13791,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13790,U_13791)),hAPP(hAPP(c_Product__Type_OSigma(U_13790,U_13791),U_13792),hAPP(c_COMBK(tc_fun(U_13791,tc_HOL_Obool),U_13790),U_13793)))) ),
    inference(variable_rename,[status(thm)],[f_3506_1]) ).

cnf(f_3506_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13790),U_13792))
    | U_13793 = c_Orderings_Obot__class_Obot(tc_fun(U_13791,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13790,U_13791)),hAPP(hAPP(c_Product__Type_OSigma(U_13790,U_13791),U_13792),hAPP(c_COMBK(tc_fun(U_13791,tc_HOL_Obool),U_13790),U_13793)))) ),
    inference(clausify,[status(thm)],[f_3506_2]) ).

fof(f_3507_1,plain,
    ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).

fof(f_3507_2,plain,
    ! [U_13797,U_13796,U_13795,U_13794] : hAPP(c_Set_OCollect(tc_prod(U_13794,U_13795)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13794,U_13795,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13794,tc_fun(U_13795,tc_HOL_Obool),tc_fun(U_13795,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13795,tc_HOL_Obool),tc_fun(U_13795,tc_HOL_Obool)),U_13794),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13795)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13794),c_fconj),U_13796))),U_13797))) = hAPP(hAPP(c_Product__Type_OSigma(U_13794,U_13795),hAPP(c_Set_OCollect(U_13794),U_13796)),hAPP(c_COMBK(tc_fun(U_13795,tc_HOL_Obool),U_13794),hAPP(c_Set_OCollect(U_13795),U_13797))),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

cnf(f_3507_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_13794,U_13795)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13794,U_13795,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13794,tc_fun(U_13795,tc_HOL_Obool),tc_fun(U_13795,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13795,tc_HOL_Obool),tc_fun(U_13795,tc_HOL_Obool)),U_13794),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13795)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13794),c_fconj),U_13796))),U_13797))) = hAPP(hAPP(c_Product__Type_OSigma(U_13794,U_13795),hAPP(c_Set_OCollect(U_13794),U_13796)),hAPP(c_COMBK(tc_fun(U_13795,tc_HOL_Obool),U_13794),hAPP(c_Set_OCollect(U_13795),U_13797))),
    inference(clausify,[status(thm)],[f_3507_2]) ).

fof(f_3508_1,plain,
    ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(f_3508_2,plain,
    ! [U_13801,U_13800,U_13799,U_13798] : hAPP(c_Set_OCollect(tc_prod(U_13798,U_13799)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13798,U_13799,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13798,tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),U_13798),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13799)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13798),c_fconj),U_13800))),U_13801))) = hAPP(hAPP(c_Product__Type_OSigma(U_13798,U_13799),hAPP(c_Set_OCollect(U_13798),U_13800)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool),U_13798),c_Set_OCollect(U_13799)),U_13801)),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

cnf(f_3508_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_13798,U_13799)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13798,U_13799,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13798,tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),U_13798),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13799)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13798),c_fconj),U_13800))),U_13801))) = hAPP(hAPP(c_Product__Type_OSigma(U_13798,U_13799),hAPP(c_Set_OCollect(U_13798),U_13800)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool),U_13798),c_Set_OCollect(U_13799)),U_13801)),
    inference(clausify,[status(thm)],[f_3508_2]) ).

fof(f_3509_1,plain,
    ! [V_A_2,T_b,T_a,V_B_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2
        | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),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_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fst__image__times]) ).

fof(f_3509_2,plain,
    ! [U_13805,U_13804,U_13803,U_13802] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_13804,U_13803),U_13804,c_Product__Type_Ofst(U_13804,U_13803)),hAPP(hAPP(c_Product__Type_OSigma(U_13804,U_13803),U_13805),hAPP(c_COMBK(tc_fun(U_13803,tc_HOL_Obool),U_13804),U_13802))) = U_13805
        | U_13802 = c_Orderings_Obot__class_Obot(tc_fun(U_13803,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_13804,U_13803),U_13804,c_Product__Type_Ofst(U_13804,U_13803)),hAPP(hAPP(c_Product__Type_OSigma(U_13804,U_13803),U_13805),hAPP(c_COMBK(tc_fun(U_13803,tc_HOL_Obool),U_13804),U_13802))) = c_Orderings_Obot__class_Obot(tc_fun(U_13804,tc_HOL_Obool))
        | U_13802 != c_Orderings_Obot__class_Obot(tc_fun(U_13803,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

fof(f_3509_3,plain,
    ( ! [U_13813,U_13811,U_13809,U_13807] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13811,U_13809),U_13811,c_Product__Type_Ofst(U_13811,U_13809)),hAPP(hAPP(c_Product__Type_OSigma(U_13811,U_13809),U_13813),hAPP(c_COMBK(tc_fun(U_13809,tc_HOL_Obool),U_13811),U_13807))) = U_13813
        | U_13807 = c_Orderings_Obot__class_Obot(tc_fun(U_13809,tc_HOL_Obool)) )
    & ! [U_13812,U_13810,U_13808,U_13806] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13810,U_13808),U_13810,c_Product__Type_Ofst(U_13810,U_13808)),hAPP(hAPP(c_Product__Type_OSigma(U_13810,U_13808),U_13812),hAPP(c_COMBK(tc_fun(U_13808,tc_HOL_Obool),U_13810),U_13806))) = c_Orderings_Obot__class_Obot(tc_fun(U_13810,tc_HOL_Obool))
        | U_13806 != c_Orderings_Obot__class_Obot(tc_fun(U_13808,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3509_2]) ).

cnf(f_3509_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13810,U_13808),U_13810,c_Product__Type_Ofst(U_13810,U_13808)),hAPP(hAPP(c_Product__Type_OSigma(U_13810,U_13808),U_13812),hAPP(c_COMBK(tc_fun(U_13808,tc_HOL_Obool),U_13810),U_13806))) = c_Orderings_Obot__class_Obot(tc_fun(U_13810,tc_HOL_Obool))
    | U_13806 != c_Orderings_Obot__class_Obot(tc_fun(U_13808,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3509_3]) ).

cnf(f_3509_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13811,U_13809),U_13811,c_Product__Type_Ofst(U_13811,U_13809)),hAPP(hAPP(c_Product__Type_OSigma(U_13811,U_13809),U_13813),hAPP(c_COMBK(tc_fun(U_13809,tc_HOL_Obool),U_13811),U_13807))) = U_13813
    | U_13807 = c_Orderings_Obot__class_Obot(tc_fun(U_13809,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3509_3]) ).

fof(f_3510_1,plain,
    ! [V_B_2,T_b,T_a,V_A_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),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_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_snd__image__times]) ).

fof(f_3510_2,plain,
    ! [U_13817,U_13816,U_13815,U_13814] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_13815,U_13816),U_13816,c_Product__Type_Osnd(U_13815,U_13816)),hAPP(hAPP(c_Product__Type_OSigma(U_13815,U_13816),U_13814),hAPP(c_COMBK(tc_fun(U_13816,tc_HOL_Obool),U_13815),U_13817))) = U_13817
        | U_13814 = c_Orderings_Obot__class_Obot(tc_fun(U_13815,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_13815,U_13816),U_13816,c_Product__Type_Osnd(U_13815,U_13816)),hAPP(hAPP(c_Product__Type_OSigma(U_13815,U_13816),U_13814),hAPP(c_COMBK(tc_fun(U_13816,tc_HOL_Obool),U_13815),U_13817))) = c_Orderings_Obot__class_Obot(tc_fun(U_13816,tc_HOL_Obool))
        | U_13814 != c_Orderings_Obot__class_Obot(tc_fun(U_13815,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

fof(f_3510_3,plain,
    ( ! [U_13825,U_13823,U_13821,U_13819] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13821,U_13823),U_13823,c_Product__Type_Osnd(U_13821,U_13823)),hAPP(hAPP(c_Product__Type_OSigma(U_13821,U_13823),U_13819),hAPP(c_COMBK(tc_fun(U_13823,tc_HOL_Obool),U_13821),U_13825))) = U_13825
        | U_13819 = c_Orderings_Obot__class_Obot(tc_fun(U_13821,tc_HOL_Obool)) )
    & ! [U_13824,U_13822,U_13820,U_13818] :
        ( hAPP(c_Set_Oimage(tc_prod(U_13820,U_13822),U_13822,c_Product__Type_Osnd(U_13820,U_13822)),hAPP(hAPP(c_Product__Type_OSigma(U_13820,U_13822),U_13818),hAPP(c_COMBK(tc_fun(U_13822,tc_HOL_Obool),U_13820),U_13824))) = c_Orderings_Obot__class_Obot(tc_fun(U_13822,tc_HOL_Obool))
        | U_13818 != c_Orderings_Obot__class_Obot(tc_fun(U_13820,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3510_2]) ).

cnf(f_3510_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13820,U_13822),U_13822,c_Product__Type_Osnd(U_13820,U_13822)),hAPP(hAPP(c_Product__Type_OSigma(U_13820,U_13822),U_13818),hAPP(c_COMBK(tc_fun(U_13822,tc_HOL_Obool),U_13820),U_13824))) = c_Orderings_Obot__class_Obot(tc_fun(U_13822,tc_HOL_Obool))
    | U_13818 != c_Orderings_Obot__class_Obot(tc_fun(U_13820,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3510_3]) ).

cnf(f_3510_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_13821,U_13823),U_13823,c_Product__Type_Osnd(U_13821,U_13823)),hAPP(hAPP(c_Product__Type_OSigma(U_13821,U_13823),U_13819),hAPP(c_COMBK(tc_fun(U_13823,tc_HOL_Obool),U_13821),U_13825))) = U_13825
    | U_13819 = c_Orderings_Obot__class_Obot(tc_fun(U_13821,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3510_3]) ).

fof(f_3511_1,plain,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__iff]) ).

fof(f_3511_2,plain,
    ! [U_13831,U_13830,U_13829,U_13828] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13828),U_13829),hAPP(c_Relation_ORange(U_13830,U_13828),U_13831)))
        | ! [U_13827] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13830,U_13828)),hAPP(hAPP(c_Product__Type_OPair(U_13830,U_13828),U_13827),U_13829)),U_13831)) )
      & ( ? [U_13826] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13830,U_13828)),hAPP(hAPP(c_Product__Type_OPair(U_13830,U_13828),U_13826),U_13829)),U_13831))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13828),U_13829),hAPP(c_Relation_ORange(U_13830,U_13828),U_13831))) ) ),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

fof(f_3511_3,plain,
    ( ! [U_13839,U_13837,U_13835,U_13833] :
        ( hBOOL(hAPP(hAPP(c_member(U_13833),U_13835),hAPP(c_Relation_ORange(U_13837,U_13833),U_13839)))
        | ! [U_13827] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13837,U_13833)),hAPP(hAPP(c_Product__Type_OPair(U_13837,U_13833),U_13827),U_13835)),U_13839)) )
    & ! [U_13838,U_13836,U_13834,U_13832] :
        ( ? [U_13826] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13836,U_13832)),hAPP(hAPP(c_Product__Type_OPair(U_13836,U_13832),U_13826),U_13834)),U_13838))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Relation_ORange(U_13836,U_13832),U_13838))) ) ),
    inference(miniscope,[status(thm)],[f_3511_2]) ).

fof(f_3511_4,plain,
    ( ! [U_13839,U_13837,U_13835,U_13833] :
        ( hBOOL(hAPP(hAPP(c_member(U_13833),U_13835),hAPP(c_Relation_ORange(U_13837,U_13833),U_13839)))
        | ! [U_13827] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13837,U_13833)),hAPP(hAPP(c_Product__Type_OPair(U_13837,U_13833),U_13827),U_13835)),U_13839)) )
    & ! [U_13838,U_13836,U_13834,U_13832] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13836,U_13832)),hAPP(hAPP(c_Product__Type_OPair(U_13836,U_13832),sK324(U_13838,U_13836,U_13834,U_13832)),U_13834)),U_13838))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Relation_ORange(U_13836,U_13832),U_13838))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_13826,sK324(U_13838,U_13836,U_13834,U_13832))],[f_3511_3]) ).

cnf(f_3511_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13836,U_13832)),hAPP(hAPP(c_Product__Type_OPair(U_13836,U_13832),sK324(U_13838,U_13836,U_13834,U_13832)),U_13834)),U_13838))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Relation_ORange(U_13836,U_13832),U_13838))) ),
    inference(clausify,[status(thm)],[f_3511_4]) ).

cnf(f_3511_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13833),U_13835),hAPP(c_Relation_ORange(U_13837,U_13833),U_13839)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13837,U_13833)),hAPP(hAPP(c_Product__Type_OPair(U_13837,U_13833),U_13827),U_13835)),U_13839)) ),
    inference(clausify,[status(thm)],[f_3511_4]) ).

fof(f_3512_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__insert]) ).

fof(f_3512_2,plain,
    ! [U_13844,U_13843,U_13842,U_13841,U_13840] : hAPP(c_Relation_ORange(U_13840,U_13841),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13840,U_13841)),hAPP(hAPP(c_Product__Type_OPair(U_13840,U_13841),U_13842),U_13843)),U_13844)) = hAPP(hAPP(c_Set_Oinsert(U_13841),U_13843),hAPP(c_Relation_ORange(U_13840,U_13841),U_13844)),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

cnf(f_3512_3,plain,
    hAPP(c_Relation_ORange(U_13840,U_13841),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13840,U_13841)),hAPP(hAPP(c_Product__Type_OPair(U_13840,U_13841),U_13842),U_13843)),U_13844)) = hAPP(hAPP(c_Set_Oinsert(U_13841),U_13843),hAPP(c_Relation_ORange(U_13840,U_13841),U_13844)),
    inference(clausify,[status(thm)],[f_3512_2]) ).

fof(f_3513_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Int__subset]) ).

fof(f_3513_2,plain,
    ! [U_13848,U_13847,U_13846,U_13845] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13845,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13846,U_13845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13846,U_13845),tc_HOL_Obool)),U_13847),U_13848))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13845,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13846,U_13845),U_13847)),hAPP(c_Relation_ORange(U_13846,U_13845),U_13848)))),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

cnf(f_3513_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13845,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13846,U_13845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13846,U_13845),tc_HOL_Obool)),U_13847),U_13848))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13845,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13846,U_13845),U_13847)),hAPP(c_Relation_ORange(U_13846,U_13845),U_13848)))),
    inference(clausify,[status(thm)],[f_3513_2]) ).

fof(f_3514_1,plain,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_insert__times__insert]) ).

fof(f_3514_2,plain,
    ! [U_13854,U_13853,U_13852,U_13851,U_13850,U_13849] : hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),hAPP(hAPP(c_Set_Oinsert(U_13849),U_13851),U_13852)),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),hAPP(hAPP(c_Set_Oinsert(U_13850),U_13853),U_13854))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13849,U_13850)),hAPP(hAPP(c_Product__Type_OPair(U_13849,U_13850),U_13851),U_13853)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13849,U_13850),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),U_13852),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),hAPP(hAPP(c_Set_Oinsert(U_13850),U_13853),U_13854)))),hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),hAPP(hAPP(c_Set_Oinsert(U_13849),U_13851),U_13852)),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),U_13854)))),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

cnf(f_3514_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),hAPP(hAPP(c_Set_Oinsert(U_13849),U_13851),U_13852)),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),hAPP(hAPP(c_Set_Oinsert(U_13850),U_13853),U_13854))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13849,U_13850)),hAPP(hAPP(c_Product__Type_OPair(U_13849,U_13850),U_13851),U_13853)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13849,U_13850),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),U_13852),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),hAPP(hAPP(c_Set_Oinsert(U_13850),U_13853),U_13854)))),hAPP(hAPP(c_Product__Type_OSigma(U_13849,U_13850),hAPP(hAPP(c_Set_Oinsert(U_13849),U_13851),U_13852)),hAPP(c_COMBK(tc_fun(U_13850,tc_HOL_Obool),U_13849),U_13854)))),
    inference(clausify,[status(thm)],[f_3514_2]) ).

fof(f_3515_1,plain,
    ! [V_X_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__equiv__class]) ).

fof(f_3515_2,plain,
    ! [U_13858,U_13857,U_13856,U_13855] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13855),U_13858))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13855,tc_HOL_Obool)),U_13858),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13855),U_13856),U_13857)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13855,U_13855),tc_HOL_Obool)),U_13857),hAPP(hAPP(c_Product__Type_OSigma(U_13855,U_13855),U_13856),hAPP(c_COMBK(tc_fun(U_13855,tc_HOL_Obool),U_13855),U_13856))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13855),U_13856)) ),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

cnf(f_3515_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13855),U_13858))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13855,tc_HOL_Obool)),U_13858),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13855),U_13856),U_13857)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13855,U_13855),tc_HOL_Obool)),U_13857),hAPP(hAPP(c_Product__Type_OSigma(U_13855,U_13855),U_13856),hAPP(c_COMBK(tc_fun(U_13855,tc_HOL_Obool),U_13855),U_13856))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13855),U_13856)) ),
    inference(clausify,[status(thm)],[f_3515_2]) ).

fof(f_3516_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Times]) ).

fof(f_3516_2,plain,
    ! [U_13864,U_13863,U_13862,U_13861,U_13860,U_13859] : hAPP(c_Set_Ovimage(U_13859,tc_prod(U_13860,U_13861),U_13862),hAPP(hAPP(c_Product__Type_OSigma(U_13860,U_13861),U_13863),hAPP(c_COMBK(tc_fun(U_13861,tc_HOL_Obool),U_13860),U_13864))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13859,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13859,U_13860,hAPP(c_Fun_Ocomp(tc_prod(U_13860,U_13861),U_13860,U_13859,c_Product__Type_Ofst(U_13860,U_13861)),U_13862)),U_13863)),hAPP(c_Set_Ovimage(U_13859,U_13861,hAPP(c_Fun_Ocomp(tc_prod(U_13860,U_13861),U_13861,U_13859,c_Product__Type_Osnd(U_13860,U_13861)),U_13862)),U_13864)),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

cnf(f_3516_3,plain,
    hAPP(c_Set_Ovimage(U_13859,tc_prod(U_13860,U_13861),U_13862),hAPP(hAPP(c_Product__Type_OSigma(U_13860,U_13861),U_13863),hAPP(c_COMBK(tc_fun(U_13861,tc_HOL_Obool),U_13860),U_13864))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13859,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13859,U_13860,hAPP(c_Fun_Ocomp(tc_prod(U_13860,U_13861),U_13860,U_13859,c_Product__Type_Ofst(U_13860,U_13861)),U_13862)),U_13863)),hAPP(c_Set_Ovimage(U_13859,U_13861,hAPP(c_Fun_Ocomp(tc_prod(U_13860,U_13861),U_13861,U_13859,c_Product__Type_Osnd(U_13860,U_13861)),U_13862)),U_13864)),
    inference(clausify,[status(thm)],[f_3516_2]) ).

fof(f_3517_1,plain,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),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(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))),
    inference(fof_nnf,[status(thm)],[fact_UN__Times__distrib]) ).

fof(f_3517_2,plain,
    ! [U_13872,U_13871,U_13870,U_13869,U_13868,U_13867,U_13866,U_13865] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_13865,U_13866),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13865,U_13866),U_13869),hAPP(c_COMBK(tc_fun(U_13866,tc_HOL_Obool),U_13865),U_13870))),hAPP(c_Product__Type_Oprod_Oprod__case(U_13865,U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_13865,tc_fun(U_13866,tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool))),tc_fun(U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),tc_fun(tc_fun(U_13866,tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool))),tc_fun(U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool))),U_13865),c_COMBB(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool),U_13866)),hAPP(hAPP(c_COMBB(tc_fun(U_13867,tc_HOL_Obool),tc_fun(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),U_13865),c_Product__Type_OSigma(U_13867,U_13868)),U_13871))),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),U_13866),c_COMBK(tc_fun(U_13868,tc_HOL_Obool),U_13867)),U_13872)))) = hAPP(hAPP(c_Product__Type_OSigma(U_13867,U_13868),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13865,tc_fun(U_13867,tc_HOL_Obool)),U_13869),U_13871)),hAPP(c_COMBK(tc_fun(U_13868,tc_HOL_Obool),U_13867),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13866,tc_fun(U_13868,tc_HOL_Obool)),U_13870),U_13872))),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

cnf(f_3517_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_13865,U_13866),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13865,U_13866),U_13869),hAPP(c_COMBK(tc_fun(U_13866,tc_HOL_Obool),U_13865),U_13870))),hAPP(c_Product__Type_Oprod_Oprod__case(U_13865,U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_13865,tc_fun(U_13866,tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool))),tc_fun(U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),tc_fun(tc_fun(U_13866,tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool))),tc_fun(U_13866,tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool))),U_13865),c_COMBB(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool),U_13866)),hAPP(hAPP(c_COMBB(tc_fun(U_13867,tc_HOL_Obool),tc_fun(tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),tc_fun(tc_prod(U_13867,U_13868),tc_HOL_Obool)),U_13865),c_Product__Type_OSigma(U_13867,U_13868)),U_13871))),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_fun(U_13867,tc_fun(U_13868,tc_HOL_Obool)),U_13866),c_COMBK(tc_fun(U_13868,tc_HOL_Obool),U_13867)),U_13872)))) = hAPP(hAPP(c_Product__Type_OSigma(U_13867,U_13868),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13865,tc_fun(U_13867,tc_HOL_Obool)),U_13869),U_13871)),hAPP(c_COMBK(tc_fun(U_13868,tc_HOL_Obool),U_13867),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13866,tc_fun(U_13868,tc_HOL_Obool)),U_13870),U_13872))),
    inference(clausify,[status(thm)],[f_3517_2]) ).

fof(f_3518_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Sigma__def]) ).

fof(f_3518_2,plain,
    ! [U_13876,U_13875,U_13874,U_13873] : hAPP(hAPP(c_Product__Type_OSigma(U_13873,U_13874),U_13875),U_13876) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13873,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13875),hAPP(hAPP(c_COMBS(U_13873,tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13873),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13876)),hAPP(hAPP(c_COMBC(U_13873,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13873),c_COMBC(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_prod(U_13873,U_13874)),tc_fun(U_13874,tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13873),hAPP(c_COMBB(tc_prod(U_13873,U_13874),tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13874),c_Set_Oinsert(tc_prod(U_13873,U_13874)))),c_Product__Type_OPair(U_13873,U_13874)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

cnf(f_3518_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_13873,U_13874),U_13875),U_13876) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13873,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13875),hAPP(hAPP(c_COMBS(U_13873,tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_HOL_Obool),tc_fun(tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13873),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13876)),hAPP(hAPP(c_COMBC(U_13873,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13873),c_COMBC(U_13874,tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13874,tc_prod(U_13873,U_13874)),tc_fun(U_13874,tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))),U_13873),hAPP(c_COMBB(tc_prod(U_13873,U_13874),tc_fun(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool),tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool)),U_13874),c_Set_Oinsert(tc_prod(U_13873,U_13874)))),c_Product__Type_OPair(U_13873,U_13874)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13873,U_13874),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3518_2]) ).

fof(f_3519_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__quotient]) ).

fof(f_3519_2,plain,
    ! [U_13879,U_13878,U_13877] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13877,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13877),U_13878),U_13879)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13877,U_13877),tc_HOL_Obool)),U_13879),hAPP(hAPP(c_Product__Type_OSigma(U_13877,U_13877),U_13878),hAPP(c_COMBK(tc_fun(U_13877,tc_HOL_Obool),U_13877),U_13878))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13877),U_13878)) ),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

cnf(f_3519_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13877,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13877),U_13878),U_13879)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13877,U_13877),tc_HOL_Obool)),U_13879),hAPP(hAPP(c_Product__Type_OSigma(U_13877,U_13877),U_13878),hAPP(c_COMBK(tc_fun(U_13877,tc_HOL_Obool),U_13877),U_13878))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13877),U_13878)) ),
    inference(clausify,[status(thm)],[f_3519_2]) ).

fof(f_3520_1,plain,
    ! [V_R_2,T_a] :
      ( c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2))
      | ~ c_Wellfounded_Owf(T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__in__rel]) ).

fof(f_3520_2,plain,
    ! [U_13881,U_13880] :
      ( c_Wellfounded_OwfP(U_13880,c_FunDef_Oin__rel(U_13880,U_13880,U_13881))
      | ~ c_Wellfounded_Owf(U_13880,U_13881) ),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

cnf(f_3520_3,plain,
    ( c_Wellfounded_OwfP(U_13880,c_FunDef_Oin__rel(U_13880,U_13880,U_13881))
    | ~ c_Wellfounded_Owf(U_13880,U_13881) ),
    inference(clausify,[status(thm)],[f_3520_2]) ).

fof(f_3521_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
        | ~ c_Wellfounded_Owf(T_a,V_r_2) )
      & ( c_Wellfounded_Owf(T_a,V_r_2)
        | ~ c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq]) ).

fof(f_3521_2,plain,
    ! [U_13883,U_13882] :
      ( ( c_Wellfounded_OwfP(U_13882,hAPP(hAPP(c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),U_13882),c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_prod(U_13882,U_13882)),tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),U_13882),hAPP(c_COMBB(tc_prod(U_13882,U_13882),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool),U_13882),c_member(tc_prod(U_13882,U_13882)))),c_Product__Type_OPair(U_13882,U_13882)))),U_13883))
        | ~ c_Wellfounded_Owf(U_13882,U_13883) )
      & ( c_Wellfounded_Owf(U_13882,U_13883)
        | ~ c_Wellfounded_OwfP(U_13882,hAPP(hAPP(c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),U_13882),c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_prod(U_13882,U_13882)),tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),U_13882),hAPP(c_COMBB(tc_prod(U_13882,U_13882),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool),U_13882),c_member(tc_prod(U_13882,U_13882)))),c_Product__Type_OPair(U_13882,U_13882)))),U_13883)) ) ),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

fof(f_3521_3,plain,
    ( ! [U_13887,U_13885] :
        ( c_Wellfounded_OwfP(U_13885,hAPP(hAPP(c_COMBC(U_13885,tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_fun(U_13885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13885,tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_fun(U_13885,tc_HOL_Obool)),U_13885),c_COMBC(U_13885,tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13885,tc_prod(U_13885,U_13885)),tc_fun(U_13885,tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),U_13885),hAPP(c_COMBB(tc_prod(U_13885,U_13885),tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool),U_13885),c_member(tc_prod(U_13885,U_13885)))),c_Product__Type_OPair(U_13885,U_13885)))),U_13887))
        | ~ c_Wellfounded_Owf(U_13885,U_13887) )
    & ! [U_13886,U_13884] :
        ( c_Wellfounded_Owf(U_13884,U_13886)
        | ~ c_Wellfounded_OwfP(U_13884,hAPP(hAPP(c_COMBC(U_13884,tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_fun(U_13884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13884,tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_fun(U_13884,tc_HOL_Obool)),U_13884),c_COMBC(U_13884,tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13884,tc_prod(U_13884,U_13884)),tc_fun(U_13884,tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),U_13884),hAPP(c_COMBB(tc_prod(U_13884,U_13884),tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool),U_13884),c_member(tc_prod(U_13884,U_13884)))),c_Product__Type_OPair(U_13884,U_13884)))),U_13886)) ) ),
    inference(miniscope,[status(thm)],[f_3521_2]) ).

cnf(f_3521_4,plain,
    ( c_Wellfounded_Owf(U_13884,U_13886)
    | ~ c_Wellfounded_OwfP(U_13884,hAPP(hAPP(c_COMBC(U_13884,tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_fun(U_13884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13884,tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_fun(U_13884,tc_HOL_Obool)),U_13884),c_COMBC(U_13884,tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13884,tc_prod(U_13884,U_13884)),tc_fun(U_13884,tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool)),U_13884),hAPP(c_COMBB(tc_prod(U_13884,U_13884),tc_fun(tc_fun(tc_prod(U_13884,U_13884),tc_HOL_Obool),tc_HOL_Obool),U_13884),c_member(tc_prod(U_13884,U_13884)))),c_Product__Type_OPair(U_13884,U_13884)))),U_13886)) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

cnf(f_3521_5,plain,
    ( c_Wellfounded_OwfP(U_13885,hAPP(hAPP(c_COMBC(U_13885,tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_fun(U_13885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13885,tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_fun(U_13885,tc_HOL_Obool)),U_13885),c_COMBC(U_13885,tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13885,tc_prod(U_13885,U_13885)),tc_fun(U_13885,tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool)),U_13885),hAPP(c_COMBB(tc_prod(U_13885,U_13885),tc_fun(tc_fun(tc_prod(U_13885,U_13885),tc_HOL_Obool),tc_HOL_Obool),U_13885),c_member(tc_prod(U_13885,U_13885)))),c_Product__Type_OPair(U_13885,U_13885)))),U_13887))
    | ~ c_Wellfounded_Owf(U_13885,U_13887) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

fof(f_3522_1,plain,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),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_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),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_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),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))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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)))))))
      | ~ c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))
      | ~ class_Rings_Osemiring__0(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj]) ).

fof(f_3522_2,plain,
    ! [U_13894,U_13893,U_13892,U_13891,U_13890,U_13889,U_13888] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13888),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13889,U_13888),U_13891),U_13893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13890,U_13888),U_13892),U_13894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13888,U_13888),c_Fun_Oid(U_13888)),hAPP(c_Set_OCollect(U_13888),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_HOL_Obool),tc_HOL_Obool,U_13888),c_HOL_OEx(U_13889)),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_HOL_Obool),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_HOL_Obool),tc_HOL_Obool,U_13889),c_HOL_OEx(U_13890))),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),tc_fun(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),U_13888),c_COMBS(U_13889,tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13889,tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),U_13889),c_COMBS(U_13890,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13889),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13890),c_fconj))),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13889,tc_fun(U_13890,U_13888)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool)),tc_fun(tc_fun(U_13889,tc_fun(U_13890,U_13888)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),U_13888),c_COMBB(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool),U_13889)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,tc_HOL_Obool),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool)),U_13888),c_COMBB(U_13888,tc_HOL_Obool,U_13890)),c_fequal))),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,U_13888),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),U_13889),c_COMBB(U_13888,U_13888,U_13890)),hAPP(hAPP(c_COMBB(U_13888,tc_fun(U_13888,U_13888),U_13889),c_Groups_Otimes__class_Otimes(U_13888)),U_13891))),U_13892)))))),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),U_13889),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13890)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13889),c_fconj),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13889,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13889)),U_13893)))),hAPP(hAPP(c_COMBC(U_13890,tc_fun(U_13890,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13890)),U_13894)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_13889,U_13890),U_13888,hAPP(c_Product__Type_Oprod_Oprod__case(U_13889,U_13890,U_13888),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,U_13888),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),U_13889),c_COMBB(U_13888,U_13888,U_13890)),hAPP(hAPP(c_COMBB(U_13888,tc_fun(U_13888,U_13888),U_13889),c_Groups_Otimes__class_Otimes(U_13888)),U_13891))),U_13892)),hAPP(hAPP(c_Product__Type_OSigma(U_13889,U_13890),U_13893),hAPP(c_COMBK(tc_fun(U_13890,tc_HOL_Obool),U_13889),U_13894)))
      | ~ class_Rings_Osemiring__0(U_13888) ),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

cnf(f_3522_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13888),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13889,U_13888),U_13891),U_13893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13890,U_13888),U_13892),U_13894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13888,U_13888),c_Fun_Oid(U_13888)),hAPP(c_Set_OCollect(U_13888),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_HOL_Obool),tc_HOL_Obool,U_13888),c_HOL_OEx(U_13889)),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_HOL_Obool),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_HOL_Obool),tc_HOL_Obool,U_13889),c_HOL_OEx(U_13890))),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),tc_fun(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),U_13888),c_COMBS(U_13889,tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13889,tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool))),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),U_13889),c_COMBS(U_13890,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool)),tc_fun(U_13889,tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13888),hAPP(c_COMBB(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13889),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13890),c_fconj))),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13889,tc_fun(U_13890,U_13888)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool)),tc_fun(tc_fun(U_13889,tc_fun(U_13890,U_13888)),tc_fun(U_13889,tc_fun(U_13890,tc_HOL_Obool))),U_13888),c_COMBB(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool),U_13889)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,tc_HOL_Obool),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,tc_HOL_Obool)),U_13888),c_COMBB(U_13888,tc_HOL_Obool,U_13890)),c_fequal))),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,U_13888),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),U_13889),c_COMBB(U_13888,U_13888,U_13890)),hAPP(hAPP(c_COMBB(U_13888,tc_fun(U_13888,U_13888),U_13889),c_Groups_Otimes__class_Otimes(U_13888)),U_13891))),U_13892)))))),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13890,tc_HOL_Obool),tc_fun(U_13890,tc_HOL_Obool)),U_13889),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13890)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13889),c_fconj),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13889,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13889)),U_13893)))),hAPP(hAPP(c_COMBC(U_13890,tc_fun(U_13890,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13890)),U_13894)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_13889,U_13890),U_13888,hAPP(c_Product__Type_Oprod_Oprod__case(U_13889,U_13890,U_13888),hAPP(hAPP(c_COMBC(U_13889,tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),hAPP(hAPP(c_COMBB(tc_fun(U_13888,U_13888),tc_fun(tc_fun(U_13890,U_13888),tc_fun(U_13890,U_13888)),U_13889),c_COMBB(U_13888,U_13888,U_13890)),hAPP(hAPP(c_COMBB(U_13888,tc_fun(U_13888,U_13888),U_13889),c_Groups_Otimes__class_Otimes(U_13888)),U_13891))),U_13892)),hAPP(hAPP(c_Product__Type_OSigma(U_13889,U_13890),U_13893),hAPP(c_COMBK(tc_fun(U_13890,tc_HOL_Obool),U_13889),U_13894)))
    | ~ class_Rings_Osemiring__0(U_13888) ),
    inference(clausify,[status(thm)],[f_3522_2]) ).

fof(f_3523_1,plain,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq]) ).

fof(f_3523_2,plain,
    ! [U_13898,U_13897,U_13896,U_13895] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13895,U_13896,hAPP(hAPP(c_COMBC(U_13895,tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_fun(U_13896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13896,tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_fun(U_13896,tc_HOL_Obool)),U_13895),c_COMBC(U_13896,tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13896,tc_prod(U_13895,U_13896)),tc_fun(U_13896,tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),U_13895),hAPP(c_COMBB(tc_prod(U_13895,U_13896),tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool),U_13896),c_member(tc_prod(U_13895,U_13896)))),c_Product__Type_OPair(U_13895,U_13896)))),U_13897)),U_13898))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13896),U_13898),hAPP(c_Relation_ORange(U_13895,U_13896),U_13897))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13896),U_13898),hAPP(c_Relation_ORange(U_13895,U_13896),U_13897)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13895,U_13896,hAPP(hAPP(c_COMBC(U_13895,tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_fun(U_13896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13896,tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_fun(U_13896,tc_HOL_Obool)),U_13895),c_COMBC(U_13896,tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13896,tc_prod(U_13895,U_13896)),tc_fun(U_13896,tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool)),U_13895),hAPP(c_COMBB(tc_prod(U_13895,U_13896),tc_fun(tc_fun(tc_prod(U_13895,U_13896),tc_HOL_Obool),tc_HOL_Obool),U_13896),c_member(tc_prod(U_13895,U_13896)))),c_Product__Type_OPair(U_13895,U_13896)))),U_13897)),U_13898)) ) ),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

fof(f_3523_3,plain,
    ( ! [U_13906,U_13904,U_13902,U_13900] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_13900,U_13902,hAPP(hAPP(c_COMBC(U_13900,tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_fun(U_13902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13902,tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_fun(U_13902,tc_HOL_Obool)),U_13900),c_COMBC(U_13902,tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13902,tc_prod(U_13900,U_13902)),tc_fun(U_13902,tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),U_13900),hAPP(c_COMBB(tc_prod(U_13900,U_13902),tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool),U_13902),c_member(tc_prod(U_13900,U_13902)))),c_Product__Type_OPair(U_13900,U_13902)))),U_13904)),U_13906))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13902),U_13906),hAPP(c_Relation_ORange(U_13900,U_13902),U_13904))) )
    & ! [U_13905,U_13903,U_13901,U_13899] :
        ( hBOOL(hAPP(hAPP(c_member(U_13901),U_13905),hAPP(c_Relation_ORange(U_13899,U_13901),U_13903)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13899,U_13901,hAPP(hAPP(c_COMBC(U_13899,tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool)),U_13899),c_COMBC(U_13901,tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_prod(U_13899,U_13901)),tc_fun(U_13901,tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),U_13899),hAPP(c_COMBB(tc_prod(U_13899,U_13901),tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool),U_13901),c_member(tc_prod(U_13899,U_13901)))),c_Product__Type_OPair(U_13899,U_13901)))),U_13903)),U_13905)) ) ),
    inference(miniscope,[status(thm)],[f_3523_2]) ).

cnf(f_3523_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13901),U_13905),hAPP(c_Relation_ORange(U_13899,U_13901),U_13903)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13899,U_13901,hAPP(hAPP(c_COMBC(U_13899,tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_fun(U_13901,tc_HOL_Obool)),U_13899),c_COMBC(U_13901,tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13901,tc_prod(U_13899,U_13901)),tc_fun(U_13901,tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool)),U_13899),hAPP(c_COMBB(tc_prod(U_13899,U_13901),tc_fun(tc_fun(tc_prod(U_13899,U_13901),tc_HOL_Obool),tc_HOL_Obool),U_13901),c_member(tc_prod(U_13899,U_13901)))),c_Product__Type_OPair(U_13899,U_13901)))),U_13903)),U_13905)) ),
    inference(clausify,[status(thm)],[f_3523_3]) ).

cnf(f_3523_5,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13900,U_13902,hAPP(hAPP(c_COMBC(U_13900,tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_fun(U_13902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13902,tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_fun(U_13902,tc_HOL_Obool)),U_13900),c_COMBC(U_13902,tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13902,tc_prod(U_13900,U_13902)),tc_fun(U_13902,tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool)),U_13900),hAPP(c_COMBB(tc_prod(U_13900,U_13902),tc_fun(tc_fun(tc_prod(U_13900,U_13902),tc_HOL_Obool),tc_HOL_Obool),U_13902),c_member(tc_prod(U_13900,U_13902)))),c_Product__Type_OPair(U_13900,U_13902)))),U_13904)),U_13906))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13902),U_13906),hAPP(c_Relation_ORange(U_13900,U_13902),U_13904))) ),
    inference(clausify,[status(thm)],[f_3523_3]) ).

fof(f_3524_1,plain,
    ! [V_A_2,V_I_2,T_b,T_a] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Ex__inj__on__UNION__Sigma]) ).

fof(f_3524_2,plain,
    ! [U_13911,U_13910,U_13909,U_13908] :
    ? [U_13907] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13909,U_13908),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13908,tc_prod(U_13909,U_13908),U_13907),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911))),hAPP(hAPP(c_Product__Type_OSigma(U_13909,U_13908),U_13910),U_13911)))
      & c_Fun_Oinj__on(U_13908,tc_prod(U_13909,U_13908),U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911)) ),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

fof(f_3524_3,plain,
    ! [U_13911,U_13910,U_13909,U_13908] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13909,U_13908),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13908,tc_prod(U_13909,U_13908),sK325(U_13911,U_13910,U_13909,U_13908)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911))),hAPP(hAPP(c_Product__Type_OSigma(U_13909,U_13908),U_13910),U_13911)))
      & c_Fun_Oinj__on(U_13908,tc_prod(U_13909,U_13908),sK325(U_13911,U_13910,U_13909,U_13908),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_13907,sK325(U_13911,U_13910,U_13909,U_13908))],[f_3524_2]) ).

cnf(f_3524_4,plain,
    c_Fun_Oinj__on(U_13908,tc_prod(U_13909,U_13908),sK325(U_13911,U_13910,U_13909,U_13908),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911)),
    inference(clausify,[status(thm)],[f_3524_3]) ).

cnf(f_3524_5,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13909,U_13908),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13908,tc_prod(U_13909,U_13908),sK325(U_13911,U_13910,U_13909,U_13908)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13908,tc_HOL_Obool)),U_13910),U_13911))),hAPP(hAPP(c_Product__Type_OSigma(U_13909,U_13908),U_13910),U_13911))),
    inference(clausify,[status(thm)],[f_3524_3]) ).

fof(f_3525_1,plain,
    ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,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_3525_2,plain,
    ! [U_13916,U_13915,U_13914,U_13913,U_13912] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_13915,U_13916,U_13912),U_13914))
      | ~ hBOOL(hAPP(hAPP(U_13912,U_13913),U_13914)) ),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

cnf(f_3525_3,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13915,U_13916,U_13912),U_13914))
    | ~ hBOOL(hAPP(hAPP(U_13912,U_13913),U_13914)) ),
    inference(clausify,[status(thm)],[f_3525_2]) ).

fof(f_3526_1,plain,
    ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__id]) ).

fof(f_3526_2,plain,
    ! [U_13918,U_13917] : hAPP(c_Set_Oimage(U_13917,U_13917,c_Fun_Oid(U_13917)),U_13918) = U_13918,
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

cnf(f_3526_3,plain,
    hAPP(c_Set_Oimage(U_13917,U_13917,c_Fun_Oid(U_13917)),U_13918) = U_13918,
    inference(clausify,[status(thm)],[f_3526_2]) ).

fof(f_3527_1,plain,
    ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_apfst__id]) ).

fof(f_3527_2,plain,
    ! [U_13920,U_13919] : c_Product__Type_Oapfst(U_13919,U_13919,U_13920,c_Fun_Oid(U_13919)) = c_Fun_Oid(tc_prod(U_13919,U_13920)),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

cnf(f_3527_3,plain,
    c_Product__Type_Oapfst(U_13919,U_13919,U_13920,c_Fun_Oid(U_13919)) = c_Fun_Oid(tc_prod(U_13919,U_13920)),
    inference(clausify,[status(thm)],[f_3527_2]) ).

fof(f_3528_1,plain,
    ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__id]) ).

fof(f_3528_2,plain,
    ! [U_13922,U_13921] : c_Product__Type_Oapsnd(U_13921,U_13921,U_13922,c_Fun_Oid(U_13921)) = c_Fun_Oid(tc_prod(U_13922,U_13921)),
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

cnf(f_3528_3,plain,
    c_Product__Type_Oapsnd(U_13921,U_13921,U_13922,c_Fun_Oid(U_13921)) = c_Fun_Oid(tc_prod(U_13922,U_13921)),
    inference(clausify,[status(thm)],[f_3528_2]) ).

fof(f_3529_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__id]) ).

fof(f_3529_2,plain,
    ! [U_13924,U_13923] : hAPP(c_Set_Ovimage(U_13923,U_13923,c_Fun_Oid(U_13923)),U_13924) = U_13924,
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

cnf(f_3529_3,plain,
    hAPP(c_Set_Ovimage(U_13923,U_13923,c_Fun_Oid(U_13923)),U_13924) = U_13924,
    inference(clausify,[status(thm)],[f_3529_2]) ).

fof(f_3530_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_3530_2,plain,
    ! [U_13926,U_13925] : hAPP(c_Fun_Oid(U_13925),U_13926) = U_13926,
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

cnf(f_3530_3,plain,
    hAPP(c_Fun_Oid(U_13925),U_13926) = U_13926,
    inference(clausify,[status(thm)],[f_3530_2]) ).

fof(f_3531_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_3531_2,plain,
    ! [U_13928,U_13927] : hAPP(c_Fun_Oid(U_13927),U_13928) = U_13928,
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

cnf(f_3531_3,plain,
    hAPP(c_Fun_Oid(U_13927),U_13928) = U_13928,
    inference(clausify,[status(thm)],[f_3531_2]) ).

fof(f_3532_1,plain,
    ! [V_a2_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,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_a,T_b,V_r_2),V_a2_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations]) ).

fof(f_3532_2,plain,
    ! [U_13934,U_13933,U_13932,U_13931] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13931,U_13932,U_13933),U_13934))
        | ! [U_13930] : ~ hBOOL(hAPP(hAPP(U_13933,U_13930),U_13934)) )
      & ( ? [U_13929] : hBOOL(hAPP(hAPP(U_13933,U_13929),U_13934))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13931,U_13932,U_13933),U_13934)) ) ),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

fof(f_3532_3,plain,
    ( ! [U_13942,U_13940] :
        ( ! [U_13938,U_13936] : hBOOL(hAPP(c_Predicate_ORangeP(U_13936,U_13938,U_13940),U_13942))
        | ! [U_13930] : ~ hBOOL(hAPP(hAPP(U_13940,U_13930),U_13942)) )
    & ! [U_13941,U_13939] :
        ( ! [U_13937,U_13935] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13935,U_13937,U_13939),U_13941))
        | ? [U_13929] : hBOOL(hAPP(hAPP(U_13939,U_13929),U_13941)) ) ),
    inference(miniscope,[status(thm)],[f_3532_2]) ).

fof(f_3532_4,plain,
    ( ! [U_13942,U_13940] :
        ( ! [U_13938,U_13936] : hBOOL(hAPP(c_Predicate_ORangeP(U_13936,U_13938,U_13940),U_13942))
        | ! [U_13930] : ~ hBOOL(hAPP(hAPP(U_13940,U_13930),U_13942)) )
    & ! [U_13941,U_13939] :
        ( ! [U_13937,U_13935] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13935,U_13937,U_13939),U_13941))
        | hBOOL(hAPP(hAPP(U_13939,sK326(U_13941,U_13939)),U_13941)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_13929,sK326(U_13941,U_13939))],[f_3532_3]) ).

cnf(f_3532_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13935,U_13937,U_13939),U_13941))
    | hBOOL(hAPP(hAPP(U_13939,sK326(U_13941,U_13939)),U_13941)) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

cnf(f_3532_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13936,U_13938,U_13940),U_13942))
    | ~ hBOOL(hAPP(hAPP(U_13940,U_13930),U_13942)) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

fof(f_3533_1,plain,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id]) ).

fof(f_3533_2,plain,
    ! [U_13944,U_13943] : c_Fun_Oinj__on(U_13943,U_13943,c_Fun_Oid(U_13943),U_13944),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

cnf(f_3533_3,plain,
    c_Fun_Oinj__on(U_13943,U_13943,c_Fun_Oid(U_13943),U_13944),
    inference(clausify,[status(thm)],[f_3533_2]) ).

fof(f_3534_1,plain,
    ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2,
    inference(fof_nnf,[status(thm)],[fact_id__o]) ).

fof(f_3534_2,plain,
    ! [U_13947,U_13946,U_13945] : hAPP(c_Fun_Ocomp(U_13945,U_13945,U_13946,c_Fun_Oid(U_13945)),U_13947) = U_13947,
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

cnf(f_3534_3,plain,
    hAPP(c_Fun_Ocomp(U_13945,U_13945,U_13946,c_Fun_Oid(U_13945)),U_13947) = U_13947,
    inference(clausify,[status(thm)],[f_3534_2]) ).

fof(f_3535_1,plain,
    ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_o__id]) ).

fof(f_3535_2,plain,
    ! [U_13950,U_13949,U_13948] : hAPP(c_Fun_Ocomp(U_13948,U_13949,U_13948,U_13950),c_Fun_Oid(U_13948)) = U_13950,
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

cnf(f_3535_3,plain,
    hAPP(c_Fun_Ocomp(U_13948,U_13949,U_13948,U_13950),c_Fun_Oid(U_13948)) = U_13950,
    inference(clausify,[status(thm)],[f_3535_2]) ).

fof(f_3536_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_c_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).

fof(f_3536_2,plain,
    ! [U_13957,U_13956,U_13955,U_13954,U_13953,U_13952,U_13951] :
      ( hAPP(U_13954,hAPP(U_13955,U_13957)) = hAPP(U_13956,U_13957)
      | hAPP(c_Fun_Ocomp(U_13951,U_13952,U_13953,U_13954),U_13955) != hAPP(c_Fun_Ocomp(U_13952,U_13952,U_13953,c_Fun_Oid(U_13952)),U_13956) ),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

fof(f_3536_3,plain,
    ! [U_13957,U_13956,U_13955,U_13954] :
      ( ! [U_13953,U_13952,U_13951] : hAPP(c_Fun_Ocomp(U_13951,U_13952,U_13953,U_13954),U_13955) != hAPP(c_Fun_Ocomp(U_13952,U_13952,U_13953,c_Fun_Oid(U_13952)),U_13956)
      | hAPP(U_13954,hAPP(U_13955,U_13957)) = hAPP(U_13956,U_13957) ),
    inference(miniscope,[status(thm)],[f_3536_2]) ).

cnf(f_3536_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13951,U_13952,U_13953,U_13954),U_13955) != hAPP(c_Fun_Ocomp(U_13952,U_13952,U_13953,c_Fun_Oid(U_13952)),U_13956)
    | hAPP(U_13954,hAPP(U_13955,U_13957)) = hAPP(U_13956,U_13957) ),
    inference(clausify,[status(thm)],[f_3536_3]) ).

fof(f_3537_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]) ).

cnf(f_3537_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3537_1]) ).

fof(f_3538_1,plain,
    ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_surj__id]) ).

fof(f_3538_2,plain,
    ! [U_13958] : hAPP(c_Set_Oimage(U_13958,U_13958,c_Fun_Oid(U_13958)),c_Orderings_Otop__class_Otop(tc_fun(U_13958,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13958,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

cnf(f_3538_3,plain,
    hAPP(c_Set_Oimage(U_13958,U_13958,c_Fun_Oid(U_13958)),c_Orderings_Otop__class_Otop(tc_fun(U_13958,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13958,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3538_2]) ).

fof(f_3539_1,plain,
    ! [V_F_2,V_f_2,T_b,T_a] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b)
      | ~ c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oempty]) ).

fof(f_3539_2,plain,
    ! [U_13962,U_13961,U_13960,U_13959] :
      ( hAPP(U_13962,c_Orderings_Obot__class_Obot(tc_fun(U_13959,tc_HOL_Obool))) = c_Fun_Oid(U_13960)
      | ~ c_Finite__Set_Ofolding(U_13959,U_13960,U_13961,U_13962) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

cnf(f_3539_3,plain,
    ( hAPP(U_13962,c_Orderings_Obot__class_Obot(tc_fun(U_13959,tc_HOL_Obool))) = c_Fun_Oid(U_13960)
    | ~ c_Finite__Set_Ofolding(U_13959,U_13960,U_13961,U_13962) ),
    inference(clausify,[status(thm)],[f_3539_2]) ).

fof(f_3540_1,plain,
    ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_split__Pair]) ).

fof(f_3540_2,plain,
    ! [U_13964,U_13963] : hAPP(c_Product__Type_Oprod_Oprod__case(U_13963,U_13964,tc_prod(U_13963,U_13964)),c_Product__Type_OPair(U_13963,U_13964)) = c_Fun_Oid(tc_prod(U_13963,U_13964)),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

cnf(f_3540_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_13963,U_13964,tc_prod(U_13963,U_13964)),c_Product__Type_OPair(U_13963,U_13964)) = c_Fun_Oid(tc_prod(U_13963,U_13964)),
    inference(clausify,[status(thm)],[f_3540_2]) ).

fof(f_3541_1,plain,
    ! [V_B_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id]) ).

fof(f_3541_2,plain,
    ! [U_13968,U_13967,U_13966,U_13965] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13966,U_13965),U_13967),U_13968) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13965,U_13965),c_Fun_Oid(U_13965)),hAPP(c_Set_Oimage(U_13966,U_13965,U_13967),U_13968))
      | ~ c_Fun_Oinj__on(U_13966,U_13965,U_13967,U_13968)
      | ~ class_Groups_Ocomm__monoid__add(U_13965) ),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

cnf(f_3541_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13966,U_13965),U_13967),U_13968) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13965,U_13965),c_Fun_Oid(U_13965)),hAPP(c_Set_Oimage(U_13966,U_13965,U_13967),U_13968))
    | ~ c_Fun_Oinj__on(U_13966,U_13965,U_13967,U_13968)
    | ~ class_Groups_Ocomm__monoid__add(U_13965) ),
    inference(clausify,[status(thm)],[f_3541_2]) ).

fof(f_3542_1,plain,
    ! [V_B_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id]) ).

fof(f_3542_2,plain,
    ! [U_13972,U_13971,U_13970,U_13969] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13970,U_13969),U_13971),U_13972) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13969,U_13969),c_Fun_Oid(U_13969)),hAPP(c_Set_Oimage(U_13970,U_13969,U_13971),U_13972))
      | ~ c_Fun_Oinj__on(U_13970,U_13969,U_13971,U_13972)
      | ~ class_Groups_Ocomm__monoid__mult(U_13969) ),
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

cnf(f_3542_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13970,U_13969),U_13971),U_13972) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13969,U_13969),c_Fun_Oid(U_13969)),hAPP(c_Set_Oimage(U_13970,U_13969,U_13971),U_13972))
    | ~ c_Fun_Oinj__on(U_13970,U_13969,U_13971,U_13972)
    | ~ class_Groups_Ocomm__monoid__mult(U_13969) ),
    inference(clausify,[status(thm)],[f_3542_2]) ).

fof(f_3543_1,plain,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Sigma]) ).

fof(f_3543_2,plain,
    ! [U_13979,U_13978,U_13977,U_13976,U_13975,U_13974] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13975,U_13974),hAPP(hAPP(c_COMBS(U_13975,tc_fun(U_13977,tc_HOL_Obool),U_13974),hAPP(hAPP(c_COMBB(tc_fun(U_13977,U_13974),tc_fun(tc_fun(U_13977,tc_HOL_Obool),U_13974),U_13975),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13977,U_13974)),U_13979)),U_13978)),U_13976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13975,U_13977),U_13974),hAPP(c_Product__Type_Oprod_Oprod__case(U_13975,U_13977,U_13974),U_13979)),hAPP(hAPP(c_Product__Type_OSigma(U_13975,U_13977),U_13976),U_13978))
      | ? [U_13973] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),hAPP(U_13978,U_13973)))
          & hBOOL(hAPP(hAPP(c_member(U_13975),U_13973),U_13976)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13975),U_13976))
      | ~ class_Groups_Ocomm__monoid__mult(U_13974) ),
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

fof(f_3543_3,plain,
    ! [U_13979,U_13978,U_13977,U_13976,U_13975,U_13974] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13975,U_13974),hAPP(hAPP(c_COMBS(U_13975,tc_fun(U_13977,tc_HOL_Obool),U_13974),hAPP(hAPP(c_COMBB(tc_fun(U_13977,U_13974),tc_fun(tc_fun(U_13977,tc_HOL_Obool),U_13974),U_13975),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13977,U_13974)),U_13979)),U_13978)),U_13976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13975,U_13977),U_13974),hAPP(c_Product__Type_Oprod_Oprod__case(U_13975,U_13977,U_13974),U_13979)),hAPP(hAPP(c_Product__Type_OSigma(U_13975,U_13977),U_13976),U_13978))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),hAPP(U_13978,sK327(U_13979,U_13978,U_13977,U_13976,U_13975,U_13974))))
        & hBOOL(hAPP(hAPP(c_member(U_13975),sK327(U_13979,U_13978,U_13977,U_13976,U_13975,U_13974)),U_13976)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13975),U_13976))
      | ~ class_Groups_Ocomm__monoid__mult(U_13974) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_13973,sK327(U_13979,U_13978,U_13977,U_13976,U_13975,U_13974))],[f_3543_2]) ).

cnf(f_3543_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13975),sK327(U_13979,U_13978,U_13977,U_13976,U_13975,U_13974)),U_13976))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13975,U_13974),hAPP(hAPP(c_COMBS(U_13975,tc_fun(U_13977,tc_HOL_Obool),U_13974),hAPP(hAPP(c_COMBB(tc_fun(U_13977,U_13974),tc_fun(tc_fun(U_13977,tc_HOL_Obool),U_13974),U_13975),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13977,U_13974)),U_13979)),U_13978)),U_13976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13975,U_13977),U_13974),hAPP(c_Product__Type_Oprod_Oprod__case(U_13975,U_13977,U_13974),U_13979)),hAPP(hAPP(c_Product__Type_OSigma(U_13975,U_13977),U_13976),U_13978))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13975),U_13976))
    | ~ class_Groups_Ocomm__monoid__mult(U_13974) ),
    inference(clausify,[status(thm)],[f_3543_3]) ).

cnf(f_3543_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),hAPP(U_13978,sK327(U_13979,U_13978,U_13977,U_13976,U_13975,U_13974))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13975,U_13974),hAPP(hAPP(c_COMBS(U_13975,tc_fun(U_13977,tc_HOL_Obool),U_13974),hAPP(hAPP(c_COMBB(tc_fun(U_13977,U_13974),tc_fun(tc_fun(U_13977,tc_HOL_Obool),U_13974),U_13975),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13977,U_13974)),U_13979)),U_13978)),U_13976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_13975,U_13977),U_13974),hAPP(c_Product__Type_Oprod_Oprod__case(U_13975,U_13977,U_13974),U_13979)),hAPP(hAPP(c_Product__Type_OSigma(U_13975,U_13977),U_13976),U_13978))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13975),U_13976))
    | ~ class_Groups_Ocomm__monoid__mult(U_13974) ),
    inference(clausify,[status(thm)],[f_3543_3]) ).

fof(f_3544_1,plain,
    ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Sigma]) ).

fof(f_3544_2,plain,
    ! [U_13986,U_13985,U_13984,U_13983,U_13982,U_13981] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13982,U_13981),hAPP(hAPP(c_COMBS(U_13982,tc_fun(U_13984,tc_HOL_Obool),U_13981),hAPP(hAPP(c_COMBB(tc_fun(U_13984,U_13981),tc_fun(tc_fun(U_13984,tc_HOL_Obool),U_13981),U_13982),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13984,U_13981)),U_13986)),U_13985)),U_13983) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13982,U_13984),U_13981),hAPP(c_Product__Type_Oprod_Oprod__case(U_13982,U_13984,U_13981),U_13986)),hAPP(hAPP(c_Product__Type_OSigma(U_13982,U_13984),U_13983),U_13985))
      | ? [U_13980] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13984),hAPP(U_13985,U_13980)))
          & hBOOL(hAPP(hAPP(c_member(U_13982),U_13980),U_13983)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13982),U_13983))
      | ~ class_Groups_Ocomm__monoid__add(U_13981) ),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

fof(f_3544_3,plain,
    ! [U_13986,U_13985,U_13984,U_13983,U_13982,U_13981] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13982,U_13981),hAPP(hAPP(c_COMBS(U_13982,tc_fun(U_13984,tc_HOL_Obool),U_13981),hAPP(hAPP(c_COMBB(tc_fun(U_13984,U_13981),tc_fun(tc_fun(U_13984,tc_HOL_Obool),U_13981),U_13982),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13984,U_13981)),U_13986)),U_13985)),U_13983) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13982,U_13984),U_13981),hAPP(c_Product__Type_Oprod_Oprod__case(U_13982,U_13984,U_13981),U_13986)),hAPP(hAPP(c_Product__Type_OSigma(U_13982,U_13984),U_13983),U_13985))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13984),hAPP(U_13985,sK328(U_13986,U_13985,U_13984,U_13983,U_13982,U_13981))))
        & hBOOL(hAPP(hAPP(c_member(U_13982),sK328(U_13986,U_13985,U_13984,U_13983,U_13982,U_13981)),U_13983)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13982),U_13983))
      | ~ class_Groups_Ocomm__monoid__add(U_13981) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_13980,sK328(U_13986,U_13985,U_13984,U_13983,U_13982,U_13981))],[f_3544_2]) ).

cnf(f_3544_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13982),sK328(U_13986,U_13985,U_13984,U_13983,U_13982,U_13981)),U_13983))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13982,U_13981),hAPP(hAPP(c_COMBS(U_13982,tc_fun(U_13984,tc_HOL_Obool),U_13981),hAPP(hAPP(c_COMBB(tc_fun(U_13984,U_13981),tc_fun(tc_fun(U_13984,tc_HOL_Obool),U_13981),U_13982),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13984,U_13981)),U_13986)),U_13985)),U_13983) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13982,U_13984),U_13981),hAPP(c_Product__Type_Oprod_Oprod__case(U_13982,U_13984,U_13981),U_13986)),hAPP(hAPP(c_Product__Type_OSigma(U_13982,U_13984),U_13983),U_13985))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13982),U_13983))
    | ~ class_Groups_Ocomm__monoid__add(U_13981) ),
    inference(clausify,[status(thm)],[f_3544_3]) ).

cnf(f_3544_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13984),hAPP(U_13985,sK328(U_13986,U_13985,U_13984,U_13983,U_13982,U_13981))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13982,U_13981),hAPP(hAPP(c_COMBS(U_13982,tc_fun(U_13984,tc_HOL_Obool),U_13981),hAPP(hAPP(c_COMBB(tc_fun(U_13984,U_13981),tc_fun(tc_fun(U_13984,tc_HOL_Obool),U_13981),U_13982),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13984,U_13981)),U_13986)),U_13985)),U_13983) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_13982,U_13984),U_13981),hAPP(c_Product__Type_Oprod_Oprod__case(U_13982,U_13984,U_13981),U_13986)),hAPP(hAPP(c_Product__Type_OSigma(U_13982,U_13984),U_13983),U_13985))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13982),U_13983))
    | ~ class_Groups_Ocomm__monoid__add(U_13981) ),
    inference(clausify,[status(thm)],[f_3544_3]) ).

fof(f_3545_1,plain,
    ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),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)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma]) ).

fof(f_3545_2,plain,
    ! [U_13993,U_13992,U_13991,U_13990,U_13989,U_13988] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,U_13989,c_Groups_Otimes__class_Otimes(U_13988)),hAPP(hAPP(c_COMBS(U_13989,tc_fun(U_13991,tc_HOL_Obool),U_13988),hAPP(hAPP(c_COMBC(U_13989,U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),hAPP(hAPP(c_COMBB(tc_fun(U_13991,U_13988),tc_fun(U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),U_13989),c_Finite__Set_Ofold__image(U_13988,U_13991,c_Groups_Otimes__class_Otimes(U_13988))),U_13993)),c_Groups_Oone__class_Oone(U_13988))),U_13992)),c_Groups_Oone__class_Oone(U_13988)),U_13990) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,tc_prod(U_13989,U_13991),c_Groups_Otimes__class_Otimes(U_13988)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13991,U_13988),U_13993)),c_Groups_Oone__class_Oone(U_13988)),hAPP(hAPP(c_Product__Type_OSigma(U_13989,U_13991),U_13990),U_13992))
      | ? [U_13987] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13991),hAPP(U_13992,U_13987)))
          & hBOOL(hAPP(hAPP(c_member(U_13989),U_13987),U_13990)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13989),U_13990))
      | ~ class_Groups_Ocomm__monoid__mult(U_13988) ),
    inference(variable_rename,[status(thm)],[f_3545_1]) ).

fof(f_3545_3,plain,
    ! [U_13993,U_13992,U_13991,U_13990,U_13989,U_13988] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,U_13989,c_Groups_Otimes__class_Otimes(U_13988)),hAPP(hAPP(c_COMBS(U_13989,tc_fun(U_13991,tc_HOL_Obool),U_13988),hAPP(hAPP(c_COMBC(U_13989,U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),hAPP(hAPP(c_COMBB(tc_fun(U_13991,U_13988),tc_fun(U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),U_13989),c_Finite__Set_Ofold__image(U_13988,U_13991,c_Groups_Otimes__class_Otimes(U_13988))),U_13993)),c_Groups_Oone__class_Oone(U_13988))),U_13992)),c_Groups_Oone__class_Oone(U_13988)),U_13990) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,tc_prod(U_13989,U_13991),c_Groups_Otimes__class_Otimes(U_13988)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13991,U_13988),U_13993)),c_Groups_Oone__class_Oone(U_13988)),hAPP(hAPP(c_Product__Type_OSigma(U_13989,U_13991),U_13990),U_13992))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13991),hAPP(U_13992,sK329(U_13993,U_13992,U_13991,U_13990,U_13989,U_13988))))
        & hBOOL(hAPP(hAPP(c_member(U_13989),sK329(U_13993,U_13992,U_13991,U_13990,U_13989,U_13988)),U_13990)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13989),U_13990))
      | ~ class_Groups_Ocomm__monoid__mult(U_13988) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_13987,sK329(U_13993,U_13992,U_13991,U_13990,U_13989,U_13988))],[f_3545_2]) ).

cnf(f_3545_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13989),sK329(U_13993,U_13992,U_13991,U_13990,U_13989,U_13988)),U_13990))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,U_13989,c_Groups_Otimes__class_Otimes(U_13988)),hAPP(hAPP(c_COMBS(U_13989,tc_fun(U_13991,tc_HOL_Obool),U_13988),hAPP(hAPP(c_COMBC(U_13989,U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),hAPP(hAPP(c_COMBB(tc_fun(U_13991,U_13988),tc_fun(U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),U_13989),c_Finite__Set_Ofold__image(U_13988,U_13991,c_Groups_Otimes__class_Otimes(U_13988))),U_13993)),c_Groups_Oone__class_Oone(U_13988))),U_13992)),c_Groups_Oone__class_Oone(U_13988)),U_13990) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,tc_prod(U_13989,U_13991),c_Groups_Otimes__class_Otimes(U_13988)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13991,U_13988),U_13993)),c_Groups_Oone__class_Oone(U_13988)),hAPP(hAPP(c_Product__Type_OSigma(U_13989,U_13991),U_13990),U_13992))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13989),U_13990))
    | ~ class_Groups_Ocomm__monoid__mult(U_13988) ),
    inference(clausify,[status(thm)],[f_3545_3]) ).

cnf(f_3545_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13991),hAPP(U_13992,sK329(U_13993,U_13992,U_13991,U_13990,U_13989,U_13988))))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,U_13989,c_Groups_Otimes__class_Otimes(U_13988)),hAPP(hAPP(c_COMBS(U_13989,tc_fun(U_13991,tc_HOL_Obool),U_13988),hAPP(hAPP(c_COMBC(U_13989,U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),hAPP(hAPP(c_COMBB(tc_fun(U_13991,U_13988),tc_fun(U_13988,tc_fun(tc_fun(U_13991,tc_HOL_Obool),U_13988)),U_13989),c_Finite__Set_Ofold__image(U_13988,U_13991,c_Groups_Otimes__class_Otimes(U_13988))),U_13993)),c_Groups_Oone__class_Oone(U_13988))),U_13992)),c_Groups_Oone__class_Oone(U_13988)),U_13990) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13988,tc_prod(U_13989,U_13991),c_Groups_Otimes__class_Otimes(U_13988)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13989,U_13991,U_13988),U_13993)),c_Groups_Oone__class_Oone(U_13988)),hAPP(hAPP(c_Product__Type_OSigma(U_13989,U_13991),U_13990),U_13992))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13989),U_13990))
    | ~ class_Groups_Ocomm__monoid__mult(U_13988) ),
    inference(clausify,[status(thm)],[f_3545_3]) ).

fof(f_3546_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__SigmaI]) ).

fof(f_3546_2,plain,
    ! [U_13998,U_13997,U_13996,U_13995] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13995,U_13997)),hAPP(hAPP(c_Product__Type_OSigma(U_13995,U_13997),U_13996),U_13998)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13995,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_Nat_Onat,U_13995),c_Finite__Set_Ocard(U_13997)),U_13998)),U_13996)
      | ? [U_13994] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(U_13998,U_13994)))
          & hBOOL(hAPP(hAPP(c_member(U_13995),U_13994),U_13996)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13995),U_13996)) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

fof(f_3546_3,plain,
    ! [U_13998,U_13997,U_13996,U_13995] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_13995,U_13997)),hAPP(hAPP(c_Product__Type_OSigma(U_13995,U_13997),U_13996),U_13998)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13995,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_Nat_Onat,U_13995),c_Finite__Set_Ocard(U_13997)),U_13998)),U_13996)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(U_13998,sK330(U_13998,U_13997,U_13996,U_13995))))
        & hBOOL(hAPP(hAPP(c_member(U_13995),sK330(U_13998,U_13997,U_13996,U_13995)),U_13996)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13995),U_13996)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_13994,sK330(U_13998,U_13997,U_13996,U_13995))],[f_3546_2]) ).

cnf(f_3546_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13995),sK330(U_13998,U_13997,U_13996,U_13995)),U_13996))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_13995,U_13997)),hAPP(hAPP(c_Product__Type_OSigma(U_13995,U_13997),U_13996),U_13998)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13995,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_Nat_Onat,U_13995),c_Finite__Set_Ocard(U_13997)),U_13998)),U_13996)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13995),U_13996)) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

cnf(f_3546_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(U_13998,sK330(U_13998,U_13997,U_13996,U_13995))))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_13995,U_13997)),hAPP(hAPP(c_Product__Type_OSigma(U_13995,U_13997),U_13996),U_13998)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13995,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13997,tc_HOL_Obool),tc_Nat_Onat,U_13995),c_Finite__Set_Ocard(U_13997)),U_13998)),U_13996)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13995),U_13996)) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

fof(f_3547_1,plain,
    ! [V_B_2,T_b,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__SigmaI]) ).

fof(f_3547_2,plain,
    ! [U_14003,U_14002,U_14001,U_14000] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14000,U_14002)),hAPP(hAPP(c_Product__Type_OSigma(U_14000,U_14002),U_14001),U_14003)))
      | ? [U_13999] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14002),hAPP(U_14003,U_13999)))
          & hBOOL(hAPP(hAPP(c_member(U_14000),U_13999),U_14001)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001)) ),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

fof(f_3547_3,plain,
    ! [U_14003,U_14002,U_14001,U_14000] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14000,U_14002)),hAPP(hAPP(c_Product__Type_OSigma(U_14000,U_14002),U_14001),U_14003)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14002),hAPP(U_14003,sK331(U_14003,U_14002,U_14001,U_14000))))
        & hBOOL(hAPP(hAPP(c_member(U_14000),sK331(U_14003,U_14002,U_14001,U_14000)),U_14001)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_13999,sK331(U_14003,U_14002,U_14001,U_14000))],[f_3547_2]) ).

cnf(f_3547_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14000),sK331(U_14003,U_14002,U_14001,U_14000)),U_14001))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14000,U_14002)),hAPP(hAPP(c_Product__Type_OSigma(U_14000,U_14002),U_14001),U_14003)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001)) ),
    inference(clausify,[status(thm)],[f_3547_3]) ).

cnf(f_3547_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14002),hAPP(U_14003,sK331(U_14003,U_14002,U_14001,U_14000))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14000,U_14002)),hAPP(hAPP(c_Product__Type_OSigma(U_14000,U_14002),U_14001),U_14003)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14000),U_14001)) ),
    inference(clausify,[status(thm)],[f_3547_3]) ).

fof(f_3548_1,plain,
    ! [V_r_2,T_b,V_b_2,T_a] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_RangeE]) ).

fof(f_3548_2,plain,
    ! [U_14008,U_14007,U_14006,U_14005] :
      ( ? [U_14004] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14007,U_14005)),hAPP(hAPP(c_Product__Type_OPair(U_14007,U_14005),U_14004),U_14006)),U_14008))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14005),U_14006),hAPP(c_Relation_ORange(U_14007,U_14005),U_14008))) ),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

fof(f_3548_3,plain,
    ! [U_14008,U_14007,U_14006,U_14005] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14007,U_14005)),hAPP(hAPP(c_Product__Type_OPair(U_14007,U_14005),sK332(U_14008,U_14007,U_14006,U_14005)),U_14006)),U_14008))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14005),U_14006),hAPP(c_Relation_ORange(U_14007,U_14005),U_14008))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_14004,sK332(U_14008,U_14007,U_14006,U_14005))],[f_3548_2]) ).

cnf(f_3548_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14007,U_14005)),hAPP(hAPP(c_Product__Type_OPair(U_14007,U_14005),sK332(U_14008,U_14007,U_14006,U_14005)),U_14006)),U_14008))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14005),U_14006),hAPP(c_Relation_ORange(U_14007,U_14005),U_14008))) ),
    inference(clausify,[status(thm)],[f_3548_3]) ).

fof(f_3549_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b,T_a] :
      ( ? [B_x] :
          ( ? [B_y] :
              ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) )
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE]) ).

fof(f_3549_2,plain,
    ! [U_14015,U_14014,U_14013,U_14012,U_14011] :
      ( ? [U_14010] :
          ( ? [U_14009] :
              ( U_14013 = hAPP(hAPP(c_Product__Type_OPair(U_14011,U_14012),U_14010),U_14009)
              & hBOOL(hAPP(hAPP(c_member(U_14012),U_14009),hAPP(U_14015,U_14010))) )
          & hBOOL(hAPP(hAPP(c_member(U_14011),U_14010),U_14014)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

fof(f_3549_3,plain,
    ! [U_14015,U_14014,U_14013,U_14012,U_14011] :
      ( ( ? [U_14009] :
            ( U_14013 = hAPP(hAPP(c_Product__Type_OPair(U_14011,U_14012),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),U_14009)
            & hBOOL(hAPP(hAPP(c_member(U_14012),U_14009),hAPP(U_14015,sK333(U_14015,U_14014,U_14013,U_14012,U_14011)))) )
        & hBOOL(hAPP(hAPP(c_member(U_14011),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),U_14014)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_14010,sK333(U_14015,U_14014,U_14013,U_14012,U_14011))],[f_3549_2]) ).

fof(f_3549_4,plain,
    ! [U_14015,U_14014,U_14013,U_14012,U_14011] :
      ( ( U_14013 = hAPP(hAPP(c_Product__Type_OPair(U_14011,U_14012),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),sK334(U_14015,U_14014,U_14013,U_14012,U_14011))
        & hBOOL(hAPP(hAPP(c_member(U_14012),sK334(U_14015,U_14014,U_14013,U_14012,U_14011)),hAPP(U_14015,sK333(U_14015,U_14014,U_14013,U_14012,U_14011))))
        & hBOOL(hAPP(hAPP(c_member(U_14011),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),U_14014)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_14009,sK334(U_14015,U_14014,U_14013,U_14012,U_14011))],[f_3549_3]) ).

cnf(f_3549_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14011),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),U_14014))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(clausify,[status(thm)],[f_3549_4]) ).

cnf(f_3549_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14012),sK334(U_14015,U_14014,U_14013,U_14012,U_14011)),hAPP(U_14015,sK333(U_14015,U_14014,U_14013,U_14012,U_14011))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(clausify,[status(thm)],[f_3549_4]) ).

cnf(f_3549_7,plain,
    ( U_14013 = hAPP(hAPP(c_Product__Type_OPair(U_14011,U_14012),sK333(U_14015,U_14014,U_14013,U_14012,U_14011)),sK334(U_14015,U_14014,U_14013,U_14012,U_14011))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14011,U_14012)),U_14013),hAPP(hAPP(c_Product__Type_OSigma(U_14011,U_14012),U_14014),U_14015))) ),
    inference(clausify,[status(thm)],[f_3549_4]) ).

fof(f_3550_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2)))
      | ~ c_Wellfounded_OwfP(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP]) ).

fof(f_3550_2,plain,
    ! [U_14017,U_14016] :
      ( c_Wellfounded_Oacyclic(U_14016,hAPP(c_Set_OCollect(tc_prod(U_14016,U_14016)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14016,U_14016,tc_HOL_Obool),U_14017)))
      | ~ c_Wellfounded_OwfP(U_14016,U_14017) ),
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

cnf(f_3550_3,plain,
    ( c_Wellfounded_Oacyclic(U_14016,hAPP(c_Set_OCollect(tc_prod(U_14016,U_14016)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14016,U_14016,tc_HOL_Obool),U_14017)))
    | ~ c_Wellfounded_OwfP(U_14016,U_14017) ),
    inference(clausify,[status(thm)],[f_3550_2]) ).

fof(f_3551_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(T_a,V_s_2)
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Un]) ).

fof(f_3551_2,plain,
    ! [U_14020,U_14019,U_14018] :
      ( c_Wellfounded_Owf(U_14018,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14018,U_14018),tc_HOL_Obool)),U_14019),U_14020))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14018,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14018,U_14018),U_14019)),hAPP(c_Relation_ORange(U_14018,U_14018),U_14020)) != c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_14018,U_14020)
      | ~ c_Wellfounded_Owf(U_14018,U_14019) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

cnf(f_3551_3,plain,
    ( c_Wellfounded_Owf(U_14018,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14018,U_14018),tc_HOL_Obool)),U_14019),U_14020))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14018,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14018,U_14018),U_14019)),hAPP(c_Relation_ORange(U_14018,U_14018),U_14020)) != c_Orderings_Obot__class_Obot(tc_fun(U_14018,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_14018,U_14020)
    | ~ c_Wellfounded_Owf(U_14018,U_14019) ),
    inference(clausify,[status(thm)],[f_3551_2]) ).

fof(f_3552_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DomainI]) ).

fof(f_3552_2,plain,
    ! [U_14025,U_14024,U_14023,U_14022,U_14021] :
      ( hBOOL(hAPP(hAPP(c_member(U_14021),U_14023),hAPP(c_Relation_ODomain(U_14021,U_14022),U_14025)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14021,U_14022)),hAPP(hAPP(c_Product__Type_OPair(U_14021,U_14022),U_14023),U_14024)),U_14025)) ),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

cnf(f_3552_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14021),U_14023),hAPP(c_Relation_ODomain(U_14021,U_14022),U_14025)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14021,U_14022)),hAPP(hAPP(c_Product__Type_OPair(U_14021,U_14022),U_14023),U_14024)),U_14025)) ),
    inference(clausify,[status(thm)],[f_3552_2]) ).

fof(f_3553_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Domain__Id__on]) ).

fof(f_3553_2,plain,
    ! [U_14027,U_14026] : hAPP(c_Relation_ODomain(U_14026,U_14026),c_Relation_OId__on(U_14026,U_14027)) = U_14027,
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

cnf(f_3553_3,plain,
    hAPP(c_Relation_ODomain(U_14026,U_14026),c_Relation_OId__on(U_14026,U_14027)) = U_14027,
    inference(clausify,[status(thm)],[f_3553_2]) ).

fof(f_3554_1,plain,
    ! [V_r_2,V_s_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,V_r_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Wellfounded_Oacyclic(T_a,V_s_2) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__subset]) ).

fof(f_3554_2,plain,
    ! [U_14030,U_14029,U_14028] :
      ( c_Wellfounded_Oacyclic(U_14028,U_14030)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14028,U_14028),tc_HOL_Obool)),U_14030),U_14029))
      | ~ c_Wellfounded_Oacyclic(U_14028,U_14029) ),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

cnf(f_3554_3,plain,
    ( c_Wellfounded_Oacyclic(U_14028,U_14030)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14028,U_14028),tc_HOL_Obool)),U_14030),U_14029))
    | ~ c_Wellfounded_Oacyclic(U_14028,U_14029) ),
    inference(clausify,[status(thm)],[f_3554_2]) ).

fof(f_3555_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,V_r_2)
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acyclic]) ).

fof(f_3555_2,plain,
    ! [U_14032,U_14031] :
      ( c_Wellfounded_Oacyclic(U_14031,U_14032)
      | ~ c_Wellfounded_Owf(U_14031,U_14032) ),
    inference(variable_rename,[status(thm)],[f_3555_1]) ).

cnf(f_3555_3,plain,
    ( c_Wellfounded_Oacyclic(U_14031,U_14032)
    | ~ c_Wellfounded_Owf(U_14031,U_14032) ),
    inference(clausify,[status(thm)],[f_3555_2]) ).

fof(f_3556_1,plain,
    ! [V_r_2,T_b,T_a] :
      ( ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff]) ).

fof(f_3556_2,plain,
    ! [U_14035,U_14034,U_14033] :
      ( ( hAPP(c_Relation_ODomain(U_14033,U_14034),U_14035) = c_Orderings_Obot__class_Obot(tc_fun(U_14033,tc_HOL_Obool))
        | U_14035 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14033,U_14034),tc_HOL_Obool)) )
      & ( U_14035 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14033,U_14034),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_14033,U_14034),U_14035) != c_Orderings_Obot__class_Obot(tc_fun(U_14033,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

fof(f_3556_3,plain,
    ( ! [U_14041,U_14039,U_14037] :
        ( hAPP(c_Relation_ODomain(U_14037,U_14039),U_14041) = c_Orderings_Obot__class_Obot(tc_fun(U_14037,tc_HOL_Obool))
        | U_14041 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14037,U_14039),tc_HOL_Obool)) )
    & ! [U_14040,U_14038,U_14036] :
        ( U_14040 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14036,U_14038),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_14036,U_14038),U_14040) != c_Orderings_Obot__class_Obot(tc_fun(U_14036,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3556_2]) ).

cnf(f_3556_4,plain,
    ( U_14040 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14036,U_14038),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_14036,U_14038),U_14040) != c_Orderings_Obot__class_Obot(tc_fun(U_14036,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3556_3]) ).

cnf(f_3556_5,plain,
    ( hAPP(c_Relation_ODomain(U_14037,U_14039),U_14041) = c_Orderings_Obot__class_Obot(tc_fun(U_14037,tc_HOL_Obool))
    | U_14041 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14037,U_14039),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3556_3]) ).

fof(f_3557_1,plain,
    ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty]) ).

fof(f_3557_2,plain,
    ! [U_14043,U_14042] : hAPP(c_Relation_ODomain(U_14042,U_14043),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14042,U_14043),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14042,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

cnf(f_3557_3,plain,
    hAPP(c_Relation_ODomain(U_14042,U_14043),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14042,U_14043),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14042,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3557_2]) ).

fof(f_3558_1,plain,
    ! [V_s_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__mono]) ).

fof(f_3558_2,plain,
    ! [U_14047,U_14046,U_14045,U_14044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14044,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14044,U_14045),U_14046)),hAPP(c_Relation_ODomain(U_14044,U_14045),U_14047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14044,U_14045),tc_HOL_Obool)),U_14046),U_14047)) ),
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

cnf(f_3558_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14044,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14044,U_14045),U_14046)),hAPP(c_Relation_ODomain(U_14044,U_14045),U_14047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14044,U_14045),tc_HOL_Obool)),U_14046),U_14047)) ),
    inference(clausify,[status(thm)],[f_3558_2]) ).

fof(f_3559_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Un__eq]) ).

fof(f_3559_2,plain,
    ! [U_14051,U_14050,U_14049,U_14048] : hAPP(c_Relation_ODomain(U_14048,U_14049),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14048,U_14049),tc_HOL_Obool)),U_14050),U_14051)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14048,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14048,U_14049),U_14050)),hAPP(c_Relation_ODomain(U_14048,U_14049),U_14051)),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

cnf(f_3559_3,plain,
    hAPP(c_Relation_ODomain(U_14048,U_14049),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14048,U_14049),tc_HOL_Obool)),U_14050),U_14051)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14048,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14048,U_14049),U_14050)),hAPP(c_Relation_ODomain(U_14048,U_14049),U_14051)),
    inference(clausify,[status(thm)],[f_3559_2]) ).

fof(f_3560_1,plain,
    ! [V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Domain]) ).

fof(f_3560_2,plain,
    ! [U_14054,U_14053,U_14052] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14052),hAPP(c_Relation_ODomain(U_14052,U_14053),U_14054)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14052,U_14053)),U_14054)) ),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

cnf(f_3560_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14052),hAPP(c_Relation_ODomain(U_14052,U_14053),U_14054)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14052,U_14053)),U_14054)) ),
    inference(clausify,[status(thm)],[f_3560_2]) ).

fof(f_3561_1,plain,
    ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_fst__eq__Domain]) ).

fof(f_3561_2,plain,
    ! [U_14057,U_14056,U_14055] : hAPP(c_Set_Oimage(tc_prod(U_14055,U_14056),U_14055,c_Product__Type_Ofst(U_14055,U_14056)),U_14057) = hAPP(c_Relation_ODomain(U_14055,U_14056),U_14057),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

cnf(f_3561_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_14055,U_14056),U_14055,c_Product__Type_Ofst(U_14055,U_14056)),U_14057) = hAPP(c_Relation_ODomain(U_14055,U_14056),U_14057),
    inference(clausify,[status(thm)],[f_3561_2]) ).

fof(f_3562_1,plain,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__iff]) ).

fof(f_3562_2,plain,
    ! [U_14063,U_14062,U_14061,U_14060] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14060),U_14061),hAPP(c_Relation_ODomain(U_14060,U_14062),U_14063)))
        | ! [U_14059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14060,U_14062)),hAPP(hAPP(c_Product__Type_OPair(U_14060,U_14062),U_14061),U_14059)),U_14063)) )
      & ( ? [U_14058] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14060,U_14062)),hAPP(hAPP(c_Product__Type_OPair(U_14060,U_14062),U_14061),U_14058)),U_14063))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14060),U_14061),hAPP(c_Relation_ODomain(U_14060,U_14062),U_14063))) ) ),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

fof(f_3562_3,plain,
    ( ! [U_14071,U_14069,U_14067,U_14065] :
        ( hBOOL(hAPP(hAPP(c_member(U_14065),U_14067),hAPP(c_Relation_ODomain(U_14065,U_14069),U_14071)))
        | ! [U_14059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14065,U_14069)),hAPP(hAPP(c_Product__Type_OPair(U_14065,U_14069),U_14067),U_14059)),U_14071)) )
    & ! [U_14070,U_14068,U_14066,U_14064] :
        ( ? [U_14058] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14068)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14068),U_14066),U_14058)),U_14070))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14066),hAPP(c_Relation_ODomain(U_14064,U_14068),U_14070))) ) ),
    inference(miniscope,[status(thm)],[f_3562_2]) ).

fof(f_3562_4,plain,
    ( ! [U_14071,U_14069,U_14067,U_14065] :
        ( hBOOL(hAPP(hAPP(c_member(U_14065),U_14067),hAPP(c_Relation_ODomain(U_14065,U_14069),U_14071)))
        | ! [U_14059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14065,U_14069)),hAPP(hAPP(c_Product__Type_OPair(U_14065,U_14069),U_14067),U_14059)),U_14071)) )
    & ! [U_14070,U_14068,U_14066,U_14064] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14068)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14068),U_14066),sK335(U_14070,U_14068,U_14066,U_14064))),U_14070))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14066),hAPP(c_Relation_ODomain(U_14064,U_14068),U_14070))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_14058,sK335(U_14070,U_14068,U_14066,U_14064))],[f_3562_3]) ).

cnf(f_3562_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14068)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14068),U_14066),sK335(U_14070,U_14068,U_14066,U_14064))),U_14070))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14066),hAPP(c_Relation_ODomain(U_14064,U_14068),U_14070))) ),
    inference(clausify,[status(thm)],[f_3562_4]) ).

cnf(f_3562_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14065),U_14067),hAPP(c_Relation_ODomain(U_14065,U_14069),U_14071)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14065,U_14069)),hAPP(hAPP(c_Product__Type_OPair(U_14065,U_14069),U_14067),U_14059)),U_14071)) ),
    inference(clausify,[status(thm)],[f_3562_4]) ).

fof(f_3563_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__insert]) ).

fof(f_3563_2,plain,
    ! [U_14076,U_14075,U_14074,U_14073,U_14072] : hAPP(c_Relation_ODomain(U_14072,U_14073),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14072,U_14073)),hAPP(hAPP(c_Product__Type_OPair(U_14072,U_14073),U_14074),U_14075)),U_14076)) = hAPP(hAPP(c_Set_Oinsert(U_14072),U_14074),hAPP(c_Relation_ODomain(U_14072,U_14073),U_14076)),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

cnf(f_3563_3,plain,
    hAPP(c_Relation_ODomain(U_14072,U_14073),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14072,U_14073)),hAPP(hAPP(c_Product__Type_OPair(U_14072,U_14073),U_14074),U_14075)),U_14076)) = hAPP(hAPP(c_Set_Oinsert(U_14072),U_14074),hAPP(c_Relation_ODomain(U_14072,U_14073),U_14076)),
    inference(clausify,[status(thm)],[f_3563_2]) ).

fof(f_3564_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_r_2)
      | ~ c_Wellfounded_Oacyclic(T_a,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf]) ).

fof(f_3564_2,plain,
    ! [U_14078,U_14077] :
      ( c_Wellfounded_Owf(U_14077,U_14078)
      | ~ c_Wellfounded_Oacyclic(U_14077,U_14078)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14077,U_14077)),U_14078)) ),
    inference(variable_rename,[status(thm)],[f_3564_1]) ).

cnf(f_3564_3,plain,
    ( c_Wellfounded_Owf(U_14077,U_14078)
    | ~ c_Wellfounded_Oacyclic(U_14077,U_14078)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14077,U_14077)),U_14078)) ),
    inference(clausify,[status(thm)],[f_3564_2]) ).

fof(f_3565_1,plain,
    ! [V_r_2,T_a] :
      ( ( ( c_Wellfounded_Owf(T_a,V_r_2)
          | ~ c_Wellfounded_Oacyclic(T_a,V_r_2) )
        & ( c_Wellfounded_Oacyclic(T_a,V_r_2)
          | ~ c_Wellfounded_Owf(T_a,V_r_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite]) ).

fof(f_3565_2,plain,
    ! [U_14080,U_14079] :
      ( ( ( c_Wellfounded_Owf(U_14079,U_14080)
          | ~ c_Wellfounded_Oacyclic(U_14079,U_14080) )
        & ( c_Wellfounded_Oacyclic(U_14079,U_14080)
          | ~ c_Wellfounded_Owf(U_14079,U_14080) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14079,U_14079)),U_14080)) ),
    inference(variable_rename,[status(thm)],[f_3565_1]) ).

cnf(f_3565_3,plain,
    ( c_Wellfounded_Oacyclic(U_14079,U_14080)
    | ~ c_Wellfounded_Owf(U_14079,U_14080)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14079,U_14079)),U_14080)) ),
    inference(clausify,[status(thm)],[f_3565_2]) ).

cnf(f_3565_4,plain,
    ( c_Wellfounded_Owf(U_14079,U_14080)
    | ~ c_Wellfounded_Oacyclic(U_14079,U_14080)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14079,U_14079)),U_14080)) ),
    inference(clausify,[status(thm)],[f_3565_2]) ).

fof(f_3566_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Int__subset]) ).

fof(f_3566_2,plain,
    ! [U_14084,U_14083,U_14082,U_14081] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14081,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14081,U_14082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),U_14083),U_14084))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14081,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14081,U_14082),U_14083)),hAPP(c_Relation_ODomain(U_14081,U_14082),U_14084)))),
    inference(variable_rename,[status(thm)],[f_3566_1]) ).

cnf(f_3566_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14081,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14081,U_14082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),U_14083),U_14084))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14081,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14081,U_14082),U_14083)),hAPP(c_Relation_ODomain(U_14081,U_14082),U_14084)))),
    inference(clausify,[status(thm)],[f_3566_2]) ).

fof(f_3567_1,plain,
    ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(f_3567_2,plain,
    ! [U_14088,U_14087,U_14086,U_14085] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14085,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14085,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14085,U_14086),U_14087)),hAPP(c_Relation_ODomain(U_14085,U_14086),U_14088))),hAPP(c_Relation_ODomain(U_14085,U_14086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14085,U_14086),tc_HOL_Obool)),U_14087),U_14088)))),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

cnf(f_3567_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14085,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14085,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14085,U_14086),U_14087)),hAPP(c_Relation_ODomain(U_14085,U_14086),U_14088))),hAPP(c_Relation_ODomain(U_14085,U_14086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14085,U_14086),tc_HOL_Obool)),U_14087),U_14088)))),
    inference(clausify,[status(thm)],[f_3567_2]) ).

fof(f_3568_1,plain,
    ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__def]) ).

fof(f_3568_2,plain,
    ! [U_14090,U_14089] : hAPP(c_Relation_OField(U_14089),U_14090) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14089,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14089,U_14089),U_14090)),hAPP(c_Relation_ORange(U_14089,U_14089),U_14090)),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

cnf(f_3568_3,plain,
    hAPP(c_Relation_OField(U_14089),U_14090) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14089,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_14089,U_14089),U_14090)),hAPP(c_Relation_ORange(U_14089,U_14089),U_14090)),
    inference(clausify,[status(thm)],[f_3568_2]) ).

fof(f_3569_1,plain,
    ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Union]) ).

fof(f_3569_2,plain,
    ! [U_14093,U_14092,U_14091] : hAPP(c_Relation_ODomain(U_14091,U_14092),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_14091,U_14092),tc_HOL_Obool),U_14093)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_14091,U_14092),tc_HOL_Obool),tc_fun(U_14091,tc_HOL_Obool)),U_14093),c_Relation_ODomain(U_14091,U_14092)),
    inference(variable_rename,[status(thm)],[f_3569_1]) ).

cnf(f_3569_3,plain,
    hAPP(c_Relation_ODomain(U_14091,U_14092),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_14091,U_14092),tc_HOL_Obool),U_14093)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_14091,U_14092),tc_HOL_Obool),tc_fun(U_14091,tc_HOL_Obool)),U_14093),c_Relation_ODomain(U_14091,U_14092)),
    inference(clausify,[status(thm)],[f_3569_2]) ).

fof(f_3570_1,plain,
    ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).

fof(f_3570_2,plain,
    ! [U_14096,U_14095,U_14094] : hAPP(c_Relation_ODomain(U_14094,U_14095),hAPP(c_Set_OCollect(tc_prod(U_14094,U_14095)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14094,U_14095,tc_HOL_Obool),U_14096))) = hAPP(c_Set_OCollect(U_14094),hAPP(hAPP(c_COMBB(tc_fun(U_14095,tc_HOL_Obool),tc_HOL_Obool,U_14094),c_HOL_OEx(U_14095)),U_14096)),
    inference(variable_rename,[status(thm)],[f_3570_1]) ).

cnf(f_3570_3,plain,
    hAPP(c_Relation_ODomain(U_14094,U_14095),hAPP(c_Set_OCollect(tc_prod(U_14094,U_14095)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14094,U_14095,tc_HOL_Obool),U_14096))) = hAPP(c_Set_OCollect(U_14094),hAPP(hAPP(c_COMBB(tc_fun(U_14095,tc_HOL_Obool),tc_HOL_Obool,U_14094),c_HOL_OEx(U_14095)),U_14096)),
    inference(clausify,[status(thm)],[f_3570_2]) ).

fof(f_3571_1,plain,
    ! [V_x_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq]) ).

fof(f_3571_2,plain,
    ! [U_14100,U_14099,U_14098,U_14097] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_14097,U_14098,hAPP(hAPP(c_COMBC(U_14097,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBC(U_14098,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14097,U_14098)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_prod(U_14097,U_14098),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14097,U_14098)))),c_Product__Type_OPair(U_14097,U_14098)))),U_14099)),U_14100))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14097),U_14100),hAPP(c_Relation_ODomain(U_14097,U_14098),U_14099))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_14097),U_14100),hAPP(c_Relation_ODomain(U_14097,U_14098),U_14099)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14097,U_14098,hAPP(hAPP(c_COMBC(U_14097,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_fun(U_14098,tc_HOL_Obool)),U_14097),c_COMBC(U_14098,tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14098,tc_prod(U_14097,U_14098)),tc_fun(U_14098,tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool)),U_14097),hAPP(c_COMBB(tc_prod(U_14097,U_14098),tc_fun(tc_fun(tc_prod(U_14097,U_14098),tc_HOL_Obool),tc_HOL_Obool),U_14098),c_member(tc_prod(U_14097,U_14098)))),c_Product__Type_OPair(U_14097,U_14098)))),U_14099)),U_14100)) ) ),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

fof(f_3571_3,plain,
    ( ! [U_14108,U_14106,U_14104,U_14102] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_14102,U_14104,hAPP(hAPP(c_COMBC(U_14102,tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_fun(U_14104,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14104,tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_fun(U_14104,tc_HOL_Obool)),U_14102),c_COMBC(U_14104,tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14104,tc_prod(U_14102,U_14104)),tc_fun(U_14104,tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),U_14102),hAPP(c_COMBB(tc_prod(U_14102,U_14104),tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool),U_14104),c_member(tc_prod(U_14102,U_14104)))),c_Product__Type_OPair(U_14102,U_14104)))),U_14106)),U_14108))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14102),U_14108),hAPP(c_Relation_ODomain(U_14102,U_14104),U_14106))) )
    & ! [U_14107,U_14105,U_14103,U_14101] :
        ( hBOOL(hAPP(hAPP(c_member(U_14101),U_14107),hAPP(c_Relation_ODomain(U_14101,U_14103),U_14105)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14101,U_14103,hAPP(hAPP(c_COMBC(U_14101,tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_fun(U_14103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14103,tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_fun(U_14103,tc_HOL_Obool)),U_14101),c_COMBC(U_14103,tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14103,tc_prod(U_14101,U_14103)),tc_fun(U_14103,tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),U_14101),hAPP(c_COMBB(tc_prod(U_14101,U_14103),tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool),U_14103),c_member(tc_prod(U_14101,U_14103)))),c_Product__Type_OPair(U_14101,U_14103)))),U_14105)),U_14107)) ) ),
    inference(miniscope,[status(thm)],[f_3571_2]) ).

cnf(f_3571_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14101),U_14107),hAPP(c_Relation_ODomain(U_14101,U_14103),U_14105)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14101,U_14103,hAPP(hAPP(c_COMBC(U_14101,tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_fun(U_14103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14103,tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_fun(U_14103,tc_HOL_Obool)),U_14101),c_COMBC(U_14103,tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14103,tc_prod(U_14101,U_14103)),tc_fun(U_14103,tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool)),U_14101),hAPP(c_COMBB(tc_prod(U_14101,U_14103),tc_fun(tc_fun(tc_prod(U_14101,U_14103),tc_HOL_Obool),tc_HOL_Obool),U_14103),c_member(tc_prod(U_14101,U_14103)))),c_Product__Type_OPair(U_14101,U_14103)))),U_14105)),U_14107)) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

cnf(f_3571_5,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14102,U_14104,hAPP(hAPP(c_COMBC(U_14102,tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_fun(U_14104,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14104,tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_fun(U_14104,tc_HOL_Obool)),U_14102),c_COMBC(U_14104,tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14104,tc_prod(U_14102,U_14104)),tc_fun(U_14104,tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool)),U_14102),hAPP(c_COMBB(tc_prod(U_14102,U_14104),tc_fun(tc_fun(tc_prod(U_14102,U_14104),tc_HOL_Obool),tc_HOL_Obool),U_14104),c_member(tc_prod(U_14102,U_14104)))),c_Product__Type_OPair(U_14102,U_14104)))),U_14106)),U_14108))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14102),U_14108),hAPP(c_Relation_ODomain(U_14102,U_14104),U_14106))) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

fof(f_3572_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Nitpick_Owf_H(T_a,V_r_2)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) )
        | ~ c_Wellfounded_Oacyclic(T_a,V_r_2) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) )
          & c_Wellfounded_Oacyclic(T_a,V_r_2) )
        | ~ c_Nitpick_Owf_H(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def]) ).

fof(f_3572_2,plain,
    ! [U_14110,U_14109] :
      ( ( c_Nitpick_Owf_H(U_14109,U_14110)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14109,U_14109)),U_14110)) )
        | ~ c_Wellfounded_Oacyclic(U_14109,U_14110) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14109,U_14109)),U_14110)) )
          & c_Wellfounded_Oacyclic(U_14109,U_14110) )
        | ~ c_Nitpick_Owf_H(U_14109,U_14110) ) ),
    inference(variable_rename,[status(thm)],[f_3572_1]) ).

fof(f_3572_3,plain,
    ( ! [U_14114,U_14112] :
        ( c_Nitpick_Owf_H(U_14112,U_14114)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14112,U_14112)),U_14114)) )
        | ~ c_Wellfounded_Oacyclic(U_14112,U_14114) )
    & ! [U_14113,U_14111] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14111,U_14111)),U_14113)) )
          & c_Wellfounded_Oacyclic(U_14111,U_14113) )
        | ~ c_Nitpick_Owf_H(U_14111,U_14113) ) ),
    inference(miniscope,[status(thm)],[f_3572_2]) ).

cnf(f_3572_4,plain,
    ( c_Wellfounded_Oacyclic(U_14111,U_14113)
    | ~ c_Nitpick_Owf_H(U_14111,U_14113) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

cnf(f_3572_5,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14111,U_14111)),U_14113))
    | ~ c_Nitpick_Owf_H(U_14111,U_14113) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

cnf(f_3572_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14112,U_14112)),U_14114))
    | ~ c_Wellfounded_Oacyclic(U_14112,U_14114)
    | c_Nitpick_Owf_H(U_14112,U_14114) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

cnf(f_3572_7,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ c_Wellfounded_Oacyclic(U_14112,U_14114)
    | c_Nitpick_Owf_H(U_14112,U_14114) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

fof(f_3573_1,plain,
    ! [V_r_2,T_b,V_a_2,T_a] :
      ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DomainE]) ).

fof(f_3573_2,plain,
    ! [U_14119,U_14118,U_14117,U_14116] :
      ( ? [U_14115] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14116,U_14118)),hAPP(hAPP(c_Product__Type_OPair(U_14116,U_14118),U_14117),U_14115)),U_14119))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14116),U_14117),hAPP(c_Relation_ODomain(U_14116,U_14118),U_14119))) ),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

fof(f_3573_3,plain,
    ! [U_14119,U_14118,U_14117,U_14116] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14116,U_14118)),hAPP(hAPP(c_Product__Type_OPair(U_14116,U_14118),U_14117),sK336(U_14119,U_14118,U_14117,U_14116))),U_14119))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14116),U_14117),hAPP(c_Relation_ODomain(U_14116,U_14118),U_14119))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_14115,sK336(U_14119,U_14118,U_14117,U_14116))],[f_3573_2]) ).

cnf(f_3573_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14116,U_14118)),hAPP(hAPP(c_Product__Type_OPair(U_14116,U_14118),U_14117),sK336(U_14119,U_14118,U_14117,U_14116))),U_14119))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14116),U_14117),hAPP(c_Relation_ODomain(U_14116,U_14118),U_14119))) ),
    inference(clausify,[status(thm)],[f_3573_3]) ).

fof(f_3574_1,plain,
    ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,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_3574_2,plain,
    ! [U_14124,U_14123,U_14122,U_14121,U_14120] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_14123,U_14124,U_14120),U_14121))
      | ~ hBOOL(hAPP(hAPP(U_14120,U_14121),U_14122)) ),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

cnf(f_3574_3,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14123,U_14124,U_14120),U_14121))
    | ~ hBOOL(hAPP(hAPP(U_14120,U_14121),U_14122)) ),
    inference(clausify,[status(thm)],[f_3574_2]) ).

fof(f_3575_1,plain,
    ! [V_a1_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,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_a,T_b,V_r_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations]) ).

fof(f_3575_2,plain,
    ! [U_14130,U_14129,U_14128,U_14127] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_14127,U_14128,U_14129),U_14130))
        | ! [U_14126] : ~ hBOOL(hAPP(hAPP(U_14129,U_14130),U_14126)) )
      & ( ? [U_14125] : hBOOL(hAPP(hAPP(U_14129,U_14130),U_14125))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14127,U_14128,U_14129),U_14130)) ) ),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

fof(f_3575_3,plain,
    ( ! [U_14138,U_14136] :
        ( ! [U_14134,U_14132] : hBOOL(hAPP(c_Predicate_ODomainP(U_14132,U_14134,U_14136),U_14138))
        | ! [U_14126] : ~ hBOOL(hAPP(hAPP(U_14136,U_14138),U_14126)) )
    & ! [U_14137,U_14135] :
        ( ! [U_14133,U_14131] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14131,U_14133,U_14135),U_14137))
        | ? [U_14125] : hBOOL(hAPP(hAPP(U_14135,U_14137),U_14125)) ) ),
    inference(miniscope,[status(thm)],[f_3575_2]) ).

fof(f_3575_4,plain,
    ( ! [U_14138,U_14136] :
        ( ! [U_14134,U_14132] : hBOOL(hAPP(c_Predicate_ODomainP(U_14132,U_14134,U_14136),U_14138))
        | ! [U_14126] : ~ hBOOL(hAPP(hAPP(U_14136,U_14138),U_14126)) )
    & ! [U_14137,U_14135] :
        ( ! [U_14133,U_14131] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14131,U_14133,U_14135),U_14137))
        | hBOOL(hAPP(hAPP(U_14135,U_14137),sK337(U_14137,U_14135))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_14125,sK337(U_14137,U_14135))],[f_3575_3]) ).

cnf(f_3575_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_14131,U_14133,U_14135),U_14137))
    | hBOOL(hAPP(hAPP(U_14135,U_14137),sK337(U_14137,U_14135))) ),
    inference(clausify,[status(thm)],[f_3575_4]) ).

cnf(f_3575_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_14132,U_14134,U_14136),U_14138))
    | ~ hBOOL(hAPP(hAPP(U_14136,U_14138),U_14126)) ),
    inference(clausify,[status(thm)],[f_3575_4]) ).

fof(f_3576_1,plain,
    ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj]) ).

fof(f_3576_2,plain,
    ! [U_14144,U_14143,U_14142,U_14141,U_14140,U_14139] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14139,U_14142),tc_prod(U_14140,U_14143),c_Product__Type_Omap__pair(U_14139,U_14140,U_14142,U_14143,U_14141,U_14144)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14139,U_14142),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14140,U_14143),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14142,U_14143,U_14144),c_Orderings_Otop__class_Otop(tc_fun(U_14142,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14143,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14139,U_14140,U_14141),c_Orderings_Otop__class_Otop(tc_fun(U_14139,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14140,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

cnf(f_3576_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14139,U_14142),tc_prod(U_14140,U_14143),c_Product__Type_Omap__pair(U_14139,U_14140,U_14142,U_14143,U_14141,U_14144)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14139,U_14142),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14140,U_14143),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14142,U_14143,U_14144),c_Orderings_Otop__class_Otop(tc_fun(U_14142,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14143,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14139,U_14140,U_14141),c_Orderings_Otop__class_Otop(tc_fun(U_14139,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14140,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3576_2]) ).

fof(f_3577_1,plain,
    ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2)))
      | ~ c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on]) ).

fof(f_3577_2,plain,
    ! [U_14152,U_14151,U_14150,U_14149,U_14148,U_14147,U_14146,U_14145] :
      ( c_Fun_Oinj__on(tc_prod(U_14145,U_14149),tc_prod(U_14146,U_14150),c_Product__Type_Omap__pair(U_14145,U_14146,U_14149,U_14150,U_14147,U_14151),hAPP(hAPP(c_Product__Type_OSigma(U_14145,U_14149),U_14148),hAPP(c_COMBK(tc_fun(U_14149,tc_HOL_Obool),U_14145),U_14152)))
      | ~ c_Fun_Oinj__on(U_14149,U_14150,U_14151,U_14152)
      | ~ c_Fun_Oinj__on(U_14145,U_14146,U_14147,U_14148) ),
    inference(variable_rename,[status(thm)],[f_3577_1]) ).

cnf(f_3577_3,plain,
    ( c_Fun_Oinj__on(tc_prod(U_14145,U_14149),tc_prod(U_14146,U_14150),c_Product__Type_Omap__pair(U_14145,U_14146,U_14149,U_14150,U_14147,U_14151),hAPP(hAPP(c_Product__Type_OSigma(U_14145,U_14149),U_14148),hAPP(c_COMBK(tc_fun(U_14149,tc_HOL_Obool),U_14145),U_14152)))
    | ~ c_Fun_Oinj__on(U_14149,U_14150,U_14151,U_14152)
    | ~ c_Fun_Oinj__on(U_14145,U_14146,U_14147,U_14148) ),
    inference(clausify,[status(thm)],[f_3577_2]) ).

fof(f_3578_1,plain,
    ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__imageI]) ).

fof(f_3578_2,plain,
    ! [U_14161,U_14160,U_14159,U_14158,U_14157,U_14156,U_14155,U_14154,U_14153] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14158,U_14159)),hAPP(hAPP(c_Product__Type_OPair(U_14158,U_14159),hAPP(U_14160,U_14155)),hAPP(U_14161,U_14156))),hAPP(c_Set_Oimage(tc_prod(U_14153,U_14154),tc_prod(U_14158,U_14159),c_Product__Type_Omap__pair(U_14153,U_14158,U_14154,U_14159,U_14160,U_14161)),U_14157)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14153,U_14154)),hAPP(hAPP(c_Product__Type_OPair(U_14153,U_14154),U_14155),U_14156)),U_14157)) ),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

cnf(f_3578_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14158,U_14159)),hAPP(hAPP(c_Product__Type_OPair(U_14158,U_14159),hAPP(U_14160,U_14155)),hAPP(U_14161,U_14156))),hAPP(c_Set_Oimage(tc_prod(U_14153,U_14154),tc_prod(U_14158,U_14159),c_Product__Type_Omap__pair(U_14153,U_14158,U_14154,U_14159,U_14160,U_14161)),U_14157)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14153,U_14154)),hAPP(hAPP(c_Product__Type_OPair(U_14153,U_14154),U_14155),U_14156)),U_14157)) ),
    inference(clausify,[status(thm)],[f_3578_2]) ).

fof(f_3579_1,plain,
    ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(f_3579_2,plain,
    ! [U_14172,U_14171,U_14170,U_14169,U_14168,U_14167,U_14166,U_14165,U_14164,U_14163,U_14162] : hAPP(c_Product__Type_Omap__pair(U_14162,U_14163,U_14164,U_14165,U_14166,U_14167),hAPP(c_Product__Type_Omap__pair(U_14168,U_14162,U_14169,U_14164,U_14170,U_14171),U_14172)) = hAPP(c_Product__Type_Omap__pair(U_14168,U_14163,U_14169,U_14165,hAPP(c_Fun_Ocomp(U_14162,U_14163,U_14168,U_14166),U_14170),hAPP(c_Fun_Ocomp(U_14164,U_14165,U_14169,U_14167),U_14171)),U_14172),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

cnf(f_3579_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_14162,U_14163,U_14164,U_14165,U_14166,U_14167),hAPP(c_Product__Type_Omap__pair(U_14168,U_14162,U_14169,U_14164,U_14170,U_14171),U_14172)) = hAPP(c_Product__Type_Omap__pair(U_14168,U_14163,U_14169,U_14165,hAPP(c_Fun_Ocomp(U_14162,U_14163,U_14168,U_14166),U_14170),hAPP(c_Fun_Ocomp(U_14164,U_14165,U_14169,U_14167),U_14171)),U_14172),
    inference(clausify,[status(thm)],[f_3579_2]) ).

fof(f_3580_1,plain,
    ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__compose]) ).

fof(f_3580_2,plain,
    ! [U_14182,U_14181,U_14180,U_14179,U_14178,U_14177,U_14176,U_14175,U_14174,U_14173] : c_Product__Type_Omap__pair(U_14173,U_14174,U_14175,U_14176,hAPP(c_Fun_Ocomp(U_14177,U_14174,U_14173,U_14178),U_14179),hAPP(c_Fun_Ocomp(U_14180,U_14176,U_14175,U_14181),U_14182)) = hAPP(c_Fun_Ocomp(tc_prod(U_14177,U_14180),tc_prod(U_14174,U_14176),tc_prod(U_14173,U_14175),c_Product__Type_Omap__pair(U_14177,U_14174,U_14180,U_14176,U_14178,U_14181)),c_Product__Type_Omap__pair(U_14173,U_14177,U_14175,U_14180,U_14179,U_14182)),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

cnf(f_3580_3,plain,
    c_Product__Type_Omap__pair(U_14173,U_14174,U_14175,U_14176,hAPP(c_Fun_Ocomp(U_14177,U_14174,U_14173,U_14178),U_14179),hAPP(c_Fun_Ocomp(U_14180,U_14176,U_14175,U_14181),U_14182)) = hAPP(c_Fun_Ocomp(tc_prod(U_14177,U_14180),tc_prod(U_14174,U_14176),tc_prod(U_14173,U_14175),c_Product__Type_Omap__pair(U_14177,U_14174,U_14180,U_14176,U_14178,U_14181)),c_Product__Type_Omap__pair(U_14173,U_14177,U_14175,U_14180,U_14179,U_14182)),
    inference(clausify,[status(thm)],[f_3580_2]) ).

fof(f_3581_1,plain,
    ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(f_3581_2,plain,
    ! [U_14192,U_14191,U_14190,U_14189,U_14188,U_14187,U_14186,U_14185,U_14184,U_14183] : hAPP(c_Fun_Ocomp(tc_prod(U_14183,U_14184),tc_prod(U_14185,U_14186),tc_prod(U_14187,U_14188),c_Product__Type_Omap__pair(U_14183,U_14185,U_14184,U_14186,U_14189,U_14190)),c_Product__Type_Omap__pair(U_14187,U_14183,U_14188,U_14184,U_14191,U_14192)) = c_Product__Type_Omap__pair(U_14187,U_14185,U_14188,U_14186,hAPP(c_Fun_Ocomp(U_14183,U_14185,U_14187,U_14189),U_14191),hAPP(c_Fun_Ocomp(U_14184,U_14186,U_14188,U_14190),U_14192)),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

cnf(f_3581_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14183,U_14184),tc_prod(U_14185,U_14186),tc_prod(U_14187,U_14188),c_Product__Type_Omap__pair(U_14183,U_14185,U_14184,U_14186,U_14189,U_14190)),c_Product__Type_Omap__pair(U_14187,U_14183,U_14188,U_14184,U_14191,U_14192)) = c_Product__Type_Omap__pair(U_14187,U_14185,U_14188,U_14186,hAPP(c_Fun_Ocomp(U_14183,U_14185,U_14187,U_14189),U_14191),hAPP(c_Fun_Ocomp(U_14184,U_14186,U_14188,U_14190),U_14192)),
    inference(clausify,[status(thm)],[f_3581_2]) ).

fof(f_3582_1,plain,
    ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(f_3582_2,plain,
    ! [U_14198,U_14197,U_14196,U_14195,U_14194,U_14193] : hAPP(c_Fun_Ocomp(tc_prod(U_14193,U_14194),U_14194,tc_prod(U_14195,U_14196),c_Product__Type_Osnd(U_14193,U_14194)),c_Product__Type_Omap__pair(U_14195,U_14193,U_14196,U_14194,U_14197,U_14198)) = hAPP(c_Fun_Ocomp(U_14196,U_14194,tc_prod(U_14195,U_14196),U_14198),c_Product__Type_Osnd(U_14195,U_14196)),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

cnf(f_3582_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14193,U_14194),U_14194,tc_prod(U_14195,U_14196),c_Product__Type_Osnd(U_14193,U_14194)),c_Product__Type_Omap__pair(U_14195,U_14193,U_14196,U_14194,U_14197,U_14198)) = hAPP(c_Fun_Ocomp(U_14196,U_14194,tc_prod(U_14195,U_14196),U_14198),c_Product__Type_Osnd(U_14195,U_14196)),
    inference(clausify,[status(thm)],[f_3582_2]) ).

fof(f_3583_1,plain,
    ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(f_3583_2,plain,
    ! [U_14204,U_14203,U_14202,U_14201,U_14200,U_14199] : hAPP(c_Fun_Ocomp(tc_prod(U_14199,U_14200),U_14199,tc_prod(U_14201,U_14202),c_Product__Type_Ofst(U_14199,U_14200)),c_Product__Type_Omap__pair(U_14201,U_14199,U_14202,U_14200,U_14203,U_14204)) = hAPP(c_Fun_Ocomp(U_14201,U_14199,tc_prod(U_14201,U_14202),U_14203),c_Product__Type_Ofst(U_14201,U_14202)),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

cnf(f_3583_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14199,U_14200),U_14199,tc_prod(U_14201,U_14202),c_Product__Type_Ofst(U_14199,U_14200)),c_Product__Type_Omap__pair(U_14201,U_14199,U_14202,U_14200,U_14203,U_14204)) = hAPP(c_Fun_Ocomp(U_14201,U_14199,tc_prod(U_14201,U_14202),U_14203),c_Product__Type_Ofst(U_14201,U_14202)),
    inference(clausify,[status(thm)],[f_3583_2]) ).

fof(f_3584_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__map__pair]) ).

fof(f_3584_2,plain,
    ! [U_14211,U_14210,U_14209,U_14208,U_14207,U_14206,U_14205] : hAPP(c_Product__Type_Ofst(U_14205,U_14206),hAPP(c_Product__Type_Omap__pair(U_14207,U_14205,U_14208,U_14206,U_14209,U_14210),U_14211)) = hAPP(U_14209,hAPP(c_Product__Type_Ofst(U_14207,U_14208),U_14211)),
    inference(variable_rename,[status(thm)],[f_3584_1]) ).

cnf(f_3584_3,plain,
    hAPP(c_Product__Type_Ofst(U_14205,U_14206),hAPP(c_Product__Type_Omap__pair(U_14207,U_14205,U_14208,U_14206,U_14209,U_14210),U_14211)) = hAPP(U_14209,hAPP(c_Product__Type_Ofst(U_14207,U_14208),U_14211)),
    inference(clausify,[status(thm)],[f_3584_2]) ).

fof(f_3585_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__prod__fun]) ).

fof(f_3585_2,plain,
    ! [U_14218,U_14217,U_14216,U_14215,U_14214,U_14213,U_14212] : hAPP(c_Product__Type_Osnd(U_14212,U_14213),hAPP(c_Product__Type_Omap__pair(U_14214,U_14212,U_14215,U_14213,U_14216,U_14217),U_14218)) = hAPP(U_14217,hAPP(c_Product__Type_Osnd(U_14214,U_14215),U_14218)),
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

cnf(f_3585_3,plain,
    hAPP(c_Product__Type_Osnd(U_14212,U_14213),hAPP(c_Product__Type_Omap__pair(U_14214,U_14212,U_14215,U_14213,U_14216,U_14217),U_14218)) = hAPP(U_14217,hAPP(c_Product__Type_Osnd(U_14214,U_14215),U_14218)),
    inference(clausify,[status(thm)],[f_3585_2]) ).

fof(f_3586_1,plain,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_3586_2,plain,
    ! [U_14226,U_14225,U_14224,U_14223,U_14222,U_14221,U_14220,U_14219] : hAPP(c_Product__Type_Omap__pair(U_14219,U_14220,U_14221,U_14222,U_14223,U_14224),hAPP(hAPP(c_Product__Type_OPair(U_14219,U_14221),U_14225),U_14226)) = hAPP(hAPP(c_Product__Type_OPair(U_14220,U_14222),hAPP(U_14223,U_14225)),hAPP(U_14224,U_14226)),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

cnf(f_3586_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_14219,U_14220,U_14221,U_14222,U_14223,U_14224),hAPP(hAPP(c_Product__Type_OPair(U_14219,U_14221),U_14225),U_14226)) = hAPP(hAPP(c_Product__Type_OPair(U_14220,U_14222),hAPP(U_14223,U_14225)),hAPP(U_14224,U_14226)),
    inference(clausify,[status(thm)],[f_3586_2]) ).

fof(f_3587_1,plain,
    ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_map__pair__ident]) ).

fof(f_3587_2,plain,
    ! [U_14229,U_14228,U_14227] : hAPP(c_Product__Type_Omap__pair(U_14227,U_14227,U_14228,U_14228,c_COMBI(U_14227),c_COMBI(U_14228)),U_14229) = U_14229,
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

cnf(f_3587_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_14227,U_14227,U_14228,U_14228,c_COMBI(U_14227),c_COMBI(U_14228)),U_14229) = U_14229,
    inference(clausify,[status(thm)],[f_3587_2]) ).

fof(f_3588_1,plain,
    ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oidentity]) ).

fof(f_3588_2,plain,
    ! [U_14231,U_14230] : c_Product__Type_Omap__pair(U_14230,U_14230,U_14231,U_14231,c_COMBI(U_14230),c_COMBI(U_14231)) = c_Fun_Oid(tc_prod(U_14230,U_14231)),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

cnf(f_3588_3,plain,
    c_Product__Type_Omap__pair(U_14230,U_14230,U_14231,U_14231,c_COMBI(U_14230),c_COMBI(U_14231)) = c_Fun_Oid(tc_prod(U_14230,U_14231)),
    inference(clausify,[status(thm)],[f_3588_2]) ).

fof(f_3589_1,plain,
    ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__def]) ).

fof(f_3589_2,plain,
    ! [U_14235,U_14234,U_14233,U_14232] : c_Product__Type_Oapsnd(U_14232,U_14233,U_14234,U_14235) = c_Product__Type_Omap__pair(U_14234,U_14234,U_14232,U_14233,c_Fun_Oid(U_14234),U_14235),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

cnf(f_3589_3,plain,
    c_Product__Type_Oapsnd(U_14232,U_14233,U_14234,U_14235) = c_Product__Type_Omap__pair(U_14234,U_14234,U_14232,U_14233,c_Fun_Oid(U_14234),U_14235),
    inference(clausify,[status(thm)],[f_3589_2]) ).

fof(f_3590_1,plain,
    ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)),
    inference(fof_nnf,[status(thm)],[fact_apfst__def]) ).

fof(f_3590_2,plain,
    ! [U_14239,U_14238,U_14237,U_14236] : c_Product__Type_Oapfst(U_14236,U_14237,U_14238,U_14239) = c_Product__Type_Omap__pair(U_14236,U_14237,U_14238,U_14238,U_14239,c_Fun_Oid(U_14238)),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

cnf(f_3590_3,plain,
    c_Product__Type_Oapfst(U_14236,U_14237,U_14238,U_14239) = c_Product__Type_Omap__pair(U_14236,U_14237,U_14238,U_14238,U_14239,c_Fun_Oid(U_14238)),
    inference(clausify,[status(thm)],[f_3590_2]) ).

fof(f_3591_1,plain,
    ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oid]) ).

fof(f_3591_2,plain,
    ! [U_14241,U_14240] : c_Product__Type_Omap__pair(U_14240,U_14240,U_14241,U_14241,c_Fun_Oid(U_14240),c_Fun_Oid(U_14241)) = c_Fun_Oid(tc_prod(U_14240,U_14241)),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

cnf(f_3591_3,plain,
    c_Product__Type_Omap__pair(U_14240,U_14240,U_14241,U_14241,c_Fun_Oid(U_14240),c_Fun_Oid(U_14241)) = c_Fun_Oid(tc_prod(U_14240,U_14241)),
    inference(clausify,[status(thm)],[f_3591_2]) ).

fof(f_3592_1,plain,
    ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,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_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__def]) ).

fof(f_3592_2,plain,
    ! [U_14247,U_14246,U_14245,U_14244,U_14243,U_14242] : c_Product__Type_Omap__pair(U_14242,U_14243,U_14244,U_14245,U_14246,U_14247) = hAPP(c_Product__Type_Oprod_Oprod__case(U_14242,U_14244,tc_prod(U_14243,U_14245)),hAPP(hAPP(c_COMBC(U_14242,tc_fun(U_14244,U_14245),tc_fun(U_14244,tc_prod(U_14243,U_14245))),hAPP(hAPP(c_COMBB(tc_fun(U_14245,tc_prod(U_14243,U_14245)),tc_fun(tc_fun(U_14244,U_14245),tc_fun(U_14244,tc_prod(U_14243,U_14245))),U_14242),c_COMBB(U_14245,tc_prod(U_14243,U_14245),U_14244)),hAPP(hAPP(c_COMBB(U_14243,tc_fun(U_14245,tc_prod(U_14243,U_14245)),U_14242),c_Product__Type_OPair(U_14243,U_14245)),U_14246))),U_14247)),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

cnf(f_3592_3,plain,
    c_Product__Type_Omap__pair(U_14242,U_14243,U_14244,U_14245,U_14246,U_14247) = hAPP(c_Product__Type_Oprod_Oprod__case(U_14242,U_14244,tc_prod(U_14243,U_14245)),hAPP(hAPP(c_COMBC(U_14242,tc_fun(U_14244,U_14245),tc_fun(U_14244,tc_prod(U_14243,U_14245))),hAPP(hAPP(c_COMBB(tc_fun(U_14245,tc_prod(U_14243,U_14245)),tc_fun(tc_fun(U_14244,U_14245),tc_fun(U_14244,tc_prod(U_14243,U_14245))),U_14242),c_COMBB(U_14245,tc_prod(U_14243,U_14245),U_14244)),hAPP(hAPP(c_COMBB(U_14243,tc_fun(U_14245,tc_prod(U_14243,U_14245)),U_14242),c_Product__Type_OPair(U_14243,U_14245)),U_14246))),U_14247)),
    inference(clausify,[status(thm)],[f_3592_2]) ).

fof(f_3593_1,plain,
    ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,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))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2))
      | hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) != V_B_H_2
      | hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) != V_A_H_2 ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on]) ).

fof(f_3593_2,plain,
    ! [U_14257,U_14256,U_14255,U_14254,U_14253,U_14252,U_14251,U_14250,U_14249,U_14248] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14248,U_14253),tc_prod(U_14249,U_14254),c_Product__Type_Omap__pair(U_14248,U_14249,U_14253,U_14254,U_14250,U_14255)),hAPP(hAPP(c_Product__Type_OSigma(U_14248,U_14253),U_14251),hAPP(c_COMBK(tc_fun(U_14253,tc_HOL_Obool),U_14248),U_14256))) = hAPP(hAPP(c_Product__Type_OSigma(U_14249,U_14254),U_14252),hAPP(c_COMBK(tc_fun(U_14254,tc_HOL_Obool),U_14249),U_14257))
      | hAPP(c_Set_Oimage(U_14253,U_14254,U_14255),U_14256) != U_14257
      | hAPP(c_Set_Oimage(U_14248,U_14249,U_14250),U_14251) != U_14252 ),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

cnf(f_3593_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14248,U_14253),tc_prod(U_14249,U_14254),c_Product__Type_Omap__pair(U_14248,U_14249,U_14253,U_14254,U_14250,U_14255)),hAPP(hAPP(c_Product__Type_OSigma(U_14248,U_14253),U_14251),hAPP(c_COMBK(tc_fun(U_14253,tc_HOL_Obool),U_14248),U_14256))) = hAPP(hAPP(c_Product__Type_OSigma(U_14249,U_14254),U_14252),hAPP(c_COMBK(tc_fun(U_14254,tc_HOL_Obool),U_14249),U_14257))
    | hAPP(c_Set_Oimage(U_14253,U_14254,U_14255),U_14256) != U_14257
    | hAPP(c_Set_Oimage(U_14248,U_14249,U_14250),U_14251) != U_14252 ),
    inference(clausify,[status(thm)],[f_3593_2]) ).

fof(f_3594_1,plain,
    ! [V_f_2,T_b,V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image]) ).

fof(f_3594_2,plain,
    ! [U_14261,U_14260,U_14259,U_14258] :
      ( c_Wellfounded_Owf(U_14260,hAPP(c_Set_Oimage(tc_prod(U_14258,U_14258),tc_prod(U_14260,U_14260),c_Product__Type_Omap__pair(U_14258,U_14260,U_14258,U_14260,U_14261,U_14261)),U_14259))
      | ~ c_Fun_Oinj__on(U_14258,U_14260,U_14261,c_Orderings_Otop__class_Otop(tc_fun(U_14258,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_14258,U_14259) ),
    inference(variable_rename,[status(thm)],[f_3594_1]) ).

cnf(f_3594_3,plain,
    ( c_Wellfounded_Owf(U_14260,hAPP(c_Set_Oimage(tc_prod(U_14258,U_14258),tc_prod(U_14260,U_14260),c_Product__Type_Omap__pair(U_14258,U_14260,U_14258,U_14260,U_14261,U_14261)),U_14259))
    | ~ c_Fun_Oinj__on(U_14258,U_14260,U_14261,c_Orderings_Otop__class_Otop(tc_fun(U_14258,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_14258,U_14259) ),
    inference(clausify,[status(thm)],[f_3594_2]) ).

fof(f_3595_1,plain,
    ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2))
          & V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_prod__fun__imageE]) ).

fof(f_3595_2,plain,
    ! [U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264] :
      ( ? [U_14263,U_14262] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14267,U_14268)),hAPP(hAPP(c_Product__Type_OPair(U_14267,U_14268),U_14263),U_14262)),U_14271))
          & U_14266 = hAPP(hAPP(c_Product__Type_OPair(U_14264,U_14265),hAPP(U_14269,U_14263)),hAPP(U_14270,U_14262)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14264,U_14265)),U_14266),hAPP(c_Set_Oimage(tc_prod(U_14267,U_14268),tc_prod(U_14264,U_14265),c_Product__Type_Omap__pair(U_14267,U_14264,U_14268,U_14265,U_14269,U_14270)),U_14271))) ),
    inference(variable_rename,[status(thm)],[f_3595_1]) ).

fof(f_3595_3,plain,
    ! [U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264] :
      ( ? [U_14262] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14267,U_14268)),hAPP(hAPP(c_Product__Type_OPair(U_14267,U_14268),sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264)),U_14262)),U_14271))
          & U_14266 = hAPP(hAPP(c_Product__Type_OPair(U_14264,U_14265),hAPP(U_14269,sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))),hAPP(U_14270,U_14262)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14264,U_14265)),U_14266),hAPP(c_Set_Oimage(tc_prod(U_14267,U_14268),tc_prod(U_14264,U_14265),c_Product__Type_Omap__pair(U_14267,U_14264,U_14268,U_14265,U_14269,U_14270)),U_14271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_14263,sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))],[f_3595_2]) ).

fof(f_3595_4,plain,
    ! [U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14267,U_14268)),hAPP(hAPP(c_Product__Type_OPair(U_14267,U_14268),sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264)),sK339(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))),U_14271))
        & U_14266 = hAPP(hAPP(c_Product__Type_OPair(U_14264,U_14265),hAPP(U_14269,sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))),hAPP(U_14270,sK339(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14264,U_14265)),U_14266),hAPP(c_Set_Oimage(tc_prod(U_14267,U_14268),tc_prod(U_14264,U_14265),c_Product__Type_Omap__pair(U_14267,U_14264,U_14268,U_14265,U_14269,U_14270)),U_14271))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_14262,sK339(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))],[f_3595_3]) ).

cnf(f_3595_5,plain,
    ( U_14266 = hAPP(hAPP(c_Product__Type_OPair(U_14264,U_14265),hAPP(U_14269,sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))),hAPP(U_14270,sK339(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14264,U_14265)),U_14266),hAPP(c_Set_Oimage(tc_prod(U_14267,U_14268),tc_prod(U_14264,U_14265),c_Product__Type_Omap__pair(U_14267,U_14264,U_14268,U_14265,U_14269,U_14270)),U_14271))) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14267,U_14268)),hAPP(hAPP(c_Product__Type_OPair(U_14267,U_14268),sK338(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264)),sK339(U_14271,U_14270,U_14269,U_14268,U_14267,U_14266,U_14265,U_14264))),U_14271))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14264,U_14265)),U_14266),hAPP(c_Set_Oimage(tc_prod(U_14267,U_14268),tc_prod(U_14264,U_14265),c_Product__Type_Omap__pair(U_14267,U_14264,U_14268,U_14265,U_14269,U_14270)),U_14271))) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

fof(f_3596_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) )
        | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def]) ).

fof(f_3596_2,plain,
    ! [U_14276,U_14275,U_14274] :
      ( ( c_Relation_Orefl__on(U_14274,U_14275,U_14276)
        | ? [U_14273] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14273),U_14273)),U_14276))
            & hBOOL(hAPP(hAPP(c_member(U_14274),U_14273),U_14275)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14276),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14275),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14275)))) )
      & ( ( ! [U_14272] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14272),U_14272)),U_14276))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14274),U_14272),U_14275)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14276),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14275),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14275)))) )
        | ~ c_Relation_Orefl__on(U_14274,U_14275,U_14276) ) ),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

fof(f_3596_3,plain,
    ( ! [U_14282,U_14280,U_14278] :
        ( c_Relation_Orefl__on(U_14278,U_14280,U_14282)
        | ? [U_14273] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14278,U_14278)),hAPP(hAPP(c_Product__Type_OPair(U_14278,U_14278),U_14273),U_14273)),U_14282))
            & hBOOL(hAPP(hAPP(c_member(U_14278),U_14273),U_14280)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14278,U_14278),tc_HOL_Obool)),U_14282),hAPP(hAPP(c_Product__Type_OSigma(U_14278,U_14278),U_14280),hAPP(c_COMBK(tc_fun(U_14278,tc_HOL_Obool),U_14278),U_14280)))) )
    & ! [U_14281,U_14279,U_14277] :
        ( ( ! [U_14272] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14277,U_14277)),hAPP(hAPP(c_Product__Type_OPair(U_14277,U_14277),U_14272),U_14272)),U_14281))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14277),U_14272),U_14279)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14277,U_14277),tc_HOL_Obool)),U_14281),hAPP(hAPP(c_Product__Type_OSigma(U_14277,U_14277),U_14279),hAPP(c_COMBK(tc_fun(U_14277,tc_HOL_Obool),U_14277),U_14279)))) )
        | ~ c_Relation_Orefl__on(U_14277,U_14279,U_14281) ) ),
    inference(miniscope,[status(thm)],[f_3596_2]) ).

fof(f_3596_4,plain,
    ( ! [U_14282,U_14280,U_14278] :
        ( c_Relation_Orefl__on(U_14278,U_14280,U_14282)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14278,U_14278)),hAPP(hAPP(c_Product__Type_OPair(U_14278,U_14278),sK340(U_14282,U_14280,U_14278)),sK340(U_14282,U_14280,U_14278))),U_14282))
          & hBOOL(hAPP(hAPP(c_member(U_14278),sK340(U_14282,U_14280,U_14278)),U_14280)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14278,U_14278),tc_HOL_Obool)),U_14282),hAPP(hAPP(c_Product__Type_OSigma(U_14278,U_14278),U_14280),hAPP(c_COMBK(tc_fun(U_14278,tc_HOL_Obool),U_14278),U_14280)))) )
    & ! [U_14281,U_14279,U_14277] :
        ( ( ! [U_14272] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14277,U_14277)),hAPP(hAPP(c_Product__Type_OPair(U_14277,U_14277),U_14272),U_14272)),U_14281))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14277),U_14272),U_14279)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14277,U_14277),tc_HOL_Obool)),U_14281),hAPP(hAPP(c_Product__Type_OSigma(U_14277,U_14277),U_14279),hAPP(c_COMBK(tc_fun(U_14277,tc_HOL_Obool),U_14277),U_14279)))) )
        | ~ c_Relation_Orefl__on(U_14277,U_14279,U_14281) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_14273,sK340(U_14282,U_14280,U_14278))],[f_3596_3]) ).

cnf(f_3596_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14277,U_14277),tc_HOL_Obool)),U_14281),hAPP(hAPP(c_Product__Type_OSigma(U_14277,U_14277),U_14279),hAPP(c_COMBK(tc_fun(U_14277,tc_HOL_Obool),U_14277),U_14279))))
    | ~ c_Relation_Orefl__on(U_14277,U_14279,U_14281) ),
    inference(clausify,[status(thm)],[f_3596_4]) ).

cnf(f_3596_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14277,U_14277)),hAPP(hAPP(c_Product__Type_OPair(U_14277,U_14277),U_14272),U_14272)),U_14281))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14277),U_14272),U_14279))
    | ~ c_Relation_Orefl__on(U_14277,U_14279,U_14281) ),
    inference(clausify,[status(thm)],[f_3596_4]) ).

cnf(f_3596_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14278),sK340(U_14282,U_14280,U_14278)),U_14280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14278,U_14278),tc_HOL_Obool)),U_14282),hAPP(hAPP(c_Product__Type_OSigma(U_14278,U_14278),U_14280),hAPP(c_COMBK(tc_fun(U_14278,tc_HOL_Obool),U_14278),U_14280))))
    | c_Relation_Orefl__on(U_14278,U_14280,U_14282) ),
    inference(clausify,[status(thm)],[f_3596_4]) ).

cnf(f_3596_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14278,U_14278)),hAPP(hAPP(c_Product__Type_OPair(U_14278,U_14278),sK340(U_14282,U_14280,U_14278)),sK340(U_14282,U_14280,U_14278))),U_14282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14278,U_14278),tc_HOL_Obool)),U_14282),hAPP(hAPP(c_Product__Type_OSigma(U_14278,U_14278),U_14280),hAPP(c_COMBK(tc_fun(U_14278,tc_HOL_Obool),U_14278),U_14280))))
    | c_Relation_Orefl__on(U_14278,U_14280,U_14282) ),
    inference(clausify,[status(thm)],[f_3596_4]) ).

fof(f_3597_1,plain,
    ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Id__on]) ).

fof(f_3597_2,plain,
    ! [U_14284,U_14283] : c_Relation_Orefl__on(U_14283,U_14284,c_Relation_OId__on(U_14283,U_14284)),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

cnf(f_3597_3,plain,
    c_Relation_Orefl__on(U_14283,U_14284,c_Relation_OId__on(U_14283,U_14284)),
    inference(clausify,[status(thm)],[f_3597_2]) ).

fof(f_3598_1,plain,
    ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_refl__on__empty]) ).

fof(f_3598_2,plain,
    ! [U_14285] : c_Relation_Orefl__on(U_14285,c_Orderings_Obot__class_Obot(tc_fun(U_14285,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14285,U_14285),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

cnf(f_3598_3,plain,
    c_Relation_Orefl__on(U_14285,c_Orderings_Obot__class_Obot(tc_fun(U_14285,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14285,U_14285),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3598_2]) ).

fof(f_3599_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Un]) ).

fof(f_3599_2,plain,
    ! [U_14290,U_14289,U_14288,U_14287,U_14286] :
      ( c_Relation_Orefl__on(U_14286,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14286,tc_HOL_Obool)),U_14287),U_14289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14286,U_14286),tc_HOL_Obool)),U_14288),U_14290))
      | ~ c_Relation_Orefl__on(U_14286,U_14289,U_14290)
      | ~ c_Relation_Orefl__on(U_14286,U_14287,U_14288) ),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

cnf(f_3599_3,plain,
    ( c_Relation_Orefl__on(U_14286,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14286,tc_HOL_Obool)),U_14287),U_14289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14286,U_14286),tc_HOL_Obool)),U_14288),U_14290))
    | ~ c_Relation_Orefl__on(U_14286,U_14289,U_14290)
    | ~ c_Relation_Orefl__on(U_14286,U_14287,U_14288) ),
    inference(clausify,[status(thm)],[f_3599_2]) ).

fof(f_3600_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Int]) ).

fof(f_3600_2,plain,
    ! [U_14295,U_14294,U_14293,U_14292,U_14291] :
      ( c_Relation_Orefl__on(U_14291,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14291,tc_HOL_Obool)),U_14292),U_14294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14291,U_14291),tc_HOL_Obool)),U_14293),U_14295))
      | ~ c_Relation_Orefl__on(U_14291,U_14294,U_14295)
      | ~ c_Relation_Orefl__on(U_14291,U_14292,U_14293) ),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

cnf(f_3600_3,plain,
    ( c_Relation_Orefl__on(U_14291,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14291,tc_HOL_Obool)),U_14292),U_14294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14291,U_14291),tc_HOL_Obool)),U_14293),U_14295))
    | ~ c_Relation_Orefl__on(U_14291,U_14294,U_14295)
    | ~ c_Relation_Orefl__on(U_14291,U_14292,U_14293) ),
    inference(clausify,[status(thm)],[f_3600_2]) ).

fof(f_3601_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD2]) ).

fof(f_3601_2,plain,
    ! [U_14300,U_14299,U_14298,U_14297,U_14296] :
      ( hBOOL(hAPP(hAPP(c_member(U_14296),U_14300),U_14297))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14299),U_14300)),U_14298))
      | ~ c_Relation_Orefl__on(U_14296,U_14297,U_14298) ),
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

cnf(f_3601_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14296),U_14300),U_14297))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14299),U_14300)),U_14298))
    | ~ c_Relation_Orefl__on(U_14296,U_14297,U_14298) ),
    inference(clausify,[status(thm)],[f_3601_2]) ).

fof(f_3602_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD1]) ).

fof(f_3602_2,plain,
    ! [U_14305,U_14304,U_14303,U_14302,U_14301] :
      ( hBOOL(hAPP(hAPP(c_member(U_14301),U_14304),U_14302))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14301,U_14301)),hAPP(hAPP(c_Product__Type_OPair(U_14301,U_14301),U_14304),U_14305)),U_14303))
      | ~ c_Relation_Orefl__on(U_14301,U_14302,U_14303) ),
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

cnf(f_3602_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14301),U_14304),U_14302))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14301,U_14301)),hAPP(hAPP(c_Product__Type_OPair(U_14301,U_14301),U_14304),U_14305)),U_14303))
    | ~ c_Relation_Orefl__on(U_14301,U_14302,U_14303) ),
    inference(clausify,[status(thm)],[f_3602_2]) ).

fof(f_3603_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD]) ).

fof(f_3603_2,plain,
    ! [U_14309,U_14308,U_14307,U_14306] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14306,U_14306)),hAPP(hAPP(c_Product__Type_OPair(U_14306,U_14306),U_14309),U_14309)),U_14308))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14306),U_14309),U_14307))
      | ~ c_Relation_Orefl__on(U_14306,U_14307,U_14308) ),
    inference(variable_rename,[status(thm)],[f_3603_1]) ).

cnf(f_3603_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14306,U_14306)),hAPP(hAPP(c_Product__Type_OPair(U_14306,U_14306),U_14309),U_14309)),U_14308))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14306),U_14309),U_14307))
    | ~ c_Relation_Orefl__on(U_14306,U_14307,U_14308) ),
    inference(clausify,[status(thm)],[f_3603_2]) ).

fof(f_3604_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Predicate_Oreflp(T_a,V_r_2)
        | ~ c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) )
      & ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2)))
        | ~ c_Predicate_Oreflp(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflp__def]) ).

fof(f_3604_2,plain,
    ! [U_14311,U_14310] :
      ( ( c_Predicate_Oreflp(U_14310,U_14311)
        | ~ c_Relation_Orefl__on(U_14310,c_Orderings_Otop__class_Otop(tc_fun(U_14310,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14310,U_14310)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14310,U_14310,tc_HOL_Obool),U_14311))) )
      & ( c_Relation_Orefl__on(U_14310,c_Orderings_Otop__class_Otop(tc_fun(U_14310,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14310,U_14310)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14310,U_14310,tc_HOL_Obool),U_14311)))
        | ~ c_Predicate_Oreflp(U_14310,U_14311) ) ),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

fof(f_3604_3,plain,
    ( ! [U_14315,U_14313] :
        ( c_Predicate_Oreflp(U_14313,U_14315)
        | ~ c_Relation_Orefl__on(U_14313,c_Orderings_Otop__class_Otop(tc_fun(U_14313,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14313,U_14313)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14313,U_14313,tc_HOL_Obool),U_14315))) )
    & ! [U_14314,U_14312] :
        ( c_Relation_Orefl__on(U_14312,c_Orderings_Otop__class_Otop(tc_fun(U_14312,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14312,U_14312)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14312,U_14312,tc_HOL_Obool),U_14314)))
        | ~ c_Predicate_Oreflp(U_14312,U_14314) ) ),
    inference(miniscope,[status(thm)],[f_3604_2]) ).

cnf(f_3604_4,plain,
    ( c_Relation_Orefl__on(U_14312,c_Orderings_Otop__class_Otop(tc_fun(U_14312,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14312,U_14312)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14312,U_14312,tc_HOL_Obool),U_14314)))
    | ~ c_Predicate_Oreflp(U_14312,U_14314) ),
    inference(clausify,[status(thm)],[f_3604_3]) ).

cnf(f_3604_5,plain,
    ( c_Predicate_Oreflp(U_14313,U_14315)
    | ~ c_Relation_Orefl__on(U_14313,c_Orderings_Otop__class_Otop(tc_fun(U_14313,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14313,U_14313)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14313,U_14313,tc_HOL_Obool),U_14315))) ),
    inference(clausify,[status(thm)],[f_3604_3]) ).

fof(f_3605_1,plain,
    ! [V_A_2,V_r_2,T_a] :
      ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onI]) ).

fof(f_3605_2,plain,
    ! [U_14319,U_14318,U_14317] :
      ( c_Relation_Orefl__on(U_14317,U_14319,U_14318)
      | ? [U_14316] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14317,U_14317)),hAPP(hAPP(c_Product__Type_OPair(U_14317,U_14317),U_14316),U_14316)),U_14318))
          & hBOOL(hAPP(hAPP(c_member(U_14317),U_14316),U_14319)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14317,U_14317),tc_HOL_Obool)),U_14318),hAPP(hAPP(c_Product__Type_OSigma(U_14317,U_14317),U_14319),hAPP(c_COMBK(tc_fun(U_14317,tc_HOL_Obool),U_14317),U_14319)))) ),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

fof(f_3605_3,plain,
    ! [U_14319,U_14318,U_14317] :
      ( c_Relation_Orefl__on(U_14317,U_14319,U_14318)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14317,U_14317)),hAPP(hAPP(c_Product__Type_OPair(U_14317,U_14317),sK341(U_14319,U_14318,U_14317)),sK341(U_14319,U_14318,U_14317))),U_14318))
        & hBOOL(hAPP(hAPP(c_member(U_14317),sK341(U_14319,U_14318,U_14317)),U_14319)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14317,U_14317),tc_HOL_Obool)),U_14318),hAPP(hAPP(c_Product__Type_OSigma(U_14317,U_14317),U_14319),hAPP(c_COMBK(tc_fun(U_14317,tc_HOL_Obool),U_14317),U_14319)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_14316,sK341(U_14319,U_14318,U_14317))],[f_3605_2]) ).

cnf(f_3605_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14317),sK341(U_14319,U_14318,U_14317)),U_14319))
    | c_Relation_Orefl__on(U_14317,U_14319,U_14318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14317,U_14317),tc_HOL_Obool)),U_14318),hAPP(hAPP(c_Product__Type_OSigma(U_14317,U_14317),U_14319),hAPP(c_COMBK(tc_fun(U_14317,tc_HOL_Obool),U_14317),U_14319)))) ),
    inference(clausify,[status(thm)],[f_3605_3]) ).

cnf(f_3605_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14317,U_14317)),hAPP(hAPP(c_Product__Type_OPair(U_14317,U_14317),sK341(U_14319,U_14318,U_14317)),sK341(U_14319,U_14318,U_14317))),U_14318))
    | c_Relation_Orefl__on(U_14317,U_14319,U_14318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14317,U_14317),tc_HOL_Obool)),U_14318),hAPP(hAPP(c_Product__Type_OSigma(U_14317,U_14317),U_14319),hAPP(c_COMBK(tc_fun(U_14317,tc_HOL_Obool),U_14317),U_14319)))) ),
    inference(clausify,[status(thm)],[f_3605_3]) ).

fof(f_3606_1,plain,
    ! [V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2))
      | ~ c_Predicate_Oreflp(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_reflpE]) ).

fof(f_3606_2,plain,
    ! [U_14322,U_14321,U_14320] :
      ( hBOOL(hAPP(hAPP(U_14321,U_14322),U_14322))
      | ~ c_Predicate_Oreflp(U_14320,U_14321) ),
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

fof(f_3606_3,plain,
    ! [U_14322,U_14321] :
      ( ! [U_14320] : ~ c_Predicate_Oreflp(U_14320,U_14321)
      | hBOOL(hAPP(hAPP(U_14321,U_14322),U_14322)) ),
    inference(miniscope,[status(thm)],[f_3606_2]) ).

cnf(f_3606_4,plain,
    ( ~ c_Predicate_Oreflp(U_14320,U_14321)
    | hBOOL(hAPP(hAPP(U_14321,U_14322),U_14322)) ),
    inference(clausify,[status(thm)],[f_3606_3]) ).

fof(f_3607_1,plain,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(V_P_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct]) ).

fof(f_3607_2,plain,
    ! [U_14325,U_14324] :
      ( hBOOL(hAPP(U_14325,U_14324))
      | ? [U_14323] : ~ hBOOL(hAPP(U_14325,hAPP(c_Int_ORep__Integ,U_14323)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14324),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

fof(f_3607_3,plain,
    ! [U_14325,U_14324] :
      ( hBOOL(hAPP(U_14325,U_14324))
      | ~ hBOOL(hAPP(U_14325,hAPP(c_Int_ORep__Integ,sK342(U_14325,U_14324))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14324),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_14323,sK342(U_14325,U_14324))],[f_3607_2]) ).

cnf(f_3607_4,plain,
    ( hBOOL(hAPP(U_14325,U_14324))
    | ~ hBOOL(hAPP(U_14325,hAPP(c_Int_ORep__Integ,sK342(U_14325,U_14324))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14324),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3607_3]) ).

fof(f_3608_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_3608_2,plain,
    ! [U_14327] :
      ( ? [U_14326] : U_14327 = hAPP(c_Int_ORep__Integ,U_14326)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14327),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

fof(f_3608_3,plain,
    ! [U_14327] :
      ( U_14327 = hAPP(c_Int_ORep__Integ,sK343(U_14327))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14327),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_14326,sK343(U_14327))],[f_3608_2]) ).

cnf(f_3608_4,plain,
    ( U_14327 = hAPP(c_Int_ORep__Integ,sK343(U_14327))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14327),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3608_3]) ).

fof(f_3609_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) ) )
        | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def_H]) ).

fof(f_3609_2,plain,
    ! [U_14334,U_14333,U_14332] :
      ( ( c_Relation_Orefl__on(U_14332,U_14333,U_14334)
        | ? [U_14331] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14332,U_14332)),hAPP(hAPP(c_Product__Type_OPair(U_14332,U_14332),U_14331),U_14331)),U_14334))
            & hBOOL(hAPP(hAPP(c_member(U_14332),U_14331),U_14333)) )
        | ? [U_14330] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14332,U_14332,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_fun(U_14332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14332,tc_HOL_Obool),tc_fun(U_14332,tc_HOL_Obool)),U_14332),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14332)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14332),c_fconj),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14332)),U_14333)))),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14332)),U_14333))),U_14330))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14332,U_14332)),U_14330),U_14334)) ) )
      & ( ( ! [U_14329] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14332,U_14332)),hAPP(hAPP(c_Product__Type_OPair(U_14332,U_14332),U_14329),U_14329)),U_14334))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14332),U_14329),U_14333)) )
          & ! [U_14328] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14332,U_14332,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_fun(U_14332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14332,tc_HOL_Obool),tc_fun(U_14332,tc_HOL_Obool)),U_14332),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14332)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14332),c_fconj),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14332)),U_14333)))),hAPP(hAPP(c_COMBC(U_14332,tc_fun(U_14332,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14332)),U_14333))),U_14328))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14332,U_14332)),U_14328),U_14334)) ) )
        | ~ c_Relation_Orefl__on(U_14332,U_14333,U_14334) ) ),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

fof(f_3609_3,plain,
    ( ! [U_14340,U_14338,U_14336] :
        ( c_Relation_Orefl__on(U_14336,U_14338,U_14340)
        | ? [U_14331] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),U_14331),U_14331)),U_14340))
            & hBOOL(hAPP(hAPP(c_member(U_14336),U_14331),U_14338)) )
        | ? [U_14330] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14336,U_14336,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),U_14336),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14336)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14336),c_fconj),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338)))),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338))),U_14330))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),U_14330),U_14340)) ) )
    & ! [U_14339,U_14337,U_14335] :
        ( ( ! [U_14329] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),hAPP(hAPP(c_Product__Type_OPair(U_14335,U_14335),U_14329),U_14329)),U_14339))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14335),U_14329),U_14337)) )
          & ! [U_14328] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14335,U_14335,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),U_14335),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14335),c_fconj),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337)))),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337))),U_14328))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),U_14328),U_14339)) ) )
        | ~ c_Relation_Orefl__on(U_14335,U_14337,U_14339) ) ),
    inference(miniscope,[status(thm)],[f_3609_2]) ).

fof(f_3609_4,plain,
    ( ! [U_14340,U_14338,U_14336] :
        ( c_Relation_Orefl__on(U_14336,U_14338,U_14340)
        | ? [U_14331] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),U_14331),U_14331)),U_14340))
            & hBOOL(hAPP(hAPP(c_member(U_14336),U_14331),U_14338)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14336,U_14336,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),U_14336),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14336)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14336),c_fconj),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338)))),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338))),sK344(U_14340,U_14338,U_14336)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),sK344(U_14340,U_14338,U_14336)),U_14340)) ) )
    & ! [U_14339,U_14337,U_14335] :
        ( ( ! [U_14329] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),hAPP(hAPP(c_Product__Type_OPair(U_14335,U_14335),U_14329),U_14329)),U_14339))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14335),U_14329),U_14337)) )
          & ! [U_14328] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14335,U_14335,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),U_14335),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14335),c_fconj),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337)))),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337))),U_14328))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),U_14328),U_14339)) ) )
        | ~ c_Relation_Orefl__on(U_14335,U_14337,U_14339) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_14330,sK344(U_14340,U_14338,U_14336))],[f_3609_3]) ).

fof(f_3609_5,plain,
    ( ! [U_14340,U_14338,U_14336] :
        ( c_Relation_Orefl__on(U_14336,U_14338,U_14340)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),sK345(U_14340,U_14338,U_14336)),sK345(U_14340,U_14338,U_14336))),U_14340))
          & hBOOL(hAPP(hAPP(c_member(U_14336),sK345(U_14340,U_14338,U_14336)),U_14338)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14336,U_14336,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),U_14336),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14336)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14336),c_fconj),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338)))),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338))),sK344(U_14340,U_14338,U_14336)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),sK344(U_14340,U_14338,U_14336)),U_14340)) ) )
    & ! [U_14339,U_14337,U_14335] :
        ( ( ! [U_14329] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),hAPP(hAPP(c_Product__Type_OPair(U_14335,U_14335),U_14329),U_14329)),U_14339))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14335),U_14329),U_14337)) )
          & ! [U_14328] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14335,U_14335,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),U_14335),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14335),c_fconj),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337)))),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337))),U_14328))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),U_14328),U_14339)) ) )
        | ~ c_Relation_Orefl__on(U_14335,U_14337,U_14339) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_14331,sK345(U_14340,U_14338,U_14336))],[f_3609_4]) ).

cnf(f_3609_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14335,U_14335,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14335,tc_HOL_Obool),tc_fun(U_14335,tc_HOL_Obool)),U_14335),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14335),c_fconj),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337)))),hAPP(hAPP(c_COMBC(U_14335,tc_fun(U_14335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14335)),U_14337))),U_14328))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),U_14328),U_14339))
    | ~ c_Relation_Orefl__on(U_14335,U_14337,U_14339) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

cnf(f_3609_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14335,U_14335)),hAPP(hAPP(c_Product__Type_OPair(U_14335,U_14335),U_14329),U_14329)),U_14339))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14335),U_14329),U_14337))
    | ~ c_Relation_Orefl__on(U_14335,U_14337,U_14339) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

cnf(f_3609_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14336),sK345(U_14340,U_14338,U_14336)),U_14338))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),sK344(U_14340,U_14338,U_14336)),U_14340))
    | c_Relation_Orefl__on(U_14336,U_14338,U_14340) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

cnf(f_3609_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),sK345(U_14340,U_14338,U_14336)),sK345(U_14340,U_14338,U_14336))),U_14340))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),sK344(U_14340,U_14338,U_14336)),U_14340))
    | c_Relation_Orefl__on(U_14336,U_14338,U_14340) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

cnf(f_3609_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14336),sK345(U_14340,U_14338,U_14336)),U_14338))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14336,U_14336,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),U_14336),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14336)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14336),c_fconj),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338)))),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338))),sK344(U_14340,U_14338,U_14336)))
    | c_Relation_Orefl__on(U_14336,U_14338,U_14340) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

cnf(f_3609_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),sK345(U_14340,U_14338,U_14336)),sK345(U_14340,U_14338,U_14336))),U_14340))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14336,U_14336,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14336,tc_HOL_Obool),tc_fun(U_14336,tc_HOL_Obool)),U_14336),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14336)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14336),c_fconj),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338)))),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14336,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14336)),U_14338))),sK344(U_14340,U_14338,U_14336)))
    | c_Relation_Orefl__on(U_14336,U_14338,U_14340) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

fof(f_3610_1,plain,
    ! [V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct]) ).

fof(f_3610_2,plain,
    ! [U_14343,U_14342] :
      ( hBOOL(hAPP(U_14342,U_14343))
      | ? [U_14341] :
          ( ~ hBOOL(hAPP(U_14342,hAPP(c_Int_OAbs__Integ,U_14341)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14341),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

fof(f_3610_3,plain,
    ! [U_14343,U_14342] :
      ( hBOOL(hAPP(U_14342,U_14343))
      | ( ~ hBOOL(hAPP(U_14342,hAPP(c_Int_OAbs__Integ,sK346(U_14343,U_14342))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK346(U_14343,U_14342)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_14341,sK346(U_14343,U_14342))],[f_3610_2]) ).

cnf(f_3610_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK346(U_14343,U_14342)),c_Int_OInteg))
    | hBOOL(hAPP(U_14342,U_14343)) ),
    inference(clausify,[status(thm)],[f_3610_3]) ).

cnf(f_3610_5,plain,
    ( ~ hBOOL(hAPP(U_14342,hAPP(c_Int_OAbs__Integ,sK346(U_14343,U_14342))))
    | hBOOL(hAPP(U_14342,U_14343)) ),
    inference(clausify,[status(thm)],[f_3610_3]) ).

fof(f_3611_1,plain,
    ! [V_P_2,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
      & ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__UNIV]) ).

fof(f_3611_2,plain,
    ! [U_14349,U_14348] :
      ( ( ! [U_14347] :
            ( hBOOL(hAPP(U_14349,U_14347))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14348),U_14347),c_Orderings_Otop__class_Otop(tc_fun(U_14348,tc_HOL_Obool)))) )
        | ? [U_14346] : ~ hBOOL(hAPP(U_14349,U_14346)) )
      & ( ! [U_14345] : hBOOL(hAPP(U_14349,U_14345))
        | ? [U_14344] :
            ( ~ hBOOL(hAPP(U_14349,U_14344))
            & hBOOL(hAPP(hAPP(c_member(U_14348),U_14344),c_Orderings_Otop__class_Otop(tc_fun(U_14348,tc_HOL_Obool)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

fof(f_3611_3,plain,
    ( ! [U_14353] :
        ( ! [U_14351,U_14347] :
            ( hBOOL(hAPP(U_14353,U_14347))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14351),U_14347),c_Orderings_Otop__class_Otop(tc_fun(U_14351,tc_HOL_Obool)))) )
        | ? [U_14346] : ~ hBOOL(hAPP(U_14353,U_14346)) )
    & ! [U_14352] :
        ( ! [U_14350] :
          ? [U_14344] :
            ( ~ hBOOL(hAPP(U_14352,U_14344))
            & hBOOL(hAPP(hAPP(c_member(U_14350),U_14344),c_Orderings_Otop__class_Otop(tc_fun(U_14350,tc_HOL_Obool)))) )
        | ! [U_14345] : hBOOL(hAPP(U_14352,U_14345)) ) ),
    inference(miniscope,[status(thm)],[f_3611_2]) ).

fof(f_3611_4,plain,
    ( ! [U_14353] :
        ( ! [U_14351,U_14347] :
            ( hBOOL(hAPP(U_14353,U_14347))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14351),U_14347),c_Orderings_Otop__class_Otop(tc_fun(U_14351,tc_HOL_Obool)))) )
        | ? [U_14346] : ~ hBOOL(hAPP(U_14353,U_14346)) )
    & ! [U_14352] :
        ( ! [U_14350] :
            ( ~ hBOOL(hAPP(U_14352,sK347(U_14352,U_14350)))
            & hBOOL(hAPP(hAPP(c_member(U_14350),sK347(U_14352,U_14350)),c_Orderings_Otop__class_Otop(tc_fun(U_14350,tc_HOL_Obool)))) )
        | ! [U_14345] : hBOOL(hAPP(U_14352,U_14345)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_14344,sK347(U_14352,U_14350))],[f_3611_3]) ).

fof(f_3611_5,plain,
    ( ! [U_14353] :
        ( ! [U_14351,U_14347] :
            ( hBOOL(hAPP(U_14353,U_14347))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14351),U_14347),c_Orderings_Otop__class_Otop(tc_fun(U_14351,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(U_14353,sK348(U_14353))) )
    & ! [U_14352] :
        ( ! [U_14350] :
            ( ~ hBOOL(hAPP(U_14352,sK347(U_14352,U_14350)))
            & hBOOL(hAPP(hAPP(c_member(U_14350),sK347(U_14352,U_14350)),c_Orderings_Otop__class_Otop(tc_fun(U_14350,tc_HOL_Obool)))) )
        | ! [U_14345] : hBOOL(hAPP(U_14352,U_14345)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_14346,sK348(U_14353))],[f_3611_4]) ).

cnf(f_3611_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14350),sK347(U_14352,U_14350)),c_Orderings_Otop__class_Otop(tc_fun(U_14350,tc_HOL_Obool))))
    | hBOOL(hAPP(U_14352,U_14345)) ),
    inference(clausify,[status(thm)],[f_3611_5]) ).

cnf(f_3611_7,plain,
    ( ~ hBOOL(hAPP(U_14352,sK347(U_14352,U_14350)))
    | hBOOL(hAPP(U_14352,U_14345)) ),
    inference(clausify,[status(thm)],[f_3611_5]) ).

cnf(f_3611_8,plain,
    ( hBOOL(hAPP(U_14353,U_14347))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14351),U_14347),c_Orderings_Otop__class_Otop(tc_fun(U_14351,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_14353,sK348(U_14353))) ),
    inference(clausify,[status(thm)],[f_3611_5]) ).

fof(f_3612_1,plain,
    ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a),
    inference(fof_nnf,[status(thm)],[fact_INFI__bool__eq]) ).

fof(f_3612_2,plain,
    ! [U_14354] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14354,tc_HOL_Obool) = c_Set_OBall(U_14354),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

cnf(f_3612_3,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14354,tc_HOL_Obool) = c_Set_OBall(U_14354),
    inference(clausify,[status(thm)],[f_3612_2]) ).

fof(f_3613_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_A_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_A_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__def]) ).

fof(f_3613_2,plain,
    ! [U_14359,U_14358,U_14357] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_14357,U_14358),U_14359))
        | ? [U_14356] :
            ( ~ hBOOL(hAPP(U_14358,U_14356))
            & hBOOL(hAPP(hAPP(c_member(U_14357),U_14356),U_14359)) ) )
      & ( ! [U_14355] :
            ( hBOOL(hAPP(U_14358,U_14355))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14357),U_14355),U_14359)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14357,U_14358),U_14359)) ) ),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

fof(f_3613_3,plain,
    ( ! [U_14365,U_14363,U_14361] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_14361,U_14363),U_14365))
        | ? [U_14356] :
            ( ~ hBOOL(hAPP(U_14363,U_14356))
            & hBOOL(hAPP(hAPP(c_member(U_14361),U_14356),U_14365)) ) )
    & ! [U_14364,U_14362,U_14360] :
        ( ! [U_14355] :
            ( hBOOL(hAPP(U_14362,U_14355))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14360),U_14355),U_14364)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14360,U_14362),U_14364)) ) ),
    inference(miniscope,[status(thm)],[f_3613_2]) ).

fof(f_3613_4,plain,
    ( ! [U_14365,U_14363,U_14361] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_14361,U_14363),U_14365))
        | ( ~ hBOOL(hAPP(U_14363,sK349(U_14365,U_14363,U_14361)))
          & hBOOL(hAPP(hAPP(c_member(U_14361),sK349(U_14365,U_14363,U_14361)),U_14365)) ) )
    & ! [U_14364,U_14362,U_14360] :
        ( ! [U_14355] :
            ( hBOOL(hAPP(U_14362,U_14355))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14360),U_14355),U_14364)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14360,U_14362),U_14364)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_14356,sK349(U_14365,U_14363,U_14361))],[f_3613_3]) ).

cnf(f_3613_5,plain,
    ( hBOOL(hAPP(U_14362,U_14355))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14360),U_14355),U_14364))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_14360,U_14362),U_14364)) ),
    inference(clausify,[status(thm)],[f_3613_4]) ).

cnf(f_3613_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14361),sK349(U_14365,U_14363,U_14361)),U_14365))
    | hBOOL(hAPP(c_Predicate_OPowp(U_14361,U_14363),U_14365)) ),
    inference(clausify,[status(thm)],[f_3613_4]) ).

cnf(f_3613_7,plain,
    ( ~ hBOOL(hAPP(U_14363,sK349(U_14365,U_14363,U_14361)))
    | hBOOL(hAPP(c_Predicate_OPowp(U_14361,U_14363),U_14365)) ),
    inference(clausify,[status(thm)],[f_3613_4]) ).

fof(f_3614_1,plain,
    ! [V_P_2,T_a,B_x] :
      ( hBOOL(hAPP(V_P_2,B_x))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_ball__empty]) ).

fof(f_3614_2,plain,
    ! [U_14368,U_14367,U_14366] :
      ( hBOOL(hAPP(U_14368,U_14366))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14367),U_14366),c_Orderings_Obot__class_Obot(tc_fun(U_14367,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

cnf(f_3614_3,plain,
    ( hBOOL(hAPP(U_14368,U_14366))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14367),U_14366),c_Orderings_Obot__class_Obot(tc_fun(U_14367,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3614_2]) ).

fof(f_3615_1,plain,
    ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).

fof(f_3615_2,plain,
    ! [U_14372,U_14371,U_14370,U_14369] : hAPP(c_Set_OCollect(U_14369),hAPP(hAPP(c_COMBB(tc_fun(U_14370,tc_HOL_Obool),tc_HOL_Obool,U_14369),c_HOL_OAll(U_14370)),hAPP(hAPP(c_COMBB(tc_fun(U_14370,tc_HOL_Obool),tc_fun(U_14370,tc_HOL_Obool),U_14369),hAPP(c_COMBS(U_14370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14370),c_fimplies),hAPP(hAPP(c_COMBC(U_14370,tc_fun(U_14370,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14370)),U_14371)))),U_14372))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14370,tc_fun(U_14369,tc_HOL_Obool)),U_14371),hAPP(hAPP(c_COMBB(tc_fun(U_14369,tc_HOL_Obool),tc_fun(U_14369,tc_HOL_Obool),U_14370),c_Set_OCollect(U_14369)),hAPP(c_COMBC(U_14369,U_14370,tc_HOL_Obool),U_14372))),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

cnf(f_3615_3,plain,
    hAPP(c_Set_OCollect(U_14369),hAPP(hAPP(c_COMBB(tc_fun(U_14370,tc_HOL_Obool),tc_HOL_Obool,U_14369),c_HOL_OAll(U_14370)),hAPP(hAPP(c_COMBB(tc_fun(U_14370,tc_HOL_Obool),tc_fun(U_14370,tc_HOL_Obool),U_14369),hAPP(c_COMBS(U_14370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14370),c_fimplies),hAPP(hAPP(c_COMBC(U_14370,tc_fun(U_14370,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14370)),U_14371)))),U_14372))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14370,tc_fun(U_14369,tc_HOL_Obool)),U_14371),hAPP(hAPP(c_COMBB(tc_fun(U_14369,tc_HOL_Obool),tc_fun(U_14369,tc_HOL_Obool),U_14370),c_Set_OCollect(U_14369)),hAPP(c_COMBC(U_14369,U_14370,tc_HOL_Obool),U_14372))),
    inference(clausify,[status(thm)],[f_3615_2]) ).

fof(f_3616_1,plain,
    ! [V_f_2,V_r_2,T_b,T_a] :
      ( ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) )
        | ~ c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_congruent__def]) ).

fof(f_3616_2,plain,
    ! [U_14378,U_14377,U_14376,U_14375] :
      ( ( c_Equiv__Relations_Ocongruent(U_14375,U_14376,U_14377,U_14378)
        | ? [U_14374] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14375,U_14375,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14375,tc_fun(U_14375,U_14376),tc_fun(U_14375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14376,tc_HOL_Obool),tc_fun(tc_fun(U_14375,U_14376),tc_fun(U_14375,tc_HOL_Obool)),U_14375),c_COMBB(U_14376,tc_HOL_Obool,U_14375)),hAPP(hAPP(c_COMBB(U_14376,tc_fun(U_14376,tc_HOL_Obool),U_14375),c_fequal),U_14378))),U_14378)),U_14374))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),U_14374),U_14377)) ) )
      & ( ! [U_14373] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14375,U_14375,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14375,tc_fun(U_14375,U_14376),tc_fun(U_14375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14376,tc_HOL_Obool),tc_fun(tc_fun(U_14375,U_14376),tc_fun(U_14375,tc_HOL_Obool)),U_14375),c_COMBB(U_14376,tc_HOL_Obool,U_14375)),hAPP(hAPP(c_COMBB(U_14376,tc_fun(U_14376,tc_HOL_Obool),U_14375),c_fequal),U_14378))),U_14378)),U_14373))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),U_14373),U_14377)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14375,U_14376,U_14377,U_14378) ) ),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

fof(f_3616_3,plain,
    ( ! [U_14386,U_14384,U_14382,U_14380] :
        ( c_Equiv__Relations_Ocongruent(U_14380,U_14382,U_14384,U_14386)
        | ? [U_14374] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14380,U_14380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14380,tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14382,tc_HOL_Obool),tc_fun(tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),U_14380),c_COMBB(U_14382,tc_HOL_Obool,U_14380)),hAPP(hAPP(c_COMBB(U_14382,tc_fun(U_14382,tc_HOL_Obool),U_14380),c_fequal),U_14386))),U_14386)),U_14374))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),U_14374),U_14384)) ) )
    & ! [U_14385,U_14383,U_14381,U_14379] :
        ( ! [U_14373] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14379,U_14379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14379,tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14381,tc_HOL_Obool),tc_fun(tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),U_14379),c_COMBB(U_14381,tc_HOL_Obool,U_14379)),hAPP(hAPP(c_COMBB(U_14381,tc_fun(U_14381,tc_HOL_Obool),U_14379),c_fequal),U_14385))),U_14385)),U_14373))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14379,U_14379)),U_14373),U_14383)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14379,U_14381,U_14383,U_14385) ) ),
    inference(miniscope,[status(thm)],[f_3616_2]) ).

fof(f_3616_4,plain,
    ( ! [U_14386,U_14384,U_14382,U_14380] :
        ( c_Equiv__Relations_Ocongruent(U_14380,U_14382,U_14384,U_14386)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14380,U_14380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14380,tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14382,tc_HOL_Obool),tc_fun(tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),U_14380),c_COMBB(U_14382,tc_HOL_Obool,U_14380)),hAPP(hAPP(c_COMBB(U_14382,tc_fun(U_14382,tc_HOL_Obool),U_14380),c_fequal),U_14386))),U_14386)),sK350(U_14386,U_14384,U_14382,U_14380)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),sK350(U_14386,U_14384,U_14382,U_14380)),U_14384)) ) )
    & ! [U_14385,U_14383,U_14381,U_14379] :
        ( ! [U_14373] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14379,U_14379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14379,tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14381,tc_HOL_Obool),tc_fun(tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),U_14379),c_COMBB(U_14381,tc_HOL_Obool,U_14379)),hAPP(hAPP(c_COMBB(U_14381,tc_fun(U_14381,tc_HOL_Obool),U_14379),c_fequal),U_14385))),U_14385)),U_14373))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14379,U_14379)),U_14373),U_14383)) )
        | ~ c_Equiv__Relations_Ocongruent(U_14379,U_14381,U_14383,U_14385) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_14374,sK350(U_14386,U_14384,U_14382,U_14380))],[f_3616_3]) ).

cnf(f_3616_5,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14379,U_14379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14379,tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14381,tc_HOL_Obool),tc_fun(tc_fun(U_14379,U_14381),tc_fun(U_14379,tc_HOL_Obool)),U_14379),c_COMBB(U_14381,tc_HOL_Obool,U_14379)),hAPP(hAPP(c_COMBB(U_14381,tc_fun(U_14381,tc_HOL_Obool),U_14379),c_fequal),U_14385))),U_14385)),U_14373))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14379,U_14379)),U_14373),U_14383))
    | ~ c_Equiv__Relations_Ocongruent(U_14379,U_14381,U_14383,U_14385) ),
    inference(clausify,[status(thm)],[f_3616_4]) ).

cnf(f_3616_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),sK350(U_14386,U_14384,U_14382,U_14380)),U_14384))
    | c_Equiv__Relations_Ocongruent(U_14380,U_14382,U_14384,U_14386) ),
    inference(clausify,[status(thm)],[f_3616_4]) ).

cnf(f_3616_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14380,U_14380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14380,tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14382,tc_HOL_Obool),tc_fun(tc_fun(U_14380,U_14382),tc_fun(U_14380,tc_HOL_Obool)),U_14380),c_COMBB(U_14382,tc_HOL_Obool,U_14380)),hAPP(hAPP(c_COMBB(U_14382,tc_fun(U_14382,tc_HOL_Obool),U_14380),c_fequal),U_14386))),U_14386)),sK350(U_14386,U_14384,U_14382,U_14380)))
    | c_Equiv__Relations_Ocongruent(U_14380,U_14382,U_14384,U_14386) ),
    inference(clausify,[status(thm)],[f_3616_4]) ).

fof(f_3617_1,plain,
    ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_INTER__def]) ).

fof(f_3617_2,plain,
    ! [U_14390,U_14389,U_14388,U_14387] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14387,tc_fun(U_14388,tc_HOL_Obool)),U_14389),U_14390) = hAPP(c_Set_OCollect(U_14388),hAPP(hAPP(c_COMBB(tc_fun(U_14387,tc_HOL_Obool),tc_HOL_Obool,U_14388),c_HOL_OAll(U_14387)),hAPP(hAPP(c_COMBB(tc_fun(U_14387,tc_HOL_Obool),tc_fun(U_14387,tc_HOL_Obool),U_14388),hAPP(c_COMBS(U_14387,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14387),c_fimplies),hAPP(hAPP(c_COMBC(U_14387,tc_fun(U_14387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14387)),U_14389)))),hAPP(hAPP(c_COMBC(U_14388,tc_fun(U_14387,tc_fun(U_14388,tc_HOL_Obool)),tc_fun(U_14387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14388,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14387,tc_fun(U_14388,tc_HOL_Obool)),tc_fun(U_14387,tc_HOL_Obool)),U_14388),c_COMBB(tc_fun(U_14388,tc_HOL_Obool),tc_HOL_Obool,U_14387)),c_member(U_14388))),U_14390)))),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

cnf(f_3617_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14387,tc_fun(U_14388,tc_HOL_Obool)),U_14389),U_14390) = hAPP(c_Set_OCollect(U_14388),hAPP(hAPP(c_COMBB(tc_fun(U_14387,tc_HOL_Obool),tc_HOL_Obool,U_14388),c_HOL_OAll(U_14387)),hAPP(hAPP(c_COMBB(tc_fun(U_14387,tc_HOL_Obool),tc_fun(U_14387,tc_HOL_Obool),U_14388),hAPP(c_COMBS(U_14387,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14387),c_fimplies),hAPP(hAPP(c_COMBC(U_14387,tc_fun(U_14387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14387)),U_14389)))),hAPP(hAPP(c_COMBC(U_14388,tc_fun(U_14387,tc_fun(U_14388,tc_HOL_Obool)),tc_fun(U_14387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14388,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14387,tc_fun(U_14388,tc_HOL_Obool)),tc_fun(U_14387,tc_HOL_Obool)),U_14388),c_COMBB(tc_fun(U_14388,tc_HOL_Obool),tc_HOL_Obool,U_14387)),c_member(U_14388))),U_14390)))),
    inference(clausify,[status(thm)],[f_3617_2]) ).

fof(f_3618_1,plain,
    ! [V_A_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__Inf]) ).

fof(f_3618_2,plain,
    ! [U_14392,U_14391] :
      ( c_Complete__Lattice_OSup__class_OSup(U_14391,U_14392) = c_Complete__Lattice_OInf__class_OInf(U_14391,hAPP(c_Set_OCollect(U_14391),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_HOL_Obool,U_14391),c_HOL_OAll(U_14391)),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_fun(U_14391,tc_HOL_Obool),U_14391),hAPP(c_COMBS(U_14391,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14391),c_fimplies),hAPP(hAPP(c_COMBC(U_14391,tc_fun(U_14391,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14391)),U_14392)))),hAPP(c_COMBC(U_14391,U_14391,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_14391))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14391) ),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

cnf(f_3618_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_14391,U_14392) = c_Complete__Lattice_OInf__class_OInf(U_14391,hAPP(c_Set_OCollect(U_14391),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_HOL_Obool,U_14391),c_HOL_OAll(U_14391)),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_fun(U_14391,tc_HOL_Obool),U_14391),hAPP(c_COMBS(U_14391,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14391),c_fimplies),hAPP(hAPP(c_COMBC(U_14391,tc_fun(U_14391,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14391)),U_14392)))),hAPP(c_COMBC(U_14391,U_14391,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_14391))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14391) ),
    inference(clausify,[status(thm)],[f_3618_2]) ).

fof(f_3619_1,plain,
    ! [V_A_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__Sup]) ).

fof(f_3619_2,plain,
    ! [U_14394,U_14393] :
      ( c_Complete__Lattice_OInf__class_OInf(U_14393,U_14394) = c_Complete__Lattice_OSup__class_OSup(U_14393,hAPP(c_Set_OCollect(U_14393),hAPP(hAPP(c_COMBB(tc_fun(U_14393,tc_HOL_Obool),tc_HOL_Obool,U_14393),c_HOL_OAll(U_14393)),hAPP(hAPP(c_COMBB(tc_fun(U_14393,tc_HOL_Obool),tc_fun(U_14393,tc_HOL_Obool),U_14393),hAPP(c_COMBS(U_14393,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14393),c_fimplies),hAPP(hAPP(c_COMBC(U_14393,tc_fun(U_14393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14393)),U_14394)))),c_Orderings_Oord__class_Oless__eq(U_14393)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14393) ),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

cnf(f_3619_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_14393,U_14394) = c_Complete__Lattice_OSup__class_OSup(U_14393,hAPP(c_Set_OCollect(U_14393),hAPP(hAPP(c_COMBB(tc_fun(U_14393,tc_HOL_Obool),tc_HOL_Obool,U_14393),c_HOL_OAll(U_14393)),hAPP(hAPP(c_COMBB(tc_fun(U_14393,tc_HOL_Obool),tc_fun(U_14393,tc_HOL_Obool),U_14393),hAPP(c_COMBS(U_14393,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14393),c_fimplies),hAPP(hAPP(c_COMBC(U_14393,tc_fun(U_14393,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14393)),U_14394)))),c_Orderings_Oord__class_Oless__eq(U_14393)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14393) ),
    inference(clausify,[status(thm)],[f_3619_2]) ).

fof(f_3620_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_3620_2,plain,
    ! [U_14396] :
    ? [U_14395] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14395),c_Int_OInteg))
      & U_14396 = hAPP(c_Int_OAbs__Integ,U_14395) ),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

fof(f_3620_3,plain,
    ! [U_14396] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK351(U_14396)),c_Int_OInteg))
      & U_14396 = hAPP(c_Int_OAbs__Integ,sK351(U_14396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_14395,sK351(U_14396))],[f_3620_2]) ).

cnf(f_3620_4,plain,
    U_14396 = hAPP(c_Int_OAbs__Integ,sK351(U_14396)),
    inference(clausify,[status(thm)],[f_3620_3]) ).

cnf(f_3620_5,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK351(U_14396)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3620_3]) ).

fof(f_3621_1,plain,
    ! [T_a,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))
      | ? [B_i,B_j] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) )
      | ? [B_i] : ~ c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__SUP]) ).

fof(f_3621_2,plain,
    ! [U_14402,U_14401,U_14400] :
      ( c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
      | ? [U_14399,U_14398] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14400,tc_HOL_Obool)),c_Predicate_ODomainP(U_14400,U_14400,hAPP(U_14401,U_14399))),c_Predicate_ORangeP(U_14400,U_14400,hAPP(U_14401,U_14398))) != c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
          & hAPP(U_14401,U_14399) != hAPP(U_14401,U_14398) )
      | ? [U_14397] : ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,U_14397)) ),
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

fof(f_3621_3,plain,
    ! [U_14402,U_14401,U_14400] :
      ( c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
      | ? [U_14399,U_14398] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14400,tc_HOL_Obool)),c_Predicate_ODomainP(U_14400,U_14400,hAPP(U_14401,U_14399))),c_Predicate_ORangeP(U_14400,U_14400,hAPP(U_14401,U_14398))) != c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
          & hAPP(U_14401,U_14399) != hAPP(U_14401,U_14398) )
      | ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,sK352(U_14402,U_14401,U_14400))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_14397,sK352(U_14402,U_14401,U_14400))],[f_3621_2]) ).

fof(f_3621_4,plain,
    ! [U_14402,U_14401,U_14400] :
      ( c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
      | ? [U_14398] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14400,tc_HOL_Obool)),c_Predicate_ODomainP(U_14400,U_14400,hAPP(U_14401,sK353(U_14402,U_14401,U_14400)))),c_Predicate_ORangeP(U_14400,U_14400,hAPP(U_14401,U_14398))) != c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
          & hAPP(U_14401,sK353(U_14402,U_14401,U_14400)) != hAPP(U_14401,U_14398) )
      | ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,sK352(U_14402,U_14401,U_14400))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_14399,sK353(U_14402,U_14401,U_14400))],[f_3621_3]) ).

fof(f_3621_5,plain,
    ! [U_14402,U_14401,U_14400] :
      ( c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14400,tc_HOL_Obool)),c_Predicate_ODomainP(U_14400,U_14400,hAPP(U_14401,sK353(U_14402,U_14401,U_14400)))),c_Predicate_ORangeP(U_14400,U_14400,hAPP(U_14401,sK354(U_14402,U_14401,U_14400)))) != c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
        & hAPP(U_14401,sK353(U_14402,U_14401,U_14400)) != hAPP(U_14401,sK354(U_14402,U_14401,U_14400)) )
      | ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,sK352(U_14402,U_14401,U_14400))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_14398,sK354(U_14402,U_14401,U_14400))],[f_3621_4]) ).

cnf(f_3621_6,plain,
    ( hAPP(U_14401,sK353(U_14402,U_14401,U_14400)) != hAPP(U_14401,sK354(U_14402,U_14401,U_14400))
    | c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
    | ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,sK352(U_14402,U_14401,U_14400))) ),
    inference(clausify,[status(thm)],[f_3621_5]) ).

cnf(f_3621_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14400,tc_HOL_Obool)),c_Predicate_ODomainP(U_14400,U_14400,hAPP(U_14401,sK353(U_14402,U_14401,U_14400)))),c_Predicate_ORangeP(U_14400,U_14400,hAPP(U_14401,sK354(U_14402,U_14401,U_14400)))) != c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
    | c_Wellfounded_OwfP(U_14400,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14402,tc_fun(U_14400,tc_fun(U_14400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14402,tc_HOL_Obool))),U_14401))
    | ~ c_Wellfounded_OwfP(U_14400,hAPP(U_14401,sK352(U_14402,U_14401,U_14400))) ),
    inference(clausify,[status(thm)],[f_3621_5]) ).

fof(f_3622_1,plain,
    ! [V_n_2,V_ts_2,T_a] :
      ( ! [B_x] :
          ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) )
      | ? [B_x] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triples__valid__Suc]) ).

fof(f_3622_2,plain,
    ! [U_14407,U_14406,U_14405] :
      ( ! [U_14404] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_14405,U_14407,U_14404)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),U_14404),U_14406)) )
      | ? [U_14403] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14405,hAPP(c_Nat_OSuc,U_14407),U_14403)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),U_14403),U_14406)) ) ),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

fof(f_3622_3,plain,
    ! [U_14407,U_14406,U_14405] :
      ( ! [U_14404] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_14405,U_14407,U_14404)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),U_14404),U_14406)) )
      | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14405,hAPP(c_Nat_OSuc,U_14407),sK355(U_14407,U_14406,U_14405))
        & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),sK355(U_14407,U_14406,U_14405)),U_14406)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_14403,sK355(U_14407,U_14406,U_14405))],[f_3622_2]) ).

cnf(f_3622_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),sK355(U_14407,U_14406,U_14405)),U_14406))
    | c_Hoare__Mirabelle_Otriple__valid(U_14405,U_14407,U_14404)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),U_14404),U_14406)) ),
    inference(clausify,[status(thm)],[f_3622_3]) ).

cnf(f_3622_5,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14405,hAPP(c_Nat_OSuc,U_14407),sK355(U_14407,U_14406,U_14405))
    | c_Hoare__Mirabelle_Otriple__valid(U_14405,U_14407,U_14404)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14405)),U_14404),U_14406)) ),
    inference(clausify,[status(thm)],[f_3622_3]) ).

fof(f_3623_1,plain,
    ! [V_ts_2,V_Ga_2,T_a] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
        | ? [B_n] :
            ( ? [B_x] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) )
            & ! [B_x] :
                ( c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) ) ) )
      & ( ! [B_n] :
            ( ! [B_x] :
                ( c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) )
            | ? [B_x] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__valids__def]) ).

fof(f_3623_2,plain,
    ! [U_14416,U_14415,U_14414] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(U_14414,U_14415,U_14416)
        | ? [U_14413] :
            ( ? [U_14412] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14414,U_14413,U_14412)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14414)),U_14412),U_14416)) )
            & ! [U_14411] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14414,U_14413,U_14411)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14414)),U_14411),U_14415)) ) ) )
      & ( ! [U_14410] :
            ( ! [U_14409] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14414,U_14410,U_14409)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14414)),U_14409),U_14416)) )
            | ? [U_14408] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14414,U_14410,U_14408)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14414)),U_14408),U_14415)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14414,U_14415,U_14416) ) ),
    inference(variable_rename,[status(thm)],[f_3623_1]) ).

fof(f_3623_3,plain,
    ( ! [U_14422,U_14420,U_14418] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422)
        | ? [U_14413] :
            ( ? [U_14412] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14418,U_14413,U_14412)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14412),U_14422)) )
            & ! [U_14411] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14418,U_14413,U_14411)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14411),U_14420)) ) ) )
    & ! [U_14421,U_14419,U_14417] :
        ( ! [U_14410] :
            ( ! [U_14409] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421)) )
            | ? [U_14408] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14408)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14408),U_14419)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ) ),
    inference(miniscope,[status(thm)],[f_3623_2]) ).

fof(f_3623_4,plain,
    ( ! [U_14422,U_14420,U_14418] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422)
        | ? [U_14413] :
            ( ? [U_14412] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14418,U_14413,U_14412)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14412),U_14422)) )
            & ! [U_14411] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14418,U_14413,U_14411)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14411),U_14420)) ) ) )
    & ! [U_14421,U_14419,U_14417] :
        ( ! [U_14410] :
            ( ! [U_14409] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,sK356(U_14421,U_14419,U_14417,U_14410))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),sK356(U_14421,U_14419,U_14417,U_14410)),U_14419)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_14408,sK356(U_14421,U_14419,U_14417,U_14410))],[f_3623_3]) ).

fof(f_3623_5,plain,
    ( ! [U_14422,U_14420,U_14418] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422)
        | ( ? [U_14412] :
              ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),U_14412)
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14412),U_14422)) )
          & ! [U_14411] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),U_14411)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14411),U_14420)) ) ) )
    & ! [U_14421,U_14419,U_14417] :
        ( ! [U_14410] :
            ( ! [U_14409] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,sK356(U_14421,U_14419,U_14417,U_14410))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),sK356(U_14421,U_14419,U_14417,U_14410)),U_14419)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_14413,sK357(U_14422,U_14420,U_14418))],[f_3623_4]) ).

fof(f_3623_6,plain,
    ( ! [U_14422,U_14420,U_14418] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422)
        | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),sK358(U_14422,U_14420,U_14418))
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),sK358(U_14422,U_14420,U_14418)),U_14422))
          & ! [U_14411] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),U_14411)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14411),U_14420)) ) ) )
    & ! [U_14421,U_14419,U_14417] :
        ( ! [U_14410] :
            ( ! [U_14409] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,sK356(U_14421,U_14419,U_14417,U_14410))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),sK356(U_14421,U_14419,U_14417,U_14410)),U_14419)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_14412,sK358(U_14422,U_14420,U_14418))],[f_3623_5]) ).

cnf(f_3623_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),sK356(U_14421,U_14419,U_14417,U_14410)),U_14419))
    | c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ),
    inference(clausify,[status(thm)],[f_3623_6]) ).

cnf(f_3623_8,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,sK356(U_14421,U_14419,U_14417,U_14410))
    | c_Hoare__Mirabelle_Otriple__valid(U_14417,U_14410,U_14409)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14417)),U_14409),U_14421))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_14417,U_14419,U_14421) ),
    inference(clausify,[status(thm)],[f_3623_6]) ).

cnf(f_3623_9,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),U_14411)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),U_14411),U_14420))
    | c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422) ),
    inference(clausify,[status(thm)],[f_3623_6]) ).

cnf(f_3623_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14418)),sK358(U_14422,U_14420,U_14418)),U_14422))
    | c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422) ),
    inference(clausify,[status(thm)],[f_3623_6]) ).

cnf(f_3623_11,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_14418,sK357(U_14422,U_14420,U_14418),sK358(U_14422,U_14420,U_14418))
    | c_Hoare__Mirabelle_Ohoare__valids(U_14418,U_14420,U_14422) ),
    inference(clausify,[status(thm)],[f_3623_6]) ).

fof(f_3624_1,plain,
    ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,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_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__eq]) ).

fof(f_3624_2,plain,
    ! [U_14424,U_14423] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_14423,tc_HOL_Obool),U_14424) = hAPP(c_Set_OCollect(U_14423),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_14423),c_HOL_OAll(tc_fun(U_14423,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),U_14423),hAPP(c_COMBS(tc_fun(U_14423,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_14423,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_14423,tc_HOL_Obool),tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_14423,tc_HOL_Obool))),U_14424)))),c_member(U_14423)))),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

cnf(f_3624_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_14423,tc_HOL_Obool),U_14424) = hAPP(c_Set_OCollect(U_14423),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_14423),c_HOL_OAll(tc_fun(U_14423,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),U_14423),hAPP(c_COMBS(tc_fun(U_14423,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_14423,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_14423,tc_HOL_Obool),tc_fun(tc_fun(U_14423,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_14423,tc_HOL_Obool))),U_14424)))),c_member(U_14423)))),
    inference(clausify,[status(thm)],[f_3624_2]) ).

fof(f_3625_1,plain,
    ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI2]) ).

fof(f_3625_2,plain,
    ! [U_14432,U_14431,U_14430,U_14429,U_14428,U_14427] :
      ( hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14428,U_14429,tc_fun(U_14430,tc_HOL_Obool)),U_14432),U_14427)))
      | ? [U_14426,U_14425] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(U_14432,U_14426),U_14425)))
          & U_14427 = hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),U_14426),U_14425) ) ),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

fof(f_3625_3,plain,
    ! [U_14432,U_14431,U_14430,U_14429,U_14428,U_14427] :
      ( hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14428,U_14429,tc_fun(U_14430,tc_HOL_Obool)),U_14432),U_14427)))
      | ? [U_14425] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(U_14432,sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),U_14425)))
          & U_14427 = hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),U_14425) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_14426,sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427))],[f_3625_2]) ).

fof(f_3625_4,plain,
    ! [U_14432,U_14431,U_14430,U_14429,U_14428,U_14427] :
      ( hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14428,U_14429,tc_fun(U_14430,tc_HOL_Obool)),U_14432),U_14427)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(U_14432,sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),sK360(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427))))
        & U_14427 = hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),sK360(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_14425,sK360(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427))],[f_3625_3]) ).

cnf(f_3625_5,plain,
    ( U_14427 = hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),sK360(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427))
    | hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14428,U_14429,tc_fun(U_14430,tc_HOL_Obool)),U_14432),U_14427))) ),
    inference(clausify,[status(thm)],[f_3625_4]) ).

cnf(f_3625_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(U_14432,sK359(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427)),sK360(U_14432,U_14431,U_14430,U_14429,U_14428,U_14427))))
    | hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14428,U_14429,tc_fun(U_14430,tc_HOL_Obool)),U_14432),U_14427))) ),
    inference(clausify,[status(thm)],[f_3625_4]) ).

fof(f_3626_1,plain,
    ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).

fof(f_3626_2,plain,
    ! [U_14440,U_14439,U_14438,U_14437,U_14436,U_14435] :
      ( ? [U_14434,U_14433] :
          ( hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(U_14439,U_14434),U_14433)))
          & U_14440 = hAPP(hAPP(c_Product__Type_OPair(U_14437,U_14438),U_14434),U_14433) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14437,U_14438,tc_fun(U_14435,tc_HOL_Obool)),U_14439),U_14440))) ),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

fof(f_3626_3,plain,
    ! [U_14440,U_14439,U_14438,U_14437,U_14436,U_14435] :
      ( ? [U_14433] :
          ( hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(U_14439,sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),U_14433)))
          & U_14440 = hAPP(hAPP(c_Product__Type_OPair(U_14437,U_14438),sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),U_14433) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14437,U_14438,tc_fun(U_14435,tc_HOL_Obool)),U_14439),U_14440))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_14434,sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435))],[f_3626_2]) ).

fof(f_3626_4,plain,
    ! [U_14440,U_14439,U_14438,U_14437,U_14436,U_14435] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(U_14439,sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),sK362(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435))))
        & U_14440 = hAPP(hAPP(c_Product__Type_OPair(U_14437,U_14438),sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),sK362(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14437,U_14438,tc_fun(U_14435,tc_HOL_Obool)),U_14439),U_14440))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_14433,sK362(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435))],[f_3626_3]) ).

cnf(f_3626_5,plain,
    ( U_14440 = hAPP(hAPP(c_Product__Type_OPair(U_14437,U_14438),sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),sK362(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14437,U_14438,tc_fun(U_14435,tc_HOL_Obool)),U_14439),U_14440))) ),
    inference(clausify,[status(thm)],[f_3626_4]) ).

cnf(f_3626_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(U_14439,sK361(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435)),sK362(U_14440,U_14439,U_14438,U_14437,U_14436,U_14435))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14435),U_14436),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14437,U_14438,tc_fun(U_14435,tc_HOL_Obool)),U_14439),U_14440))) ),
    inference(clausify,[status(thm)],[f_3626_4]) ).

fof(f_3627_1,plain,
    ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))),
    inference(fof_nnf,[status(thm)],[fact_Eps__split]) ).

fof(f_3627_2,plain,
    ! [U_14443,U_14442,U_14441] : c_Hilbert__Choice_OEps(tc_prod(U_14441,U_14442),hAPP(c_Product__Type_Oprod_Oprod__case(U_14441,U_14442,tc_HOL_Obool),U_14443)) = c_Hilbert__Choice_OEps(tc_prod(U_14441,U_14442),hAPP(hAPP(c_COMBS(tc_prod(U_14441,U_14442),U_14442,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14441,tc_fun(U_14442,tc_HOL_Obool),tc_prod(U_14441,U_14442)),U_14443),c_Product__Type_Ofst(U_14441,U_14442))),c_Product__Type_Osnd(U_14441,U_14442))),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

cnf(f_3627_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14441,U_14442),hAPP(c_Product__Type_Oprod_Oprod__case(U_14441,U_14442,tc_HOL_Obool),U_14443)) = c_Hilbert__Choice_OEps(tc_prod(U_14441,U_14442),hAPP(hAPP(c_COMBS(tc_prod(U_14441,U_14442),U_14442,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14441,tc_fun(U_14442,tc_HOL_Obool),tc_prod(U_14441,U_14442)),U_14443),c_Product__Type_Ofst(U_14441,U_14442))),c_Product__Type_Osnd(U_14441,U_14442))),
    inference(clausify,[status(thm)],[f_3627_2]) ).

fof(f_3628_1,plain,
    ! [V_R_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
      | ? [B_A] :
          ( B_A != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfI__pf]) ).

fof(f_3628_2,plain,
    ! [U_14446,U_14445] :
      ( c_Wellfounded_Owf(U_14445,U_14446)
      | ? [U_14444] :
          ( U_14444 != c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14445,tc_HOL_Obool)),U_14444),hAPP(c_Relation_OImage(U_14445,U_14445,U_14446),U_14444))) ) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

fof(f_3628_3,plain,
    ! [U_14446,U_14445] :
      ( c_Wellfounded_Owf(U_14445,U_14446)
      | ( sK363(U_14446,U_14445) != c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14445,tc_HOL_Obool)),sK363(U_14446,U_14445)),hAPP(c_Relation_OImage(U_14445,U_14445,U_14446),sK363(U_14446,U_14445)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_14444,sK363(U_14446,U_14445))],[f_3628_2]) ).

cnf(f_3628_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14445,tc_HOL_Obool)),sK363(U_14446,U_14445)),hAPP(c_Relation_OImage(U_14445,U_14445,U_14446),sK363(U_14446,U_14445))))
    | c_Wellfounded_Owf(U_14445,U_14446) ),
    inference(clausify,[status(thm)],[f_3628_3]) ).

cnf(f_3628_5,plain,
    ( sK363(U_14446,U_14445) != c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
    | c_Wellfounded_Owf(U_14445,U_14446) ),
    inference(clausify,[status(thm)],[f_3628_3]) ).

fof(f_3629_1,plain,
    ! [T_a,V_c_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_c_2))
      | V_c_2 != c_Hilbert__Choice_OEps(T_a,V_P_2)
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_exE__some]) ).

fof(f_3629_2,plain,
    ! [U_14450,U_14449,U_14448] :
      ( hBOOL(hAPP(U_14448,U_14449))
      | U_14449 != c_Hilbert__Choice_OEps(U_14450,U_14448)
      | ! [U_14447] : ~ hBOOL(hAPP(U_14448,U_14447)) ),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

cnf(f_3629_3,plain,
    ( hBOOL(hAPP(U_14448,U_14449))
    | U_14449 != c_Hilbert__Choice_OEps(U_14450,U_14448)
    | ~ hBOOL(hAPP(U_14448,U_14447)) ),
    inference(clausify,[status(thm)],[f_3629_2]) ).

fof(f_3630_1,plain,
    ! [T_a,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_someI]) ).

fof(f_3630_2,plain,
    ! [U_14453,U_14452,U_14451] :
      ( hBOOL(hAPP(U_14451,c_Hilbert__Choice_OEps(U_14453,U_14451)))
      | ~ hBOOL(hAPP(U_14451,U_14452)) ),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

cnf(f_3630_3,plain,
    ( hBOOL(hAPP(U_14451,c_Hilbert__Choice_OEps(U_14453,U_14451)))
    | ~ hBOOL(hAPP(U_14451,U_14452)) ),
    inference(clausify,[status(thm)],[f_3630_2]) ).

fof(f_3631_1,plain,
    ! [T_a,B_P] :
      ( hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P)))
      | ! [B_x] : ~ hBOOL(hAPP(B_P,B_x)) ),
    inference(fof_nnf,[status(thm)],[fact_tfl__some]) ).

fof(f_3631_2,plain,
    ! [U_14456,U_14455] :
      ( hBOOL(hAPP(U_14455,c_Hilbert__Choice_OEps(U_14456,U_14455)))
      | ! [U_14454] : ~ hBOOL(hAPP(U_14455,U_14454)) ),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

cnf(f_3631_3,plain,
    ( hBOOL(hAPP(U_14455,c_Hilbert__Choice_OEps(U_14456,U_14455)))
    | ~ hBOOL(hAPP(U_14455,U_14454)) ),
    inference(clausify,[status(thm)],[f_3631_2]) ).

fof(f_3632_1,plain,
    ! [T_a,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).

fof(f_3632_2,plain,
    ! [U_14459,U_14458] :
      ( hBOOL(hAPP(U_14458,c_Hilbert__Choice_OEps(U_14459,U_14458)))
      | ! [U_14457] : ~ hBOOL(hAPP(U_14458,U_14457)) ),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

cnf(f_3632_3,plain,
    ( hBOOL(hAPP(U_14458,c_Hilbert__Choice_OEps(U_14459,U_14458)))
    | ~ hBOOL(hAPP(U_14458,U_14457)) ),
    inference(clausify,[status(thm)],[f_3632_2]) ).

fof(f_3633_1,plain,
    ! [T_a,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ~ hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).

fof(f_3633_2,plain,
    ! [U_14463,U_14462] :
      ( ( hBOOL(hAPP(U_14462,c_Hilbert__Choice_OEps(U_14463,U_14462)))
        | ! [U_14461] : ~ hBOOL(hAPP(U_14462,U_14461)) )
      & ( ? [U_14460] : hBOOL(hAPP(U_14462,U_14460))
        | ~ hBOOL(hAPP(U_14462,c_Hilbert__Choice_OEps(U_14463,U_14462))) ) ),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

fof(f_3633_3,plain,
    ( ! [U_14467,U_14465] :
        ( hBOOL(hAPP(U_14465,c_Hilbert__Choice_OEps(U_14467,U_14465)))
        | ! [U_14461] : ~ hBOOL(hAPP(U_14465,U_14461)) )
    & ! [U_14466,U_14464] :
        ( ? [U_14460] : hBOOL(hAPP(U_14464,U_14460))
        | ~ hBOOL(hAPP(U_14464,c_Hilbert__Choice_OEps(U_14466,U_14464))) ) ),
    inference(miniscope,[status(thm)],[f_3633_2]) ).

fof(f_3633_4,plain,
    ( ! [U_14467,U_14465] :
        ( hBOOL(hAPP(U_14465,c_Hilbert__Choice_OEps(U_14467,U_14465)))
        | ! [U_14461] : ~ hBOOL(hAPP(U_14465,U_14461)) )
    & ! [U_14466,U_14464] :
        ( hBOOL(hAPP(U_14464,sK364(U_14466,U_14464)))
        | ~ hBOOL(hAPP(U_14464,c_Hilbert__Choice_OEps(U_14466,U_14464))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_14460,sK364(U_14466,U_14464))],[f_3633_3]) ).

cnf(f_3633_5,plain,
    ( hBOOL(hAPP(U_14464,sK364(U_14466,U_14464)))
    | ~ hBOOL(hAPP(U_14464,c_Hilbert__Choice_OEps(U_14466,U_14464))) ),
    inference(clausify,[status(thm)],[f_3633_4]) ).

cnf(f_3633_6,plain,
    ( hBOOL(hAPP(U_14465,c_Hilbert__Choice_OEps(U_14467,U_14465)))
    | ~ hBOOL(hAPP(U_14465,U_14461)) ),
    inference(clausify,[status(thm)],[f_3633_4]) ).

fof(f_3634_1,plain,
    ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__eq__trivial]) ).

fof(f_3634_2,plain,
    ! [U_14469,U_14468] : c_Hilbert__Choice_OEps(U_14468,hAPP(hAPP(c_COMBC(U_14468,U_14468,tc_HOL_Obool),c_fequal),U_14469)) = U_14469,
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

cnf(f_3634_3,plain,
    c_Hilbert__Choice_OEps(U_14468,hAPP(hAPP(c_COMBC(U_14468,U_14468,tc_HOL_Obool),c_fequal),U_14469)) = U_14469,
    inference(clausify,[status(thm)],[f_3634_2]) ).

fof(f_3635_1,plain,
    ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(f_3635_2,plain,
    ! [U_14471,U_14470] : c_Hilbert__Choice_OEps(U_14470,hAPP(c_fequal,U_14471)) = U_14471,
    inference(variable_rename,[status(thm)],[f_3635_1]) ).

cnf(f_3635_3,plain,
    c_Hilbert__Choice_OEps(U_14470,hAPP(c_fequal,U_14471)) = U_14471,
    inference(clausify,[status(thm)],[f_3635_2]) ).

fof(f_3636_1,plain,
    ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_Eps__split__eq]) ).

fof(f_3636_2,plain,
    ! [U_14475,U_14474,U_14473,U_14472] : c_Hilbert__Choice_OEps(tc_prod(U_14472,U_14473),hAPP(c_Product__Type_Oprod_Oprod__case(U_14472,U_14473,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14472,tc_fun(U_14473,tc_HOL_Obool),tc_fun(U_14473,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14473,tc_HOL_Obool),tc_fun(U_14473,tc_HOL_Obool)),U_14472),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14473)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14472),c_fconj),hAPP(c_fequal,U_14474)))),hAPP(c_fequal,U_14475)))) = hAPP(hAPP(c_Product__Type_OPair(U_14472,U_14473),U_14474),U_14475),
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

cnf(f_3636_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14472,U_14473),hAPP(c_Product__Type_Oprod_Oprod__case(U_14472,U_14473,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14472,tc_fun(U_14473,tc_HOL_Obool),tc_fun(U_14473,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14473,tc_HOL_Obool),tc_fun(U_14473,tc_HOL_Obool)),U_14472),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14473)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14472),c_fconj),hAPP(c_fequal,U_14474)))),hAPP(c_fequal,U_14475)))) = hAPP(hAPP(c_Product__Type_OPair(U_14472,U_14473),U_14474),U_14475),
    inference(clausify,[status(thm)],[f_3636_2]) ).

fof(f_3637_1,plain,
    ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).

fof(f_3637_2,plain,
    ! [U_14478,U_14477,U_14476] : c_Hilbert__Choice_OEps(tc_prod(U_14476,U_14477),U_14478) = c_Hilbert__Choice_OEps(tc_prod(U_14476,U_14477),hAPP(c_Product__Type_Oprod_Oprod__case(U_14476,U_14477,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14477,tc_prod(U_14476,U_14477)),tc_fun(U_14477,tc_HOL_Obool),U_14476),hAPP(c_COMBB(tc_prod(U_14476,U_14477),tc_HOL_Obool,U_14477),U_14478)),c_Product__Type_OPair(U_14476,U_14477)))),
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

cnf(f_3637_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14476,U_14477),U_14478) = c_Hilbert__Choice_OEps(tc_prod(U_14476,U_14477),hAPP(c_Product__Type_Oprod_Oprod__case(U_14476,U_14477,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14477,tc_prod(U_14476,U_14477)),tc_fun(U_14477,tc_HOL_Obool),U_14476),hAPP(c_COMBB(tc_prod(U_14476,U_14477),tc_HOL_Obool,U_14477),U_14478)),c_Product__Type_OPair(U_14476,U_14477)))),
    inference(clausify,[status(thm)],[f_3637_2]) ).

fof(f_3638_1,plain,
    ! [V_P_2,V_m_2,T_a,T_b] :
      ( c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2)))))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_LeastM__def]) ).

fof(f_3638_2,plain,
    ! [U_14482,U_14481,U_14480,U_14479] :
      ( c_Hilbert__Choice_OLeastM(U_14480,U_14479,U_14481,U_14482) = c_Hilbert__Choice_OEps(U_14480,hAPP(hAPP(c_COMBS(U_14480,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14480),c_fconj),U_14482)),hAPP(hAPP(c_COMBB(tc_fun(U_14480,tc_HOL_Obool),tc_HOL_Obool,U_14480),c_HOL_OAll(U_14480)),hAPP(hAPP(c_COMBB(tc_fun(U_14480,tc_HOL_Obool),tc_fun(U_14480,tc_HOL_Obool),U_14480),hAPP(c_COMBS(U_14480,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14480),c_fimplies),U_14482))),hAPP(hAPP(c_COMBC(U_14480,tc_fun(U_14480,U_14479),tc_fun(U_14480,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14479,tc_HOL_Obool),tc_fun(tc_fun(U_14480,U_14479),tc_fun(U_14480,tc_HOL_Obool)),U_14480),c_COMBB(U_14479,tc_HOL_Obool,U_14480)),hAPP(hAPP(c_COMBB(U_14479,tc_fun(U_14479,tc_HOL_Obool),U_14480),c_Orderings_Oord__class_Oless__eq(U_14479)),U_14481))),U_14481)))))
      | ~ class_Orderings_Oord(U_14479) ),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

cnf(f_3638_3,plain,
    ( c_Hilbert__Choice_OLeastM(U_14480,U_14479,U_14481,U_14482) = c_Hilbert__Choice_OEps(U_14480,hAPP(hAPP(c_COMBS(U_14480,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14480),c_fconj),U_14482)),hAPP(hAPP(c_COMBB(tc_fun(U_14480,tc_HOL_Obool),tc_HOL_Obool,U_14480),c_HOL_OAll(U_14480)),hAPP(hAPP(c_COMBB(tc_fun(U_14480,tc_HOL_Obool),tc_fun(U_14480,tc_HOL_Obool),U_14480),hAPP(c_COMBS(U_14480,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14480),c_fimplies),U_14482))),hAPP(hAPP(c_COMBC(U_14480,tc_fun(U_14480,U_14479),tc_fun(U_14480,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14479,tc_HOL_Obool),tc_fun(tc_fun(U_14480,U_14479),tc_fun(U_14480,tc_HOL_Obool)),U_14480),c_COMBB(U_14479,tc_HOL_Obool,U_14480)),hAPP(hAPP(c_COMBB(U_14479,tc_fun(U_14479,tc_HOL_Obool),U_14480),c_Orderings_Oord__class_Oless__eq(U_14479)),U_14481))),U_14481)))))
    | ~ class_Orderings_Oord(U_14479) ),
    inference(clausify,[status(thm)],[f_3638_2]) ).

fof(f_3639_1,plain,
    ! [V_P_2,V_m_2,T_a,T_b] :
      ( hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2)))))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_GreatestM__def]) ).

fof(f_3639_2,plain,
    ! [U_14486,U_14485,U_14484,U_14483] :
      ( hAPP(c_Hilbert__Choice_OGreatestM(U_14484,U_14483,U_14485),U_14486) = c_Hilbert__Choice_OEps(U_14484,hAPP(hAPP(c_COMBS(U_14484,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14484),c_fconj),U_14486)),hAPP(hAPP(c_COMBB(tc_fun(U_14484,tc_HOL_Obool),tc_HOL_Obool,U_14484),c_HOL_OAll(U_14484)),hAPP(hAPP(c_COMBB(tc_fun(U_14484,tc_HOL_Obool),tc_fun(U_14484,tc_HOL_Obool),U_14484),hAPP(c_COMBS(U_14484,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14484),c_fimplies),U_14486))),hAPP(hAPP(c_COMBB(U_14483,tc_fun(U_14484,tc_HOL_Obool),U_14484),hAPP(c_COMBC(U_14484,U_14483,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14483,tc_fun(U_14483,tc_HOL_Obool),U_14484),c_Orderings_Oord__class_Oless__eq(U_14483)),U_14485))),U_14485)))))
      | ~ class_Orderings_Oord(U_14483) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

cnf(f_3639_3,plain,
    ( hAPP(c_Hilbert__Choice_OGreatestM(U_14484,U_14483,U_14485),U_14486) = c_Hilbert__Choice_OEps(U_14484,hAPP(hAPP(c_COMBS(U_14484,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14484),c_fconj),U_14486)),hAPP(hAPP(c_COMBB(tc_fun(U_14484,tc_HOL_Obool),tc_HOL_Obool,U_14484),c_HOL_OAll(U_14484)),hAPP(hAPP(c_COMBB(tc_fun(U_14484,tc_HOL_Obool),tc_fun(U_14484,tc_HOL_Obool),U_14484),hAPP(c_COMBS(U_14484,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14484),c_fimplies),U_14486))),hAPP(hAPP(c_COMBB(U_14483,tc_fun(U_14484,tc_HOL_Obool),U_14484),hAPP(c_COMBC(U_14484,U_14483,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14483,tc_fun(U_14483,tc_HOL_Obool),U_14484),c_Orderings_Oord__class_Oless__eq(U_14483)),U_14485))),U_14485)))))
    | ~ class_Orderings_Oord(U_14483) ),
    inference(clausify,[status(thm)],[f_3639_2]) ).

fof(f_3640_1,plain,
    ! [V_m_2,T_a,V_k_2,V_P_2] :
      ( ( ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y)))
            | ~ hBOOL(hAPP(V_P_2,B_y)) )
        & hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) )
      | ~ hBOOL(hAPP(V_P_2,V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_LeastM__nat__lemma]) ).

fof(f_3640_2,plain,
    ! [U_14491,U_14490,U_14489,U_14488] :
      ( ( ! [U_14487] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_14491,c_Hilbert__Choice_OLeastM(U_14490,tc_Nat_Onat,U_14491,U_14488))),hAPP(U_14491,U_14487)))
            | ~ hBOOL(hAPP(U_14488,U_14487)) )
        & hBOOL(hAPP(U_14488,c_Hilbert__Choice_OLeastM(U_14490,tc_Nat_Onat,U_14491,U_14488))) )
      | ~ hBOOL(hAPP(U_14488,U_14489)) ),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

cnf(f_3640_3,plain,
    ( hBOOL(hAPP(U_14488,c_Hilbert__Choice_OLeastM(U_14490,tc_Nat_Onat,U_14491,U_14488)))
    | ~ hBOOL(hAPP(U_14488,U_14489)) ),
    inference(clausify,[status(thm)],[f_3640_2]) ).

cnf(f_3640_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_14491,c_Hilbert__Choice_OLeastM(U_14490,tc_Nat_Onat,U_14491,U_14488))),hAPP(U_14491,U_14487)))
    | ~ hBOOL(hAPP(U_14488,U_14487))
    | ~ hBOOL(hAPP(U_14488,U_14489)) ),
    inference(clausify,[status(thm)],[f_3640_2]) ).

fof(f_3641_1,plain,
    ! [T_a,V_m_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_LeastM__nat__le]) ).

fof(f_3641_2,plain,
    ! [U_14495,U_14494,U_14493,U_14492] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_14494,c_Hilbert__Choice_OLeastM(U_14495,tc_Nat_Onat,U_14494,U_14492))),hAPP(U_14494,U_14493)))
      | ~ hBOOL(hAPP(U_14492,U_14493)) ),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

cnf(f_3641_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_14494,c_Hilbert__Choice_OLeastM(U_14495,tc_Nat_Onat,U_14494,U_14492))),hAPP(U_14494,U_14493)))
    | ~ hBOOL(hAPP(U_14492,U_14493)) ),
    inference(clausify,[status(thm)],[f_3641_2]) ).

fof(f_3642_1,plain,
    ! [T_a] :
      ( c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Greatest__def]) ).

fof(f_3642_2,plain,
    ! [U_14496] :
      ( c_Hilbert__Choice_OGreatest(U_14496) = c_Hilbert__Choice_OGreatestM(U_14496,U_14496,c_COMBI(U_14496))
      | ~ class_Orderings_Oord(U_14496) ),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

cnf(f_3642_3,plain,
    ( c_Hilbert__Choice_OGreatest(U_14496) = c_Hilbert__Choice_OGreatestM(U_14496,U_14496,c_COMBI(U_14496))
    | ~ class_Orderings_Oord(U_14496) ),
    inference(clausify,[status(thm)],[f_3642_2]) ).

fof(f_3643_1,plain,
    ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_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)),hAPP(V_D_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Sigma__mono]) ).

fof(f_3643_2,plain,
    ! [U_14503,U_14502,U_14501,U_14500,U_14499,U_14498] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14498,U_14501),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14499),U_14502)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14500),U_14503)))
      | ? [U_14497] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14501,tc_HOL_Obool)),hAPP(U_14502,U_14497)),hAPP(U_14503,U_14497)))
          & hBOOL(hAPP(hAPP(c_member(U_14498),U_14497),U_14499)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14498,tc_HOL_Obool)),U_14499),U_14500)) ),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

fof(f_3643_3,plain,
    ! [U_14503,U_14502,U_14501,U_14500,U_14499,U_14498] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14498,U_14501),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14499),U_14502)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14500),U_14503)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14501,tc_HOL_Obool)),hAPP(U_14502,sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498))),hAPP(U_14503,sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498))))
        & hBOOL(hAPP(hAPP(c_member(U_14498),sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498)),U_14499)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14498,tc_HOL_Obool)),U_14499),U_14500)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_14497,sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498))],[f_3643_2]) ).

cnf(f_3643_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14498),sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498)),U_14499))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14498,U_14501),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14499),U_14502)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14500),U_14503)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14498,tc_HOL_Obool)),U_14499),U_14500)) ),
    inference(clausify,[status(thm)],[f_3643_3]) ).

cnf(f_3643_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14501,tc_HOL_Obool)),hAPP(U_14502,sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498))),hAPP(U_14503,sK365(U_14503,U_14502,U_14501,U_14500,U_14499,U_14498))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14498,U_14501),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14499),U_14502)),hAPP(hAPP(c_Product__Type_OSigma(U_14498,U_14501),U_14500),U_14503)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14498,tc_HOL_Obool)),U_14499),U_14500)) ),
    inference(clausify,[status(thm)],[f_3643_3]) ).

fof(f_3644_1,plain,
    ! [V_m_2,T_a,V_k_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_LeastM__natI]) ).

fof(f_3644_2,plain,
    ! [U_14507,U_14506,U_14505,U_14504] :
      ( hBOOL(hAPP(U_14504,c_Hilbert__Choice_OLeastM(U_14506,tc_Nat_Onat,U_14507,U_14504)))
      | ~ hBOOL(hAPP(U_14504,U_14505)) ),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

cnf(f_3644_3,plain,
    ( hBOOL(hAPP(U_14504,c_Hilbert__Choice_OLeastM(U_14506,tc_Nat_Onat,U_14507,U_14504)))
    | ~ hBOOL(hAPP(U_14504,U_14505)) ),
    inference(clausify,[status(thm)],[f_3644_2]) ).

fof(f_3645_1,plain,
    ! [V_r_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_OaccI]) ).

fof(f_3645_2,plain,
    ! [U_14511,U_14510,U_14509] :
      ( hBOOL(hAPP(hAPP(c_member(U_14509),U_14510),c_Wellfounded_Oacc(U_14509,U_14511)))
      | ? [U_14508] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14509),U_14508),c_Wellfounded_Oacc(U_14509,U_14511)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14509,U_14509)),hAPP(hAPP(c_Product__Type_OPair(U_14509,U_14509),U_14508),U_14510)),U_14511)) ) ),
    inference(variable_rename,[status(thm)],[f_3645_1]) ).

fof(f_3645_3,plain,
    ! [U_14511,U_14510,U_14509] :
      ( hBOOL(hAPP(hAPP(c_member(U_14509),U_14510),c_Wellfounded_Oacc(U_14509,U_14511)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_14509),sK366(U_14511,U_14510,U_14509)),c_Wellfounded_Oacc(U_14509,U_14511)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14509,U_14509)),hAPP(hAPP(c_Product__Type_OPair(U_14509,U_14509),sK366(U_14511,U_14510,U_14509)),U_14510)),U_14511)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_14508,sK366(U_14511,U_14510,U_14509))],[f_3645_2]) ).

cnf(f_3645_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14509,U_14509)),hAPP(hAPP(c_Product__Type_OPair(U_14509,U_14509),sK366(U_14511,U_14510,U_14509)),U_14510)),U_14511))
    | hBOOL(hAPP(hAPP(c_member(U_14509),U_14510),c_Wellfounded_Oacc(U_14509,U_14511))) ),
    inference(clausify,[status(thm)],[f_3645_3]) ).

cnf(f_3645_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14509),sK366(U_14511,U_14510,U_14509)),c_Wellfounded_Oacc(U_14509,U_14511)))
    | hBOOL(hAPP(hAPP(c_member(U_14509),U_14510),c_Wellfounded_Oacc(U_14509,U_14511))) ),
    inference(clausify,[status(thm)],[f_3645_3]) ).

fof(f_3646_1,plain,
    ! [V_R_2,V_x_2,T_a] :
      ( ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) )
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_not__acc__down]) ).

fof(f_3646_2,plain,
    ! [U_14515,U_14514,U_14513] :
      ( ? [U_14512] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14513),U_14512),c_Wellfounded_Oacc(U_14513,U_14515)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14513,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14513,U_14513),U_14512),U_14514)),U_14515)) )
      | hBOOL(hAPP(hAPP(c_member(U_14513),U_14514),c_Wellfounded_Oacc(U_14513,U_14515))) ),
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

fof(f_3646_3,plain,
    ! [U_14515,U_14514,U_14513] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14513),sK367(U_14515,U_14514,U_14513)),c_Wellfounded_Oacc(U_14513,U_14515)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14513,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14513,U_14513),sK367(U_14515,U_14514,U_14513)),U_14514)),U_14515)) )
      | hBOOL(hAPP(hAPP(c_member(U_14513),U_14514),c_Wellfounded_Oacc(U_14513,U_14515))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_14512,sK367(U_14515,U_14514,U_14513))],[f_3646_2]) ).

cnf(f_3646_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14513,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14513,U_14513),sK367(U_14515,U_14514,U_14513)),U_14514)),U_14515))
    | hBOOL(hAPP(hAPP(c_member(U_14513),U_14514),c_Wellfounded_Oacc(U_14513,U_14515))) ),
    inference(clausify,[status(thm)],[f_3646_3]) ).

cnf(f_3646_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14513),sK367(U_14515,U_14514,U_14513)),c_Wellfounded_Oacc(U_14513,U_14515)))
    | hBOOL(hAPP(hAPP(c_member(U_14513),U_14514),c_Wellfounded_Oacc(U_14513,U_14515))) ),
    inference(clausify,[status(thm)],[f_3646_3]) ).

fof(f_3647_1,plain,
    ! [V_R_2,V_a2_2,V_a1_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2))
                  & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Osimps]) ).

fof(f_3647_2,plain,
    ! [U_14523,U_14522,U_14521,U_14520] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14520,tc_HOL_Obool),tc_fun(U_14520,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14520,tc_HOL_Obool),tc_fun(U_14520,tc_HOL_Obool)),U_14521),U_14522)),c_Wellfounded_Omax__ext(U_14520,U_14523)))
        | ? [U_14519] :
            ( ! [U_14518] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14520,U_14520),U_14519),U_14518)),U_14523))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14520),U_14518),U_14522)) )
            & hBOOL(hAPP(hAPP(c_member(U_14520),U_14519),U_14521)) )
        | U_14522 = c_Orderings_Obot__class_Obot(tc_fun(U_14520,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14520),U_14522))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14520),U_14521)) )
      & ( ( ! [U_14517] :
              ( ? [U_14516] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),hAPP(hAPP(c_Product__Type_OPair(U_14520,U_14520),U_14517),U_14516)),U_14523))
                  & hBOOL(hAPP(hAPP(c_member(U_14520),U_14516),U_14522)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14520),U_14517),U_14521)) )
          & U_14522 != c_Orderings_Obot__class_Obot(tc_fun(U_14520,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14520),U_14522))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14520),U_14521)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14520,tc_HOL_Obool),tc_fun(U_14520,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14520,tc_HOL_Obool),tc_fun(U_14520,tc_HOL_Obool)),U_14521),U_14522)),c_Wellfounded_Omax__ext(U_14520,U_14523))) ) ),
    inference(variable_rename,[status(thm)],[f_3647_1]) ).

fof(f_3647_3,plain,
    ( ! [U_14531,U_14529,U_14527,U_14525] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool)),U_14527),U_14529)),c_Wellfounded_Omax__ext(U_14525,U_14531)))
        | ? [U_14519] :
            ( ! [U_14518] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14525,U_14525)),hAPP(hAPP(c_Product__Type_OPair(U_14525,U_14525),U_14519),U_14518)),U_14531))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14525),U_14518),U_14529)) )
            & hBOOL(hAPP(hAPP(c_member(U_14525),U_14519),U_14527)) )
        | U_14529 = c_Orderings_Obot__class_Obot(tc_fun(U_14525,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14529))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14527)) )
    & ! [U_14530,U_14528,U_14526,U_14524] :
        ( ( ! [U_14517] :
              ( ? [U_14516] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14524),U_14517),U_14516)),U_14530))
                  & hBOOL(hAPP(hAPP(c_member(U_14524),U_14516),U_14528)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14524),U_14517),U_14526)) )
          & U_14528 != c_Orderings_Obot__class_Obot(tc_fun(U_14524,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14528))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14526)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ) ),
    inference(miniscope,[status(thm)],[f_3647_2]) ).

fof(f_3647_4,plain,
    ( ! [U_14531,U_14529,U_14527,U_14525] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool)),U_14527),U_14529)),c_Wellfounded_Omax__ext(U_14525,U_14531)))
        | ? [U_14519] :
            ( ! [U_14518] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14525,U_14525)),hAPP(hAPP(c_Product__Type_OPair(U_14525,U_14525),U_14519),U_14518)),U_14531))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14525),U_14518),U_14529)) )
            & hBOOL(hAPP(hAPP(c_member(U_14525),U_14519),U_14527)) )
        | U_14529 = c_Orderings_Obot__class_Obot(tc_fun(U_14525,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14529))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14527)) )
    & ! [U_14530,U_14528,U_14526,U_14524] :
        ( ( ! [U_14517] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14524),U_14517),sK368(U_14530,U_14528,U_14526,U_14524,U_14517))),U_14530))
                & hBOOL(hAPP(hAPP(c_member(U_14524),sK368(U_14530,U_14528,U_14526,U_14524,U_14517)),U_14528)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14524),U_14517),U_14526)) )
          & U_14528 != c_Orderings_Obot__class_Obot(tc_fun(U_14524,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14528))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14526)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_14516,sK368(U_14530,U_14528,U_14526,U_14524,U_14517))],[f_3647_3]) ).

fof(f_3647_5,plain,
    ( ! [U_14531,U_14529,U_14527,U_14525] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool)),U_14527),U_14529)),c_Wellfounded_Omax__ext(U_14525,U_14531)))
        | ( ! [U_14518] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14525,U_14525)),hAPP(hAPP(c_Product__Type_OPair(U_14525,U_14525),sK369(U_14531,U_14529,U_14527,U_14525)),U_14518)),U_14531))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14525),U_14518),U_14529)) )
          & hBOOL(hAPP(hAPP(c_member(U_14525),sK369(U_14531,U_14529,U_14527,U_14525)),U_14527)) )
        | U_14529 = c_Orderings_Obot__class_Obot(tc_fun(U_14525,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14529))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14527)) )
    & ! [U_14530,U_14528,U_14526,U_14524] :
        ( ( ! [U_14517] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14524),U_14517),sK368(U_14530,U_14528,U_14526,U_14524,U_14517))),U_14530))
                & hBOOL(hAPP(hAPP(c_member(U_14524),sK368(U_14530,U_14528,U_14526,U_14524,U_14517)),U_14528)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14524),U_14517),U_14526)) )
          & U_14528 != c_Orderings_Obot__class_Obot(tc_fun(U_14524,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14528))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14526)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_14519,sK369(U_14531,U_14529,U_14527,U_14525))],[f_3647_4]) ).

cnf(f_3647_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14526))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14524),U_14528))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_8,plain,
    ( U_14528 != c_Orderings_Obot__class_Obot(tc_fun(U_14524,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14524),sK368(U_14530,U_14528,U_14526,U_14524,U_14517)),U_14528))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14524),U_14517),U_14526))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14524),U_14517),sK368(U_14530,U_14528,U_14526,U_14524,U_14517))),U_14530))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14524),U_14517),U_14526))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14524,tc_HOL_Obool),tc_fun(U_14524,tc_HOL_Obool)),U_14526),U_14528)),c_Wellfounded_Omax__ext(U_14524,U_14530))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14525),sK369(U_14531,U_14529,U_14527,U_14525)),U_14527))
    | U_14529 = c_Orderings_Obot__class_Obot(tc_fun(U_14525,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14529))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14527))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool)),U_14527),U_14529)),c_Wellfounded_Omax__ext(U_14525,U_14531))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

cnf(f_3647_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14525,U_14525)),hAPP(hAPP(c_Product__Type_OPair(U_14525,U_14525),sK369(U_14531,U_14529,U_14527,U_14525)),U_14518)),U_14531))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14525),U_14518),U_14529))
    | U_14529 = c_Orderings_Obot__class_Obot(tc_fun(U_14525,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14529))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14525),U_14527))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14525,tc_HOL_Obool),tc_fun(U_14525,tc_HOL_Obool)),U_14527),U_14529)),c_Wellfounded_Omax__ext(U_14525,U_14531))) ),
    inference(clausify,[status(thm)],[f_3647_5]) ).

fof(f_3648_1,plain,
    ! [V_f_2,V_r_2,T_a] :
      ( ? [B_k] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE]) ).

fof(f_3648_2,plain,
    ! [U_14535,U_14534,U_14533] :
      ( ? [U_14532] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14533,U_14533)),hAPP(hAPP(c_Product__Type_OPair(U_14533,U_14533),hAPP(U_14535,hAPP(c_Nat_OSuc,U_14532))),hAPP(U_14535,U_14532))),U_14534))
      | ~ c_Wellfounded_Owf(U_14533,U_14534) ),
    inference(variable_rename,[status(thm)],[f_3648_1]) ).

fof(f_3648_3,plain,
    ! [U_14535,U_14534,U_14533] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14533,U_14533)),hAPP(hAPP(c_Product__Type_OPair(U_14533,U_14533),hAPP(U_14535,hAPP(c_Nat_OSuc,sK370(U_14535,U_14534,U_14533)))),hAPP(U_14535,sK370(U_14535,U_14534,U_14533)))),U_14534))
      | ~ c_Wellfounded_Owf(U_14533,U_14534) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_14532,sK370(U_14535,U_14534,U_14533))],[f_3648_2]) ).

cnf(f_3648_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14533,U_14533)),hAPP(hAPP(c_Product__Type_OPair(U_14533,U_14533),hAPP(U_14535,hAPP(c_Nat_OSuc,sK370(U_14535,U_14534,U_14533)))),hAPP(U_14535,sK370(U_14535,U_14534,U_14533)))),U_14534))
    | ~ c_Wellfounded_Owf(U_14533,U_14534) ),
    inference(clausify,[status(thm)],[f_3648_3]) ).

fof(f_3649_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_3649_2,plain,
    ! [U_14538,U_14537,U_14536] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_14536,U_14537,U_14538)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_14538)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

cnf(f_3649_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_14536,U_14537,U_14538)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_14538)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3649_2]) ).

fof(f_3650_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_3650_2,plain,
    ! [U_14541,U_14540,U_14539] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_14539,U_14540,U_14541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_14541)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

cnf(f_3650_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_14539,U_14540,U_14541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_14541)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3650_2]) ).

fof(f_3651_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_3651_2,plain,
    ! [U_14544,U_14543,U_14542] :
      ( hBOOL(hAPP(c_Com_OWT,U_14544))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14542,U_14543,U_14544))) ),
    inference(variable_rename,[status(thm)],[f_3651_1]) ).

fof(f_3651_3,plain,
    ! [U_14544] :
      ( ! [U_14543,U_14542] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14542,U_14543,U_14544)))
      | hBOOL(hAPP(c_Com_OWT,U_14544)) ),
    inference(miniscope,[status(thm)],[f_3651_2]) ).

cnf(f_3651_4,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14542,U_14543,U_14544)))
    | hBOOL(hAPP(c_Com_OWT,U_14544)) ),
    inference(clausify,[status(thm)],[f_3651_3]) ).

fof(f_3652_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_3652_2,plain,
    ! [U_14549,U_14548,U_14547,U_14546,U_14545] : c_Com_Ocom_OWhile(U_14545,U_14546) != c_Com_Ocom_OLocal(U_14547,U_14548,U_14549),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

cnf(f_3652_3,plain,
    c_Com_Ocom_OWhile(U_14545,U_14546) != c_Com_Ocom_OLocal(U_14547,U_14548,U_14549),
    inference(clausify,[status(thm)],[f_3652_2]) ).

fof(f_3653_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_3653_2,plain,
    ! [U_14554,U_14553,U_14552,U_14551,U_14550] : c_Com_Ocom_OLocal(U_14550,U_14551,U_14552) != c_Com_Ocom_OWhile(U_14553,U_14554),
    inference(variable_rename,[status(thm)],[f_3653_1]) ).

cnf(f_3653_3,plain,
    c_Com_Ocom_OLocal(U_14550,U_14551,U_14552) != c_Com_Ocom_OWhile(U_14553,U_14554),
    inference(clausify,[status(thm)],[f_3653_2]) ).

fof(f_3654_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_3654_2,plain,
    ! [U_14560,U_14559,U_14558,U_14557,U_14556,U_14555] :
      ( ( c_Com_Ocom_OLocal(U_14555,U_14556,U_14557) = c_Com_Ocom_OLocal(U_14558,U_14559,U_14560)
        | U_14557 != U_14560
        | U_14556 != U_14559
        | U_14555 != U_14558 )
      & ( ( U_14557 = U_14560
          & U_14556 = U_14559
          & U_14555 = U_14558 )
        | c_Com_Ocom_OLocal(U_14555,U_14556,U_14557) != c_Com_Ocom_OLocal(U_14558,U_14559,U_14560) ) ),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

fof(f_3654_3,plain,
    ( ! [U_14572,U_14570,U_14568,U_14566,U_14564,U_14562] :
        ( c_Com_Ocom_OLocal(U_14562,U_14564,U_14566) = c_Com_Ocom_OLocal(U_14568,U_14570,U_14572)
        | U_14566 != U_14572
        | U_14564 != U_14570
        | U_14562 != U_14568 )
    & ! [U_14571,U_14569,U_14567,U_14565,U_14563,U_14561] :
        ( ( U_14565 = U_14571
          & U_14563 = U_14569
          & U_14561 = U_14567 )
        | c_Com_Ocom_OLocal(U_14561,U_14563,U_14565) != c_Com_Ocom_OLocal(U_14567,U_14569,U_14571) ) ),
    inference(miniscope,[status(thm)],[f_3654_2]) ).

cnf(f_3654_4,plain,
    ( U_14561 = U_14567
    | c_Com_Ocom_OLocal(U_14561,U_14563,U_14565) != c_Com_Ocom_OLocal(U_14567,U_14569,U_14571) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_5,plain,
    ( U_14563 = U_14569
    | c_Com_Ocom_OLocal(U_14561,U_14563,U_14565) != c_Com_Ocom_OLocal(U_14567,U_14569,U_14571) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_6,plain,
    ( U_14565 = U_14571
    | c_Com_Ocom_OLocal(U_14561,U_14563,U_14565) != c_Com_Ocom_OLocal(U_14567,U_14569,U_14571) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_7,plain,
    ( c_Com_Ocom_OLocal(U_14562,U_14564,U_14566) = c_Com_Ocom_OLocal(U_14568,U_14570,U_14572)
    | U_14566 != U_14572
    | U_14564 != U_14570
    | U_14562 != U_14568 ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

fof(f_3655_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_3655_2,plain,
    ! [U_14576,U_14575,U_14574,U_14573] : c_Com_Ocom_OLocal(U_14573,U_14574,U_14575) != hAPP(c_Com_Ocom_OBODY,U_14576),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

cnf(f_3655_3,plain,
    c_Com_Ocom_OLocal(U_14573,U_14574,U_14575) != hAPP(c_Com_Ocom_OBODY,U_14576),
    inference(clausify,[status(thm)],[f_3655_2]) ).

fof(f_3656_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_3656_2,plain,
    ! [U_14580,U_14579,U_14578,U_14577] : hAPP(c_Com_Ocom_OBODY,U_14577) != c_Com_Ocom_OLocal(U_14578,U_14579,U_14580),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

cnf(f_3656_3,plain,
    hAPP(c_Com_Ocom_OBODY,U_14577) != c_Com_Ocom_OLocal(U_14578,U_14579,U_14580),
    inference(clausify,[status(thm)],[f_3656_2]) ).

fof(f_3657_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_3657_2,plain,
    ! [U_14583,U_14582,U_14581] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14582,U_14583,U_14581)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_14581)) ),
    inference(variable_rename,[status(thm)],[f_3657_1]) ).

cnf(f_3657_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14582,U_14583,U_14581)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_14581)) ),
    inference(clausify,[status(thm)],[f_3657_2]) ).

fof(f_3658_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_3658_2,plain,
    ! [U_14586,U_14585,U_14584] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14584,U_14585,U_14586)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_14586)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_14586))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14584,U_14585,U_14586))) ) ),
    inference(variable_rename,[status(thm)],[f_3658_1]) ).

fof(f_3658_3,plain,
    ( ! [U_14592] :
        ( ! [U_14590,U_14588] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14588,U_14590,U_14592)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_14592)) )
    & ! [U_14591] :
        ( ! [U_14589,U_14587] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14587,U_14589,U_14591)))
        | hBOOL(hAPP(c_Com_OWT,U_14591)) ) ),
    inference(miniscope,[status(thm)],[f_3658_2]) ).

cnf(f_3658_4,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14587,U_14589,U_14591)))
    | hBOOL(hAPP(c_Com_OWT,U_14591)) ),
    inference(clausify,[status(thm)],[f_3658_3]) ).

cnf(f_3658_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_14588,U_14590,U_14592)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_14592)) ),
    inference(clausify,[status(thm)],[f_3658_3]) ).

fof(f_3659_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_3659_2,plain,
    ! [U_14595,U_14594,U_14593] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_14593,U_14594,U_14595),
    inference(variable_rename,[status(thm)],[f_3659_1]) ).

cnf(f_3659_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_14593,U_14594,U_14595),
    inference(clausify,[status(thm)],[f_3659_2]) ).

fof(f_3660_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_3660_2,plain,
    ! [U_14598,U_14597,U_14596] : c_Com_Ocom_OLocal(U_14596,U_14597,U_14598) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

cnf(f_3660_3,plain,
    c_Com_Ocom_OLocal(U_14596,U_14597,U_14598) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_3660_2]) ).

fof(f_3661_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_3661_2,plain,
    ! [U_14603,U_14602,U_14601,U_14600,U_14599] : c_Com_Ocom_OSemi(U_14599,U_14600) != c_Com_Ocom_OLocal(U_14601,U_14602,U_14603),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

cnf(f_3661_3,plain,
    c_Com_Ocom_OSemi(U_14599,U_14600) != c_Com_Ocom_OLocal(U_14601,U_14602,U_14603),
    inference(clausify,[status(thm)],[f_3661_2]) ).

fof(f_3662_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_3662_2,plain,
    ! [U_14608,U_14607,U_14606,U_14605,U_14604] : c_Com_Ocom_OLocal(U_14604,U_14605,U_14606) != c_Com_Ocom_OSemi(U_14607,U_14608),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

cnf(f_3662_3,plain,
    c_Com_Ocom_OLocal(U_14604,U_14605,U_14606) != c_Com_Ocom_OSemi(U_14607,U_14608),
    inference(clausify,[status(thm)],[f_3662_2]) ).

fof(f_3663_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_3663_2,plain,
    ! [U_14614,U_14613,U_14612,U_14611,U_14610,U_14609] : c_Com_Ocom_OLocal(U_14609,U_14610,U_14611) != c_Com_Ocom_OCond(U_14612,U_14613,U_14614),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

cnf(f_3663_3,plain,
    c_Com_Ocom_OLocal(U_14609,U_14610,U_14611) != c_Com_Ocom_OCond(U_14612,U_14613,U_14614),
    inference(clausify,[status(thm)],[f_3663_2]) ).

fof(f_3664_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_3664_2,plain,
    ! [U_14620,U_14619,U_14618,U_14617,U_14616,U_14615] : c_Com_Ocom_OCond(U_14615,U_14616,U_14617) != c_Com_Ocom_OLocal(U_14618,U_14619,U_14620),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

cnf(f_3664_3,plain,
    c_Com_Ocom_OCond(U_14615,U_14616,U_14617) != c_Com_Ocom_OLocal(U_14618,U_14619,U_14620),
    inference(clausify,[status(thm)],[f_3664_2]) ).

fof(f_3665_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),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_a),B_a),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong]) ).

fof(f_3665_2,plain,
    ! [U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14624,U_14622),U_14629),U_14627) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14623,U_14622),U_14628),U_14626)
      | ? [U_14621] :
          ( hAPP(U_14628,U_14621) != hAPP(U_14629,hAPP(U_14625,U_14621))
          & hBOOL(hAPP(hAPP(c_member(U_14623),U_14621),U_14626)) )
      | U_14627 != hAPP(c_Set_Oimage(U_14623,U_14624,U_14625),U_14626)
      | ~ c_Fun_Oinj__on(U_14623,U_14624,U_14625,U_14626)
      | ~ class_Groups_Ocomm__monoid__add(U_14622) ),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

fof(f_3665_3,plain,
    ! [U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14624,U_14622),U_14629),U_14627) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14623,U_14622),U_14628),U_14626)
      | ( hAPP(U_14628,sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)) != hAPP(U_14629,hAPP(U_14625,sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)))
        & hBOOL(hAPP(hAPP(c_member(U_14623),sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)),U_14626)) )
      | U_14627 != hAPP(c_Set_Oimage(U_14623,U_14624,U_14625),U_14626)
      | ~ c_Fun_Oinj__on(U_14623,U_14624,U_14625,U_14626)
      | ~ class_Groups_Ocomm__monoid__add(U_14622) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_14621,sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622))],[f_3665_2]) ).

cnf(f_3665_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14623),sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)),U_14626))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14624,U_14622),U_14629),U_14627) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14623,U_14622),U_14628),U_14626)
    | U_14627 != hAPP(c_Set_Oimage(U_14623,U_14624,U_14625),U_14626)
    | ~ c_Fun_Oinj__on(U_14623,U_14624,U_14625,U_14626)
    | ~ class_Groups_Ocomm__monoid__add(U_14622) ),
    inference(clausify,[status(thm)],[f_3665_3]) ).

cnf(f_3665_5,plain,
    ( hAPP(U_14628,sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)) != hAPP(U_14629,hAPP(U_14625,sK371(U_14629,U_14628,U_14627,U_14626,U_14625,U_14624,U_14623,U_14622)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14624,U_14622),U_14629),U_14627) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14623,U_14622),U_14628),U_14626)
    | U_14627 != hAPP(c_Set_Oimage(U_14623,U_14624,U_14625),U_14626)
    | ~ c_Fun_Oinj__on(U_14623,U_14624,U_14625,U_14626)
    | ~ class_Groups_Ocomm__monoid__add(U_14622) ),
    inference(clausify,[status(thm)],[f_3665_3]) ).

fof(f_3666_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_scomp__unfold]) ).

fof(f_3666_2,plain,
    ! [U_14636,U_14635,U_14634,U_14633,U_14632,U_14631,U_14630] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14630,U_14631,U_14632,U_14633),U_14634),U_14635),U_14636) = hAPP(hAPP(U_14635,hAPP(c_Product__Type_Ofst(U_14631,U_14632),hAPP(U_14634,U_14636))),hAPP(c_Product__Type_Osnd(U_14631,U_14632),hAPP(U_14634,U_14636))),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

cnf(f_3666_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14630,U_14631,U_14632,U_14633),U_14634),U_14635),U_14636) = hAPP(hAPP(U_14635,hAPP(c_Product__Type_Ofst(U_14631,U_14632),hAPP(U_14634,U_14636))),hAPP(c_Product__Type_Osnd(U_14631,U_14632),hAPP(U_14634,U_14636))),
    inference(clausify,[status(thm)],[f_3666_2]) ).

fof(f_3667_1,plain,
    ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__scomp]) ).

fof(f_3667_2,plain,
    ! [U_14645,U_14644,U_14643,U_14642,U_14641,U_14640,U_14639,U_14638,U_14637] : hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14638,U_14639,U_14640),hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14641,U_14642,tc_prod(U_14638,U_14639)),U_14643),U_14644)),U_14645) = hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14641,U_14642,U_14640),U_14643),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14638,tc_fun(U_14639,U_14640)),tc_fun(U_14642,U_14640)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_prod(U_14638,U_14639)),tc_fun(tc_fun(U_14638,tc_fun(U_14639,U_14640)),tc_fun(U_14642,U_14640)),U_14641),c_Product__Type_Oscomp(U_14642,U_14638,U_14639,U_14640)),U_14644)),U_14645)),
    inference(variable_rename,[status(thm)],[f_3667_1]) ).

cnf(f_3667_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14638,U_14639,U_14640),hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14641,U_14642,tc_prod(U_14638,U_14639)),U_14643),U_14644)),U_14645) = hAPP(hAPP(c_Product__Type_Oscomp(U_14637,U_14641,U_14642,U_14640),U_14643),hAPP(hAPP(c_COMBC(U_14641,tc_fun(U_14638,tc_fun(U_14639,U_14640)),tc_fun(U_14642,U_14640)),hAPP(hAPP(c_COMBB(tc_fun(U_14642,tc_prod(U_14638,U_14639)),tc_fun(tc_fun(U_14638,tc_fun(U_14639,U_14640)),tc_fun(U_14642,U_14640)),U_14641),c_Product__Type_Oscomp(U_14642,U_14638,U_14639,U_14640)),U_14644)),U_14645)),
    inference(clausify,[status(thm)],[f_3667_2]) ).

fof(f_3668_1,plain,
    ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_Pair__scomp]) ).

fof(f_3668_2,plain,
    ! [U_14650,U_14649,U_14648,U_14647,U_14646] : hAPP(hAPP(c_Product__Type_Oscomp(U_14646,U_14647,U_14646,U_14648),hAPP(c_Product__Type_OPair(U_14647,U_14646),U_14649)),U_14650) = hAPP(U_14650,U_14649),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

cnf(f_3668_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14646,U_14647,U_14646,U_14648),hAPP(c_Product__Type_OPair(U_14647,U_14646),U_14649)),U_14650) = hAPP(U_14650,U_14649),
    inference(clausify,[status(thm)],[f_3668_2]) ).

fof(f_3669_1,plain,
    ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_scomp__Pair]) ).

fof(f_3669_2,plain,
    ! [U_14654,U_14653,U_14652,U_14651] : hAPP(hAPP(c_Product__Type_Oscomp(U_14651,U_14652,U_14653,tc_prod(U_14652,U_14653)),U_14654),c_Product__Type_OPair(U_14652,U_14653)) = U_14654,
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

cnf(f_3669_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14651,U_14652,U_14653,tc_prod(U_14652,U_14653)),U_14654),c_Product__Type_OPair(U_14652,U_14653)) = U_14654,
    inference(clausify,[status(thm)],[f_3669_2]) ).

fof(f_3670_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__apply]) ).

fof(f_3670_2,plain,
    ! [U_14661,U_14660,U_14659,U_14658,U_14657,U_14656,U_14655] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14655,U_14656,U_14657,U_14658),U_14659),U_14660),U_14661) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14656,U_14657,U_14658),U_14660),hAPP(U_14659,U_14661)),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

cnf(f_3670_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14655,U_14656,U_14657,U_14658),U_14659),U_14660),U_14661) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14656,U_14657,U_14658),U_14660),hAPP(U_14659,U_14661)),
    inference(clausify,[status(thm)],[f_3670_2]) ).

fof(f_3671_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__def]) ).

fof(f_3671_2,plain,
    ! [U_14668,U_14667,U_14666,U_14665,U_14664,U_14663,U_14662] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14662,U_14663,U_14664,U_14665),U_14666),U_14667),U_14668) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14663,U_14664,U_14665),U_14667),hAPP(U_14666,U_14668)),
    inference(variable_rename,[status(thm)],[f_3671_1]) ).

cnf(f_3671_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14662,U_14663,U_14664,U_14665),U_14666),U_14667),U_14668) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14663,U_14664,U_14665),U_14667),hAPP(U_14666,U_14668)),
    inference(clausify,[status(thm)],[f_3671_2]) ).

fof(f_3672_1,plain,
    ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
      ( ( hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,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_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),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_3672_2,plain,
    ! [U_14673,U_14672,U_14671,U_14670,U_14669] :
      ( ( hAPP(c_Random_Oiterate(U_14670,U_14671,U_14669,U_14672),U_14673) = hAPP(hAPP(c_Product__Type_Oscomp(U_14671,U_14670,U_14671,tc_prod(U_14670,U_14671)),hAPP(U_14672,U_14673)),c_Random_Oiterate(U_14670,U_14671,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14669),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14672))
        | U_14669 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_14670,U_14671,U_14669,U_14672),U_14673) = hAPP(c_Product__Type_OPair(U_14670,U_14671),U_14673)
        | U_14669 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

fof(f_3672_3,plain,
    ( ! [U_14683,U_14681,U_14679,U_14677,U_14675] :
        ( hAPP(c_Random_Oiterate(U_14677,U_14679,U_14675,U_14681),U_14683) = hAPP(hAPP(c_Product__Type_Oscomp(U_14679,U_14677,U_14679,tc_prod(U_14677,U_14679)),hAPP(U_14681,U_14683)),c_Random_Oiterate(U_14677,U_14679,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14675),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14681))
        | U_14675 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_14682,U_14680,U_14678,U_14676,U_14674] :
        ( hAPP(c_Random_Oiterate(U_14676,U_14678,U_14674,U_14680),U_14682) = hAPP(c_Product__Type_OPair(U_14676,U_14678),U_14682)
        | U_14674 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3672_2]) ).

cnf(f_3672_4,plain,
    ( hAPP(c_Random_Oiterate(U_14676,U_14678,U_14674,U_14680),U_14682) = hAPP(c_Product__Type_OPair(U_14676,U_14678),U_14682)
    | U_14674 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3672_3]) ).

cnf(f_3672_5,plain,
    ( hAPP(c_Random_Oiterate(U_14677,U_14679,U_14675,U_14681),U_14683) = hAPP(hAPP(c_Product__Type_Oscomp(U_14679,U_14677,U_14679,tc_prod(U_14677,U_14679)),hAPP(U_14681,U_14683)),c_Random_Oiterate(U_14677,U_14679,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14675),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14681))
    | U_14675 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3672_3]) ).

fof(f_3673_1,plain,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,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_a),B_x),V_d_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x)) )
      | V_b_2 != V_d_2
      | V_a_2 != V_c_2
      | ~ class_Orderings_Oord(T_a)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).

fof(f_3673_2,plain,
    ! [U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14691),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14687),U_14689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14692),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14688),U_14690))
      | ? [U_14684] :
          ( hAPP(U_14691,U_14684) != hAPP(U_14692,U_14684)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14686),U_14684),U_14690))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14686),U_14688),U_14684)) )
      | U_14689 != U_14690
      | U_14687 != U_14688
      | ~ class_Orderings_Oord(U_14686)
      | ~ class_Groups_Ocomm__monoid__add(U_14685) ),
    inference(variable_rename,[status(thm)],[f_3673_1]) ).

fof(f_3673_3,plain,
    ! [U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14691),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14687),U_14689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14692),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14688),U_14690))
      | ( hAPP(U_14691,sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685)) != hAPP(U_14692,sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14686),sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685)),U_14690))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14686),U_14688),sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685))) )
      | U_14689 != U_14690
      | U_14687 != U_14688
      | ~ class_Orderings_Oord(U_14686)
      | ~ class_Groups_Ocomm__monoid__add(U_14685) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_14684,sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685))],[f_3673_2]) ).

cnf(f_3673_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14686),U_14688),sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14691),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14687),U_14689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14692),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14688),U_14690))
    | U_14689 != U_14690
    | U_14687 != U_14688
    | ~ class_Orderings_Oord(U_14686)
    | ~ class_Groups_Ocomm__monoid__add(U_14685) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

cnf(f_3673_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14686),sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685)),U_14690))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14691),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14687),U_14689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14692),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14688),U_14690))
    | U_14689 != U_14690
    | U_14687 != U_14688
    | ~ class_Orderings_Oord(U_14686)
    | ~ class_Groups_Ocomm__monoid__add(U_14685) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

cnf(f_3673_6,plain,
    ( hAPP(U_14691,sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685)) != hAPP(U_14692,sK372(U_14692,U_14691,U_14690,U_14689,U_14688,U_14687,U_14686,U_14685))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14691),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14687),U_14689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14686,U_14685),U_14692),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14686,U_14688),U_14690))
    | U_14689 != U_14690
    | U_14687 != U_14688
    | ~ class_Orderings_Oord(U_14686)
    | ~ class_Groups_Ocomm__monoid__add(U_14685) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

fof(f_3674_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_3674_2,plain,
    ! [U_14694,U_14693] :
      ( ( c_Random_Olog(U_14693,U_14694) = 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_14693,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_14694),U_14693)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14694),U_14693))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14693),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_14693,U_14694) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14694),U_14693))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14693),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

fof(f_3674_3,plain,
    ( ! [U_14698,U_14696] :
        ( c_Random_Olog(U_14696,U_14698) = 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_14696,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_14698),U_14696)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14698),U_14696))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14696),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_14697,U_14695] :
        ( c_Random_Olog(U_14695,U_14697) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14697),U_14695))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14695),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_3674_2]) ).

cnf(f_3674_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14695),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | c_Random_Olog(U_14695,U_14697) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3674_3]) ).

cnf(f_3674_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14697),U_14695))
    | c_Random_Olog(U_14695,U_14697) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3674_3]) ).

cnf(f_3674_6,plain,
    ( c_Random_Olog(U_14696,U_14698) = 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_14696,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_14698),U_14696)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14698),U_14696))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_14696),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_3674_3]) ).

fof(f_3675_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_3675_2,plain,
    ! [U_14701,U_14700,U_14699] :
      ( ( c_Random_Ominus__shift(U_14701,U_14699,U_14700) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14699),U_14700)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14699),U_14700)) )
      & ( c_Random_Ominus__shift(U_14701,U_14699,U_14700) = 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_14701),U_14699)),U_14700)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14699),U_14700)) ) ),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

fof(f_3675_3,plain,
    ( ! [U_14707,U_14705,U_14703] :
        ( c_Random_Ominus__shift(U_14707,U_14703,U_14705) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14703),U_14705)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14703),U_14705)) )
    & ! [U_14706,U_14704,U_14702] :
        ( c_Random_Ominus__shift(U_14706,U_14702,U_14704) = 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_14706),U_14702)),U_14704)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14702),U_14704)) ) ),
    inference(miniscope,[status(thm)],[f_3675_2]) ).

cnf(f_3675_4,plain,
    ( c_Random_Ominus__shift(U_14706,U_14702,U_14704) = 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_14706),U_14702)),U_14704)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14702),U_14704)) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

cnf(f_3675_5,plain,
    ( c_Random_Ominus__shift(U_14707,U_14703,U_14705) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14703),U_14705)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14703),U_14705)) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

fof(f_3676_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_3676_2,plain,
    ! [U_14709,U_14708] :
      ( ( c_Random_Oinc__shift(U_14708,U_14709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_14709),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_14708 = U_14709 )
      & ( c_Random_Oinc__shift(U_14708,U_14709) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_14708 != U_14709 ) ),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

fof(f_3676_3,plain,
    ( ! [U_14713,U_14711] :
        ( c_Random_Oinc__shift(U_14711,U_14713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_14713),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_14711 = U_14713 )
    & ! [U_14712,U_14710] :
        ( c_Random_Oinc__shift(U_14710,U_14712) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_14710 != U_14712 ) ),
    inference(miniscope,[status(thm)],[f_3676_2]) ).

cnf(f_3676_4,plain,
    ( c_Random_Oinc__shift(U_14710,U_14712) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_14710 != U_14712 ),
    inference(clausify,[status(thm)],[f_3676_3]) ).

cnf(f_3676_5,plain,
    ( c_Random_Oinc__shift(U_14711,U_14713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_14713),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_14711 = U_14713 ),
    inference(clausify,[status(thm)],[f_3676_3]) ).

fof(f_3677_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_3677_2,plain,
    ! [U_14715,U_14714] :
      ( 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_14714),U_14715))),U_14714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14714)) ),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

cnf(f_3677_3,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_14714),U_14715))),U_14714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14714)) ),
    inference(clausify,[status(thm)],[f_3677_2]) ).

fof(f_3678_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_3678_2,plain,
    ! [U_14717,U_14716] :
      ( ( 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_14716),U_14717)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14716),U_14717)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14716),U_14717))
        | ~ 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_14716),U_14717)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

fof(f_3678_3,plain,
    ( ! [U_14721,U_14719] :
        ( 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_14719),U_14721)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14719),U_14721)) )
    & ! [U_14720,U_14718] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14718),U_14720))
        | ~ 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_14718),U_14720)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3678_2]) ).

cnf(f_3678_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14718),U_14720))
    | ~ 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_14718),U_14720)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3678_3]) ).

cnf(f_3678_5,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_14719),U_14721)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14719),U_14721)) ),
    inference(clausify,[status(thm)],[f_3678_3]) ).

fof(f_3679_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_3679_2,plain,
    ! [U_14727,U_14726,U_14725,U_14724] :
      ( ? [U_14723] :
          ( hAPP(U_14726,U_14723) = U_14727
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14723),U_14725))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),U_14723)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
      | ? [U_14722] :
          ( ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14722),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,U_14722)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14722),U_14725))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),U_14722)) ) ),
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

fof(f_3679_3,plain,
    ! [U_14727,U_14726,U_14725,U_14724] :
      ( ? [U_14723] :
          ( hAPP(U_14726,U_14723) = U_14727
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14723),U_14725))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),U_14723)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
      | ( ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,sK373(U_14727,U_14726,U_14725,U_14724))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),U_14725))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK373(U_14727,U_14726,U_14725,U_14724))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_14722,sK373(U_14727,U_14726,U_14725,U_14724))],[f_3679_2]) ).

fof(f_3679_4,plain,
    ! [U_14727,U_14726,U_14725,U_14724] :
      ( ( hAPP(U_14726,sK374(U_14727,U_14726,U_14725,U_14724)) = U_14727
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK374(U_14727,U_14726,U_14725,U_14724)),U_14725))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK374(U_14727,U_14726,U_14725,U_14724))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
      | ( ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,sK373(U_14727,U_14726,U_14725,U_14724))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),U_14725))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK373(U_14727,U_14726,U_14725,U_14724))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_14723,sK374(U_14727,U_14726,U_14725,U_14724))],[f_3679_3]) ).

cnf(f_3679_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK374(U_14727,U_14726,U_14725,U_14724)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK373(U_14727,U_14726,U_14725,U_14724))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK374(U_14727,U_14726,U_14725,U_14724)),U_14725))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK373(U_14727,U_14726,U_14725,U_14724))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_7,plain,
    ( hAPP(U_14726,sK374(U_14727,U_14726,U_14725,U_14724)) = U_14727
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK373(U_14727,U_14726,U_14725,U_14724))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK374(U_14727,U_14726,U_14725,U_14724)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),U_14725)) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK374(U_14727,U_14726,U_14725,U_14724)),U_14725))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),U_14725)) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_10,plain,
    ( hAPP(U_14726,sK374(U_14727,U_14726,U_14725,U_14724)) = U_14727
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),U_14725)) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14724),sK374(U_14727,U_14726,U_14725,U_14724)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,sK373(U_14727,U_14726,U_14725,U_14724))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK374(U_14727,U_14726,U_14725,U_14724)),U_14725))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,sK373(U_14727,U_14726,U_14725,U_14724))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

cnf(f_3679_13,plain,
    ( hAPP(U_14726,sK374(U_14727,U_14726,U_14725,U_14724)) = U_14727
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_14727),hAPP(U_14726,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_14726,U_14724)),U_14727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14724),U_14725))
    | ~ 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_14726,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK373(U_14727,U_14726,U_14725,U_14724)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_14726,sK373(U_14727,U_14726,U_14725,U_14724))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3679_4]) ).

fof(f_3680_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))
      | ~ c_Wellfounded_Owf(T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__trancl]) ).

fof(f_3680_2,plain,
    ! [U_14729,U_14728] :
      ( c_Wellfounded_Owf(U_14728,c_Transitive__Closure_Otrancl(U_14728,U_14729))
      | ~ c_Wellfounded_Owf(U_14728,U_14729) ),
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

cnf(f_3680_3,plain,
    ( c_Wellfounded_Owf(U_14728,c_Transitive__Closure_Otrancl(U_14728,U_14729))
    | ~ c_Wellfounded_Owf(U_14728,U_14729) ),
    inference(clausify,[status(thm)],[f_3680_2]) ).

fof(f_3681_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]) ).

cnf(f_3681_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3681_1]) ).

fof(f_3682_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Oacyclic(T_a,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__def]) ).

fof(f_3682_2,plain,
    ! [U_14733,U_14732] :
      ( ( c_Wellfounded_Oacyclic(U_14732,U_14733)
        | ? [U_14731] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14732,U_14732)),hAPP(hAPP(c_Product__Type_OPair(U_14732,U_14732),U_14731),U_14731)),c_Transitive__Closure_Otrancl(U_14732,U_14733))) )
      & ( ! [U_14730] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14732,U_14732)),hAPP(hAPP(c_Product__Type_OPair(U_14732,U_14732),U_14730),U_14730)),c_Transitive__Closure_Otrancl(U_14732,U_14733)))
        | ~ c_Wellfounded_Oacyclic(U_14732,U_14733) ) ),
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

fof(f_3682_3,plain,
    ( ! [U_14737,U_14735] :
        ( c_Wellfounded_Oacyclic(U_14735,U_14737)
        | ? [U_14731] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14731),U_14731)),c_Transitive__Closure_Otrancl(U_14735,U_14737))) )
    & ! [U_14736,U_14734] :
        ( ! [U_14730] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14734,U_14734)),hAPP(hAPP(c_Product__Type_OPair(U_14734,U_14734),U_14730),U_14730)),c_Transitive__Closure_Otrancl(U_14734,U_14736)))
        | ~ c_Wellfounded_Oacyclic(U_14734,U_14736) ) ),
    inference(miniscope,[status(thm)],[f_3682_2]) ).

fof(f_3682_4,plain,
    ( ! [U_14737,U_14735] :
        ( c_Wellfounded_Oacyclic(U_14735,U_14737)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),sK375(U_14737,U_14735)),sK375(U_14737,U_14735))),c_Transitive__Closure_Otrancl(U_14735,U_14737))) )
    & ! [U_14736,U_14734] :
        ( ! [U_14730] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14734,U_14734)),hAPP(hAPP(c_Product__Type_OPair(U_14734,U_14734),U_14730),U_14730)),c_Transitive__Closure_Otrancl(U_14734,U_14736)))
        | ~ c_Wellfounded_Oacyclic(U_14734,U_14736) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_14731,sK375(U_14737,U_14735))],[f_3682_3]) ).

cnf(f_3682_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14734,U_14734)),hAPP(hAPP(c_Product__Type_OPair(U_14734,U_14734),U_14730),U_14730)),c_Transitive__Closure_Otrancl(U_14734,U_14736)))
    | ~ c_Wellfounded_Oacyclic(U_14734,U_14736) ),
    inference(clausify,[status(thm)],[f_3682_4]) ).

cnf(f_3682_6,plain,
    ( c_Wellfounded_Oacyclic(U_14735,U_14737)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),sK375(U_14737,U_14735)),sK375(U_14737,U_14735))),c_Transitive__Closure_Otrancl(U_14735,U_14737))) ),
    inference(clausify,[status(thm)],[f_3682_4]) ).

fof(f_3683_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl]) ).

fof(f_3683_2,plain,
    ! [U_14741,U_14740,U_14739,U_14738] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),c_Transitive__Closure_Otrancl(U_14738,U_14741)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),U_14741)) ),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

cnf(f_3683_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),c_Transitive__Closure_Otrancl(U_14738,U_14741)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),U_14741)) ),
    inference(clausify,[status(thm)],[f_3683_2]) ).

fof(f_3684_1,plain,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(f_3684_2,plain,
    ! [U_14743,U_14742] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14742,U_14742),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14742,U_14743)),hAPP(hAPP(c_Product__Type_OSigma(U_14742,U_14742),hAPP(c_Relation_OField(U_14742),U_14743)),hAPP(c_COMBK(tc_fun(U_14742,tc_HOL_Obool),U_14742),hAPP(c_Relation_OField(U_14742),U_14743))))),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

cnf(f_3684_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14742,U_14742),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14742,U_14743)),hAPP(hAPP(c_Product__Type_OSigma(U_14742,U_14742),hAPP(c_Relation_OField(U_14742),U_14743)),hAPP(c_COMBK(tc_fun(U_14742,tc_HOL_Obool),U_14742),hAPP(c_Relation_OField(U_14742),U_14743))))),
    inference(clausify,[status(thm)],[f_3684_2]) ).

fof(f_3685_1,plain,
    ! [V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H]) ).

fof(f_3685_2,plain,
    ! [U_14746,U_14745,U_14744] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14744,U_14744)),U_14745),c_Transitive__Closure_Otrancl(U_14744,U_14746)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14744,U_14744)),U_14745),U_14746)) ),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

cnf(f_3685_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14744,U_14744)),U_14745),c_Transitive__Closure_Otrancl(U_14744,U_14746)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14744,U_14744)),U_14745),U_14746)) ),
    inference(clausify,[status(thm)],[f_3685_2]) ).

fof(f_3686_1,plain,
    ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_trancl__empty]) ).

fof(f_3686_2,plain,
    ! [U_14747] : c_Transitive__Closure_Otrancl(U_14747,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14747,U_14747),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14747,U_14747),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

cnf(f_3686_3,plain,
    c_Transitive__Closure_Otrancl(U_14747,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14747,U_14747),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14747,U_14747),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3686_2]) ).

fof(f_3687_1,plain,
    ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__domain]) ).

fof(f_3687_2,plain,
    ! [U_14749,U_14748] : hAPP(c_Relation_ODomain(U_14748,U_14748),c_Transitive__Closure_Otrancl(U_14748,U_14749)) = hAPP(c_Relation_ODomain(U_14748,U_14748),U_14749),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

cnf(f_3687_3,plain,
    hAPP(c_Relation_ODomain(U_14748,U_14748),c_Transitive__Closure_Otrancl(U_14748,U_14749)) = hAPP(c_Relation_ODomain(U_14748,U_14748),U_14749),
    inference(clausify,[status(thm)],[f_3687_2]) ).

fof(f_3688_1,plain,
    ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__range]) ).

fof(f_3688_2,plain,
    ! [U_14751,U_14750] : hAPP(c_Relation_ORange(U_14750,U_14750),c_Transitive__Closure_Otrancl(U_14750,U_14751)) = hAPP(c_Relation_ORange(U_14750,U_14750),U_14751),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

cnf(f_3688_3,plain,
    hAPP(c_Relation_ORange(U_14750,U_14750),c_Transitive__Closure_Otrancl(U_14750,U_14751)) = hAPP(c_Relation_ORange(U_14750,U_14750),U_14751),
    inference(clausify,[status(thm)],[f_3688_2]) ).

fof(f_3689_1,plain,
    ! [V_r_2,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__trancl]) ).

fof(f_3689_2,plain,
    ! [U_14753,U_14752] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14752,U_14752)),c_Transitive__Closure_Otrancl(U_14752,U_14753)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14752,U_14752)),U_14753)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14752,U_14752)),U_14753))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14752,U_14752)),c_Transitive__Closure_Otrancl(U_14752,U_14753))) ) ),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

fof(f_3689_3,plain,
    ( ! [U_14757,U_14755] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14755,U_14755)),c_Transitive__Closure_Otrancl(U_14755,U_14757)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14755,U_14755)),U_14757)) )
    & ! [U_14756,U_14754] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14754,U_14754)),U_14756))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14754,U_14754)),c_Transitive__Closure_Otrancl(U_14754,U_14756))) ) ),
    inference(miniscope,[status(thm)],[f_3689_2]) ).

cnf(f_3689_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14754,U_14754)),U_14756))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14754,U_14754)),c_Transitive__Closure_Otrancl(U_14754,U_14756))) ),
    inference(clausify,[status(thm)],[f_3689_3]) ).

cnf(f_3689_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14755,U_14755)),c_Transitive__Closure_Otrancl(U_14755,U_14757)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14755,U_14755)),U_14757)) ),
    inference(clausify,[status(thm)],[f_3689_3]) ).

fof(f_3690_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__trans]) ).

fof(f_3690_2,plain,
    ! [U_14762,U_14761,U_14760,U_14759,U_14758] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14759),U_14762)),c_Transitive__Closure_Otrancl(U_14758,U_14761)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14760),U_14762)),c_Transitive__Closure_Otrancl(U_14758,U_14761)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14759),U_14760)),c_Transitive__Closure_Otrancl(U_14758,U_14761))) ),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

cnf(f_3690_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14759),U_14762)),c_Transitive__Closure_Otrancl(U_14758,U_14761)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14760),U_14762)),c_Transitive__Closure_Otrancl(U_14758,U_14761)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),hAPP(hAPP(c_Product__Type_OPair(U_14758,U_14758),U_14759),U_14760)),c_Transitive__Closure_Otrancl(U_14758,U_14761))) ),
    inference(clausify,[status(thm)],[f_3690_2]) ).

fof(f_3691_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).

fof(f_3691_2,plain,
    ! [U_14767,U_14766,U_14765,U_14764,U_14763] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14764),U_14767)),c_Transitive__Closure_Otrancl(U_14763,U_14766)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14765),U_14767)),U_14766))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14764),U_14765)),c_Transitive__Closure_Otrancl(U_14763,U_14766))) ),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

cnf(f_3691_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14764),U_14767)),c_Transitive__Closure_Otrancl(U_14763,U_14766)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14765),U_14767)),U_14766))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14763,U_14763)),hAPP(hAPP(c_Product__Type_OPair(U_14763,U_14763),U_14764),U_14765)),c_Transitive__Closure_Otrancl(U_14763,U_14766))) ),
    inference(clausify,[status(thm)],[f_3691_2]) ).

fof(f_3692_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).

fof(f_3692_2,plain,
    ! [U_14772,U_14771,U_14770,U_14769,U_14768] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14772)),c_Transitive__Closure_Otrancl(U_14768,U_14771)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14770),U_14772)),c_Transitive__Closure_Otrancl(U_14768,U_14771)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),U_14771)) ),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

cnf(f_3692_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14772)),c_Transitive__Closure_Otrancl(U_14768,U_14771)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14770),U_14772)),c_Transitive__Closure_Otrancl(U_14768,U_14771)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),U_14771)) ),
    inference(clausify,[status(thm)],[f_3692_2]) ).

fof(f_3693_1,plain,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).

fof(f_3693_2,plain,
    ! [U_14777,U_14776,U_14775,U_14774,U_14773] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14774),U_14777)),c_Transitive__Closure_Otrancl(U_14773,U_14776)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14775),U_14777)),U_14776))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14774),U_14775)),U_14776)) ),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

cnf(f_3693_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14774),U_14777)),c_Transitive__Closure_Otrancl(U_14773,U_14776)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14775),U_14777)),U_14776))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14773,U_14773)),hAPP(hAPP(c_Product__Type_OPair(U_14773,U_14773),U_14774),U_14775)),U_14776)) ),
    inference(clausify,[status(thm)],[f_3693_2]) ).

fof(f_3694_1,plain,
    ! [V_s_2,V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__mono]) ).

fof(f_3694_2,plain,
    ! [U_14781,U_14780,U_14779,U_14778] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14778,U_14778)),U_14779),c_Transitive__Closure_Otrancl(U_14778,U_14781)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14778,U_14778),tc_HOL_Obool)),U_14780),U_14781))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14778,U_14778)),U_14779),c_Transitive__Closure_Otrancl(U_14778,U_14780))) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

cnf(f_3694_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14778,U_14778)),U_14779),c_Transitive__Closure_Otrancl(U_14778,U_14781)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14778,U_14778),tc_HOL_Obool)),U_14780),U_14781))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14778,U_14778)),U_14779),c_Transitive__Closure_Otrancl(U_14778,U_14780))) ),
    inference(clausify,[status(thm)],[f_3694_2]) ).

fof(f_3695_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold]) ).

fof(f_3695_2,plain,
    ! [U_14783,U_14782] : c_Transitive__Closure_Otrancl(U_14782,U_14783) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14783),hAPP(hAPP(c_Relation_Orel__comp(U_14782,U_14782,U_14782),c_Transitive__Closure_Otrancl(U_14782,U_14783)),U_14783)),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

cnf(f_3695_3,plain,
    c_Transitive__Closure_Otrancl(U_14782,U_14783) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14783),hAPP(hAPP(c_Relation_Orel__comp(U_14782,U_14782,U_14782),c_Transitive__Closure_Otrancl(U_14782,U_14783)),U_14783)),
    inference(clausify,[status(thm)],[f_3695_2]) ).

fof(f_3696_1,plain,
    ! [V_A_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma]) ).

fof(f_3696_2,plain,
    ! [U_14786,U_14785,U_14784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14784,U_14784),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14784,U_14785)),hAPP(hAPP(c_Product__Type_OSigma(U_14784,U_14784),U_14786),hAPP(c_COMBK(tc_fun(U_14784,tc_HOL_Obool),U_14784),U_14786))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14784,U_14784),tc_HOL_Obool)),U_14785),hAPP(hAPP(c_Product__Type_OSigma(U_14784,U_14784),U_14786),hAPP(c_COMBK(tc_fun(U_14784,tc_HOL_Obool),U_14784),U_14786)))) ),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

cnf(f_3696_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14784,U_14784),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14784,U_14785)),hAPP(hAPP(c_Product__Type_OSigma(U_14784,U_14784),U_14786),hAPP(c_COMBK(tc_fun(U_14784,tc_HOL_Obool),U_14784),U_14786))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14784,U_14784),tc_HOL_Obool)),U_14785),hAPP(hAPP(c_Product__Type_OSigma(U_14784,U_14784),U_14786),hAPP(c_COMBK(tc_fun(U_14784,tc_HOL_Obool),U_14784),U_14786)))) ),
    inference(clausify,[status(thm)],[f_3696_2]) ).

fof(f_3697_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,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_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset]) ).

fof(f_3697_2,plain,
    ! [U_14789,U_14788,U_14787] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14787,U_14788)),U_14789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14787,U_14787,U_14787),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14787,U_14788)),U_14789)),U_14788)),U_14789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),U_14788),U_14789)) ),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

cnf(f_3697_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14787,U_14788)),U_14789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14787,U_14787,U_14787),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14787,U_14788)),U_14789)),U_14788)),U_14789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14787,U_14787),tc_HOL_Obool)),U_14788),U_14789)) ),
    inference(clausify,[status(thm)],[f_3697_2]) ).

fof(f_3698_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__insert]) ).

fof(f_3698_2,plain,
    ! [U_14793,U_14792,U_14791,U_14790] : c_Transitive__Closure_Otrancl(U_14790,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14790,U_14790)),hAPP(hAPP(c_Product__Type_OPair(U_14790,U_14790),U_14791),U_14792)),U_14793)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14790,U_14793)),hAPP(c_Set_OCollect(tc_prod(U_14790,U_14790)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14790,U_14790,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14790,tc_fun(U_14790,tc_HOL_Obool),tc_fun(U_14790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14790,tc_HOL_Obool),tc_fun(U_14790,tc_HOL_Obool)),U_14790),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14790)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14790),c_fconj),hAPP(hAPP(c_COMBC(U_14790,tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14790,U_14790),tc_fun(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),U_14790),c_member(tc_prod(U_14790,U_14790))),hAPP(hAPP(c_COMBC(U_14790,U_14790,tc_prod(U_14790,U_14790)),c_Product__Type_OPair(U_14790,U_14790)),U_14791))),c_Transitive__Closure_Ortrancl(U_14790,U_14793))))),hAPP(hAPP(c_COMBC(U_14790,tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14790,U_14790),tc_fun(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),U_14790),c_member(tc_prod(U_14790,U_14790))),hAPP(c_Product__Type_OPair(U_14790,U_14790),U_14792))),c_Transitive__Closure_Ortrancl(U_14790,U_14793)))))),
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

cnf(f_3698_3,plain,
    c_Transitive__Closure_Otrancl(U_14790,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14790,U_14790)),hAPP(hAPP(c_Product__Type_OPair(U_14790,U_14790),U_14791),U_14792)),U_14793)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14790,U_14793)),hAPP(c_Set_OCollect(tc_prod(U_14790,U_14790)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14790,U_14790,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14790,tc_fun(U_14790,tc_HOL_Obool),tc_fun(U_14790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14790,tc_HOL_Obool),tc_fun(U_14790,tc_HOL_Obool)),U_14790),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14790)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14790),c_fconj),hAPP(hAPP(c_COMBC(U_14790,tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14790,U_14790),tc_fun(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),U_14790),c_member(tc_prod(U_14790,U_14790))),hAPP(hAPP(c_COMBC(U_14790,U_14790,tc_prod(U_14790,U_14790)),c_Product__Type_OPair(U_14790,U_14790)),U_14791))),c_Transitive__Closure_Ortrancl(U_14790,U_14793))))),hAPP(hAPP(c_COMBC(U_14790,tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14790,U_14790),tc_fun(tc_fun(tc_prod(U_14790,U_14790),tc_HOL_Obool),tc_HOL_Obool),U_14790),c_member(tc_prod(U_14790,U_14790))),hAPP(c_Product__Type_OPair(U_14790,U_14790),U_14792))),c_Transitive__Closure_Ortrancl(U_14790,U_14793)))))),
    inference(clausify,[status(thm)],[f_3698_2]) ).

fof(f_3699_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq]) ).

fof(f_3699_2,plain,
    ! [U_14797,U_14796,U_14795,U_14794] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14794,tc_fun(U_14794,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14794,tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_fun(U_14794,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14794,tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_fun(U_14794,tc_HOL_Obool)),U_14794),c_COMBC(U_14794,tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14794,tc_prod(U_14794,U_14794)),tc_fun(U_14794,tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),U_14794),hAPP(c_COMBB(tc_prod(U_14794,U_14794),tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool),U_14794),c_member(tc_prod(U_14794,U_14794)))),c_Product__Type_OPair(U_14794,U_14794)))),U_14795)),c_fequal),U_14796),U_14797))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14794,U_14794)),hAPP(hAPP(c_Product__Type_OPair(U_14794,U_14794),U_14796),U_14797)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool)),U_14795),c_Relation_OId(U_14794)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14794,U_14794)),hAPP(hAPP(c_Product__Type_OPair(U_14794,U_14794),U_14796),U_14797)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool)),U_14795),c_Relation_OId(U_14794))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14794,tc_fun(U_14794,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14794,tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_fun(U_14794,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14794,tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_fun(U_14794,tc_HOL_Obool)),U_14794),c_COMBC(U_14794,tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14794,tc_prod(U_14794,U_14794)),tc_fun(U_14794,tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool)),U_14794),hAPP(c_COMBB(tc_prod(U_14794,U_14794),tc_fun(tc_fun(tc_prod(U_14794,U_14794),tc_HOL_Obool),tc_HOL_Obool),U_14794),c_member(tc_prod(U_14794,U_14794)))),c_Product__Type_OPair(U_14794,U_14794)))),U_14795)),c_fequal),U_14796),U_14797)) ) ),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

fof(f_3699_3,plain,
    ( ! [U_14805,U_14803,U_14801,U_14799] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14799,tc_fun(U_14799,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14799,tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_fun(U_14799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14799,tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_fun(U_14799,tc_HOL_Obool)),U_14799),c_COMBC(U_14799,tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14799,tc_prod(U_14799,U_14799)),tc_fun(U_14799,tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),U_14799),hAPP(c_COMBB(tc_prod(U_14799,U_14799),tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool),U_14799),c_member(tc_prod(U_14799,U_14799)))),c_Product__Type_OPair(U_14799,U_14799)))),U_14801)),c_fequal),U_14803),U_14805))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14799,U_14799)),hAPP(hAPP(c_Product__Type_OPair(U_14799,U_14799),U_14803),U_14805)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool)),U_14801),c_Relation_OId(U_14799)))) )
    & ! [U_14804,U_14802,U_14800,U_14798] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14798,U_14798)),hAPP(hAPP(c_Product__Type_OPair(U_14798,U_14798),U_14802),U_14804)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool)),U_14800),c_Relation_OId(U_14798))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14798,tc_fun(U_14798,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14798,tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_fun(U_14798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14798,tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_fun(U_14798,tc_HOL_Obool)),U_14798),c_COMBC(U_14798,tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14798,tc_prod(U_14798,U_14798)),tc_fun(U_14798,tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),U_14798),hAPP(c_COMBB(tc_prod(U_14798,U_14798),tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool),U_14798),c_member(tc_prod(U_14798,U_14798)))),c_Product__Type_OPair(U_14798,U_14798)))),U_14800)),c_fequal),U_14802),U_14804)) ) ),
    inference(miniscope,[status(thm)],[f_3699_2]) ).

cnf(f_3699_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14798,U_14798)),hAPP(hAPP(c_Product__Type_OPair(U_14798,U_14798),U_14802),U_14804)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool)),U_14800),c_Relation_OId(U_14798))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14798,tc_fun(U_14798,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14798,tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_fun(U_14798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14798,tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_fun(U_14798,tc_HOL_Obool)),U_14798),c_COMBC(U_14798,tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14798,tc_prod(U_14798,U_14798)),tc_fun(U_14798,tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool)),U_14798),hAPP(c_COMBB(tc_prod(U_14798,U_14798),tc_fun(tc_fun(tc_prod(U_14798,U_14798),tc_HOL_Obool),tc_HOL_Obool),U_14798),c_member(tc_prod(U_14798,U_14798)))),c_Product__Type_OPair(U_14798,U_14798)))),U_14800)),c_fequal),U_14802),U_14804)) ),
    inference(clausify,[status(thm)],[f_3699_3]) ).

cnf(f_3699_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14799,tc_fun(U_14799,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14799,tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_fun(U_14799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14799,tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_fun(U_14799,tc_HOL_Obool)),U_14799),c_COMBC(U_14799,tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14799,tc_prod(U_14799,U_14799)),tc_fun(U_14799,tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool)),U_14799),hAPP(c_COMBB(tc_prod(U_14799,U_14799),tc_fun(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool),tc_HOL_Obool),U_14799),c_member(tc_prod(U_14799,U_14799)))),c_Product__Type_OPair(U_14799,U_14799)))),U_14801)),c_fequal),U_14803),U_14805))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14799,U_14799)),hAPP(hAPP(c_Product__Type_OPair(U_14799,U_14799),U_14803),U_14805)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14799,U_14799),tc_HOL_Obool)),U_14801),c_Relation_OId(U_14799)))) ),
    inference(clausify,[status(thm)],[f_3699_3]) ).

fof(f_3700_1,plain,
    ! [V_r_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl]) ).

fof(f_3700_2,plain,
    ! [U_14808,U_14807,U_14806] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),U_14807),c_Transitive__Closure_Ortrancl(U_14806,U_14808)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),U_14807),U_14808)) ),
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

cnf(f_3700_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),U_14807),c_Transitive__Closure_Ortrancl(U_14806,U_14808)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),U_14807),U_14808)) ),
    inference(clausify,[status(thm)],[f_3700_2]) ).

fof(f_3701_1,plain,
    ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

fof(f_3701_2,plain,
    ! [U_14811,U_14810,U_14809] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14809,U_14809)),hAPP(hAPP(c_Product__Type_OPair(U_14809,U_14809),U_14810),U_14810)),c_Transitive__Closure_Ortrancl(U_14809,U_14811))),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

cnf(f_3701_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14809,U_14809)),hAPP(hAPP(c_Product__Type_OPair(U_14809,U_14809),U_14810),U_14810)),c_Transitive__Closure_Ortrancl(U_14809,U_14811))),
    inference(clausify,[status(thm)],[f_3701_2]) ).

fof(f_3702_1,plain,
    ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))),
    inference(fof_nnf,[status(thm)],[fact_IdI]) ).

fof(f_3702_2,plain,
    ! [U_14813,U_14812] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14813)),c_Relation_OId(U_14812))),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

cnf(f_3702_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14813)),c_Relation_OId(U_14812))),
    inference(clausify,[status(thm)],[f_3702_2]) ).

fof(f_3703_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl]) ).

fof(f_3703_2,plain,
    ! [U_14817,U_14816,U_14815,U_14814] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14814),U_14815),U_14816)),c_Transitive__Closure_Ortrancl(U_14814,U_14817)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14814),U_14815),U_14816)),c_Transitive__Closure_Otrancl(U_14814,U_14817))) ),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

cnf(f_3703_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14814),U_14815),U_14816)),c_Transitive__Closure_Ortrancl(U_14814,U_14817)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14814),U_14815),U_14816)),c_Transitive__Closure_Otrancl(U_14814,U_14817))) ),
    inference(clausify,[status(thm)],[f_3703_2]) ).

fof(f_3704_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__left]) ).

fof(f_3704_2,plain,
    ! [U_14819,U_14818] : c_Transitive__Closure_Otrancl(U_14818,U_14819) = hAPP(hAPP(c_Relation_Orel__comp(U_14818,U_14818,U_14818),U_14819),c_Transitive__Closure_Ortrancl(U_14818,U_14819)),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

cnf(f_3704_3,plain,
    c_Transitive__Closure_Otrancl(U_14818,U_14819) = hAPP(hAPP(c_Relation_Orel__comp(U_14818,U_14818,U_14818),U_14819),c_Transitive__Closure_Ortrancl(U_14818,U_14819)),
    inference(clausify,[status(thm)],[f_3704_2]) ).

fof(f_3705_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__right]) ).

fof(f_3705_2,plain,
    ! [U_14821,U_14820] : c_Transitive__Closure_Otrancl(U_14820,U_14821) = hAPP(hAPP(c_Relation_Orel__comp(U_14820,U_14820,U_14820),c_Transitive__Closure_Ortrancl(U_14820,U_14821)),U_14821),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

cnf(f_3705_3,plain,
    c_Transitive__Closure_Otrancl(U_14820,U_14821) = hAPP(hAPP(c_Relation_Orel__comp(U_14820,U_14820,U_14820),c_Transitive__Closure_Ortrancl(U_14820,U_14821)),U_14821),
    inference(clausify,[status(thm)],[f_3705_2]) ).

fof(f_3706_1,plain,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_reflcl__trancl]) ).

fof(f_3706_2,plain,
    ! [U_14823,U_14822] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14822,U_14822),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14822,U_14823)),c_Relation_OId(U_14822)) = c_Transitive__Closure_Ortrancl(U_14822,U_14823),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

cnf(f_3706_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14822,U_14822),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14822,U_14823)),c_Relation_OId(U_14822)) = c_Transitive__Closure_Ortrancl(U_14822,U_14823),
    inference(clausify,[status(thm)],[f_3706_2]) ).

fof(f_3707_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__reflcl]) ).

fof(f_3707_2,plain,
    ! [U_14825,U_14824] : c_Transitive__Closure_Otrancl(U_14824,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14824,U_14824),tc_HOL_Obool)),U_14825),c_Relation_OId(U_14824))) = c_Transitive__Closure_Ortrancl(U_14824,U_14825),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

cnf(f_3707_3,plain,
    c_Transitive__Closure_Otrancl(U_14824,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14824,U_14824),tc_HOL_Obool)),U_14825),c_Relation_OId(U_14824))) = c_Transitive__Closure_Ortrancl(U_14824,U_14825),
    inference(clausify,[status(thm)],[f_3707_2]) ).

fof(f_3708_1,plain,
    ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(f_3708_2,plain,
    ! [U_14827,U_14826] : c_Transitive__Closure_Otrancl(U_14826,c_Transitive__Closure_Ortrancl(U_14826,U_14827)) = c_Transitive__Closure_Ortrancl(U_14826,U_14827),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

cnf(f_3708_3,plain,
    c_Transitive__Closure_Otrancl(U_14826,c_Transitive__Closure_Ortrancl(U_14826,U_14827)) = c_Transitive__Closure_Ortrancl(U_14826,U_14827),
    inference(clausify,[status(thm)],[f_3708_2]) ).

fof(f_3709_1,plain,
    ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(f_3709_2,plain,
    ! [U_14829,U_14828] : c_Transitive__Closure_Ortrancl(U_14828,c_Transitive__Closure_Otrancl(U_14828,U_14829)) = c_Transitive__Closure_Ortrancl(U_14828,U_14829),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

cnf(f_3709_3,plain,
    c_Transitive__Closure_Ortrancl(U_14828,c_Transitive__Closure_Otrancl(U_14828,U_14829)) = c_Transitive__Closure_Ortrancl(U_14828,U_14829),
    inference(clausify,[status(thm)],[f_3709_2]) ).

fof(f_3710_1,plain,
    ! [V_r_2,V_s_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,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_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset]) ).

fof(f_3710_2,plain,
    ! [U_14832,U_14831,U_14830] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14830,U_14832)),U_14831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14830,U_14830,U_14830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14830,U_14832)),U_14831)),U_14832)),U_14831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Relation_OId(U_14830)),U_14831)) ),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

cnf(f_3710_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14830,U_14832)),U_14831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14830,U_14830,U_14830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14830,U_14832)),U_14831)),U_14832)),U_14831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14830,U_14830),tc_HOL_Obool)),c_Relation_OId(U_14830)),U_14831)) ),
    inference(clausify,[status(thm)],[f_3710_2]) ).

fof(f_3711_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl]) ).

fof(f_3711_2,plain,
    ! [U_14835,U_14834,U_14833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14833,U_14833),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14833,U_14834)),c_Transitive__Closure_Ortrancl(U_14833,U_14835)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14833,U_14833),tc_HOL_Obool)),U_14834),c_Transitive__Closure_Ortrancl(U_14833,U_14835))) ),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

cnf(f_3711_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14833,U_14833),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14833,U_14834)),c_Transitive__Closure_Ortrancl(U_14833,U_14835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14833,U_14833),tc_HOL_Obool)),U_14834),c_Transitive__Closure_Ortrancl(U_14833,U_14835))) ),
    inference(clausify,[status(thm)],[f_3711_2]) ).

fof(f_3712_1,plain,
    ! [V_S_2,V_R_2,T_a] :
      ( c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset]) ).

fof(f_3712_2,plain,
    ! [U_14838,U_14837,U_14836] :
      ( c_Transitive__Closure_Ortrancl(U_14836,U_14838) = c_Transitive__Closure_Ortrancl(U_14836,U_14837)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14836,U_14836),tc_HOL_Obool)),U_14838),c_Transitive__Closure_Ortrancl(U_14836,U_14837)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14836,U_14836),tc_HOL_Obool)),U_14837),U_14838)) ),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

cnf(f_3712_3,plain,
    ( c_Transitive__Closure_Ortrancl(U_14836,U_14838) = c_Transitive__Closure_Ortrancl(U_14836,U_14837)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14836,U_14836),tc_HOL_Obool)),U_14838),c_Transitive__Closure_Ortrancl(U_14836,U_14837)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14836,U_14836),tc_HOL_Obool)),U_14837),U_14838)) ),
    inference(clausify,[status(thm)],[f_3712_2]) ).

fof(f_3713_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__mono]) ).

fof(f_3713_2,plain,
    ! [U_14841,U_14840,U_14839] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14839,U_14839),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14839,U_14840)),c_Transitive__Closure_Ortrancl(U_14839,U_14841)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14839,U_14839),tc_HOL_Obool)),U_14840),U_14841)) ),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

cnf(f_3713_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14839,U_14839),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14839,U_14840)),c_Transitive__Closure_Ortrancl(U_14839,U_14841)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14839,U_14839),tc_HOL_Obool)),U_14840),U_14841)) ),
    inference(clausify,[status(thm)],[f_3713_2]) ).

fof(f_3714_1,plain,
    ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(f_3714_2,plain,
    ! [U_14844,U_14843,U_14842] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14842,U_14843)),c_Transitive__Closure_Ortrancl(U_14842,U_14844))),c_Transitive__Closure_Ortrancl(U_14842,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),U_14843),U_14844)))),
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

cnf(f_3714_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14842,U_14843)),c_Transitive__Closure_Ortrancl(U_14842,U_14844))),c_Transitive__Closure_Ortrancl(U_14842,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14842,U_14842),tc_HOL_Obool)),U_14843),U_14844)))),
    inference(clausify,[status(thm)],[f_3714_2]) ).

fof(f_3715_1,plain,
    ! [V_X_2,V_r_2,T_a] :
      ( hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl]) ).

fof(f_3715_2,plain,
    ! [U_14847,U_14846,U_14845] :
      ( hAPP(c_Relation_OImage(U_14845,U_14845,c_Transitive__Closure_Ortrancl(U_14845,U_14846)),U_14847) = U_14847
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14845,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14845,U_14845,U_14846),U_14847)),U_14847)) ),
    inference(variable_rename,[status(thm)],[f_3715_1]) ).

cnf(f_3715_3,plain,
    ( hAPP(c_Relation_OImage(U_14845,U_14845,c_Transitive__Closure_Ortrancl(U_14845,U_14846)),U_14847) = U_14847
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14845,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14845,U_14845,U_14846),U_14847)),U_14847)) ),
    inference(clausify,[status(thm)],[f_3715_2]) ).

fof(f_3716_1,plain,
    ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__rtrancl]) ).

fof(f_3716_2,plain,
    ! [U_14849,U_14848] : c_Relation_Orefl__on(U_14848,c_Orderings_Otop__class_Otop(tc_fun(U_14848,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14848,U_14849)),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

cnf(f_3716_3,plain,
    c_Relation_Orefl__on(U_14848,c_Orderings_Otop__class_Otop(tc_fun(U_14848,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14848,U_14849)),
    inference(clausify,[status(thm)],[f_3716_2]) ).

fof(f_3717_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(f_3717_2,plain,
    ! [U_14851,U_14850] : c_Transitive__Closure_Ortrancl(U_14850,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14850,U_14850),tc_HOL_Obool)),U_14851),c_Relation_OId(U_14850))) = c_Transitive__Closure_Ortrancl(U_14850,U_14851),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

cnf(f_3717_3,plain,
    c_Transitive__Closure_Ortrancl(U_14850,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14850,U_14850),tc_HOL_Obool)),U_14851),c_Relation_OId(U_14850))) = c_Transitive__Closure_Ortrancl(U_14850,U_14851),
    inference(clausify,[status(thm)],[f_3717_2]) ).

fof(f_3718_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trans]) ).

fof(f_3718_2,plain,
    ! [U_14856,U_14855,U_14854,U_14853,U_14852] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14853),U_14856)),c_Transitive__Closure_Ortrancl(U_14852,U_14855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14854),U_14856)),c_Transitive__Closure_Ortrancl(U_14852,U_14855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14853),U_14854)),c_Transitive__Closure_Ortrancl(U_14852,U_14855))) ),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

cnf(f_3718_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14853),U_14856)),c_Transitive__Closure_Ortrancl(U_14852,U_14855)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14854),U_14856)),c_Transitive__Closure_Ortrancl(U_14852,U_14855)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14852,U_14852)),hAPP(hAPP(c_Product__Type_OPair(U_14852,U_14852),U_14853),U_14854)),c_Transitive__Closure_Ortrancl(U_14852,U_14855))) ),
    inference(clausify,[status(thm)],[f_3718_2]) ).

fof(f_3719_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl]) ).

fof(f_3719_2,plain,
    ! [U_14861,U_14860,U_14859,U_14858,U_14857] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14858),U_14861)),c_Transitive__Closure_Ortrancl(U_14857,U_14860)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14859),U_14861)),U_14860))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14858),U_14859)),c_Transitive__Closure_Ortrancl(U_14857,U_14860))) ),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

cnf(f_3719_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14858),U_14861)),c_Transitive__Closure_Ortrancl(U_14857,U_14860)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14859),U_14861)),U_14860))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14857),U_14858),U_14859)),c_Transitive__Closure_Ortrancl(U_14857,U_14860))) ),
    inference(clausify,[status(thm)],[f_3719_2]) ).

fof(f_3720_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).

fof(f_3720_2,plain,
    ! [U_14866,U_14865,U_14864,U_14863,U_14862] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14863),U_14866)),c_Transitive__Closure_Ortrancl(U_14862,U_14865)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14864),U_14866)),c_Transitive__Closure_Ortrancl(U_14862,U_14865)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14863),U_14864)),U_14865)) ),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

cnf(f_3720_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14863),U_14866)),c_Transitive__Closure_Ortrancl(U_14862,U_14865)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14864),U_14866)),c_Transitive__Closure_Ortrancl(U_14862,U_14865)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14862,U_14862)),hAPP(hAPP(c_Product__Type_OPair(U_14862,U_14862),U_14863),U_14864)),U_14865)) ),
    inference(clausify,[status(thm)],[f_3720_2]) ).

fof(f_3721_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp]) ).

fof(f_3721_2,plain,
    ! [U_14868,U_14867] : c_Transitive__Closure_Ortrancl(U_14867,c_Transitive__Closure_Ortrancl(U_14867,U_14868)) = c_Transitive__Closure_Ortrancl(U_14867,U_14868),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

cnf(f_3721_3,plain,
    c_Transitive__Closure_Ortrancl(U_14867,c_Transitive__Closure_Ortrancl(U_14867,U_14868)) = c_Transitive__Closure_Ortrancl(U_14867,U_14868),
    inference(clausify,[status(thm)],[f_3721_2]) ).

fof(f_3722_1,plain,
    ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(f_3722_2,plain,
    ! [U_14870,U_14869] : c_Transitive__Closure_Ortrancl(U_14869,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14869,U_14869),tc_HOL_Obool)),U_14870),c_Relation_OId(U_14869))) = c_Transitive__Closure_Ortrancl(U_14869,U_14870),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

cnf(f_3722_3,plain,
    c_Transitive__Closure_Ortrancl(U_14869,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14869,U_14869),tc_HOL_Obool)),U_14870),c_Relation_OId(U_14869))) = c_Transitive__Closure_Ortrancl(U_14869,U_14870),
    inference(clausify,[status(thm)],[f_3722_2]) ).

fof(f_3723_1,plain,
    ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

fof(f_3723_2,plain,
    ! [U_14873,U_14872,U_14871] : c_Transitive__Closure_Ortrancl(U_14871,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14871,U_14871),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14871,U_14872)),c_Transitive__Closure_Ortrancl(U_14871,U_14873))) = c_Transitive__Closure_Ortrancl(U_14871,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14871,U_14871),tc_HOL_Obool)),U_14872),U_14873)),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

cnf(f_3723_3,plain,
    c_Transitive__Closure_Ortrancl(U_14871,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14871,U_14871),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14871,U_14872)),c_Transitive__Closure_Ortrancl(U_14871,U_14873))) = c_Transitive__Closure_Ortrancl(U_14871,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14871,U_14871),tc_HOL_Obool)),U_14872),U_14873)),
    inference(clausify,[status(thm)],[f_3723_2]) ).

fof(f_3724_1,plain,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(f_3724_2,plain,
    ! [U_14875,U_14874] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14874,U_14874),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14874,U_14875)),c_Relation_OId(U_14874)) = c_Transitive__Closure_Ortrancl(U_14874,U_14875),
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

cnf(f_3724_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14874,U_14874),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14874,U_14875)),c_Relation_OId(U_14874)) = c_Transitive__Closure_Ortrancl(U_14874,U_14875),
    inference(clausify,[status(thm)],[f_3724_2]) ).

fof(f_3725_1,plain,
    ! [V_S_2,V_R_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI]) ).

fof(f_3725_2,plain,
    ! [U_14879,U_14878,U_14877,U_14876] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14876,U_14876),tc_HOL_Obool)),U_14878),U_14879))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,U_14879)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,U_14878))) ) ),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

cnf(f_3725_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,U_14878)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14876,U_14876),tc_HOL_Obool)),U_14878),U_14879)))) ),
    inference(clausify,[status(thm)],[f_3725_2]) ).

cnf(f_3725_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,U_14879)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14876,U_14876)),U_14877),c_Transitive__Closure_Ortrancl(U_14876,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14876,U_14876),tc_HOL_Obool)),U_14878),U_14879)))) ),
    inference(clausify,[status(thm)],[f_3725_2]) ).

fof(f_3726_1,plain,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(f_3726_2,plain,
    ! [U_14881,U_14880] : hAPP(hAPP(c_Relation_Orel__comp(U_14880,U_14880,U_14880),c_Transitive__Closure_Ortrancl(U_14880,U_14881)),c_Transitive__Closure_Ortrancl(U_14880,U_14881)) = c_Transitive__Closure_Ortrancl(U_14880,U_14881),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

cnf(f_3726_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14880,U_14880,U_14880),c_Transitive__Closure_Ortrancl(U_14880,U_14881)),c_Transitive__Closure_Ortrancl(U_14880,U_14881)) = c_Transitive__Closure_Ortrancl(U_14880,U_14881),
    inference(clausify,[status(thm)],[f_3726_2]) ).

fof(f_3727_1,plain,
    ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

fof(f_3727_2,plain,
    ! [U_14883,U_14882] : hAPP(hAPP(c_Relation_Orel__comp(U_14882,U_14882,U_14882),U_14883),c_Transitive__Closure_Ortrancl(U_14882,U_14883)) = hAPP(hAPP(c_Relation_Orel__comp(U_14882,U_14882,U_14882),c_Transitive__Closure_Ortrancl(U_14882,U_14883)),U_14883),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

cnf(f_3727_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14882,U_14882,U_14882),U_14883),c_Transitive__Closure_Ortrancl(U_14882,U_14883)) = hAPP(hAPP(c_Relation_Orel__comp(U_14882,U_14882,U_14882),c_Transitive__Closure_Ortrancl(U_14882,U_14883)),U_14883),
    inference(clausify,[status(thm)],[f_3727_2]) ).

fof(f_3728_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__unfold]) ).

fof(f_3728_2,plain,
    ! [U_14885,U_14884] : c_Transitive__Closure_Ortrancl(U_14884,U_14885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14884,U_14884),tc_HOL_Obool)),c_Relation_OId(U_14884)),hAPP(hAPP(c_Relation_Orel__comp(U_14884,U_14884,U_14884),c_Transitive__Closure_Ortrancl(U_14884,U_14885)),U_14885)),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

cnf(f_3728_3,plain,
    c_Transitive__Closure_Ortrancl(U_14884,U_14885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14884,U_14884),tc_HOL_Obool)),c_Relation_OId(U_14884)),hAPP(hAPP(c_Relation_Orel__comp(U_14884,U_14884,U_14884),c_Transitive__Closure_Ortrancl(U_14884,U_14885)),U_14885)),
    inference(clausify,[status(thm)],[f_3728_2]) ).

fof(f_3729_1,plain,
    ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__empty]) ).

fof(f_3729_2,plain,
    ! [U_14886] : c_Transitive__Closure_Ortrancl(U_14886,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14886,U_14886),tc_HOL_Obool))) = c_Relation_OId(U_14886),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

cnf(f_3729_3,plain,
    c_Transitive__Closure_Ortrancl(U_14886,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14886,U_14886),tc_HOL_Obool))) = c_Relation_OId(U_14886),
    inference(clausify,[status(thm)],[f_3729_2]) ).

fof(f_3730_1,plain,
    ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__rtrancl]) ).

fof(f_3730_2,plain,
    ! [U_14888,U_14887] : hAPP(c_Relation_ORange(U_14887,U_14887),c_Transitive__Closure_Ortrancl(U_14887,U_14888)) = c_Orderings_Otop__class_Otop(tc_fun(U_14887,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

cnf(f_3730_3,plain,
    hAPP(c_Relation_ORange(U_14887,U_14887),c_Transitive__Closure_Ortrancl(U_14887,U_14888)) = c_Orderings_Otop__class_Otop(tc_fun(U_14887,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3730_2]) ).

fof(f_3731_1,plain,
    ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__rtrancl]) ).

fof(f_3731_2,plain,
    ! [U_14890,U_14889] : hAPP(c_Relation_ODomain(U_14889,U_14889),c_Transitive__Closure_Ortrancl(U_14889,U_14890)) = c_Orderings_Otop__class_Otop(tc_fun(U_14889,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

cnf(f_3731_3,plain,
    hAPP(c_Relation_ODomain(U_14889,U_14889),c_Transitive__Closure_Ortrancl(U_14889,U_14890)) = c_Orderings_Otop__class_Otop(tc_fun(U_14889,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3731_2]) ).

fof(f_3732_1,plain,
    ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_R__O__Id]) ).

fof(f_3732_2,plain,
    ! [U_14893,U_14892,U_14891] : hAPP(hAPP(c_Relation_Orel__comp(U_14891,U_14892,U_14892),U_14893),c_Relation_OId(U_14892)) = U_14893,
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

cnf(f_3732_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14891,U_14892,U_14892),U_14893),c_Relation_OId(U_14892)) = U_14893,
    inference(clausify,[status(thm)],[f_3732_2]) ).

fof(f_3733_1,plain,
    ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_Id__O__R]) ).

fof(f_3733_2,plain,
    ! [U_14896,U_14895,U_14894] : hAPP(hAPP(c_Relation_Orel__comp(U_14894,U_14894,U_14895),c_Relation_OId(U_14894)),U_14896) = U_14896,
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

cnf(f_3733_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14894,U_14894,U_14895),c_Relation_OId(U_14894)),U_14896) = U_14896,
    inference(clausify,[status(thm)],[f_3733_2]) ).

fof(f_3734_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Image__Id]) ).

fof(f_3734_2,plain,
    ! [U_14898,U_14897] : hAPP(c_Relation_OImage(U_14897,U_14897,c_Relation_OId(U_14897)),U_14898) = U_14898,
    inference(variable_rename,[status(thm)],[f_3734_1]) ).

cnf(f_3734_3,plain,
    hAPP(c_Relation_OImage(U_14897,U_14897,c_Relation_OId(U_14897)),U_14898) = U_14898,
    inference(clausify,[status(thm)],[f_3734_2]) ).

fof(f_3735_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a)))
        | V_a_2 != V_b_2 )
      & ( V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv]) ).

fof(f_3735_2,plain,
    ! [U_14901,U_14900,U_14899] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14899,U_14899)),hAPP(hAPP(c_Product__Type_OPair(U_14899,U_14899),U_14900),U_14901)),c_Relation_OId(U_14899)))
        | U_14900 != U_14901 )
      & ( U_14900 = U_14901
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14899,U_14899)),hAPP(hAPP(c_Product__Type_OPair(U_14899,U_14899),U_14900),U_14901)),c_Relation_OId(U_14899))) ) ),
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

fof(f_3735_3,plain,
    ( ! [U_14907,U_14905] :
        ( ! [U_14903] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14903,U_14903)),hAPP(hAPP(c_Product__Type_OPair(U_14903,U_14903),U_14905),U_14907)),c_Relation_OId(U_14903)))
        | U_14905 != U_14907 )
    & ! [U_14906,U_14904] :
        ( ! [U_14902] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14902,U_14902)),hAPP(hAPP(c_Product__Type_OPair(U_14902,U_14902),U_14904),U_14906)),c_Relation_OId(U_14902)))
        | U_14904 = U_14906 ) ),
    inference(miniscope,[status(thm)],[f_3735_2]) ).

cnf(f_3735_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14902,U_14902)),hAPP(hAPP(c_Product__Type_OPair(U_14902,U_14902),U_14904),U_14906)),c_Relation_OId(U_14902)))
    | U_14904 = U_14906 ),
    inference(clausify,[status(thm)],[f_3735_3]) ).

cnf(f_3735_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14903,U_14903)),hAPP(hAPP(c_Product__Type_OPair(U_14903,U_14903),U_14905),U_14907)),c_Relation_OId(U_14903)))
    | U_14905 != U_14907 ),
    inference(clausify,[status(thm)],[f_3735_3]) ).

fof(f_3736_1,plain,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl]) ).

fof(f_3736_2,plain,
    ! [U_14912,U_14911,U_14910,U_14909,U_14908] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14909),U_14912)),c_Transitive__Closure_Otrancl(U_14908,U_14911)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14910),U_14912)),c_Transitive__Closure_Otrancl(U_14908,U_14911)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14909),U_14910)),c_Transitive__Closure_Ortrancl(U_14908,U_14911))) ),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

cnf(f_3736_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14909),U_14912)),c_Transitive__Closure_Otrancl(U_14908,U_14911)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14910),U_14912)),c_Transitive__Closure_Otrancl(U_14908,U_14911)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14908,U_14908)),hAPP(hAPP(c_Product__Type_OPair(U_14908,U_14908),U_14909),U_14910)),c_Transitive__Closure_Ortrancl(U_14908,U_14911))) ),
    inference(clausify,[status(thm)],[f_3736_2]) ).

fof(f_3737_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).

fof(f_3737_2,plain,
    ! [U_14917,U_14916,U_14915,U_14914,U_14913] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14914),U_14917)),c_Transitive__Closure_Otrancl(U_14913,U_14916)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14915),U_14917)),c_Transitive__Closure_Ortrancl(U_14913,U_14916)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14914),U_14915)),c_Transitive__Closure_Otrancl(U_14913,U_14916))) ),
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

cnf(f_3737_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14914),U_14917)),c_Transitive__Closure_Otrancl(U_14913,U_14916)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14915),U_14917)),c_Transitive__Closure_Ortrancl(U_14913,U_14916)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14913,U_14913)),hAPP(hAPP(c_Product__Type_OPair(U_14913,U_14913),U_14914),U_14915)),c_Transitive__Closure_Otrancl(U_14913,U_14916))) ),
    inference(clausify,[status(thm)],[f_3737_2]) ).

fof(f_3738_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).

fof(f_3738_2,plain,
    ! [U_14922,U_14921,U_14920,U_14919,U_14918] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14919),U_14922)),c_Transitive__Closure_Otrancl(U_14918,U_14921)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14920),U_14922)),U_14921))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14919),U_14920)),c_Transitive__Closure_Ortrancl(U_14918,U_14921))) ),
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

cnf(f_3738_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14919),U_14922)),c_Transitive__Closure_Otrancl(U_14918,U_14921)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14920),U_14922)),U_14921))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14918,U_14918)),hAPP(hAPP(c_Product__Type_OPair(U_14918,U_14918),U_14919),U_14920)),c_Transitive__Closure_Ortrancl(U_14918,U_14921))) ),
    inference(clausify,[status(thm)],[f_3738_2]) ).

fof(f_3739_1,plain,
    ! [V_R_2,V_b_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
        & V_a_2 != V_b_2 )
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtranclD]) ).

fof(f_3739_2,plain,
    ! [U_14926,U_14925,U_14924,U_14923] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14923,U_14923)),hAPP(hAPP(c_Product__Type_OPair(U_14923,U_14923),U_14924),U_14925)),c_Transitive__Closure_Otrancl(U_14923,U_14926)))
        & U_14924 != U_14925 )
      | U_14924 = U_14925
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14923,U_14923)),hAPP(hAPP(c_Product__Type_OPair(U_14923,U_14923),U_14924),U_14925)),c_Transitive__Closure_Ortrancl(U_14923,U_14926))) ),
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

cnf(f_3739_3,plain,
    ( U_14924 != U_14925
    | U_14924 = U_14925
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14923,U_14923)),hAPP(hAPP(c_Product__Type_OPair(U_14923,U_14923),U_14924),U_14925)),c_Transitive__Closure_Ortrancl(U_14923,U_14926))) ),
    inference(clausify,[status(thm)],[f_3739_2]) ).

cnf(f_3739_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14923,U_14923)),hAPP(hAPP(c_Product__Type_OPair(U_14923,U_14923),U_14924),U_14925)),c_Transitive__Closure_Otrancl(U_14923,U_14926)))
    | U_14924 = U_14925
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14923,U_14923)),hAPP(hAPP(c_Product__Type_OPair(U_14923,U_14923),U_14924),U_14925)),c_Transitive__Closure_Ortrancl(U_14923,U_14926))) ),
    inference(clausify,[status(thm)],[f_3739_2]) ).

fof(f_3740_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).

fof(f_3740_2,plain,
    ! [U_14931,U_14930,U_14929,U_14928,U_14927] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14928),U_14931)),c_Transitive__Closure_Otrancl(U_14927,U_14930)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14929),U_14931)),c_Transitive__Closure_Ortrancl(U_14927,U_14930)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14928),U_14929)),U_14930)) ),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

cnf(f_3740_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14928),U_14931)),c_Transitive__Closure_Otrancl(U_14927,U_14930)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14929),U_14931)),c_Transitive__Closure_Ortrancl(U_14927,U_14930)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14927,U_14927)),hAPP(hAPP(c_Product__Type_OPair(U_14927,U_14927),U_14928),U_14929)),U_14930)) ),
    inference(clausify,[status(thm)],[f_3740_2]) ).

fof(f_3741_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
            | V_x_2 = V_y_2 )
          & V_x_2 != V_y_2 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
          & V_x_2 != V_y_2 )
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl]) ).

fof(f_3741_2,plain,
    ! [U_14935,U_14934,U_14933,U_14932] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14932,U_14932)),hAPP(hAPP(c_Product__Type_OPair(U_14932,U_14932),U_14933),U_14934)),c_Transitive__Closure_Ortrancl(U_14932,U_14935)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14932,U_14932)),hAPP(hAPP(c_Product__Type_OPair(U_14932,U_14932),U_14933),U_14934)),c_Transitive__Closure_Otrancl(U_14932,U_14935)))
            | U_14933 = U_14934 )
          & U_14933 != U_14934 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14932,U_14932)),hAPP(hAPP(c_Product__Type_OPair(U_14932,U_14932),U_14933),U_14934)),c_Transitive__Closure_Otrancl(U_14932,U_14935)))
          & U_14933 != U_14934 )
        | U_14933 = U_14934
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14932,U_14932)),hAPP(hAPP(c_Product__Type_OPair(U_14932,U_14932),U_14933),U_14934)),c_Transitive__Closure_Ortrancl(U_14932,U_14935))) ) ),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ( ! [U_14943,U_14941,U_14939,U_14937] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14937,U_14937)),hAPP(hAPP(c_Product__Type_OPair(U_14937,U_14937),U_14939),U_14941)),c_Transitive__Closure_Ortrancl(U_14937,U_14943)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14937,U_14937)),hAPP(hAPP(c_Product__Type_OPair(U_14937,U_14937),U_14939),U_14941)),c_Transitive__Closure_Otrancl(U_14937,U_14943)))
            | U_14939 = U_14941 )
          & U_14939 != U_14941 ) )
    & ! [U_14942,U_14940,U_14938,U_14936] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14936,U_14936)),hAPP(hAPP(c_Product__Type_OPair(U_14936,U_14936),U_14938),U_14940)),c_Transitive__Closure_Otrancl(U_14936,U_14942)))
          & U_14938 != U_14940 )
        | U_14938 = U_14940
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14936,U_14936)),hAPP(hAPP(c_Product__Type_OPair(U_14936,U_14936),U_14938),U_14940)),c_Transitive__Closure_Ortrancl(U_14936,U_14942))) ) ),
    inference(miniscope,[status(thm)],[f_3741_2]) ).

cnf(f_3741_4,plain,
    ( U_14938 != U_14940
    | U_14938 = U_14940
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14936,U_14936)),hAPP(hAPP(c_Product__Type_OPair(U_14936,U_14936),U_14938),U_14940)),c_Transitive__Closure_Ortrancl(U_14936,U_14942))) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

cnf(f_3741_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14936,U_14936)),hAPP(hAPP(c_Product__Type_OPair(U_14936,U_14936),U_14938),U_14940)),c_Transitive__Closure_Otrancl(U_14936,U_14942)))
    | U_14938 = U_14940
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14936,U_14936)),hAPP(hAPP(c_Product__Type_OPair(U_14936,U_14936),U_14938),U_14940)),c_Transitive__Closure_Ortrancl(U_14936,U_14942))) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

cnf(f_3741_6,plain,
    ( U_14939 != U_14941
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14937,U_14937)),hAPP(hAPP(c_Product__Type_OPair(U_14937,U_14937),U_14939),U_14941)),c_Transitive__Closure_Ortrancl(U_14937,U_14943))) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

cnf(f_3741_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14937,U_14937)),hAPP(hAPP(c_Product__Type_OPair(U_14937,U_14937),U_14939),U_14941)),c_Transitive__Closure_Otrancl(U_14937,U_14943)))
    | U_14939 = U_14941
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14937,U_14937)),hAPP(hAPP(c_Product__Type_OPair(U_14937,U_14937),U_14939),U_14941)),c_Transitive__Closure_Ortrancl(U_14937,U_14943))) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

fof(f_3742_1,plain,
    ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Id]) ).

fof(f_3742_2,plain,
    ! [U_14944] : hAPP(c_Relation_ODomain(U_14944,U_14944),c_Relation_OId(U_14944)) = c_Orderings_Otop__class_Otop(tc_fun(U_14944,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

cnf(f_3742_3,plain,
    hAPP(c_Relation_ODomain(U_14944,U_14944),c_Relation_OId(U_14944)) = c_Orderings_Otop__class_Otop(tc_fun(U_14944,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3742_2]) ).

fof(f_3743_1,plain,
    ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__Id]) ).

fof(f_3743_2,plain,
    ! [U_14945] : hAPP(c_Relation_ORange(U_14945,U_14945),c_Relation_OId(U_14945)) = c_Orderings_Otop__class_Otop(tc_fun(U_14945,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

cnf(f_3743_3,plain,
    hAPP(c_Relation_ORange(U_14945,U_14945),c_Relation_OId(U_14945)) = c_Orderings_Otop__class_Otop(tc_fun(U_14945,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3743_2]) ).

fof(f_3744_1,plain,
    ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)),
    inference(fof_nnf,[status(thm)],[fact_refl__Id]) ).

fof(f_3744_2,plain,
    ! [U_14946] : c_Relation_Orefl__on(U_14946,c_Orderings_Otop__class_Otop(tc_fun(U_14946,tc_HOL_Obool)),c_Relation_OId(U_14946)),
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

cnf(f_3744_3,plain,
    c_Relation_Orefl__on(U_14946,c_Orderings_Otop__class_Otop(tc_fun(U_14946,tc_HOL_Obool)),c_Relation_OId(U_14946)),
    inference(clausify,[status(thm)],[f_3744_2]) ).

fof(f_3745_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]) ).

cnf(f_3745_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(clausify,[status(thm)],[f_3745_1]) ).

fof(f_3746_1,plain,
    ! [V_y_2,V_R_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(f_3746_2,plain,
    ! [U_14950,U_14949,U_14948,U_14947] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14948),U_14950)),c_Transitive__Closure_Ortrancl(U_14947,U_14949)))
          | U_14948 != U_14950 )
        & ( U_14948 = U_14950
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14948),U_14950)),c_Transitive__Closure_Ortrancl(U_14947,U_14949))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_14947),U_14948),hAPP(c_Relation_ODomain(U_14947,U_14947),U_14949))) ),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

cnf(f_3746_3,plain,
    ( U_14948 = U_14950
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14948),U_14950)),c_Transitive__Closure_Ortrancl(U_14947,U_14949)))
    | hBOOL(hAPP(hAPP(c_member(U_14947),U_14948),hAPP(c_Relation_ODomain(U_14947,U_14947),U_14949))) ),
    inference(clausify,[status(thm)],[f_3746_2]) ).

cnf(f_3746_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14948),U_14950)),c_Transitive__Closure_Ortrancl(U_14947,U_14949)))
    | U_14948 != U_14950
    | hBOOL(hAPP(hAPP(c_member(U_14947),U_14948),hAPP(c_Relation_ODomain(U_14947,U_14947),U_14949))) ),
    inference(clausify,[status(thm)],[f_3746_2]) ).

fof(f_3747_1,plain,
    ! [V_b_2,V_r_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards]) ).

fof(f_3747_2,plain,
    ! [U_14954,U_14953,U_14952,U_14951] :
      ( hBOOL(hAPP(hAPP(c_member(U_14951),U_14954),c_Wellfounded_Oacc(U_14951,U_14953)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14951,U_14951)),hAPP(hAPP(c_Product__Type_OPair(U_14951,U_14951),U_14954),U_14952)),c_Transitive__Closure_Ortrancl(U_14951,U_14953)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14951),U_14952),c_Wellfounded_Oacc(U_14951,U_14953))) ),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

cnf(f_3747_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14951),U_14954),c_Wellfounded_Oacc(U_14951,U_14953)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14951,U_14951)),hAPP(hAPP(c_Product__Type_OPair(U_14951,U_14951),U_14954),U_14952)),c_Transitive__Closure_Ortrancl(U_14951,U_14953)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14951),U_14952),c_Wellfounded_Oacc(U_14951,U_14953))) ),
    inference(clausify,[status(thm)],[f_3747_2]) ).

fof(f_3748_1,plain,
    ! [V_r_2,V_a_2,V_b_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux]) ).

fof(f_3748_2,plain,
    ! [U_14958,U_14957,U_14956,U_14955] :
      ( hBOOL(hAPP(hAPP(c_member(U_14955),U_14956),c_Wellfounded_Oacc(U_14955,U_14958)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14955),U_14957),c_Wellfounded_Oacc(U_14955,U_14958)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14955,U_14955)),hAPP(hAPP(c_Product__Type_OPair(U_14955,U_14955),U_14956),U_14957)),c_Transitive__Closure_Ortrancl(U_14955,U_14958))) ),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

cnf(f_3748_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14955),U_14956),c_Wellfounded_Oacc(U_14955,U_14958)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14955),U_14957),c_Wellfounded_Oacc(U_14955,U_14958)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14955,U_14955)),hAPP(hAPP(c_Product__Type_OPair(U_14955,U_14955),U_14956),U_14957)),c_Transitive__Closure_Ortrancl(U_14955,U_14958))) ),
    inference(clausify,[status(thm)],[f_3748_2]) ).

fof(f_3749_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
        | ~ c_Wellfounded_Owf(T_a,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
          & c_Wellfounded_Owf(T_a,V_r_2) )
        | ~ c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__insert]) ).

fof(f_3749_2,plain,
    ! [U_14962,U_14961,U_14960,U_14959] :
      ( ( c_Wellfounded_Owf(U_14959,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14959,U_14959)),hAPP(hAPP(c_Product__Type_OPair(U_14959,U_14959),U_14960),U_14961)),U_14962))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14959,U_14959)),hAPP(hAPP(c_Product__Type_OPair(U_14959,U_14959),U_14961),U_14960)),c_Transitive__Closure_Ortrancl(U_14959,U_14962)))
        | ~ c_Wellfounded_Owf(U_14959,U_14962) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14959,U_14959)),hAPP(hAPP(c_Product__Type_OPair(U_14959,U_14959),U_14961),U_14960)),c_Transitive__Closure_Ortrancl(U_14959,U_14962)))
          & c_Wellfounded_Owf(U_14959,U_14962) )
        | ~ c_Wellfounded_Owf(U_14959,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14959,U_14959)),hAPP(hAPP(c_Product__Type_OPair(U_14959,U_14959),U_14960),U_14961)),U_14962)) ) ),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ( ! [U_14970,U_14968,U_14966,U_14964] :
        ( c_Wellfounded_Owf(U_14964,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14964,U_14964)),hAPP(hAPP(c_Product__Type_OPair(U_14964,U_14964),U_14966),U_14968)),U_14970))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14964,U_14964)),hAPP(hAPP(c_Product__Type_OPair(U_14964,U_14964),U_14968),U_14966)),c_Transitive__Closure_Ortrancl(U_14964,U_14970)))
        | ~ c_Wellfounded_Owf(U_14964,U_14970) )
    & ! [U_14969,U_14967,U_14965,U_14963] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14963,U_14963)),hAPP(hAPP(c_Product__Type_OPair(U_14963,U_14963),U_14967),U_14965)),c_Transitive__Closure_Ortrancl(U_14963,U_14969)))
          & c_Wellfounded_Owf(U_14963,U_14969) )
        | ~ c_Wellfounded_Owf(U_14963,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14963,U_14963)),hAPP(hAPP(c_Product__Type_OPair(U_14963,U_14963),U_14965),U_14967)),U_14969)) ) ),
    inference(miniscope,[status(thm)],[f_3749_2]) ).

cnf(f_3749_4,plain,
    ( c_Wellfounded_Owf(U_14963,U_14969)
    | ~ c_Wellfounded_Owf(U_14963,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14963,U_14963)),hAPP(hAPP(c_Product__Type_OPair(U_14963,U_14963),U_14965),U_14967)),U_14969)) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

cnf(f_3749_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14963,U_14963)),hAPP(hAPP(c_Product__Type_OPair(U_14963,U_14963),U_14967),U_14965)),c_Transitive__Closure_Ortrancl(U_14963,U_14969)))
    | ~ c_Wellfounded_Owf(U_14963,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14963,U_14963)),hAPP(hAPP(c_Product__Type_OPair(U_14963,U_14963),U_14965),U_14967)),U_14969)) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

cnf(f_3749_6,plain,
    ( c_Wellfounded_Owf(U_14964,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14964,U_14964)),hAPP(hAPP(c_Product__Type_OPair(U_14964,U_14964),U_14966),U_14968)),U_14970))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14964,U_14964)),hAPP(hAPP(c_Product__Type_OPair(U_14964,U_14964),U_14968),U_14966)),c_Transitive__Closure_Ortrancl(U_14964,U_14970)))
    | ~ c_Wellfounded_Owf(U_14964,U_14970) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_a] :
      ( ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_a,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
          & c_Wellfounded_Oacyclic(T_a,V_r_2) )
        | ~ c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__insert]) ).

fof(f_3750_2,plain,
    ! [U_14974,U_14973,U_14972,U_14971] :
      ( ( c_Wellfounded_Oacyclic(U_14971,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14971,U_14971)),hAPP(hAPP(c_Product__Type_OPair(U_14971,U_14971),U_14972),U_14973)),U_14974))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14971,U_14971)),hAPP(hAPP(c_Product__Type_OPair(U_14971,U_14971),U_14973),U_14972)),c_Transitive__Closure_Ortrancl(U_14971,U_14974)))
        | ~ c_Wellfounded_Oacyclic(U_14971,U_14974) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14971,U_14971)),hAPP(hAPP(c_Product__Type_OPair(U_14971,U_14971),U_14973),U_14972)),c_Transitive__Closure_Ortrancl(U_14971,U_14974)))
          & c_Wellfounded_Oacyclic(U_14971,U_14974) )
        | ~ c_Wellfounded_Oacyclic(U_14971,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14971,U_14971)),hAPP(hAPP(c_Product__Type_OPair(U_14971,U_14971),U_14972),U_14973)),U_14974)) ) ),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ( ! [U_14982,U_14980,U_14978,U_14976] :
        ( c_Wellfounded_Oacyclic(U_14976,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14978),U_14980)),U_14982))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14980),U_14978)),c_Transitive__Closure_Ortrancl(U_14976,U_14982)))
        | ~ c_Wellfounded_Oacyclic(U_14976,U_14982) )
    & ! [U_14981,U_14979,U_14977,U_14975] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14975,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14975),U_14979),U_14977)),c_Transitive__Closure_Ortrancl(U_14975,U_14981)))
          & c_Wellfounded_Oacyclic(U_14975,U_14981) )
        | ~ c_Wellfounded_Oacyclic(U_14975,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14975,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14975),U_14977),U_14979)),U_14981)) ) ),
    inference(miniscope,[status(thm)],[f_3750_2]) ).

cnf(f_3750_4,plain,
    ( c_Wellfounded_Oacyclic(U_14975,U_14981)
    | ~ c_Wellfounded_Oacyclic(U_14975,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14975,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14975),U_14977),U_14979)),U_14981)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14975,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14975),U_14979),U_14977)),c_Transitive__Closure_Ortrancl(U_14975,U_14981)))
    | ~ c_Wellfounded_Oacyclic(U_14975,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14975,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14975),U_14977),U_14979)),U_14981)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_6,plain,
    ( c_Wellfounded_Oacyclic(U_14976,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14978),U_14980)),U_14982))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14980),U_14978)),c_Transitive__Closure_Ortrancl(U_14976,U_14982)))
    | ~ c_Wellfounded_Oacyclic(U_14976,U_14982) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_1,plain,
    ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))),
    inference(fof_nnf,[status(thm)],[fact_refl__reflcl]) ).

fof(f_3751_2,plain,
    ! [U_14984,U_14983] : c_Relation_Orefl__on(U_14983,c_Orderings_Otop__class_Otop(tc_fun(U_14983,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14983,U_14983),tc_HOL_Obool)),U_14984),c_Relation_OId(U_14983))),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

cnf(f_3751_3,plain,
    c_Relation_Orefl__on(U_14983,c_Orderings_Otop__class_Otop(tc_fun(U_14983,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14983,U_14983),tc_HOL_Obool)),U_14984),c_Relation_OId(U_14983))),
    inference(clausify,[status(thm)],[f_3751_2]) ).

fof(f_3752_1,plain,
    ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))),
    inference(fof_nnf,[status(thm)],[fact_Id__def]) ).

fof(f_3752_2,plain,
    ! [U_14985] : c_Relation_OId(U_14985) = hAPP(c_Set_OCollect(tc_prod(U_14985,U_14985)),hAPP(hAPP(c_COMBB(tc_fun(U_14985,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14985,U_14985)),c_HOL_OEx(U_14985)),hAPP(hAPP(c_COMBC(tc_prod(U_14985,U_14985),tc_fun(U_14985,tc_prod(U_14985,U_14985)),tc_fun(U_14985,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14985,U_14985),tc_HOL_Obool),tc_fun(tc_fun(U_14985,tc_prod(U_14985,U_14985)),tc_fun(U_14985,tc_HOL_Obool)),tc_prod(U_14985,U_14985)),c_COMBB(tc_prod(U_14985,U_14985),tc_HOL_Obool,U_14985)),c_fequal)),hAPP(hAPP(c_COMBS(U_14985,U_14985,tc_prod(U_14985,U_14985)),c_Product__Type_OPair(U_14985,U_14985)),c_COMBI(U_14985))))),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

cnf(f_3752_3,plain,
    c_Relation_OId(U_14985) = hAPP(c_Set_OCollect(tc_prod(U_14985,U_14985)),hAPP(hAPP(c_COMBB(tc_fun(U_14985,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14985,U_14985)),c_HOL_OEx(U_14985)),hAPP(hAPP(c_COMBC(tc_prod(U_14985,U_14985),tc_fun(U_14985,tc_prod(U_14985,U_14985)),tc_fun(U_14985,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14985,U_14985),tc_HOL_Obool),tc_fun(tc_fun(U_14985,tc_prod(U_14985,U_14985)),tc_fun(U_14985,tc_HOL_Obool)),tc_prod(U_14985,U_14985)),c_COMBB(tc_prod(U_14985,U_14985),tc_HOL_Obool,U_14985)),c_fequal)),hAPP(hAPP(c_COMBS(U_14985,U_14985,tc_prod(U_14985,U_14985)),c_Product__Type_OPair(U_14985,U_14985)),c_COMBI(U_14985))))),
    inference(clausify,[status(thm)],[f_3752_2]) ).

fof(f_3753_1,plain,
    ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))),
    inference(fof_nnf,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(f_3753_2,plain,
    ! [U_14987,U_14986] : c_Relation_Oirrefl(U_14986,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14986,U_14986),tc_HOL_Obool)),U_14987),c_Relation_OId(U_14986))),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

cnf(f_3753_3,plain,
    c_Relation_Oirrefl(U_14986,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14986,U_14986),tc_HOL_Obool)),U_14987),c_Relation_OId(U_14986))),
    inference(clausify,[status(thm)],[f_3753_2]) ).

fof(f_3754_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_3754_2,plain,
    ! [U_14989,U_14988] :
      ( ( 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_14988),U_14989)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14988),U_14989)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14988),U_14989))
        | ~ 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_14988),U_14989)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3754_1]) ).

fof(f_3754_3,plain,
    ( ! [U_14993,U_14991] :
        ( 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_14991),U_14993)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14991),U_14993)) )
    & ! [U_14992,U_14990] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14990),U_14992))
        | ~ 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_14990),U_14992)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3754_2]) ).

cnf(f_3754_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14990),U_14992))
    | ~ 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_14990),U_14992)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3754_3]) ).

cnf(f_3754_5,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_14991),U_14993)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14991),U_14993)) ),
    inference(clausify,[status(thm)],[f_3754_3]) ).

fof(f_3755_1,plain,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),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_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux]) ).

fof(f_3755_2,plain,
    ! [U_14998,U_14997,U_14996,U_14995,U_14994] :
      ( hBOOL(hAPP(hAPP(c_member(U_14994),U_14995),U_14998))
      | U_14995 = U_14996
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14994,U_14994),tc_HOL_Obool)),U_14997),hAPP(hAPP(c_Product__Type_OSigma(U_14994,U_14994),U_14998),hAPP(c_COMBK(tc_fun(U_14994,tc_HOL_Obool),U_14994),U_14998))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14995),U_14996)),c_Transitive__Closure_Ortrancl(U_14994,U_14997))) ),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

cnf(f_3755_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14994),U_14995),U_14998))
    | U_14995 = U_14996
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14994,U_14994),tc_HOL_Obool)),U_14997),hAPP(hAPP(c_Product__Type_OSigma(U_14994,U_14994),U_14998),hAPP(c_COMBK(tc_fun(U_14994,tc_HOL_Obool),U_14994),U_14998))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14995),U_14996)),c_Transitive__Closure_Ortrancl(U_14994,U_14997))) ),
    inference(clausify,[status(thm)],[f_3755_2]) ).

fof(f_3756_1,plain,
    ! [V_x_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__tranclI]) ).

fof(f_3756_2,plain,
    ! [U_15001,U_15000,U_14999] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14999,U_14999)),hAPP(hAPP(c_Product__Type_OPair(U_14999,U_14999),U_15001),U_15001)),c_Transitive__Closure_Otrancl(U_14999,U_15000)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14999,U_14999),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14999,U_14999),U_15000)),c_Transitive__Closure_Ortrancl(U_14999,U_15000)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14999,U_14999),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3756_1]) ).

cnf(f_3756_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14999,U_14999)),hAPP(hAPP(c_Product__Type_OPair(U_14999,U_14999),U_15001),U_15001)),c_Transitive__Closure_Otrancl(U_14999,U_15000)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14999,U_14999),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14999,U_14999),U_15000)),c_Transitive__Closure_Ortrancl(U_14999,U_15000)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14999,U_14999),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3756_2]) ).

fof(f_3757_1,plain,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,V_r_2)))
      | ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_sequence__trans]) ).

fof(f_3757_2,plain,
    ! [U_15007,U_15006,U_15005,U_15004,U_15003] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15006),U_15007))),hAPP(U_15004,U_15006))),c_Transitive__Closure_Ortrancl(U_15003,U_15005)))
      | ? [U_15002] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(c_Nat_OSuc,U_15002))),hAPP(U_15004,U_15002))),c_Transitive__Closure_Ortrancl(U_15003,U_15005))) ),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

fof(f_3757_3,plain,
    ! [U_15007,U_15006,U_15005,U_15004,U_15003] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15006),U_15007))),hAPP(U_15004,U_15006))),c_Transitive__Closure_Ortrancl(U_15003,U_15005)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(c_Nat_OSuc,sK376(U_15007,U_15006,U_15005,U_15004,U_15003)))),hAPP(U_15004,sK376(U_15007,U_15006,U_15005,U_15004,U_15003)))),c_Transitive__Closure_Ortrancl(U_15003,U_15005))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_15002,sK376(U_15007,U_15006,U_15005,U_15004,U_15003))],[f_3757_2]) ).

cnf(f_3757_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15006),U_15007))),hAPP(U_15004,U_15006))),c_Transitive__Closure_Ortrancl(U_15003,U_15005)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15003,U_15003)),hAPP(hAPP(c_Product__Type_OPair(U_15003,U_15003),hAPP(U_15004,hAPP(c_Nat_OSuc,sK376(U_15007,U_15006,U_15005,U_15004,U_15003)))),hAPP(U_15004,sK376(U_15007,U_15006,U_15005,U_15004,U_15003)))),c_Transitive__Closure_Ortrancl(U_15003,U_15005))) ),
    inference(clausify,[status(thm)],[f_3757_3]) ).

fof(f_3758_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converse]) ).

fof(f_3758_2,plain,
    ! [U_15009,U_15008] : c_Transitive__Closure_Ortrancl(U_15008,hAPP(c_Relation_Oconverse(U_15008,U_15008),U_15009)) = hAPP(c_Relation_Oconverse(U_15008,U_15008),c_Transitive__Closure_Ortrancl(U_15008,U_15009)),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

cnf(f_3758_3,plain,
    c_Transitive__Closure_Ortrancl(U_15008,hAPP(c_Relation_Oconverse(U_15008,U_15008),U_15009)) = hAPP(c_Relation_Oconverse(U_15008,U_15008),c_Transitive__Closure_Ortrancl(U_15008,U_15009)),
    inference(clausify,[status(thm)],[f_3758_2]) ).

fof(f_3759_1,plain,
    ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a),
    inference(fof_nnf,[status(thm)],[fact_converse__Id]) ).

fof(f_3759_2,plain,
    ! [U_15010] : hAPP(c_Relation_Oconverse(U_15010,U_15010),c_Relation_OId(U_15010)) = c_Relation_OId(U_15010),
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

cnf(f_3759_3,plain,
    hAPP(c_Relation_Oconverse(U_15010,U_15010),c_Relation_OId(U_15010)) = c_Relation_OId(U_15010),
    inference(clausify,[status(thm)],[f_3759_2]) ).

fof(f_3760_1,plain,
    ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__INTER]) ).

fof(f_3760_2,plain,
    ! [U_15015,U_15014,U_15013,U_15012,U_15011] : hAPP(c_Relation_Oconverse(U_15011,U_15012),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15013,tc_fun(tc_prod(U_15011,U_15012),tc_HOL_Obool)),U_15014),U_15015)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15013,tc_fun(tc_prod(U_15012,U_15011),tc_HOL_Obool)),U_15014),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15011,U_15012),tc_HOL_Obool),tc_fun(tc_prod(U_15012,U_15011),tc_HOL_Obool),U_15013),c_Relation_Oconverse(U_15011,U_15012)),U_15015)),
    inference(variable_rename,[status(thm)],[f_3760_1]) ).

cnf(f_3760_3,plain,
    hAPP(c_Relation_Oconverse(U_15011,U_15012),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15013,tc_fun(tc_prod(U_15011,U_15012),tc_HOL_Obool)),U_15014),U_15015)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15013,tc_fun(tc_prod(U_15012,U_15011),tc_HOL_Obool)),U_15014),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15011,U_15012),tc_HOL_Obool),tc_fun(tc_prod(U_15012,U_15011),tc_HOL_Obool),U_15013),c_Relation_Oconverse(U_15011,U_15012)),U_15015)),
    inference(clausify,[status(thm)],[f_3760_2]) ).

fof(f_3761_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
        | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) )
      & ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
        | ~ c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__converse]) ).

fof(f_3761_2,plain,
    ! [U_15018,U_15017,U_15016] :
      ( ( c_Relation_Orefl__on(U_15016,U_15017,hAPP(c_Relation_Oconverse(U_15016,U_15016),U_15018))
        | ~ c_Relation_Orefl__on(U_15016,U_15017,U_15018) )
      & ( c_Relation_Orefl__on(U_15016,U_15017,U_15018)
        | ~ c_Relation_Orefl__on(U_15016,U_15017,hAPP(c_Relation_Oconverse(U_15016,U_15016),U_15018)) ) ),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

fof(f_3761_3,plain,
    ( ! [U_15024,U_15022,U_15020] :
        ( c_Relation_Orefl__on(U_15020,U_15022,hAPP(c_Relation_Oconverse(U_15020,U_15020),U_15024))
        | ~ c_Relation_Orefl__on(U_15020,U_15022,U_15024) )
    & ! [U_15023,U_15021,U_15019] :
        ( c_Relation_Orefl__on(U_15019,U_15021,U_15023)
        | ~ c_Relation_Orefl__on(U_15019,U_15021,hAPP(c_Relation_Oconverse(U_15019,U_15019),U_15023)) ) ),
    inference(miniscope,[status(thm)],[f_3761_2]) ).

cnf(f_3761_4,plain,
    ( c_Relation_Orefl__on(U_15019,U_15021,U_15023)
    | ~ c_Relation_Orefl__on(U_15019,U_15021,hAPP(c_Relation_Oconverse(U_15019,U_15019),U_15023)) ),
    inference(clausify,[status(thm)],[f_3761_3]) ).

cnf(f_3761_5,plain,
    ( c_Relation_Orefl__on(U_15020,U_15022,hAPP(c_Relation_Oconverse(U_15020,U_15020),U_15024))
    | ~ c_Relation_Orefl__on(U_15020,U_15022,U_15024) ),
    inference(clausify,[status(thm)],[f_3761_3]) ).

fof(f_3762_1,plain,
    ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__UNION]) ).

fof(f_3762_2,plain,
    ! [U_15029,U_15028,U_15027,U_15026,U_15025] : hAPP(c_Relation_Oconverse(U_15025,U_15026),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15027,tc_fun(tc_prod(U_15025,U_15026),tc_HOL_Obool)),U_15028),U_15029)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15027,tc_fun(tc_prod(U_15026,U_15025),tc_HOL_Obool)),U_15028),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15025,U_15026),tc_HOL_Obool),tc_fun(tc_prod(U_15026,U_15025),tc_HOL_Obool),U_15027),c_Relation_Oconverse(U_15025,U_15026)),U_15029)),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

cnf(f_3762_3,plain,
    hAPP(c_Relation_Oconverse(U_15025,U_15026),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15027,tc_fun(tc_prod(U_15025,U_15026),tc_HOL_Obool)),U_15028),U_15029)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15027,tc_fun(tc_prod(U_15026,U_15025),tc_HOL_Obool)),U_15028),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15025,U_15026),tc_HOL_Obool),tc_fun(tc_prod(U_15026,U_15025),tc_HOL_Obool),U_15027),c_Relation_Oconverse(U_15025,U_15026)),U_15029)),
    inference(clausify,[status(thm)],[f_3762_2]) ).

fof(f_3763_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_converse__iff]) ).

fof(f_3763_2,plain,
    ! [U_15034,U_15033,U_15032,U_15031,U_15030] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15030,U_15031)),hAPP(hAPP(c_Product__Type_OPair(U_15030,U_15031),U_15032),U_15033)),hAPP(c_Relation_Oconverse(U_15031,U_15030),U_15034)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15031,U_15030)),hAPP(hAPP(c_Product__Type_OPair(U_15031,U_15030),U_15033),U_15032)),U_15034)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15031,U_15030)),hAPP(hAPP(c_Product__Type_OPair(U_15031,U_15030),U_15033),U_15032)),U_15034))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15030,U_15031)),hAPP(hAPP(c_Product__Type_OPair(U_15030,U_15031),U_15032),U_15033)),hAPP(c_Relation_Oconverse(U_15031,U_15030),U_15034))) ) ),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

fof(f_3763_3,plain,
    ( ! [U_15044,U_15042,U_15040,U_15038,U_15036] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15036,U_15038)),hAPP(hAPP(c_Product__Type_OPair(U_15036,U_15038),U_15040),U_15042)),hAPP(c_Relation_Oconverse(U_15038,U_15036),U_15044)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15038,U_15036)),hAPP(hAPP(c_Product__Type_OPair(U_15038,U_15036),U_15042),U_15040)),U_15044)) )
    & ! [U_15043,U_15041,U_15039,U_15037,U_15035] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15037,U_15035)),hAPP(hAPP(c_Product__Type_OPair(U_15037,U_15035),U_15041),U_15039)),U_15043))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15035,U_15037)),hAPP(hAPP(c_Product__Type_OPair(U_15035,U_15037),U_15039),U_15041)),hAPP(c_Relation_Oconverse(U_15037,U_15035),U_15043))) ) ),
    inference(miniscope,[status(thm)],[f_3763_2]) ).

cnf(f_3763_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15037,U_15035)),hAPP(hAPP(c_Product__Type_OPair(U_15037,U_15035),U_15041),U_15039)),U_15043))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15035,U_15037)),hAPP(hAPP(c_Product__Type_OPair(U_15035,U_15037),U_15039),U_15041)),hAPP(c_Relation_Oconverse(U_15037,U_15035),U_15043))) ),
    inference(clausify,[status(thm)],[f_3763_3]) ).

cnf(f_3763_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15036,U_15038)),hAPP(hAPP(c_Product__Type_OPair(U_15036,U_15038),U_15040),U_15042)),hAPP(c_Relation_Oconverse(U_15038,U_15036),U_15044)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15038,U_15036)),hAPP(hAPP(c_Product__Type_OPair(U_15038,U_15036),U_15042),U_15040)),U_15044)) ),
    inference(clausify,[status(thm)],[f_3763_3]) ).

fof(f_3764_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converseI]) ).

fof(f_3764_2,plain,
    ! [U_15049,U_15048,U_15047,U_15046,U_15045] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15045)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15045),U_15048),U_15047)),hAPP(c_Relation_Oconverse(U_15045,U_15046),U_15049)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15046)),hAPP(hAPP(c_Product__Type_OPair(U_15045,U_15046),U_15047),U_15048)),U_15049)) ),
    inference(variable_rename,[status(thm)],[f_3764_1]) ).

cnf(f_3764_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15045)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15045),U_15048),U_15047)),hAPP(c_Relation_Oconverse(U_15045,U_15046),U_15049)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15046)),hAPP(hAPP(c_Product__Type_OPair(U_15045,U_15046),U_15047),U_15048)),U_15049)) ),
    inference(clausify,[status(thm)],[f_3764_2]) ).

fof(f_3765_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseD]) ).

fof(f_3765_2,plain,
    ! [U_15054,U_15053,U_15052,U_15051,U_15050] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15051,U_15050)),hAPP(hAPP(c_Product__Type_OPair(U_15051,U_15050),U_15053),U_15052)),U_15054))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15051)),hAPP(hAPP(c_Product__Type_OPair(U_15050,U_15051),U_15052),U_15053)),hAPP(c_Relation_Oconverse(U_15051,U_15050),U_15054))) ),
    inference(variable_rename,[status(thm)],[f_3765_1]) ).

cnf(f_3765_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15051,U_15050)),hAPP(hAPP(c_Product__Type_OPair(U_15051,U_15050),U_15053),U_15052)),U_15054))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15051)),hAPP(hAPP(c_Product__Type_OPair(U_15050,U_15051),U_15052),U_15053)),hAPP(c_Relation_Oconverse(U_15051,U_15050),U_15054))) ),
    inference(clausify,[status(thm)],[f_3765_2]) ).

fof(f_3766_1,plain,
    ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_converse__inv__image]) ).

fof(f_3766_2,plain,
    ! [U_15058,U_15057,U_15056,U_15055] : hAPP(c_Relation_Oconverse(U_15055,U_15055),hAPP(hAPP(c_Relation_Oinv__image(U_15056,U_15055),U_15057),U_15058)) = hAPP(hAPP(c_Relation_Oinv__image(U_15056,U_15055),hAPP(c_Relation_Oconverse(U_15056,U_15056),U_15057)),U_15058),
    inference(variable_rename,[status(thm)],[f_3766_1]) ).

cnf(f_3766_3,plain,
    hAPP(c_Relation_Oconverse(U_15055,U_15055),hAPP(hAPP(c_Relation_Oinv__image(U_15056,U_15055),U_15057),U_15058)) = hAPP(hAPP(c_Relation_Oinv__image(U_15056,U_15055),hAPP(c_Relation_Oconverse(U_15056,U_15056),U_15057)),U_15058),
    inference(clausify,[status(thm)],[f_3766_2]) ).

fof(f_3767_1,plain,
    ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Field__converse]) ).

fof(f_3767_2,plain,
    ! [U_15060,U_15059] : hAPP(c_Relation_OField(U_15059),hAPP(c_Relation_Oconverse(U_15059,U_15059),U_15060)) = hAPP(c_Relation_OField(U_15059),U_15060),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

cnf(f_3767_3,plain,
    hAPP(c_Relation_OField(U_15059),hAPP(c_Relation_Oconverse(U_15059,U_15059),U_15060)) = hAPP(c_Relation_OField(U_15059),U_15060),
    inference(clausify,[status(thm)],[f_3767_2]) ).

fof(f_3768_1,plain,
    ! [V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__converse]) ).

fof(f_3768_2,plain,
    ! [U_15063,U_15062,U_15061] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15061,U_15062)),hAPP(c_Relation_Oconverse(U_15062,U_15061),U_15063)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15062,U_15061)),U_15063)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15062,U_15061)),U_15063))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15061,U_15062)),hAPP(c_Relation_Oconverse(U_15062,U_15061),U_15063))) ) ),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

fof(f_3768_3,plain,
    ( ! [U_15069,U_15067,U_15065] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15065,U_15067)),hAPP(c_Relation_Oconverse(U_15067,U_15065),U_15069)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15067,U_15065)),U_15069)) )
    & ! [U_15068,U_15066,U_15064] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15066,U_15064)),U_15068))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15064,U_15066)),hAPP(c_Relation_Oconverse(U_15066,U_15064),U_15068))) ) ),
    inference(miniscope,[status(thm)],[f_3768_2]) ).

cnf(f_3768_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15066,U_15064)),U_15068))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15064,U_15066)),hAPP(c_Relation_Oconverse(U_15066,U_15064),U_15068))) ),
    inference(clausify,[status(thm)],[f_3768_3]) ).

cnf(f_3768_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15065,U_15067)),hAPP(c_Relation_Oconverse(U_15067,U_15065),U_15069)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15067,U_15065)),U_15069)) ),
    inference(clausify,[status(thm)],[f_3768_3]) ).

fof(f_3769_1,plain,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_converse__converse]) ).

fof(f_3769_2,plain,
    ! [U_15072,U_15071,U_15070] : hAPP(c_Relation_Oconverse(U_15070,U_15071),hAPP(c_Relation_Oconverse(U_15071,U_15070),U_15072)) = U_15072,
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

cnf(f_3769_3,plain,
    hAPP(c_Relation_Oconverse(U_15070,U_15071),hAPP(c_Relation_Oconverse(U_15071,U_15070),U_15072)) = U_15072,
    inference(clausify,[status(thm)],[f_3769_2]) ).

fof(f_3770_1,plain,
    ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Int]) ).

fof(f_3770_2,plain,
    ! [U_15076,U_15075,U_15074,U_15073] : hAPP(c_Relation_Oconverse(U_15073,U_15074),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15073,U_15074),tc_HOL_Obool)),U_15075),U_15076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15074,U_15073),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15073,U_15074),U_15075)),hAPP(c_Relation_Oconverse(U_15073,U_15074),U_15076)),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

cnf(f_3770_3,plain,
    hAPP(c_Relation_Oconverse(U_15073,U_15074),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15073,U_15074),tc_HOL_Obool)),U_15075),U_15076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15074,U_15073),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15073,U_15074),U_15075)),hAPP(c_Relation_Oconverse(U_15073,U_15074),U_15076)),
    inference(clausify,[status(thm)],[f_3770_2]) ).

fof(f_3771_1,plain,
    ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2),
    inference(fof_nnf,[status(thm)],[fact_converse__Id__on]) ).

fof(f_3771_2,plain,
    ! [U_15078,U_15077] : hAPP(c_Relation_Oconverse(U_15077,U_15077),c_Relation_OId__on(U_15077,U_15078)) = c_Relation_OId__on(U_15077,U_15078),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

cnf(f_3771_3,plain,
    hAPP(c_Relation_Oconverse(U_15077,U_15077),c_Relation_OId__on(U_15077,U_15078)) = c_Relation_OId__on(U_15077,U_15078),
    inference(clausify,[status(thm)],[f_3771_2]) ).

fof(f_3772_1,plain,
    ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Un]) ).

fof(f_3772_2,plain,
    ! [U_15082,U_15081,U_15080,U_15079] : hAPP(c_Relation_Oconverse(U_15079,U_15080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15079,U_15080),tc_HOL_Obool)),U_15081),U_15082)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15080,U_15079),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15079,U_15080),U_15081)),hAPP(c_Relation_Oconverse(U_15079,U_15080),U_15082)),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

cnf(f_3772_3,plain,
    hAPP(c_Relation_Oconverse(U_15079,U_15080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15079,U_15080),tc_HOL_Obool)),U_15081),U_15082)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15080,U_15079),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_15079,U_15080),U_15081)),hAPP(c_Relation_Oconverse(U_15079,U_15080),U_15082)),
    inference(clausify,[status(thm)],[f_3772_2]) ).

fof(f_3773_1,plain,
    ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__rel__comp]) ).

fof(f_3773_2,plain,
    ! [U_15087,U_15086,U_15085,U_15084,U_15083] : hAPP(c_Relation_Oconverse(U_15083,U_15084),hAPP(hAPP(c_Relation_Orel__comp(U_15083,U_15085,U_15084),U_15086),U_15087)) = hAPP(hAPP(c_Relation_Orel__comp(U_15084,U_15085,U_15083),hAPP(c_Relation_Oconverse(U_15085,U_15084),U_15087)),hAPP(c_Relation_Oconverse(U_15083,U_15085),U_15086)),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

cnf(f_3773_3,plain,
    hAPP(c_Relation_Oconverse(U_15083,U_15084),hAPP(hAPP(c_Relation_Orel__comp(U_15083,U_15085,U_15084),U_15086),U_15087)) = hAPP(hAPP(c_Relation_Orel__comp(U_15084,U_15085,U_15083),hAPP(c_Relation_Oconverse(U_15085,U_15084),U_15087)),hAPP(c_Relation_Oconverse(U_15083,U_15085),U_15086)),
    inference(clausify,[status(thm)],[f_3773_2]) ).

fof(f_3774_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
        | ~ c_Wellfounded_Oacyclic(T_a,V_r_2) )
      & ( c_Wellfounded_Oacyclic(T_a,V_r_2)
        | ~ c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__converse]) ).

fof(f_3774_2,plain,
    ! [U_15089,U_15088] :
      ( ( c_Wellfounded_Oacyclic(U_15088,hAPP(c_Relation_Oconverse(U_15088,U_15088),U_15089))
        | ~ c_Wellfounded_Oacyclic(U_15088,U_15089) )
      & ( c_Wellfounded_Oacyclic(U_15088,U_15089)
        | ~ c_Wellfounded_Oacyclic(U_15088,hAPP(c_Relation_Oconverse(U_15088,U_15088),U_15089)) ) ),
    inference(variable_rename,[status(thm)],[f_3774_1]) ).

fof(f_3774_3,plain,
    ( ! [U_15093,U_15091] :
        ( c_Wellfounded_Oacyclic(U_15091,hAPP(c_Relation_Oconverse(U_15091,U_15091),U_15093))
        | ~ c_Wellfounded_Oacyclic(U_15091,U_15093) )
    & ! [U_15092,U_15090] :
        ( c_Wellfounded_Oacyclic(U_15090,U_15092)
        | ~ c_Wellfounded_Oacyclic(U_15090,hAPP(c_Relation_Oconverse(U_15090,U_15090),U_15092)) ) ),
    inference(miniscope,[status(thm)],[f_3774_2]) ).

cnf(f_3774_4,plain,
    ( c_Wellfounded_Oacyclic(U_15090,U_15092)
    | ~ c_Wellfounded_Oacyclic(U_15090,hAPP(c_Relation_Oconverse(U_15090,U_15090),U_15092)) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

cnf(f_3774_5,plain,
    ( c_Wellfounded_Oacyclic(U_15091,hAPP(c_Relation_Oconverse(U_15091,U_15091),U_15093))
    | ~ c_Wellfounded_Oacyclic(U_15091,U_15093) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

fof(f_3775_1,plain,
    ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__converse]) ).

fof(f_3775_2,plain,
    ! [U_15095,U_15094] : c_Transitive__Closure_Otrancl(U_15094,hAPP(c_Relation_Oconverse(U_15094,U_15094),U_15095)) = hAPP(c_Relation_Oconverse(U_15094,U_15094),c_Transitive__Closure_Otrancl(U_15094,U_15095)),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

cnf(f_3775_3,plain,
    c_Transitive__Closure_Otrancl(U_15094,hAPP(c_Relation_Oconverse(U_15094,U_15094),U_15095)) = hAPP(c_Relation_Oconverse(U_15094,U_15094),c_Transitive__Closure_Otrancl(U_15094,U_15095)),
    inference(clausify,[status(thm)],[f_3775_2]) ).

fof(f_3776_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
      | ~ c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl]) ).

fof(f_3776_2,plain,
    ! [U_15097,U_15096] :
      ( c_Wellfounded_Owf(U_15096,hAPP(c_Relation_Oconverse(U_15096,U_15096),c_Transitive__Closure_Otrancl(U_15096,U_15097)))
      | ~ c_Wellfounded_Owf(U_15096,hAPP(c_Relation_Oconverse(U_15096,U_15096),U_15097)) ),
    inference(variable_rename,[status(thm)],[f_3776_1]) ).

cnf(f_3776_3,plain,
    ( c_Wellfounded_Owf(U_15096,hAPP(c_Relation_Oconverse(U_15096,U_15096),c_Transitive__Closure_Otrancl(U_15096,U_15097)))
    | ~ c_Wellfounded_Owf(U_15096,hAPP(c_Relation_Oconverse(U_15096,U_15096),U_15097)) ),
    inference(clausify,[status(thm)],[f_3776_2]) ).

fof(f_3777_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq]) ).

fof(f_3777_2,plain,
    ! [U_15100,U_15099,U_15098] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),hAPP(c_Relation_Oconverse(U_15098,U_15098),U_15100)),U_15100) = U_15100
      | ~ c_Equiv__Relations_Oequiv(U_15098,U_15099,U_15100) ),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

cnf(f_3777_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),hAPP(c_Relation_Oconverse(U_15098,U_15098),U_15100)),U_15100) = U_15100
    | ~ c_Equiv__Relations_Oequiv(U_15098,U_15099,U_15100) ),
    inference(clausify,[status(thm)],[f_3777_2]) ).

fof(f_3778_1,plain,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__def]) ).

fof(f_3778_2,plain,
    ! [U_15103,U_15102,U_15101] : hAPP(c_Relation_ORange(U_15101,U_15102),U_15103) = hAPP(c_Relation_ODomain(U_15102,U_15101),hAPP(c_Relation_Oconverse(U_15101,U_15102),U_15103)),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

cnf(f_3778_3,plain,
    hAPP(c_Relation_ORange(U_15101,U_15102),U_15103) = hAPP(c_Relation_ODomain(U_15102,U_15101),hAPP(c_Relation_Oconverse(U_15101,U_15102),U_15103)),
    inference(clausify,[status(thm)],[f_3778_2]) ).

fof(f_3779_1,plain,
    ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Domain__converse]) ).

fof(f_3779_2,plain,
    ! [U_15106,U_15105,U_15104] : hAPP(c_Relation_ODomain(U_15104,U_15105),hAPP(c_Relation_Oconverse(U_15105,U_15104),U_15106)) = hAPP(c_Relation_ORange(U_15105,U_15104),U_15106),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

cnf(f_3779_3,plain,
    hAPP(c_Relation_ODomain(U_15104,U_15105),hAPP(c_Relation_Oconverse(U_15105,U_15104),U_15106)) = hAPP(c_Relation_ORange(U_15105,U_15104),U_15106),
    inference(clausify,[status(thm)],[f_3779_2]) ).

fof(f_3780_1,plain,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Range__converse]) ).

fof(f_3780_2,plain,
    ! [U_15109,U_15108,U_15107] : hAPP(c_Relation_ORange(U_15107,U_15108),hAPP(c_Relation_Oconverse(U_15108,U_15107),U_15109)) = hAPP(c_Relation_ODomain(U_15108,U_15107),U_15109),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

cnf(f_3780_3,plain,
    hAPP(c_Relation_ORange(U_15107,U_15108),hAPP(c_Relation_Oconverse(U_15108,U_15107),U_15109)) = hAPP(c_Relation_ODomain(U_15108,U_15107),U_15109),
    inference(clausify,[status(thm)],[f_3780_2]) ).

fof(f_3781_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI]) ).

fof(f_3781_2,plain,
    ! [U_15113,U_15112,U_15111,U_15110] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15110,U_15110)),hAPP(hAPP(c_Product__Type_OPair(U_15110,U_15110),U_15112),U_15111)),c_Transitive__Closure_Ortrancl(U_15110,hAPP(c_Relation_Oconverse(U_15110,U_15110),U_15113))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15110,U_15110)),hAPP(hAPP(c_Product__Type_OPair(U_15110,U_15110),U_15111),U_15112)),c_Transitive__Closure_Ortrancl(U_15110,U_15113))) ),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

cnf(f_3781_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15110,U_15110)),hAPP(hAPP(c_Product__Type_OPair(U_15110,U_15110),U_15112),U_15111)),c_Transitive__Closure_Ortrancl(U_15110,hAPP(c_Relation_Oconverse(U_15110,U_15110),U_15113))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15110,U_15110)),hAPP(hAPP(c_Product__Type_OPair(U_15110,U_15110),U_15111),U_15112)),c_Transitive__Closure_Ortrancl(U_15110,U_15113))) ),
    inference(clausify,[status(thm)],[f_3781_2]) ).

fof(f_3782_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD]) ).

fof(f_3782_2,plain,
    ! [U_15117,U_15116,U_15115,U_15114] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15116),U_15115)),c_Transitive__Closure_Ortrancl(U_15114,U_15117)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),c_Transitive__Closure_Ortrancl(U_15114,hAPP(c_Relation_Oconverse(U_15114,U_15114),U_15117)))) ),
    inference(variable_rename,[status(thm)],[f_3782_1]) ).

cnf(f_3782_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15116),U_15115)),c_Transitive__Closure_Ortrancl(U_15114,U_15117)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),c_Transitive__Closure_Ortrancl(U_15114,hAPP(c_Relation_Oconverse(U_15114,U_15114),U_15117)))) ),
    inference(clausify,[status(thm)],[f_3782_2]) ).

fof(f_3783_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseI]) ).

fof(f_3783_2,plain,
    ! [U_15121,U_15120,U_15119,U_15118] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),c_Transitive__Closure_Otrancl(U_15118,hAPP(c_Relation_Oconverse(U_15118,U_15118),U_15121))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),hAPP(c_Relation_Oconverse(U_15118,U_15118),c_Transitive__Closure_Otrancl(U_15118,U_15121)))) ),
    inference(variable_rename,[status(thm)],[f_3783_1]) ).

cnf(f_3783_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),c_Transitive__Closure_Otrancl(U_15118,hAPP(c_Relation_Oconverse(U_15118,U_15118),U_15121))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),hAPP(c_Relation_Oconverse(U_15118,U_15118),c_Transitive__Closure_Otrancl(U_15118,U_15121)))) ),
    inference(clausify,[status(thm)],[f_3783_2]) ).

fof(f_3784_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseD]) ).

fof(f_3784_2,plain,
    ! [U_15125,U_15124,U_15123,U_15122] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15122,U_15122)),hAPP(hAPP(c_Product__Type_OPair(U_15122,U_15122),U_15123),U_15124)),hAPP(c_Relation_Oconverse(U_15122,U_15122),c_Transitive__Closure_Otrancl(U_15122,U_15125))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15122,U_15122)),hAPP(hAPP(c_Product__Type_OPair(U_15122,U_15122),U_15123),U_15124)),c_Transitive__Closure_Otrancl(U_15122,hAPP(c_Relation_Oconverse(U_15122,U_15122),U_15125)))) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

cnf(f_3784_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15122,U_15122)),hAPP(hAPP(c_Product__Type_OPair(U_15122,U_15122),U_15123),U_15124)),hAPP(c_Relation_Oconverse(U_15122,U_15122),c_Transitive__Closure_Otrancl(U_15122,U_15125))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15122,U_15122)),hAPP(hAPP(c_Product__Type_OPair(U_15122,U_15122),U_15123),U_15124)),c_Transitive__Closure_Otrancl(U_15122,hAPP(c_Relation_Oconverse(U_15122,U_15122),U_15125)))) ),
    inference(clausify,[status(thm)],[f_3784_2]) ).

fof(f_3785_1,plain,
    ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,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)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset__eq]) ).

fof(f_3785_2,plain,
    ! [U_15130,U_15129,U_15128,U_15127,U_15126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15126,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15127,U_15126,U_15128),U_15129)),U_15130))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15127,tc_HOL_Obool)),U_15129),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15127,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15126,U_15127,hAPP(c_Relation_Oconverse(U_15127,U_15126),U_15128)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15126,tc_HOL_Obool)),U_15130))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15127,tc_HOL_Obool)),U_15129),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15127,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15126,U_15127,hAPP(c_Relation_Oconverse(U_15127,U_15126),U_15128)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15126,tc_HOL_Obool)),U_15130)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15126,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15127,U_15126,U_15128),U_15129)),U_15130)) ) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

fof(f_3785_3,plain,
    ( ! [U_15140,U_15138,U_15136,U_15134,U_15132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15132,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15134,U_15132,U_15136),U_15138)),U_15140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15134,tc_HOL_Obool)),U_15138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15134,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15132,U_15134,hAPP(c_Relation_Oconverse(U_15134,U_15132),U_15136)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15132,tc_HOL_Obool)),U_15140))))) )
    & ! [U_15139,U_15137,U_15135,U_15133,U_15131] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15133,tc_HOL_Obool)),U_15137),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15133,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15131,U_15133,hAPP(c_Relation_Oconverse(U_15133,U_15131),U_15135)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15131,tc_HOL_Obool)),U_15139)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15131,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15133,U_15131,U_15135),U_15137)),U_15139)) ) ),
    inference(miniscope,[status(thm)],[f_3785_2]) ).

cnf(f_3785_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15133,tc_HOL_Obool)),U_15137),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15133,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15131,U_15133,hAPP(c_Relation_Oconverse(U_15133,U_15131),U_15135)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15131,tc_HOL_Obool)),U_15139)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15131,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15133,U_15131,U_15135),U_15137)),U_15139)) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

cnf(f_3785_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15132,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15134,U_15132,U_15136),U_15138)),U_15140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15134,tc_HOL_Obool)),U_15138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15134,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15132,U_15134,hAPP(c_Relation_Oconverse(U_15134,U_15132),U_15136)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_15132,tc_HOL_Obool)),U_15140))))) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

fof(f_3786_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2)))
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset]) ).

fof(f_3786_2,plain,
    ! [U_15143,U_15142,U_15141] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool)),U_15143),hAPP(hAPP(c_Relation_Orel__comp(U_15141,U_15141,U_15141),hAPP(c_Relation_Oconverse(U_15141,U_15141),U_15143)),U_15143)))
      | ~ c_Relation_Orefl__on(U_15141,U_15142,U_15143) ),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

cnf(f_3786_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool)),U_15143),hAPP(hAPP(c_Relation_Orel__comp(U_15141,U_15141,U_15141),hAPP(c_Relation_Oconverse(U_15141,U_15141),U_15143)),U_15143)))
    | ~ c_Relation_Orefl__on(U_15141,U_15142,U_15143) ),
    inference(clausify,[status(thm)],[f_3786_2]) ).

fof(f_3787_1,plain,
    ! [V_A_2,V_r_2,T_a] :
      ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
      | hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) != V_A_2
      | hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) != V_r_2 ),
    inference(fof_nnf,[status(thm)],[fact_comp__equivI]) ).

fof(f_3787_2,plain,
    ! [U_15146,U_15145,U_15144] :
      ( c_Equiv__Relations_Oequiv(U_15144,U_15146,U_15145)
      | hAPP(c_Relation_ODomain(U_15144,U_15144),U_15145) != U_15146
      | hAPP(hAPP(c_Relation_Orel__comp(U_15144,U_15144,U_15144),hAPP(c_Relation_Oconverse(U_15144,U_15144),U_15145)),U_15145) != U_15145 ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

cnf(f_3787_3,plain,
    ( c_Equiv__Relations_Oequiv(U_15144,U_15146,U_15145)
    | hAPP(c_Relation_ODomain(U_15144,U_15144),U_15145) != U_15146
    | hAPP(hAPP(c_Relation_Orel__comp(U_15144,U_15144,U_15144),hAPP(c_Relation_Oconverse(U_15144,U_15144),U_15145)),U_15145) != U_15145 ),
    inference(clausify,[status(thm)],[f_3787_2]) ).

fof(f_3788_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
      | ~ c_Wellfounded_Oacyclic(T_a,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse]) ).

fof(f_3788_2,plain,
    ! [U_15148,U_15147] :
      ( c_Wellfounded_Owf(U_15147,hAPP(c_Relation_Oconverse(U_15147,U_15147),U_15148))
      | ~ c_Wellfounded_Oacyclic(U_15147,U_15148)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15147,U_15147)),U_15148)) ),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

cnf(f_3788_3,plain,
    ( c_Wellfounded_Owf(U_15147,hAPP(c_Relation_Oconverse(U_15147,U_15147),U_15148))
    | ~ c_Wellfounded_Oacyclic(U_15147,U_15148)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15147,U_15147)),U_15148)) ),
    inference(clausify,[status(thm)],[f_3788_2]) ).

fof(f_3789_1,plain,
    ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),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_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_converse__def]) ).

fof(f_3789_2,plain,
    ! [U_15151,U_15150,U_15149] : hAPP(c_Relation_Oconverse(U_15149,U_15150),U_15151) = hAPP(c_Set_OCollect(tc_prod(U_15150,U_15149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15150,U_15149,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15150,tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_fun(U_15149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15149,tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_fun(U_15149,tc_HOL_Obool)),U_15150),c_COMBC(U_15149,tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15149,tc_prod(U_15149,U_15150)),tc_fun(U_15149,tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),U_15150),hAPP(c_COMBB(tc_prod(U_15149,U_15150),tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool),U_15149),c_member(tc_prod(U_15149,U_15150)))),hAPP(c_COMBC(U_15149,U_15150,tc_prod(U_15149,U_15150)),c_Product__Type_OPair(U_15149,U_15150))))),U_15151))),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

cnf(f_3789_3,plain,
    hAPP(c_Relation_Oconverse(U_15149,U_15150),U_15151) = hAPP(c_Set_OCollect(tc_prod(U_15150,U_15149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15150,U_15149,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15150,tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_fun(U_15149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15149,tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_fun(U_15149,tc_HOL_Obool)),U_15150),c_COMBC(U_15149,tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15149,tc_prod(U_15149,U_15150)),tc_fun(U_15149,tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool)),U_15150),hAPP(c_COMBB(tc_prod(U_15149,U_15150),tc_fun(tc_fun(tc_prod(U_15149,U_15150),tc_HOL_Obool),tc_HOL_Obool),U_15149),c_member(tc_prod(U_15149,U_15150)))),hAPP(c_COMBC(U_15149,U_15150,tc_prod(U_15149,U_15150)),c_Product__Type_OPair(U_15149,U_15150))))),U_15151))),
    inference(clausify,[status(thm)],[f_3789_2]) ).

fof(f_3790_1,plain,
    ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
      ( hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__eq]) ).

fof(f_3790_2,plain,
    ! [U_15157,U_15156,U_15155,U_15154,U_15153,U_15152] :
      ( hAPP(c_Relation_OImage(U_15153,U_15152,U_15154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15156,tc_fun(U_15153,tc_HOL_Obool)),U_15155),U_15157)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15156,tc_fun(U_15152,tc_HOL_Obool)),U_15155),hAPP(hAPP(c_COMBB(tc_fun(U_15153,tc_HOL_Obool),tc_fun(U_15152,tc_HOL_Obool),U_15156),c_Relation_OImage(U_15153,U_15152,U_15154)),U_15157))
      | U_15155 = c_Orderings_Obot__class_Obot(tc_fun(U_15156,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_15152,U_15153,hAPP(c_Relation_Oconverse(U_15153,U_15152),U_15154)) ),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

cnf(f_3790_3,plain,
    ( hAPP(c_Relation_OImage(U_15153,U_15152,U_15154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15156,tc_fun(U_15153,tc_HOL_Obool)),U_15155),U_15157)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15156,tc_fun(U_15152,tc_HOL_Obool)),U_15155),hAPP(hAPP(c_COMBB(tc_fun(U_15153,tc_HOL_Obool),tc_fun(U_15152,tc_HOL_Obool),U_15156),c_Relation_OImage(U_15153,U_15152,U_15154)),U_15157))
    | U_15155 = c_Orderings_Obot__class_Obot(tc_fun(U_15156,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_15152,U_15153,hAPP(c_Relation_Oconverse(U_15153,U_15152),U_15154)) ),
    inference(clausify,[status(thm)],[f_3790_2]) ).

fof(f_3791_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))
        | ~ c_Relation_Ototal__on(T_a,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id]) ).

fof(f_3791_2,plain,
    ! [U_15160,U_15159,U_15158] :
      ( ( c_Relation_Ototal__on(U_15158,U_15159,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15158,U_15158),tc_HOL_Obool)),U_15160),c_Relation_OId(U_15158)))
        | ~ c_Relation_Ototal__on(U_15158,U_15159,U_15160) )
      & ( c_Relation_Ototal__on(U_15158,U_15159,U_15160)
        | ~ c_Relation_Ototal__on(U_15158,U_15159,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15158,U_15158),tc_HOL_Obool)),U_15160),c_Relation_OId(U_15158))) ) ),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

fof(f_3791_3,plain,
    ( ! [U_15166,U_15164,U_15162] :
        ( c_Relation_Ototal__on(U_15162,U_15164,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15162,U_15162),tc_HOL_Obool)),U_15166),c_Relation_OId(U_15162)))
        | ~ c_Relation_Ototal__on(U_15162,U_15164,U_15166) )
    & ! [U_15165,U_15163,U_15161] :
        ( c_Relation_Ototal__on(U_15161,U_15163,U_15165)
        | ~ c_Relation_Ototal__on(U_15161,U_15163,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15161,U_15161),tc_HOL_Obool)),U_15165),c_Relation_OId(U_15161))) ) ),
    inference(miniscope,[status(thm)],[f_3791_2]) ).

cnf(f_3791_4,plain,
    ( c_Relation_Ototal__on(U_15161,U_15163,U_15165)
    | ~ c_Relation_Ototal__on(U_15161,U_15163,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15161,U_15161),tc_HOL_Obool)),U_15165),c_Relation_OId(U_15161))) ),
    inference(clausify,[status(thm)],[f_3791_3]) ).

cnf(f_3791_5,plain,
    ( c_Relation_Ototal__on(U_15162,U_15164,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15162,U_15162),tc_HOL_Obool)),U_15166),c_Relation_OId(U_15162)))
    | ~ c_Relation_Ototal__on(U_15162,U_15164,U_15166) ),
    inference(clausify,[status(thm)],[f_3791_3]) ).

fof(f_3792_1,plain,
    ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id]) ).

fof(f_3792_2,plain,
    ! [U_15167] : c_Relation_Osingle__valued(U_15167,U_15167,c_Relation_OId(U_15167)),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

cnf(f_3792_3,plain,
    c_Relation_Osingle__valued(U_15167,U_15167,c_Relation_OId(U_15167)),
    inference(clausify,[status(thm)],[f_3792_2]) ).

fof(f_3793_1,plain,
    ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id__on]) ).

fof(f_3793_2,plain,
    ! [U_15169,U_15168] : c_Relation_Osingle__valued(U_15168,U_15168,c_Relation_OId__on(U_15168,U_15169)),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

cnf(f_3793_3,plain,
    c_Relation_Osingle__valued(U_15168,U_15168,c_Relation_OId__on(U_15168,U_15169)),
    inference(clausify,[status(thm)],[f_3793_2]) ).

fof(f_3794_1,plain,
    ! [V_s_2,T_c,V_r_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_s_2)
      | ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp]) ).

fof(f_3794_2,plain,
    ! [U_15174,U_15173,U_15172,U_15171,U_15170] :
      ( c_Relation_Osingle__valued(U_15170,U_15173,hAPP(hAPP(c_Relation_Orel__comp(U_15170,U_15171,U_15173),U_15172),U_15174))
      | ~ c_Relation_Osingle__valued(U_15171,U_15173,U_15174)
      | ~ c_Relation_Osingle__valued(U_15170,U_15171,U_15172) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

cnf(f_3794_3,plain,
    ( c_Relation_Osingle__valued(U_15170,U_15173,hAPP(hAPP(c_Relation_Orel__comp(U_15170,U_15171,U_15173),U_15172),U_15174))
    | ~ c_Relation_Osingle__valued(U_15171,U_15173,U_15174)
    | ~ c_Relation_Osingle__valued(U_15170,U_15171,U_15172) ),
    inference(clausify,[status(thm)],[f_3794_2]) ).

fof(f_3795_1,plain,
    ! [V_s_2,V_r_2,T_b,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
      | ~ c_Relation_Osingle__valued(T_a,T_b,V_s_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__subset]) ).

fof(f_3795_2,plain,
    ! [U_15178,U_15177,U_15176,U_15175] :
      ( c_Relation_Osingle__valued(U_15175,U_15176,U_15177)
      | ~ c_Relation_Osingle__valued(U_15175,U_15176,U_15178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15175,U_15176),tc_HOL_Obool)),U_15177),U_15178)) ),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

cnf(f_3795_3,plain,
    ( c_Relation_Osingle__valued(U_15175,U_15176,U_15177)
    | ~ c_Relation_Osingle__valued(U_15175,U_15176,U_15178)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15175,U_15176),tc_HOL_Obool)),U_15177),U_15178)) ),
    inference(clausify,[status(thm)],[f_3795_2]) ).

fof(f_3796_1,plain,
    ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_total__on__empty]) ).

fof(f_3796_2,plain,
    ! [U_15180,U_15179] : c_Relation_Ototal__on(U_15179,c_Orderings_Obot__class_Obot(tc_fun(U_15179,tc_HOL_Obool)),U_15180),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

cnf(f_3796_3,plain,
    c_Relation_Ototal__on(U_15179,c_Orderings_Obot__class_Obot(tc_fun(U_15179,tc_HOL_Obool)),U_15180),
    inference(clausify,[status(thm)],[f_3796_2]) ).

fof(f_3797_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
        | ~ c_Relation_Ototal__on(T_a,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__converse]) ).

fof(f_3797_2,plain,
    ! [U_15183,U_15182,U_15181] :
      ( ( c_Relation_Ototal__on(U_15181,U_15182,hAPP(c_Relation_Oconverse(U_15181,U_15181),U_15183))
        | ~ c_Relation_Ototal__on(U_15181,U_15182,U_15183) )
      & ( c_Relation_Ototal__on(U_15181,U_15182,U_15183)
        | ~ c_Relation_Ototal__on(U_15181,U_15182,hAPP(c_Relation_Oconverse(U_15181,U_15181),U_15183)) ) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

fof(f_3797_3,plain,
    ( ! [U_15189,U_15187,U_15185] :
        ( c_Relation_Ototal__on(U_15185,U_15187,hAPP(c_Relation_Oconverse(U_15185,U_15185),U_15189))
        | ~ c_Relation_Ototal__on(U_15185,U_15187,U_15189) )
    & ! [U_15188,U_15186,U_15184] :
        ( c_Relation_Ototal__on(U_15184,U_15186,U_15188)
        | ~ c_Relation_Ototal__on(U_15184,U_15186,hAPP(c_Relation_Oconverse(U_15184,U_15184),U_15188)) ) ),
    inference(miniscope,[status(thm)],[f_3797_2]) ).

cnf(f_3797_4,plain,
    ( c_Relation_Ototal__on(U_15184,U_15186,U_15188)
    | ~ c_Relation_Ototal__on(U_15184,U_15186,hAPP(c_Relation_Oconverse(U_15184,U_15184),U_15188)) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_5,plain,
    ( c_Relation_Ototal__on(U_15185,U_15187,hAPP(c_Relation_Oconverse(U_15185,U_15185),U_15189))
    | ~ c_Relation_Ototal__on(U_15185,U_15187,U_15189) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

fof(f_3798_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
      ( V_y_2 = V_z_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valuedD]) ).

fof(f_3798_2,plain,
    ! [U_15195,U_15194,U_15193,U_15192,U_15191,U_15190] :
      ( U_15194 = U_15195
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15190,U_15191)),hAPP(hAPP(c_Product__Type_OPair(U_15190,U_15191),U_15193),U_15195)),U_15192))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15190,U_15191)),hAPP(hAPP(c_Product__Type_OPair(U_15190,U_15191),U_15193),U_15194)),U_15192))
      | ~ c_Relation_Osingle__valued(U_15190,U_15191,U_15192) ),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

cnf(f_3798_3,plain,
    ( U_15194 = U_15195
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15190,U_15191)),hAPP(hAPP(c_Product__Type_OPair(U_15190,U_15191),U_15193),U_15195)),U_15192))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15190,U_15191)),hAPP(hAPP(c_Product__Type_OPair(U_15190,U_15191),U_15193),U_15194)),U_15192))
    | ~ c_Relation_Osingle__valued(U_15190,U_15191,U_15192) ),
    inference(clausify,[status(thm)],[f_3798_2]) ).

fof(f_3799_1,plain,
    ! [V_r_2,T_b,T_a] :
      ( ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
        | ? [B_x,B_y] :
            ( ? [B_z] :
                ( B_y != B_z
                & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),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_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__def]) ).

fof(f_3799_2,plain,
    ! [U_15204,U_15203,U_15202] :
      ( ( c_Relation_Osingle__valued(U_15202,U_15203,U_15204)
        | ? [U_15201,U_15200] :
            ( ? [U_15199] :
                ( U_15200 != U_15199
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15203),U_15201),U_15199)),U_15204)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15203),U_15201),U_15200)),U_15204)) ) )
      & ( ! [U_15198,U_15197] :
            ( ! [U_15196] :
                ( U_15197 = U_15196
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15203),U_15198),U_15196)),U_15204)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15203),U_15198),U_15197)),U_15204)) )
        | ~ c_Relation_Osingle__valued(U_15202,U_15203,U_15204) ) ),
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

fof(f_3799_3,plain,
    ( ! [U_15210,U_15208,U_15206] :
        ( c_Relation_Osingle__valued(U_15206,U_15208,U_15210)
        | ? [U_15201,U_15200] :
            ( ? [U_15199] :
                ( U_15200 != U_15199
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),U_15201),U_15199)),U_15210)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),U_15201),U_15200)),U_15210)) ) )
    & ! [U_15209,U_15207,U_15205] :
        ( ! [U_15198,U_15197] :
            ( ! [U_15196] :
                ( U_15197 = U_15196
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15196)),U_15209)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15197)),U_15209)) )
        | ~ c_Relation_Osingle__valued(U_15205,U_15207,U_15209) ) ),
    inference(miniscope,[status(thm)],[f_3799_2]) ).

fof(f_3799_4,plain,
    ( ! [U_15210,U_15208,U_15206] :
        ( c_Relation_Osingle__valued(U_15206,U_15208,U_15210)
        | ? [U_15200] :
            ( ? [U_15199] :
                ( U_15200 != U_15199
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),U_15199)),U_15210)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),U_15200)),U_15210)) ) )
    & ! [U_15209,U_15207,U_15205] :
        ( ! [U_15198,U_15197] :
            ( ! [U_15196] :
                ( U_15197 = U_15196
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15196)),U_15209)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15197)),U_15209)) )
        | ~ c_Relation_Osingle__valued(U_15205,U_15207,U_15209) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_15201,sK377(U_15210,U_15208,U_15206))],[f_3799_3]) ).

fof(f_3799_5,plain,
    ( ! [U_15210,U_15208,U_15206] :
        ( c_Relation_Osingle__valued(U_15206,U_15208,U_15210)
        | ( ? [U_15199] :
              ( sK378(U_15210,U_15208,U_15206) != U_15199
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),U_15199)),U_15210)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),sK378(U_15210,U_15208,U_15206))),U_15210)) ) )
    & ! [U_15209,U_15207,U_15205] :
        ( ! [U_15198,U_15197] :
            ( ! [U_15196] :
                ( U_15197 = U_15196
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15196)),U_15209)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15197)),U_15209)) )
        | ~ c_Relation_Osingle__valued(U_15205,U_15207,U_15209) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_15200,sK378(U_15210,U_15208,U_15206))],[f_3799_4]) ).

fof(f_3799_6,plain,
    ( ! [U_15210,U_15208,U_15206] :
        ( c_Relation_Osingle__valued(U_15206,U_15208,U_15210)
        | ( sK378(U_15210,U_15208,U_15206) != sK379(U_15210,U_15208,U_15206)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),sK379(U_15210,U_15208,U_15206))),U_15210))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),sK378(U_15210,U_15208,U_15206))),U_15210)) ) )
    & ! [U_15209,U_15207,U_15205] :
        ( ! [U_15198,U_15197] :
            ( ! [U_15196] :
                ( U_15197 = U_15196
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15196)),U_15209)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15197)),U_15209)) )
        | ~ c_Relation_Osingle__valued(U_15205,U_15207,U_15209) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_15199,sK379(U_15210,U_15208,U_15206))],[f_3799_5]) ).

cnf(f_3799_7,plain,
    ( U_15197 = U_15196
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15196)),U_15209))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15205,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15205,U_15207),U_15198),U_15197)),U_15209))
    | ~ c_Relation_Osingle__valued(U_15205,U_15207,U_15209) ),
    inference(clausify,[status(thm)],[f_3799_6]) ).

cnf(f_3799_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),sK378(U_15210,U_15208,U_15206))),U_15210))
    | c_Relation_Osingle__valued(U_15206,U_15208,U_15210) ),
    inference(clausify,[status(thm)],[f_3799_6]) ).

cnf(f_3799_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15206,U_15208)),hAPP(hAPP(c_Product__Type_OPair(U_15206,U_15208),sK377(U_15210,U_15208,U_15206)),sK379(U_15210,U_15208,U_15206))),U_15210))
    | c_Relation_Osingle__valued(U_15206,U_15208,U_15210) ),
    inference(clausify,[status(thm)],[f_3799_6]) ).

cnf(f_3799_10,plain,
    ( sK378(U_15210,U_15208,U_15206) != sK379(U_15210,U_15208,U_15206)
    | c_Relation_Osingle__valued(U_15206,U_15208,U_15210) ),
    inference(clausify,[status(thm)],[f_3799_6]) ).

fof(f_3800_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
                & B_x != B_xa
                & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
                | B_x = B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
        | ~ c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__def]) ).

fof(f_3800_2,plain,
    ! [U_15217,U_15216,U_15215] :
      ( ( c_Relation_Ototal__on(U_15215,U_15216,U_15217)
        | ? [U_15214] :
            ( ? [U_15213] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15215,U_15215)),hAPP(hAPP(c_Product__Type_OPair(U_15215,U_15215),U_15213),U_15214)),U_15217))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15215,U_15215)),hAPP(hAPP(c_Product__Type_OPair(U_15215,U_15215),U_15214),U_15213)),U_15217))
                & U_15214 != U_15213
                & hBOOL(hAPP(hAPP(c_member(U_15215),U_15213),U_15216)) )
            & hBOOL(hAPP(hAPP(c_member(U_15215),U_15214),U_15216)) ) )
      & ( ! [U_15212] :
            ( ! [U_15211] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15215,U_15215)),hAPP(hAPP(c_Product__Type_OPair(U_15215,U_15215),U_15211),U_15212)),U_15217))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15215,U_15215)),hAPP(hAPP(c_Product__Type_OPair(U_15215,U_15215),U_15212),U_15211)),U_15217))
                | U_15212 = U_15211
                | ~ hBOOL(hAPP(hAPP(c_member(U_15215),U_15211),U_15216)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_15215),U_15212),U_15216)) )
        | ~ c_Relation_Ototal__on(U_15215,U_15216,U_15217) ) ),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

fof(f_3800_3,plain,
    ( ! [U_15223,U_15221,U_15219] :
        ( c_Relation_Ototal__on(U_15219,U_15221,U_15223)
        | ? [U_15214] :
            ( ? [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_15214)),U_15223))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15214),U_15213)),U_15223))
                & U_15214 != U_15213
                & hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221)) )
            & hBOOL(hAPP(hAPP(c_member(U_15219),U_15214),U_15221)) ) )
    & ! [U_15222,U_15220,U_15218] :
        ( ! [U_15212] :
            ( ! [U_15211] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15211),U_15212)),U_15222))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15212),U_15211)),U_15222))
                | U_15212 = U_15211
                | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15211),U_15220)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15212),U_15220)) )
        | ~ c_Relation_Ototal__on(U_15218,U_15220,U_15222) ) ),
    inference(miniscope,[status(thm)],[f_3800_2]) ).

fof(f_3800_4,plain,
    ( ! [U_15223,U_15221,U_15219] :
        ( c_Relation_Ototal__on(U_15219,U_15221,U_15223)
        | ( ? [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),sK380(U_15223,U_15221,U_15219))),U_15223))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),sK380(U_15223,U_15221,U_15219)),U_15213)),U_15223))
              & sK380(U_15223,U_15221,U_15219) != U_15213
              & hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221)) )
          & hBOOL(hAPP(hAPP(c_member(U_15219),sK380(U_15223,U_15221,U_15219)),U_15221)) ) )
    & ! [U_15222,U_15220,U_15218] :
        ( ! [U_15212] :
            ( ! [U_15211] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15211),U_15212)),U_15222))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15212),U_15211)),U_15222))
                | U_15212 = U_15211
                | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15211),U_15220)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15212),U_15220)) )
        | ~ c_Relation_Ototal__on(U_15218,U_15220,U_15222) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_15214,sK380(U_15223,U_15221,U_15219))],[f_3800_3]) ).

fof(f_3800_5,plain,
    ( ! [U_15223,U_15221,U_15219] :
        ( c_Relation_Ototal__on(U_15219,U_15221,U_15223)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),sK381(U_15223,U_15221,U_15219)),sK380(U_15223,U_15221,U_15219))),U_15223))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),sK380(U_15223,U_15221,U_15219)),sK381(U_15223,U_15221,U_15219))),U_15223))
          & sK380(U_15223,U_15221,U_15219) != sK381(U_15223,U_15221,U_15219)
          & hBOOL(hAPP(hAPP(c_member(U_15219),sK381(U_15223,U_15221,U_15219)),U_15221))
          & hBOOL(hAPP(hAPP(c_member(U_15219),sK380(U_15223,U_15221,U_15219)),U_15221)) ) )
    & ! [U_15222,U_15220,U_15218] :
        ( ! [U_15212] :
            ( ! [U_15211] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15211),U_15212)),U_15222))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15212),U_15211)),U_15222))
                | U_15212 = U_15211
                | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15211),U_15220)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15212),U_15220)) )
        | ~ c_Relation_Ototal__on(U_15218,U_15220,U_15222) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_15213,sK381(U_15223,U_15221,U_15219))],[f_3800_4]) ).

cnf(f_3800_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15211),U_15212)),U_15222))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),U_15212),U_15211)),U_15222))
    | U_15212 = U_15211
    | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15211),U_15220))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15218),U_15212),U_15220))
    | ~ c_Relation_Ototal__on(U_15218,U_15220,U_15222) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

cnf(f_3800_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15219),sK380(U_15223,U_15221,U_15219)),U_15221))
    | c_Relation_Ototal__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

cnf(f_3800_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15219),sK381(U_15223,U_15221,U_15219)),U_15221))
    | c_Relation_Ototal__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

cnf(f_3800_9,plain,
    ( sK380(U_15223,U_15221,U_15219) != sK381(U_15223,U_15221,U_15219)
    | c_Relation_Ototal__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

cnf(f_3800_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),sK380(U_15223,U_15221,U_15219)),sK381(U_15223,U_15221,U_15219))),U_15223))
    | c_Relation_Ototal__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

cnf(f_3800_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),sK381(U_15223,U_15221,U_15219)),sK380(U_15223,U_15221,U_15219))),U_15223))
    | c_Relation_Ototal__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3800_5]) ).

fof(f_3801_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
      | ~ c_Relation_Osingle__valued(T_a,T_a,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__confluent]) ).

fof(f_3801_2,plain,
    ! [U_15228,U_15227,U_15226,U_15225,U_15224] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15228),U_15227)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15227),U_15228)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15226),U_15228)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15226),U_15227)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
      | ~ c_Relation_Osingle__valued(U_15224,U_15224,U_15225) ),
    inference(variable_rename,[status(thm)],[f_3801_1]) ).

cnf(f_3801_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15228),U_15227)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15227),U_15228)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15226),U_15228)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),U_15226),U_15227)),c_Transitive__Closure_Ortrancl(U_15224,U_15225)))
    | ~ c_Relation_Osingle__valued(U_15224,U_15224,U_15225) ),
    inference(clausify,[status(thm)],[f_3801_2]) ).

fof(f_3802_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
      ( hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2))
      | ~ c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__eq]) ).

fof(f_3802_2,plain,
    ! [U_15233,U_15232,U_15231,U_15230,U_15229] :
      ( hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15230,tc_HOL_Obool)),U_15232),U_15233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15229,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),U_15232)),hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),U_15233))
      | ~ c_Relation_Osingle__valued(U_15229,U_15230,hAPP(c_Relation_Oconverse(U_15230,U_15229),U_15231)) ),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

cnf(f_3802_3,plain,
    ( hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15230,tc_HOL_Obool)),U_15232),U_15233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15229,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),U_15232)),hAPP(c_Relation_OImage(U_15230,U_15229,U_15231),U_15233))
    | ~ c_Relation_Osingle__valued(U_15229,U_15230,hAPP(c_Relation_Oconverse(U_15230,U_15229),U_15231)) ),
    inference(clausify,[status(thm)],[f_3802_2]) ).

fof(f_3803_1,plain,
    ! [V_R_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow]) ).

fof(f_3803_2,plain,
    ! [U_15236,U_15235,U_15234] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),U_15235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15234,U_15234),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_15234,U_15234),tc_HOL_Obool),tc_fun(tc_prod(U_15234,U_15234),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15234,U_15234),tc_HOL_Obool)),U_15236))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),U_15235),c_Transitive__Closure_Ortrancl(U_15234,U_15236))) ),
    inference(variable_rename,[status(thm)],[f_3803_1]) ).

cnf(f_3803_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),U_15235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15234,U_15234),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_15234,U_15234),tc_HOL_Obool),tc_fun(tc_prod(U_15234,U_15234),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15234,U_15234),tc_HOL_Obool)),U_15236))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15234)),U_15235),c_Transitive__Closure_Ortrancl(U_15234,U_15236))) ),
    inference(clausify,[status(thm)],[f_3803_2]) ).

fof(f_3804_1,plain,
    ! [V_r_2,T_a] :
      ( c_Wellfounded_Oacyclic(T_a,V_r_2)
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicI]) ).

fof(f_3804_2,plain,
    ! [U_15239,U_15238] :
      ( c_Wellfounded_Oacyclic(U_15238,U_15239)
      | ? [U_15237] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),U_15237),U_15237)),c_Transitive__Closure_Otrancl(U_15238,U_15239))) ),
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

fof(f_3804_3,plain,
    ! [U_15239,U_15238] :
      ( c_Wellfounded_Oacyclic(U_15238,U_15239)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),sK382(U_15239,U_15238)),sK382(U_15239,U_15238))),c_Transitive__Closure_Otrancl(U_15238,U_15239))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_15237,sK382(U_15239,U_15238))],[f_3804_2]) ).

cnf(f_3804_4,plain,
    ( c_Wellfounded_Oacyclic(U_15238,U_15239)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15238,U_15238)),hAPP(hAPP(c_Product__Type_OPair(U_15238,U_15238),sK382(U_15239,U_15238)),sK382(U_15239,U_15238))),c_Transitive__Closure_Otrancl(U_15238,U_15239))) ),
    inference(clausify,[status(thm)],[f_3804_3]) ).

fof(f_3805_1,plain,
    ! [V_n_2,V_R_2,T_a] :
      ( c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))
      | ~ c_Relation_Osingle__valued(T_a,T_a,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow]) ).

fof(f_3805_2,plain,
    ! [U_15242,U_15241,U_15240] :
      ( c_Relation_Osingle__valued(U_15240,U_15240,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15240,U_15240),tc_HOL_Obool),U_15242),U_15241))
      | ~ c_Relation_Osingle__valued(U_15240,U_15240,U_15241) ),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

cnf(f_3805_3,plain,
    ( c_Relation_Osingle__valued(U_15240,U_15240,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15240,U_15240),tc_HOL_Obool),U_15242),U_15241))
    | ~ c_Relation_Osingle__valued(U_15240,U_15240,U_15241) ),
    inference(clausify,[status(thm)],[f_3805_2]) ).

fof(f_3806_1,plain,
    ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_comp__funpow]) ).

fof(f_3806_2,plain,
    ! [U_15246,U_15245,U_15244,U_15243] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15243,U_15244),tc_fun(U_15243,U_15244)),U_15245),c_Fun_Ocomp(U_15244,U_15244,U_15243,U_15246)) = c_Fun_Ocomp(U_15244,U_15244,U_15243,hAPP(hAPP(c_Nat_Ocompow(U_15244,U_15244),U_15245),U_15246)),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

cnf(f_3806_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15243,U_15244),tc_fun(U_15243,U_15244)),U_15245),c_Fun_Ocomp(U_15244,U_15244,U_15243,U_15246)) = c_Fun_Ocomp(U_15244,U_15244,U_15243,hAPP(hAPP(c_Nat_Ocompow(U_15244,U_15244),U_15245),U_15246)),
    inference(clausify,[status(thm)],[f_3806_2]) ).

fof(f_3807_1,plain,
    ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__swap1]) ).

fof(f_3807_2,plain,
    ! [U_15250,U_15249,U_15248,U_15247] : hAPP(U_15247,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15248,U_15248),U_15249),U_15247),U_15250)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15248,U_15248),U_15249),U_15247),hAPP(U_15247,U_15250)),
    inference(variable_rename,[status(thm)],[f_3807_1]) ).

cnf(f_3807_3,plain,
    hAPP(U_15247,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15248,U_15248),U_15249),U_15247),U_15250)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15248,U_15248),U_15249),U_15247),hAPP(U_15247,U_15250)),
    inference(clausify,[status(thm)],[f_3807_2]) ).

fof(f_3808_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),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_3808_2,plain,
    ! [U_15254,U_15253,U_15252,U_15251] : hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),U_15252),hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),U_15253),U_15254)) = hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15253),U_15252)),U_15254),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

cnf(f_3808_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),U_15252),hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),U_15253),U_15254)) = hAPP(hAPP(c_Nat_Ocompow(U_15251,U_15251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15253),U_15252)),U_15254),
    inference(clausify,[status(thm)],[f_3808_2]) ).

fof(f_3809_1,plain,
    ! [V_R_2,V_n_2,T_a] :
      ( c_Wellfounded_Owf(T_a,V_R_2)
      | ~ c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__exp]) ).

fof(f_3809_2,plain,
    ! [U_15257,U_15256,U_15255] :
      ( c_Wellfounded_Owf(U_15255,U_15257)
      | ~ c_Wellfounded_Owf(U_15255,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15255,U_15255),tc_HOL_Obool),U_15256),U_15257)) ),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

cnf(f_3809_3,plain,
    ( c_Wellfounded_Owf(U_15255,U_15257)
    | ~ c_Wellfounded_Owf(U_15255,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15255,U_15255),tc_HOL_Obool),U_15256),U_15257)) ),
    inference(clausify,[status(thm)],[f_3809_2]) ).

fof(f_3810_1,plain,
    ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__commute]) ).

fof(f_3810_2,plain,
    ! [U_15260,U_15259,U_15258] : hAPP(hAPP(c_Relation_Orel__comp(U_15258,U_15258,U_15258),U_15259),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15258,U_15258),tc_HOL_Obool),U_15260),U_15259)) = hAPP(hAPP(c_Relation_Orel__comp(U_15258,U_15258,U_15258),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15258,U_15258),tc_HOL_Obool),U_15260),U_15259)),U_15259),
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

cnf(f_3810_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15258,U_15258,U_15258),U_15259),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15258,U_15258),tc_HOL_Obool),U_15260),U_15259)) = hAPP(hAPP(c_Relation_Orel__comp(U_15258,U_15258,U_15258),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15258,U_15258),tc_HOL_Obool),U_15260),U_15259)),U_15259),
    inference(clausify,[status(thm)],[f_3810_2]) ).

fof(f_3811_1,plain,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3811_2,plain,
    ! [U_15262,U_15261] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15261,U_15261),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_15262) = U_15262,
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

cnf(f_3811_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15261,U_15261),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_15262) = U_15262,
    inference(clausify,[status(thm)],[f_3811_2]) ).

fof(f_3812_1,plain,
    ! [V_R_2,V_n_2,V_p_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl]) ).

fof(f_3812_2,plain,
    ! [U_15266,U_15265,U_15264,U_15263] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15263,U_15263)),U_15264),c_Transitive__Closure_Ortrancl(U_15263,U_15266)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15263,U_15263)),U_15264),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15263,U_15263),tc_HOL_Obool),U_15265),U_15266))) ),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

cnf(f_3812_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15263,U_15263)),U_15264),c_Transitive__Closure_Ortrancl(U_15263,U_15266)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15263,U_15263)),U_15264),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15263,U_15263),tc_HOL_Obool),U_15265),U_15266))) ),
    inference(clausify,[status(thm)],[f_3812_2]) ).

fof(f_3813_1,plain,
    ! [V_R_2,V_p_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
        | ! [B_n] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) )
      & ( ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__power]) ).

fof(f_3813_2,plain,
    ! [U_15271,U_15270,U_15269] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15269,U_15269)),U_15270),c_Transitive__Closure_Ortrancl(U_15269,U_15271)))
        | ! [U_15268] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15269,U_15269)),U_15270),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15269,U_15269),tc_HOL_Obool),U_15268),U_15271))) )
      & ( ? [U_15267] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15269,U_15269)),U_15270),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15269,U_15269),tc_HOL_Obool),U_15267),U_15271)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15269,U_15269)),U_15270),c_Transitive__Closure_Ortrancl(U_15269,U_15271))) ) ),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

fof(f_3813_3,plain,
    ( ! [U_15277,U_15275,U_15273] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),c_Transitive__Closure_Ortrancl(U_15273,U_15277)))
        | ! [U_15268] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15273,U_15273),tc_HOL_Obool),U_15268),U_15277))) )
    & ! [U_15276,U_15274,U_15272] :
        ( ? [U_15267] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15272,U_15272),tc_HOL_Obool),U_15267),U_15276)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),c_Transitive__Closure_Ortrancl(U_15272,U_15276))) ) ),
    inference(miniscope,[status(thm)],[f_3813_2]) ).

fof(f_3813_4,plain,
    ( ! [U_15277,U_15275,U_15273] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),c_Transitive__Closure_Ortrancl(U_15273,U_15277)))
        | ! [U_15268] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15273,U_15273),tc_HOL_Obool),U_15268),U_15277))) )
    & ! [U_15276,U_15274,U_15272] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15272,U_15272),tc_HOL_Obool),sK383(U_15276,U_15274,U_15272)),U_15276)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),c_Transitive__Closure_Ortrancl(U_15272,U_15276))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_15267,sK383(U_15276,U_15274,U_15272))],[f_3813_3]) ).

cnf(f_3813_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15272,U_15272),tc_HOL_Obool),sK383(U_15276,U_15274,U_15272)),U_15276)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15272)),U_15274),c_Transitive__Closure_Ortrancl(U_15272,U_15276))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),c_Transitive__Closure_Ortrancl(U_15273,U_15277)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15273)),U_15275),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15273,U_15273),tc_HOL_Obool),U_15268),U_15277))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

fof(f_3814_1,plain,
    ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(f_3814_2,plain,
    ! [U_15280,U_15279,U_15278] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15278,U_15278),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15279)),U_15280) = hAPP(hAPP(c_Relation_Orel__comp(U_15278,U_15278,U_15278),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15278,U_15278),tc_HOL_Obool),U_15279),U_15280)),U_15280),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

cnf(f_3814_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15278,U_15278),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15279)),U_15280) = hAPP(hAPP(c_Relation_Orel__comp(U_15278,U_15278,U_15278),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15278,U_15278),tc_HOL_Obool),U_15279),U_15280)),U_15280),
    inference(clausify,[status(thm)],[f_3814_2]) ).

fof(f_3815_1,plain,
    ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__add]) ).

fof(f_3815_2,plain,
    ! [U_15284,U_15283,U_15282,U_15281] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15282),U_15283)),U_15284) = hAPP(hAPP(c_Relation_Orel__comp(U_15281,U_15281,U_15281),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),U_15282),U_15284)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),U_15283),U_15284)),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

cnf(f_3815_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15282),U_15283)),U_15284) = hAPP(hAPP(c_Relation_Orel__comp(U_15281,U_15281,U_15281),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),U_15282),U_15284)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15281,U_15281),tc_HOL_Obool),U_15283),U_15284)),
    inference(clausify,[status(thm)],[f_3815_2]) ).

fof(f_3816_1,plain,
    ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(f_3816_2,plain,
    ! [U_15286,U_15285] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15285,U_15285),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15286) = c_Relation_OId(U_15285),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

cnf(f_3816_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15285,U_15285),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15286) = c_Relation_OId(U_15285),
    inference(clausify,[status(thm)],[f_3816_2]) ).

fof(f_3817_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3817_2,plain,
    ! [U_15290,U_15289,U_15288,U_15287] :
      ( U_15288 = U_15289
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15287,U_15287)),hAPP(hAPP(c_Product__Type_OPair(U_15287,U_15287),U_15288),U_15289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15287,U_15287),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15290))) ),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

fof(f_3817_3,plain,
    ! [U_15290,U_15289,U_15288] :
      ( ! [U_15287] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15287,U_15287)),hAPP(hAPP(c_Product__Type_OPair(U_15287,U_15287),U_15288),U_15289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15287,U_15287),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15290)))
      | U_15288 = U_15289 ),
    inference(miniscope,[status(thm)],[f_3817_2]) ).

cnf(f_3817_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15287,U_15287)),hAPP(hAPP(c_Product__Type_OPair(U_15287,U_15287),U_15288),U_15289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15287,U_15287),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15290)))
    | U_15288 = U_15289 ),
    inference(clausify,[status(thm)],[f_3817_3]) ).

fof(f_3818_1,plain,
    ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3818_2,plain,
    ! [U_15293,U_15292,U_15291] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15291,U_15291)),hAPP(hAPP(c_Product__Type_OPair(U_15291,U_15291),U_15292),U_15292)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15291,U_15291),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15293))),
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

cnf(f_3818_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_15291,U_15291)),hAPP(hAPP(c_Product__Type_OPair(U_15291,U_15291),U_15292),U_15292)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15291,U_15291),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15293))),
    inference(clausify,[status(thm)],[f_3818_2]) ).

fof(f_3819_1,plain,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2]) ).

fof(f_3819_2,plain,
    ! [U_15299,U_15298,U_15297,U_15296,U_15295,U_15294] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15295),U_15298)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15294,U_15294),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15299)),U_15297)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15296),U_15298)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15294,U_15294),tc_HOL_Obool),U_15299),U_15297)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15295),U_15296)),U_15297)) ),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

cnf(f_3819_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15295),U_15298)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15294,U_15294),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15299)),U_15297)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15296),U_15298)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15294,U_15294),tc_HOL_Obool),U_15299),U_15297)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15294,U_15294)),hAPP(hAPP(c_Product__Type_OPair(U_15294,U_15294),U_15295),U_15296)),U_15297)) ),
    inference(clausify,[status(thm)],[f_3819_2]) ).

fof(f_3820_1,plain,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I]) ).

fof(f_3820_2,plain,
    ! [U_15305,U_15304,U_15303,U_15302,U_15301,U_15300] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15301),U_15305)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15300,U_15300),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15303)),U_15304)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15302),U_15305)),U_15304))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15301),U_15302)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15300,U_15300),tc_HOL_Obool),U_15303),U_15304))) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

cnf(f_3820_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15301),U_15305)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15300,U_15300),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15303)),U_15304)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15302),U_15305)),U_15304))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15300,U_15300)),hAPP(hAPP(c_Product__Type_OPair(U_15300,U_15300),U_15301),U_15302)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15300,U_15300),tc_HOL_Obool),U_15303),U_15304))) ),
    inference(clausify,[status(thm)],[f_3820_2]) ).

fof(f_3821_1,plain,
    ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(f_3821_2,plain,
    ! [U_15308,U_15307,U_15306] : hAPP(hAPP(c_Nat_Ocompow(U_15306,U_15306),hAPP(c_Nat_OSuc,U_15307)),U_15308) = hAPP(c_Fun_Ocomp(U_15306,U_15306,U_15306,U_15308),hAPP(hAPP(c_Nat_Ocompow(U_15306,U_15306),U_15307),U_15308)),
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

cnf(f_3821_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15306,U_15306),hAPP(c_Nat_OSuc,U_15307)),U_15308) = hAPP(c_Fun_Ocomp(U_15306,U_15306,U_15306,U_15308),hAPP(hAPP(c_Nat_Ocompow(U_15306,U_15306),U_15307),U_15308)),
    inference(clausify,[status(thm)],[f_3821_2]) ).

fof(f_3822_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__add]) ).

fof(f_3822_2,plain,
    ! [U_15312,U_15311,U_15310,U_15309] : hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15310),U_15311)),U_15312) = hAPP(c_Fun_Ocomp(U_15309,U_15309,U_15309,hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),U_15310),U_15312)),hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),U_15311),U_15312)),
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

cnf(f_3822_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15310),U_15311)),U_15312) = hAPP(c_Fun_Ocomp(U_15309,U_15309,U_15309,hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),U_15310),U_15312)),hAPP(hAPP(c_Nat_Ocompow(U_15309,U_15309),U_15311),U_15312)),
    inference(clausify,[status(thm)],[f_3822_2]) ).

fof(f_3823_1,plain,
    ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(f_3823_2,plain,
    ! [U_15314,U_15313] : hAPP(hAPP(c_Nat_Ocompow(U_15313,U_15313),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15314) = c_Fun_Oid(U_15313),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

cnf(f_3823_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15313,U_15313),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15314) = c_Fun_Oid(U_15313),
    inference(clausify,[status(thm)],[f_3823_2]) ).

fof(f_3824_1,plain,
    ! [V_R_2,V_p_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
        | ! [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__power]) ).

fof(f_3824_2,plain,
    ! [U_15319,U_15318,U_15317] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15317,U_15317)),U_15318),c_Transitive__Closure_Otrancl(U_15317,U_15319)))
        | ! [U_15316] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15317,U_15317)),U_15318),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15317,U_15317),tc_HOL_Obool),U_15316),U_15319)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15316)) ) )
      & ( ? [U_15315] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15317,U_15317)),U_15318),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15317,U_15317),tc_HOL_Obool),U_15315),U_15319)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15315)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15317,U_15317)),U_15318),c_Transitive__Closure_Otrancl(U_15317,U_15319))) ) ),
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

fof(f_3824_3,plain,
    ( ! [U_15325,U_15323,U_15321] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),c_Transitive__Closure_Otrancl(U_15321,U_15325)))
        | ! [U_15316] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15321,U_15321),tc_HOL_Obool),U_15316),U_15325)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15316)) ) )
    & ! [U_15324,U_15322,U_15320] :
        ( ? [U_15315] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15320,U_15320),tc_HOL_Obool),U_15315),U_15324)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15315)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),c_Transitive__Closure_Otrancl(U_15320,U_15324))) ) ),
    inference(miniscope,[status(thm)],[f_3824_2]) ).

fof(f_3824_4,plain,
    ( ! [U_15325,U_15323,U_15321] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),c_Transitive__Closure_Otrancl(U_15321,U_15325)))
        | ! [U_15316] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15321,U_15321),tc_HOL_Obool),U_15316),U_15325)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15316)) ) )
    & ! [U_15324,U_15322,U_15320] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15320,U_15320),tc_HOL_Obool),sK384(U_15324,U_15322,U_15320)),U_15324)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK384(U_15324,U_15322,U_15320))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),c_Transitive__Closure_Otrancl(U_15320,U_15324))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_15315,sK384(U_15324,U_15322,U_15320))],[f_3824_3]) ).

cnf(f_3824_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK384(U_15324,U_15322,U_15320)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),c_Transitive__Closure_Otrancl(U_15320,U_15324))) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

cnf(f_3824_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15320,U_15320),tc_HOL_Obool),sK384(U_15324,U_15322,U_15320)),U_15324)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15320,U_15320)),U_15322),c_Transitive__Closure_Otrancl(U_15320,U_15324))) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

cnf(f_3824_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),c_Transitive__Closure_Otrancl(U_15321,U_15325)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15321,U_15321)),U_15323),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15321,U_15321),tc_HOL_Obool),U_15316),U_15325)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15316)) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

fof(f_3825_1,plain,
    ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(f_3825_2,plain,
    ! [U_15327,U_15326] : c_Transitive__Closure_Ortrancl(U_15326,U_15327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15326,U_15326),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_15326,U_15326),tc_HOL_Obool),tc_fun(tc_prod(U_15326,U_15326),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15326,U_15326),tc_HOL_Obool)),U_15327)),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

cnf(f_3825_3,plain,
    c_Transitive__Closure_Ortrancl(U_15326,U_15327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15326,U_15326),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_15326,U_15326),tc_HOL_Obool),tc_fun(tc_prod(U_15326,U_15326),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15326,U_15326),tc_HOL_Obool)),U_15327)),
    inference(clausify,[status(thm)],[f_3825_2]) ).

fof(f_3826_1,plain,
    ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a),
    inference(fof_nnf,[status(thm)],[fact_funpow__code__def]) ).

fof(f_3826_2,plain,
    ! [U_15328] : c_Nat_Ofunpow(U_15328) = c_Nat_Ocompow(U_15328,U_15328),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

cnf(f_3826_3,plain,
    c_Nat_Ofunpow(U_15328) = c_Nat_Ocompow(U_15328,U_15328),
    inference(clausify,[status(thm)],[f_3826_2]) ).

fof(f_3827_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E]) ).

fof(f_3827_2,plain,
    ! [U_15335,U_15334,U_15333,U_15332,U_15331] :
      ( ? [U_15330,U_15329] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15330),U_15333)),U_15335))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15330)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15329),U_15335)))
          & U_15334 = hAPP(c_Nat_OSuc,U_15329) )
      | ( U_15332 = U_15333
        & U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

fof(f_3827_3,plain,
    ! [U_15335,U_15334,U_15333,U_15332,U_15331] :
      ( ? [U_15329] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),sK385(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15333)),U_15335))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),sK385(U_15335,U_15334,U_15333,U_15332,U_15331))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15329),U_15335)))
          & U_15334 = hAPP(c_Nat_OSuc,U_15329) )
      | ( U_15332 = U_15333
        & U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_15330,sK385(U_15335,U_15334,U_15333,U_15332,U_15331))],[f_3827_2]) ).

fof(f_3827_4,plain,
    ! [U_15335,U_15334,U_15333,U_15332,U_15331] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),sK385(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15333)),U_15335))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),sK385(U_15335,U_15334,U_15333,U_15332,U_15331))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),sK386(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15335)))
        & U_15334 = hAPP(c_Nat_OSuc,sK386(U_15335,U_15334,U_15333,U_15332,U_15331)) )
      | ( U_15332 = U_15333
        & U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_15329,sK386(U_15335,U_15334,U_15333,U_15332,U_15331))],[f_3827_3]) ).

cnf(f_3827_5,plain,
    ( U_15334 = hAPP(c_Nat_OSuc,sK386(U_15335,U_15334,U_15333,U_15332,U_15331))
    | U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

cnf(f_3827_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),sK385(U_15335,U_15334,U_15333,U_15332,U_15331))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),sK386(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15335)))
    | U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

cnf(f_3827_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),sK385(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15333)),U_15335))
    | U_15334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

cnf(f_3827_8,plain,
    ( U_15334 = hAPP(c_Nat_OSuc,sK386(U_15335,U_15334,U_15333,U_15332,U_15331))
    | U_15332 = U_15333
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

cnf(f_3827_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),sK385(U_15335,U_15334,U_15333,U_15332,U_15331))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),sK386(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15335)))
    | U_15332 = U_15333
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

cnf(f_3827_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),sK385(U_15335,U_15334,U_15333,U_15332,U_15331)),U_15333)),U_15335))
    | U_15332 = U_15333
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15331,U_15331)),hAPP(hAPP(c_Product__Type_OPair(U_15331,U_15331),U_15332),U_15333)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15331,U_15331),tc_HOL_Obool),U_15334),U_15335))) ),
    inference(clausify,[status(thm)],[f_3827_4]) ).

fof(f_3828_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E2]) ).

fof(f_3828_2,plain,
    ! [U_15342,U_15341,U_15340,U_15339,U_15338] :
      ( ? [U_15337,U_15336] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15337),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15336),U_15342)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15337)),U_15342))
          & U_15341 = hAPP(c_Nat_OSuc,U_15336) )
      | ( U_15339 = U_15340
        & U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

fof(f_3828_3,plain,
    ! [U_15342,U_15341,U_15340,U_15339,U_15338] :
      ( ? [U_15336] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),sK387(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15336),U_15342)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),sK387(U_15342,U_15341,U_15340,U_15339,U_15338))),U_15342))
          & U_15341 = hAPP(c_Nat_OSuc,U_15336) )
      | ( U_15339 = U_15340
        & U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_15337,sK387(U_15342,U_15341,U_15340,U_15339,U_15338))],[f_3828_2]) ).

fof(f_3828_4,plain,
    ! [U_15342,U_15341,U_15340,U_15339,U_15338] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),sK387(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),sK388(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15342)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),sK387(U_15342,U_15341,U_15340,U_15339,U_15338))),U_15342))
        & U_15341 = hAPP(c_Nat_OSuc,sK388(U_15342,U_15341,U_15340,U_15339,U_15338)) )
      | ( U_15339 = U_15340
        & U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_15336,sK388(U_15342,U_15341,U_15340,U_15339,U_15338))],[f_3828_3]) ).

cnf(f_3828_5,plain,
    ( U_15341 = hAPP(c_Nat_OSuc,sK388(U_15342,U_15341,U_15340,U_15339,U_15338))
    | U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

cnf(f_3828_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),sK387(U_15342,U_15341,U_15340,U_15339,U_15338))),U_15342))
    | U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

cnf(f_3828_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),sK387(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),sK388(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15342)))
    | U_15341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

cnf(f_3828_8,plain,
    ( U_15341 = hAPP(c_Nat_OSuc,sK388(U_15342,U_15341,U_15340,U_15339,U_15338))
    | U_15339 = U_15340
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

cnf(f_3828_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),sK387(U_15342,U_15341,U_15340,U_15339,U_15338))),U_15342))
    | U_15339 = U_15340
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

cnf(f_3828_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),sK387(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),sK388(U_15342,U_15341,U_15340,U_15339,U_15338)),U_15342)))
    | U_15339 = U_15340
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15338,U_15338)),hAPP(hAPP(c_Product__Type_OPair(U_15338,U_15338),U_15339),U_15340)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15338,U_15338),tc_HOL_Obool),U_15341),U_15342))) ),
    inference(clausify,[status(thm)],[f_3828_4]) ).

fof(f_3829_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).

fof(f_3829_2,plain,
    ! [U_15349,U_15348,U_15347,U_15346,U_15345] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
      | ? [U_15344] :
          ( ? [U_15343] :
              ( U_15344 != U_15343
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15344),U_15343)),U_15349)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15344)),c_Transitive__Closure_Ortrancl(U_15345,U_15348))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

fof(f_3829_3,plain,
    ! [U_15349,U_15348,U_15347,U_15346,U_15345] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
      | ( ? [U_15343] :
            ( sK389(U_15349,U_15348,U_15347,U_15346,U_15345) != U_15343
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),sK389(U_15349,U_15348,U_15347,U_15346,U_15345)),U_15343)),U_15349)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),sK389(U_15349,U_15348,U_15347,U_15346,U_15345))),c_Transitive__Closure_Ortrancl(U_15345,U_15348))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_15344,sK389(U_15349,U_15348,U_15347,U_15346,U_15345))],[f_3829_2]) ).

fof(f_3829_4,plain,
    ! [U_15349,U_15348,U_15347,U_15346,U_15345] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
      | ( sK389(U_15349,U_15348,U_15347,U_15346,U_15345) != sK390(U_15349,U_15348,U_15347,U_15346,U_15345)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),sK389(U_15349,U_15348,U_15347,U_15346,U_15345)),sK390(U_15349,U_15348,U_15347,U_15346,U_15345))),U_15349))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),sK389(U_15349,U_15348,U_15347,U_15346,U_15345))),c_Transitive__Closure_Ortrancl(U_15345,U_15348))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_15343,sK390(U_15349,U_15348,U_15347,U_15346,U_15345))],[f_3829_3]) ).

cnf(f_3829_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),sK389(U_15349,U_15348,U_15347,U_15346,U_15345))),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

cnf(f_3829_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),sK389(U_15349,U_15348,U_15347,U_15346,U_15345)),sK390(U_15349,U_15348,U_15347,U_15346,U_15345))),U_15349))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

cnf(f_3829_7,plain,
    ( sK389(U_15349,U_15348,U_15347,U_15346,U_15345) != sK390(U_15349,U_15348,U_15347,U_15346,U_15345)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,U_15348)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15345,U_15345)),hAPP(hAPP(c_Product__Type_OPair(U_15345,U_15345),U_15346),U_15347)),c_Transitive__Closure_Ortrancl(U_15345,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15345,U_15345),tc_HOL_Obool)),U_15348),U_15349)))) ),
    inference(clausify,[status(thm)],[f_3829_4]) ).

fof(f_3830_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_y != B_x
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).

fof(f_3830_2,plain,
    ! [U_15356,U_15355,U_15354,U_15353,U_15352] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
      | ? [U_15351] :
          ( ? [U_15350] :
              ( U_15350 != U_15351
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15350),U_15351)),U_15356)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15351),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

fof(f_3830_3,plain,
    ! [U_15356,U_15355,U_15354,U_15353,U_15352] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
      | ( ? [U_15350] :
            ( U_15350 != sK391(U_15356,U_15355,U_15354,U_15353,U_15352)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15350),sK391(U_15356,U_15355,U_15354,U_15353,U_15352))),U_15356)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),sK391(U_15356,U_15355,U_15354,U_15353,U_15352)),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_15351,sK391(U_15356,U_15355,U_15354,U_15353,U_15352))],[f_3830_2]) ).

fof(f_3830_4,plain,
    ! [U_15356,U_15355,U_15354,U_15353,U_15352] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
      | ( sK392(U_15356,U_15355,U_15354,U_15353,U_15352) != sK391(U_15356,U_15355,U_15354,U_15353,U_15352)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),sK392(U_15356,U_15355,U_15354,U_15353,U_15352)),sK391(U_15356,U_15355,U_15354,U_15353,U_15352))),U_15356))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),sK391(U_15356,U_15355,U_15354,U_15353,U_15352)),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_15350,sK392(U_15356,U_15355,U_15354,U_15353,U_15352))],[f_3830_3]) ).

cnf(f_3830_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),sK391(U_15356,U_15355,U_15354,U_15353,U_15352)),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

cnf(f_3830_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),sK392(U_15356,U_15355,U_15354,U_15353,U_15352)),sK391(U_15356,U_15355,U_15354,U_15353,U_15352))),U_15356))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

cnf(f_3830_7,plain,
    ( sK392(U_15356,U_15355,U_15354,U_15353,U_15352) != sK391(U_15356,U_15355,U_15354,U_15353,U_15352)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,U_15355)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15352,U_15352)),hAPP(hAPP(c_Product__Type_OPair(U_15352,U_15352),U_15353),U_15354)),c_Transitive__Closure_Ortrancl(U_15352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15352,U_15352),tc_HOL_Obool)),U_15355),U_15356)))) ),
    inference(clausify,[status(thm)],[f_3830_4]) ).

fof(f_3831_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3831_2,plain,
    ! [U_15362,U_15361,U_15360,U_15359,U_15358] :
      ( ? [U_15357] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15357),U_15360)),U_15362))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),U_15357)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),U_15361),U_15362))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),U_15360)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15361)),U_15362))) ),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

fof(f_3831_3,plain,
    ! [U_15362,U_15361,U_15360,U_15359,U_15358] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),sK393(U_15362,U_15361,U_15360,U_15359,U_15358)),U_15360)),U_15362))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),sK393(U_15362,U_15361,U_15360,U_15359,U_15358))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),U_15361),U_15362))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),U_15360)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15361)),U_15362))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_15357,sK393(U_15362,U_15361,U_15360,U_15359,U_15358))],[f_3831_2]) ).

cnf(f_3831_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),sK393(U_15362,U_15361,U_15360,U_15359,U_15358))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),U_15361),U_15362)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),U_15360)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15361)),U_15362))) ),
    inference(clausify,[status(thm)],[f_3831_3]) ).

cnf(f_3831_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),sK393(U_15362,U_15361,U_15360,U_15359,U_15358)),U_15360)),U_15362))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15358,U_15358)),hAPP(hAPP(c_Product__Type_OPair(U_15358,U_15358),U_15359),U_15360)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15358,U_15358),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15361)),U_15362))) ),
    inference(clausify,[status(thm)],[f_3831_3]) ).

fof(f_3832_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3832_2,plain,
    ! [U_15368,U_15367,U_15366,U_15365,U_15364] :
      ( ? [U_15363] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15363),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),U_15367),U_15368)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),U_15363)),U_15368)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15367)),U_15368))) ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

fof(f_3832_3,plain,
    ! [U_15368,U_15367,U_15366,U_15365,U_15364] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),sK394(U_15368,U_15367,U_15366,U_15365,U_15364)),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),U_15367),U_15368)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),sK394(U_15368,U_15367,U_15366,U_15365,U_15364))),U_15368)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15367)),U_15368))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_15363,sK394(U_15368,U_15367,U_15366,U_15365,U_15364))],[f_3832_2]) ).

cnf(f_3832_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),sK394(U_15368,U_15367,U_15366,U_15365,U_15364))),U_15368))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15367)),U_15368))) ),
    inference(clausify,[status(thm)],[f_3832_3]) ).

cnf(f_3832_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),sK394(U_15368,U_15367,U_15366,U_15365,U_15364)),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),U_15367),U_15368)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15364,U_15364)),hAPP(hAPP(c_Product__Type_OPair(U_15364,U_15364),U_15365),U_15366)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15364,U_15364),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15367)),U_15368))) ),
    inference(clausify,[status(thm)],[f_3832_3]) ).

fof(f_3833_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_3833_2,plain,
    ! [U_15374,U_15373,U_15372,U_15371,U_15370] :
      ( ? [U_15369] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15369),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),U_15373),U_15374)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),U_15369)),U_15374)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15373)),U_15374))) ),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

fof(f_3833_3,plain,
    ! [U_15374,U_15373,U_15372,U_15371,U_15370] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),sK395(U_15374,U_15373,U_15372,U_15371,U_15370)),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),U_15373),U_15374)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),sK395(U_15374,U_15373,U_15372,U_15371,U_15370))),U_15374)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15373)),U_15374))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_15369,sK395(U_15374,U_15373,U_15372,U_15371,U_15370))],[f_3833_2]) ).

cnf(f_3833_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),sK395(U_15374,U_15373,U_15372,U_15371,U_15370))),U_15374))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15373)),U_15374))) ),
    inference(clausify,[status(thm)],[f_3833_3]) ).

cnf(f_3833_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),sK395(U_15374,U_15373,U_15372,U_15371,U_15370)),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),U_15373),U_15374)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15370,U_15370)),hAPP(hAPP(c_Product__Type_OPair(U_15370,U_15370),U_15371),U_15372)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15370,U_15370),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15373)),U_15374))) ),
    inference(clausify,[status(thm)],[f_3833_3]) ).

fof(f_3834_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD2]) ).

fof(f_3834_2,plain,
    ! [U_15379,U_15378,U_15377,U_15376] :
      ( ? [U_15375] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15375),U_15378)),U_15379))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),U_15375)),c_Transitive__Closure_Ortrancl(U_15376,U_15379))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),U_15378)),c_Transitive__Closure_Otrancl(U_15376,U_15379))) ),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

fof(f_3834_3,plain,
    ! [U_15379,U_15378,U_15377,U_15376] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),sK396(U_15379,U_15378,U_15377,U_15376)),U_15378)),U_15379))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),sK396(U_15379,U_15378,U_15377,U_15376))),c_Transitive__Closure_Ortrancl(U_15376,U_15379))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),U_15378)),c_Transitive__Closure_Otrancl(U_15376,U_15379))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_15375,sK396(U_15379,U_15378,U_15377,U_15376))],[f_3834_2]) ).

cnf(f_3834_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),sK396(U_15379,U_15378,U_15377,U_15376))),c_Transitive__Closure_Ortrancl(U_15376,U_15379)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),U_15378)),c_Transitive__Closure_Otrancl(U_15376,U_15379))) ),
    inference(clausify,[status(thm)],[f_3834_3]) ).

cnf(f_3834_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),sK396(U_15379,U_15378,U_15377,U_15376)),U_15378)),U_15379))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15376,U_15376)),hAPP(hAPP(c_Product__Type_OPair(U_15376,U_15376),U_15377),U_15378)),c_Transitive__Closure_Otrancl(U_15376,U_15379))) ),
    inference(clausify,[status(thm)],[f_3834_3]) ).

fof(f_3835_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_a] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD]) ).

fof(f_3835_2,plain,
    ! [U_15384,U_15383,U_15382,U_15381] :
      ( ? [U_15380] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15380),U_15383)),c_Transitive__Closure_Ortrancl(U_15381,U_15384)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),U_15380)),U_15384)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),U_15383)),c_Transitive__Closure_Otrancl(U_15381,U_15384))) ),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

fof(f_3835_3,plain,
    ! [U_15384,U_15383,U_15382,U_15381] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),sK397(U_15384,U_15383,U_15382,U_15381)),U_15383)),c_Transitive__Closure_Ortrancl(U_15381,U_15384)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),sK397(U_15384,U_15383,U_15382,U_15381))),U_15384)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),U_15383)),c_Transitive__Closure_Otrancl(U_15381,U_15384))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_15380,sK397(U_15384,U_15383,U_15382,U_15381))],[f_3835_2]) ).

cnf(f_3835_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),sK397(U_15384,U_15383,U_15382,U_15381))),U_15384))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),U_15383)),c_Transitive__Closure_Otrancl(U_15381,U_15384))) ),
    inference(clausify,[status(thm)],[f_3835_3]) ).

cnf(f_3835_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),sK397(U_15384,U_15383,U_15382,U_15381)),U_15383)),c_Transitive__Closure_Ortrancl(U_15381,U_15384)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15381,U_15381)),hAPP(hAPP(c_Product__Type_OPair(U_15381,U_15381),U_15382),U_15383)),c_Transitive__Closure_Otrancl(U_15381,U_15384))) ),
    inference(clausify,[status(thm)],[f_3835_3]) ).

fof(f_3836_1,plain,
    ! [V_p_2,T_a] :
      ( ? [B_x] : V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) ),
    inference(fof_nnf,[status(thm)],[fact_IdE]) ).

fof(f_3836_2,plain,
    ! [U_15387,U_15386] :
      ( ? [U_15385] : U_15387 = hAPP(hAPP(c_Product__Type_OPair(U_15386,U_15386),U_15385),U_15385)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15386,U_15386)),U_15387),c_Relation_OId(U_15386))) ),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

fof(f_3836_3,plain,
    ! [U_15387,U_15386] :
      ( U_15387 = hAPP(hAPP(c_Product__Type_OPair(U_15386,U_15386),sK398(U_15387,U_15386)),sK398(U_15387,U_15386))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15386,U_15386)),U_15387),c_Relation_OId(U_15386))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_15385,sK398(U_15387,U_15386))],[f_3836_2]) ).

cnf(f_3836_4,plain,
    ( U_15387 = hAPP(hAPP(c_Product__Type_OPair(U_15386,U_15386),sK398(U_15387,U_15386)),sK398(U_15387,U_15386))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15386,U_15386)),U_15387),c_Relation_OId(U_15386))) ),
    inference(clausify,[status(thm)],[f_3836_3]) ).

fof(f_3837_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_3837_2,plain,
    ! [U_15390,U_15389,U_15388] :
      ( U_15389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_15388),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_15388),U_15389),U_15390)),U_15390)),c_Divides_Odiv__class_Omod(U_15388,U_15389,U_15390))
      | ~ class_Divides_Osemiring__div(U_15388) ),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

cnf(f_3837_3,plain,
    ( U_15389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_15388),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_15388),U_15389),U_15390)),U_15390)),c_Divides_Odiv__class_Omod(U_15388,U_15389,U_15390))
    | ~ class_Divides_Osemiring__div(U_15388) ),
    inference(clausify,[status(thm)],[f_3837_2]) ).

fof(f_3838_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Owf(T_a,V_r_2)
        | ? [B_Q] :
            ( ! [B_x] :
                ( ? [B_y] :
                    ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
            & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) ) )
      & ( ! [B_Q] :
            ( ? [B_x] :
                ( ! [B_y] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) )
                & hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
            | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) )
        | ~ c_Wellfounded_Owf(T_a,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__eq__minimal]) ).

fof(f_3838_2,plain,
    ! [U_15400,U_15399] :
      ( ( c_Wellfounded_Owf(U_15399,U_15400)
        | ? [U_15398] :
            ( ! [U_15397] :
                ( ? [U_15396] :
                    ( hBOOL(hAPP(hAPP(c_member(U_15399),U_15396),U_15398))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15399,U_15399)),hAPP(hAPP(c_Product__Type_OPair(U_15399,U_15399),U_15396),U_15397)),U_15400)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15397),U_15398)) )
            & ? [U_15395] : hBOOL(hAPP(hAPP(c_member(U_15399),U_15395),U_15398)) ) )
      & ( ! [U_15394] :
            ( ? [U_15393] :
                ( ! [U_15392] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15392),U_15394))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15399,U_15399)),hAPP(hAPP(c_Product__Type_OPair(U_15399,U_15399),U_15392),U_15393)),U_15400)) )
                & hBOOL(hAPP(hAPP(c_member(U_15399),U_15393),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15399,U_15400) ) ),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

fof(f_3838_3,plain,
    ( ! [U_15404,U_15402] :
        ( c_Wellfounded_Owf(U_15402,U_15404)
        | ? [U_15398] :
            ( ! [U_15397] :
                ( ? [U_15396] :
                    ( hBOOL(hAPP(hAPP(c_member(U_15402),U_15396),U_15398))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),U_15396),U_15397)),U_15404)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),U_15398)) )
            & ? [U_15395] : hBOOL(hAPP(hAPP(c_member(U_15402),U_15395),U_15398)) ) )
    & ! [U_15403,U_15401] :
        ( ! [U_15394] :
            ( ? [U_15393] :
                ( ! [U_15392] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),U_15393)),U_15403)) )
                & hBOOL(hAPP(hAPP(c_member(U_15401),U_15393),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15401,U_15403) ) ),
    inference(miniscope,[status(thm)],[f_3838_2]) ).

fof(f_3838_4,plain,
    ( ! [U_15404,U_15402] :
        ( c_Wellfounded_Owf(U_15402,U_15404)
        | ? [U_15398] :
            ( ! [U_15397] :
                ( ? [U_15396] :
                    ( hBOOL(hAPP(hAPP(c_member(U_15402),U_15396),U_15398))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),U_15396),U_15397)),U_15404)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),U_15398)) )
            & ? [U_15395] : hBOOL(hAPP(hAPP(c_member(U_15402),U_15395),U_15398)) ) )
    & ! [U_15403,U_15401] :
        ( ! [U_15394] :
            ( ( ! [U_15392] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),sK399(U_15403,U_15401,U_15394))),U_15403)) )
              & hBOOL(hAPP(hAPP(c_member(U_15401),sK399(U_15403,U_15401,U_15394)),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15401,U_15403) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_15393,sK399(U_15403,U_15401,U_15394))],[f_3838_3]) ).

fof(f_3838_5,plain,
    ( ! [U_15404,U_15402] :
        ( c_Wellfounded_Owf(U_15402,U_15404)
        | ( ! [U_15397] :
              ( ? [U_15396] :
                  ( hBOOL(hAPP(hAPP(c_member(U_15402),U_15396),sK400(U_15404,U_15402)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),U_15396),U_15397)),U_15404)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),sK400(U_15404,U_15402))) )
          & ? [U_15395] : hBOOL(hAPP(hAPP(c_member(U_15402),U_15395),sK400(U_15404,U_15402))) ) )
    & ! [U_15403,U_15401] :
        ( ! [U_15394] :
            ( ( ! [U_15392] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),sK399(U_15403,U_15401,U_15394))),U_15403)) )
              & hBOOL(hAPP(hAPP(c_member(U_15401),sK399(U_15403,U_15401,U_15394)),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15401,U_15403) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_15398,sK400(U_15404,U_15402))],[f_3838_4]) ).

fof(f_3838_6,plain,
    ( ! [U_15404,U_15402] :
        ( c_Wellfounded_Owf(U_15402,U_15404)
        | ( ! [U_15397] :
              ( ? [U_15396] :
                  ( hBOOL(hAPP(hAPP(c_member(U_15402),U_15396),sK400(U_15404,U_15402)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),U_15396),U_15397)),U_15404)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),sK400(U_15404,U_15402))) )
          & hBOOL(hAPP(hAPP(c_member(U_15402),sK401(U_15404,U_15402)),sK400(U_15404,U_15402))) ) )
    & ! [U_15403,U_15401] :
        ( ! [U_15394] :
            ( ( ! [U_15392] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),sK399(U_15403,U_15401,U_15394))),U_15403)) )
              & hBOOL(hAPP(hAPP(c_member(U_15401),sK399(U_15403,U_15401,U_15394)),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15401,U_15403) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15395,sK401(U_15404,U_15402))],[f_3838_5]) ).

fof(f_3838_7,plain,
    ( ! [U_15404,U_15402] :
        ( c_Wellfounded_Owf(U_15402,U_15404)
        | ( ! [U_15397] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_15402),sK402(U_15404,U_15402,U_15397)),sK400(U_15404,U_15402)))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),sK402(U_15404,U_15402,U_15397)),U_15397)),U_15404)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),sK400(U_15404,U_15402))) )
          & hBOOL(hAPP(hAPP(c_member(U_15402),sK401(U_15404,U_15402)),sK400(U_15404,U_15402))) ) )
    & ! [U_15403,U_15401] :
        ( ! [U_15394] :
            ( ( ! [U_15392] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),sK399(U_15403,U_15401,U_15394))),U_15403)) )
              & hBOOL(hAPP(hAPP(c_member(U_15401),sK399(U_15403,U_15401,U_15394)),U_15394)) )
            | ! [U_15391] : ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394)) )
        | ~ c_Wellfounded_Owf(U_15401,U_15403) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15396,sK402(U_15404,U_15402,U_15397))],[f_3838_6]) ).

cnf(f_3838_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15401),sK399(U_15403,U_15401,U_15394)),U_15394))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394))
    | ~ c_Wellfounded_Owf(U_15401,U_15403) ),
    inference(clausify,[status(thm)],[f_3838_7]) ).

cnf(f_3838_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15392),U_15394))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15401,U_15401)),hAPP(hAPP(c_Product__Type_OPair(U_15401,U_15401),U_15392),sK399(U_15403,U_15401,U_15394))),U_15403))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15401),U_15391),U_15394))
    | ~ c_Wellfounded_Owf(U_15401,U_15403) ),
    inference(clausify,[status(thm)],[f_3838_7]) ).

cnf(f_3838_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15402),sK401(U_15404,U_15402)),sK400(U_15404,U_15402)))
    | c_Wellfounded_Owf(U_15402,U_15404) ),
    inference(clausify,[status(thm)],[f_3838_7]) ).

cnf(f_3838_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15402,U_15402)),hAPP(hAPP(c_Product__Type_OPair(U_15402,U_15402),sK402(U_15404,U_15402,U_15397)),U_15397)),U_15404))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),sK400(U_15404,U_15402)))
    | c_Wellfounded_Owf(U_15402,U_15404) ),
    inference(clausify,[status(thm)],[f_3838_7]) ).

cnf(f_3838_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15402),sK402(U_15404,U_15402,U_15397)),sK400(U_15404,U_15402)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15397),sK400(U_15404,U_15402)))
    | c_Wellfounded_Owf(U_15402,U_15404) ),
    inference(clausify,[status(thm)],[f_3838_7]) ).

fof(f_3839_1,plain,
    ! [V_P_H_2,V_P_2] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2))
      | ? [B_x] :
          ( ( ( ~ hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(V_P_H_2,B_x)) )
            | ( ~ hBOOL(hAPP(V_P_H_2,B_x))
              & hBOOL(hAPP(V_P_2,B_x)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong]) ).

fof(f_3839_2,plain,
    ! [U_15407,U_15406] :
      ( 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_15406)) = 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_15407))
      | ? [U_15405] :
          ( ( ( ~ hBOOL(hAPP(U_15406,U_15405))
              & hBOOL(hAPP(U_15407,U_15405)) )
            | ( ~ hBOOL(hAPP(U_15407,U_15405))
              & hBOOL(hAPP(U_15406,U_15405)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_15405)) ) ),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

fof(f_3839_3,plain,
    ! [U_15407,U_15406] :
      ( 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_15406)) = 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_15407))
      | ( ( ( ~ hBOOL(hAPP(U_15406,sK403(U_15407,U_15406)))
            & hBOOL(hAPP(U_15407,sK403(U_15407,U_15406))) )
          | ( ~ hBOOL(hAPP(U_15407,sK403(U_15407,U_15406)))
            & hBOOL(hAPP(U_15406,sK403(U_15407,U_15406))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK403(U_15407,U_15406))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15405,sK403(U_15407,U_15406))],[f_3839_2]) ).

cnf(f_3839_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK403(U_15407,U_15406)))
    | 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_15406)) = 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_15407)) ),
    inference(clausify,[status(thm)],[f_3839_3]) ).

cnf(f_3839_5,plain,
    ( hBOOL(hAPP(U_15407,sK403(U_15407,U_15406)))
    | hBOOL(hAPP(U_15406,sK403(U_15407,U_15406)))
    | 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_15406)) = 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_15407)) ),
    inference(clausify,[status(thm)],[f_3839_3]) ).

cnf(f_3839_6,plain,
    ( ~ hBOOL(hAPP(U_15406,sK403(U_15407,U_15406)))
    | hBOOL(hAPP(U_15406,sK403(U_15407,U_15406)))
    | 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_15406)) = 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_15407)) ),
    inference(clausify,[status(thm)],[f_3839_3]) ).

cnf(f_3839_7,plain,
    ( hBOOL(hAPP(U_15407,sK403(U_15407,U_15406)))
    | ~ hBOOL(hAPP(U_15407,sK403(U_15407,U_15406)))
    | 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_15406)) = 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_15407)) ),
    inference(clausify,[status(thm)],[f_3839_3]) ).

cnf(f_3839_8,plain,
    ( ~ hBOOL(hAPP(U_15406,sK403(U_15407,U_15406)))
    | ~ hBOOL(hAPP(U_15407,sK403(U_15407,U_15406)))
    | 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_15406)) = 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_15407)) ),
    inference(clausify,[status(thm)],[f_3839_3]) ).

fof(f_3840_1,plain,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Q_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).

fof(f_3840_2,plain,
    ! [U_15413,U_15412,U_15411,U_15410,U_15409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15410),hAPP(c_Set_OCollect(U_15409),U_15412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15411),hAPP(c_Set_OCollect(U_15409),U_15413))))
      | ? [U_15408] :
          ( ~ hBOOL(hAPP(U_15413,U_15408))
          & hBOOL(hAPP(U_15412,U_15408))
          & hBOOL(hAPP(hAPP(c_member(U_15409),U_15408),U_15410)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),U_15410),U_15411)) ),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

fof(f_3840_3,plain,
    ! [U_15413,U_15412,U_15411,U_15410,U_15409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15410),hAPP(c_Set_OCollect(U_15409),U_15412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15411),hAPP(c_Set_OCollect(U_15409),U_15413))))
      | ( ~ hBOOL(hAPP(U_15413,sK404(U_15413,U_15412,U_15411,U_15410,U_15409)))
        & hBOOL(hAPP(U_15412,sK404(U_15413,U_15412,U_15411,U_15410,U_15409)))
        & hBOOL(hAPP(hAPP(c_member(U_15409),sK404(U_15413,U_15412,U_15411,U_15410,U_15409)),U_15410)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),U_15410),U_15411)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15408,sK404(U_15413,U_15412,U_15411,U_15410,U_15409))],[f_3840_2]) ).

cnf(f_3840_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15409),sK404(U_15413,U_15412,U_15411,U_15410,U_15409)),U_15410))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15410),hAPP(c_Set_OCollect(U_15409),U_15412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15411),hAPP(c_Set_OCollect(U_15409),U_15413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),U_15410),U_15411)) ),
    inference(clausify,[status(thm)],[f_3840_3]) ).

cnf(f_3840_5,plain,
    ( hBOOL(hAPP(U_15412,sK404(U_15413,U_15412,U_15411,U_15410,U_15409)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15410),hAPP(c_Set_OCollect(U_15409),U_15412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15411),hAPP(c_Set_OCollect(U_15409),U_15413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),U_15410),U_15411)) ),
    inference(clausify,[status(thm)],[f_3840_3]) ).

cnf(f_3840_6,plain,
    ( ~ hBOOL(hAPP(U_15413,sK404(U_15413,U_15412,U_15411,U_15410,U_15409)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15410),hAPP(c_Set_OCollect(U_15409),U_15412))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15409,tc_HOL_Obool)),U_15411),hAPP(c_Set_OCollect(U_15409),U_15413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15409,tc_HOL_Obool)),U_15410),U_15411)) ),
    inference(clausify,[status(thm)],[f_3840_3]) ).

fof(f_3841_1,plain,
    ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
      ( ? [B_x,B_y,B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2))
          & V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compE]) ).

fof(f_3841_2,plain,
    ! [U_15422,U_15421,U_15420,U_15419,U_15418,U_15417] :
      ( ? [U_15416,U_15415,U_15414] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15418)),hAPP(hAPP(c_Product__Type_OPair(U_15420,U_15418),U_15415),U_15414)),U_15422))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15420)),hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15420),U_15416),U_15415)),U_15421))
          & U_15419 = hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15418),U_15416),U_15414) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

fof(f_3841_3,plain,
    ! [U_15422,U_15421,U_15420,U_15419,U_15418,U_15417] :
      ( ? [U_15415,U_15414] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15418)),hAPP(hAPP(c_Product__Type_OPair(U_15420,U_15418),U_15415),U_15414)),U_15422))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15420)),hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15420),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),U_15415)),U_15421))
          & U_15419 = hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15418),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),U_15414) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_15416,sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))],[f_3841_2]) ).

fof(f_3841_4,plain,
    ! [U_15422,U_15421,U_15420,U_15419,U_15418,U_15417] :
      ( ? [U_15414] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15418)),hAPP(hAPP(c_Product__Type_OPair(U_15420,U_15418),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),U_15414)),U_15422))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15420)),hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15420),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))),U_15421))
          & U_15419 = hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15418),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),U_15414) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_15415,sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))],[f_3841_3]) ).

fof(f_3841_5,plain,
    ! [U_15422,U_15421,U_15420,U_15419,U_15418,U_15417] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15418)),hAPP(hAPP(c_Product__Type_OPair(U_15420,U_15418),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK407(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))),U_15422))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15420)),hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15420),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))),U_15421))
        & U_15419 = hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15418),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK407(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_15414,sK407(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))],[f_3841_4]) ).

cnf(f_3841_6,plain,
    ( U_15419 = hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15418),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK407(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

cnf(f_3841_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15420)),hAPP(hAPP(c_Product__Type_OPair(U_15417,U_15420),sK405(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))),U_15421))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

cnf(f_3841_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15418)),hAPP(hAPP(c_Product__Type_OPair(U_15420,U_15418),sK406(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417)),sK407(U_15422,U_15421,U_15420,U_15419,U_15418,U_15417))),U_15422))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15417,U_15418)),U_15419),hAPP(hAPP(c_Relation_Orel__comp(U_15417,U_15420,U_15418),U_15421),U_15422))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

fof(f_3842_1,plain,
    ! [V_r_2,V_yx_2,T_b,T_a] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2))
          & V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseE]) ).

fof(f_3842_2,plain,
    ! [U_15428,U_15427,U_15426,U_15425] :
      ( ? [U_15424,U_15423] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15426,U_15425)),hAPP(hAPP(c_Product__Type_OPair(U_15426,U_15425),U_15424),U_15423)),U_15428))
          & U_15427 = hAPP(hAPP(c_Product__Type_OPair(U_15425,U_15426),U_15423),U_15424) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15426)),U_15427),hAPP(c_Relation_Oconverse(U_15426,U_15425),U_15428))) ),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

fof(f_3842_3,plain,
    ! [U_15428,U_15427,U_15426,U_15425] :
      ( ? [U_15423] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15426,U_15425)),hAPP(hAPP(c_Product__Type_OPair(U_15426,U_15425),sK408(U_15428,U_15427,U_15426,U_15425)),U_15423)),U_15428))
          & U_15427 = hAPP(hAPP(c_Product__Type_OPair(U_15425,U_15426),U_15423),sK408(U_15428,U_15427,U_15426,U_15425)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15426)),U_15427),hAPP(c_Relation_Oconverse(U_15426,U_15425),U_15428))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_15424,sK408(U_15428,U_15427,U_15426,U_15425))],[f_3842_2]) ).

fof(f_3842_4,plain,
    ! [U_15428,U_15427,U_15426,U_15425] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15426,U_15425)),hAPP(hAPP(c_Product__Type_OPair(U_15426,U_15425),sK408(U_15428,U_15427,U_15426,U_15425)),sK409(U_15428,U_15427,U_15426,U_15425))),U_15428))
        & U_15427 = hAPP(hAPP(c_Product__Type_OPair(U_15425,U_15426),sK409(U_15428,U_15427,U_15426,U_15425)),sK408(U_15428,U_15427,U_15426,U_15425)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15426)),U_15427),hAPP(c_Relation_Oconverse(U_15426,U_15425),U_15428))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_15423,sK409(U_15428,U_15427,U_15426,U_15425))],[f_3842_3]) ).

cnf(f_3842_5,plain,
    ( U_15427 = hAPP(hAPP(c_Product__Type_OPair(U_15425,U_15426),sK409(U_15428,U_15427,U_15426,U_15425)),sK408(U_15428,U_15427,U_15426,U_15425))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15426)),U_15427),hAPP(c_Relation_Oconverse(U_15426,U_15425),U_15428))) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

cnf(f_3842_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15426,U_15425)),hAPP(hAPP(c_Product__Type_OPair(U_15426,U_15425),sK408(U_15428,U_15427,U_15426,U_15425)),sK409(U_15428,U_15427,U_15426,U_15425))),U_15428))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15426)),U_15427),hAPP(c_Relation_Oconverse(U_15426,U_15425),U_15428))) ),
    inference(clausify,[status(thm)],[f_3842_4]) ).

fof(f_3843_1,plain,
    ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),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_a),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_a),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_a),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_a),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(f_3843_2,plain,
    ! [U_15431,U_15430,U_15429] : c_Nitpick_Oplus__frac(U_15429,U_15430,U_15431) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_15429),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_15429),U_15430),hAPP(c_Nitpick_Odenom(U_15429),U_15431))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_15429),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_15429),tc_Int_Oint),c_Nitpick_Ofrac(U_15429)),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_15429),U_15430))),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_15429),U_15430))))),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_15429),U_15431))),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_15429),U_15431)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

cnf(f_3843_3,plain,
    c_Nitpick_Oplus__frac(U_15429,U_15430,U_15431) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_15429),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_15429),U_15430),hAPP(c_Nitpick_Odenom(U_15429),U_15431))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_15429),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_15429),tc_Int_Oint),c_Nitpick_Ofrac(U_15429)),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_15429),U_15430))),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_15429),U_15430))))),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_15429),U_15431))),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_15429),U_15431)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3843_2]) ).

fof(f_3844_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_3844_2,plain,
    ! [U_15434,U_15433,U_15432] : c_Nitpick_Otimes__frac(U_15432,U_15433,U_15434) = hAPP(hAPP(c_Nitpick_Ofrac(U_15432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15432),U_15433)),hAPP(c_Nitpick_Onum(U_15432),U_15434))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_15432),U_15433)),hAPP(c_Nitpick_Odenom(U_15432),U_15434))),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

cnf(f_3844_3,plain,
    c_Nitpick_Otimes__frac(U_15432,U_15433,U_15434) = hAPP(hAPP(c_Nitpick_Ofrac(U_15432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15432),U_15433)),hAPP(c_Nitpick_Onum(U_15432),U_15434))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_15432),U_15433)),hAPP(c_Nitpick_Odenom(U_15432),U_15434))),
    inference(clausify,[status(thm)],[f_3844_2]) ).

fof(f_3845_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_3845_2,plain,
    ! [U_15437,U_15436,U_15435] :
      ( c_Nitpick_Oof__frac(U_15436,U_15435,U_15437) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_15435),hAPP(c_Int_Oring__1__class_Oof__int(U_15435),hAPP(c_Nitpick_Onum(U_15436),U_15437))),hAPP(c_Int_Oring__1__class_Oof__int(U_15435),hAPP(c_Nitpick_Odenom(U_15436),U_15437)))
      | ~ class_Rings_Oring__1(U_15435)
      | ~ class_Rings_Oinverse(U_15435) ),
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

cnf(f_3845_3,plain,
    ( c_Nitpick_Oof__frac(U_15436,U_15435,U_15437) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_15435),hAPP(c_Int_Oring__1__class_Oof__int(U_15435),hAPP(c_Nitpick_Onum(U_15436),U_15437))),hAPP(c_Int_Oring__1__class_Oof__int(U_15435),hAPP(c_Nitpick_Odenom(U_15436),U_15437)))
    | ~ class_Rings_Oring__1(U_15435)
    | ~ class_Rings_Oinverse(U_15435) ),
    inference(clausify,[status(thm)],[f_3845_2]) ).

fof(f_3846_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_3846_2,plain,
    ! [U_15439,U_15438] : c_Nitpick_Oinverse__frac(U_15438,U_15439) = hAPP(hAPP(c_Nitpick_Ofrac(U_15438),hAPP(c_Nitpick_Odenom(U_15438),U_15439)),hAPP(c_Nitpick_Onum(U_15438),U_15439)),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

cnf(f_3846_3,plain,
    c_Nitpick_Oinverse__frac(U_15438,U_15439) = hAPP(hAPP(c_Nitpick_Ofrac(U_15438),hAPP(c_Nitpick_Odenom(U_15438),U_15439)),hAPP(c_Nitpick_Onum(U_15438),U_15439)),
    inference(clausify,[status(thm)],[f_3846_2]) ).

fof(f_3847_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_3847_2,plain,
    ! [U_15441,U_15440] : c_Nitpick_Ouminus__frac(U_15440,U_15441) = c_Nitpick_OAbs__Frac(U_15440,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_15440),U_15441))),hAPP(c_Nitpick_Odenom(U_15440),U_15441))),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

cnf(f_3847_3,plain,
    c_Nitpick_Ouminus__frac(U_15440,U_15441) = c_Nitpick_OAbs__Frac(U_15440,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_15440),U_15441))),hAPP(c_Nitpick_Odenom(U_15440),U_15441))),
    inference(clausify,[status(thm)],[f_3847_2]) ).

fof(f_3848_1,plain,
    ! [V_r_2,V_q_2,T_a] :
      ( ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,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_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def]) ).

fof(f_3848_2,plain,
    ! [U_15444,U_15443,U_15442] :
      ( ( c_Nitpick_Oless__frac(U_15442,U_15443,U_15444)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15442),c_Nitpick_Oplus__frac(U_15442,U_15443,c_Nitpick_Ouminus__frac(U_15442,U_15444)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15442),c_Nitpick_Oplus__frac(U_15442,U_15443,c_Nitpick_Ouminus__frac(U_15442,U_15444)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_15442,U_15443,U_15444) ) ),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

fof(f_3848_3,plain,
    ( ! [U_15450,U_15448,U_15446] :
        ( c_Nitpick_Oless__frac(U_15446,U_15448,U_15450)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15446),c_Nitpick_Oplus__frac(U_15446,U_15448,c_Nitpick_Ouminus__frac(U_15446,U_15450)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_15449,U_15447,U_15445] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15445),c_Nitpick_Oplus__frac(U_15445,U_15447,c_Nitpick_Ouminus__frac(U_15445,U_15449)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_15445,U_15447,U_15449) ) ),
    inference(miniscope,[status(thm)],[f_3848_2]) ).

cnf(f_3848_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15445),c_Nitpick_Oplus__frac(U_15445,U_15447,c_Nitpick_Ouminus__frac(U_15445,U_15449)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_15445,U_15447,U_15449) ),
    inference(clausify,[status(thm)],[f_3848_3]) ).

cnf(f_3848_5,plain,
    ( c_Nitpick_Oless__frac(U_15446,U_15448,U_15450)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15446),c_Nitpick_Oplus__frac(U_15446,U_15448,c_Nitpick_Ouminus__frac(U_15446,U_15450)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3848_3]) ).

fof(f_3849_1,plain,
    ! [V_r_2,V_q_2,T_a] :
      ( ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,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_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def]) ).

fof(f_3849_2,plain,
    ! [U_15453,U_15452,U_15451] :
      ( ( c_Nitpick_Oless__eq__frac(U_15451,U_15452,U_15453)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15451),c_Nitpick_Oplus__frac(U_15451,U_15452,c_Nitpick_Ouminus__frac(U_15451,U_15453)))),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_15451),c_Nitpick_Oplus__frac(U_15451,U_15452,c_Nitpick_Ouminus__frac(U_15451,U_15453)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_15451,U_15452,U_15453) ) ),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

fof(f_3849_3,plain,
    ( ! [U_15459,U_15457,U_15455] :
        ( c_Nitpick_Oless__eq__frac(U_15455,U_15457,U_15459)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15455),c_Nitpick_Oplus__frac(U_15455,U_15457,c_Nitpick_Ouminus__frac(U_15455,U_15459)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_15458,U_15456,U_15454] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15454),c_Nitpick_Oplus__frac(U_15454,U_15456,c_Nitpick_Ouminus__frac(U_15454,U_15458)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_15454,U_15456,U_15458) ) ),
    inference(miniscope,[status(thm)],[f_3849_2]) ).

cnf(f_3849_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15454),c_Nitpick_Oplus__frac(U_15454,U_15456,c_Nitpick_Ouminus__frac(U_15454,U_15458)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_15454,U_15456,U_15458) ),
    inference(clausify,[status(thm)],[f_3849_3]) ).

cnf(f_3849_5,plain,
    ( c_Nitpick_Oless__eq__frac(U_15455,U_15457,U_15459)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_15455),c_Nitpick_Oplus__frac(U_15455,U_15457,c_Nitpick_Ouminus__frac(U_15455,U_15459)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3849_3]) ).

fof(f_3850_1,plain,
    ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(f_3850_2,plain,
    ! [U_15460] : c_Nitpick_Odenom(U_15460) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15460,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15460)),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

cnf(f_3850_3,plain,
    c_Nitpick_Odenom(U_15460) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15460,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15460)),
    inference(clausify,[status(thm)],[f_3850_2]) ).

fof(f_3851_1,plain,
    ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(f_3851_2,plain,
    ! [U_15461] : c_Nitpick_Onum(U_15461) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15461,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15461)),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

cnf(f_3851_3,plain,
    c_Nitpick_Onum(U_15461) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15461,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15461)),
    inference(clausify,[status(thm)],[f_3851_2]) ).

fof(f_3852_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos]) ).

fof(f_3852_2,plain,
    ! [U_15466,U_15465,U_15464,U_15463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15464,U_15463),U_15466),U_15465)))
      | ? [U_15462] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(U_15466,U_15462)))
          & hBOOL(hAPP(hAPP(c_member(U_15464),U_15462),U_15465)) )
      | ~ class_Rings_Olinordered__semidom(U_15463) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

fof(f_3852_3,plain,
    ! [U_15466,U_15465,U_15464,U_15463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15464,U_15463),U_15466),U_15465)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(U_15466,sK410(U_15466,U_15465,U_15464,U_15463))))
        & hBOOL(hAPP(hAPP(c_member(U_15464),sK410(U_15466,U_15465,U_15464,U_15463)),U_15465)) )
      | ~ class_Rings_Olinordered__semidom(U_15463) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_15462,sK410(U_15466,U_15465,U_15464,U_15463))],[f_3852_2]) ).

cnf(f_3852_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15464),sK410(U_15466,U_15465,U_15464,U_15463)),U_15465))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15464,U_15463),U_15466),U_15465)))
    | ~ class_Rings_Olinordered__semidom(U_15463) ),
    inference(clausify,[status(thm)],[f_3852_3]) ).

cnf(f_3852_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(U_15466,sK410(U_15466,U_15465,U_15464,U_15463))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15463),c_Groups_Ozero__class_Ozero(U_15463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15464,U_15463),U_15466),U_15465)))
    | ~ class_Rings_Olinordered__semidom(U_15463) ),
    inference(clausify,[status(thm)],[f_3852_3]) ).

fof(f_3853_1,plain,
    ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),
    inference(fof_nnf,[status(thm)],[fact_internal__split__def]) ).

fof(f_3853_2,plain,
    ! [U_15469,U_15468,U_15467] : c_Product__Type_Ointernal__split(U_15467,U_15468,U_15469) = c_Product__Type_Oprod_Oprod__case(U_15467,U_15468,U_15469),
    inference(variable_rename,[status(thm)],[f_3853_1]) ).

cnf(f_3853_3,plain,
    c_Product__Type_Ointernal__split(U_15467,U_15468,U_15469) = c_Product__Type_Oprod_Oprod__case(U_15467,U_15468,U_15469),
    inference(clausify,[status(thm)],[f_3853_2]) ).

fof(f_3854_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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_3854_2,plain,
    ! [U_15475,U_15474,U_15473,U_15472,U_15471,U_15470] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_15470,U_15471,U_15472),U_15473),hAPP(hAPP(c_Product__Type_OPair(U_15470,U_15471),U_15474),U_15475)) = hAPP(hAPP(U_15473,U_15474),U_15475),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

cnf(f_3854_3,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_15470,U_15471,U_15472),U_15473),hAPP(hAPP(c_Product__Type_OPair(U_15470,U_15471),U_15474),U_15475)) = hAPP(hAPP(U_15473,U_15474),U_15475),
    inference(clausify,[status(thm)],[f_3854_2]) ).

fof(f_3855_1,plain,
    ! [V_f_2,V_A_2,T_a,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__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__nonneg]) ).

fof(f_3855_2,plain,
    ! [U_15480,U_15479,U_15478,U_15477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15478,U_15477),U_15480),U_15479)))
      | ? [U_15476] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(U_15480,U_15476)))
          & hBOOL(hAPP(hAPP(c_member(U_15478),U_15476),U_15479)) )
      | ~ class_Rings_Olinordered__semidom(U_15477) ),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

fof(f_3855_3,plain,
    ! [U_15480,U_15479,U_15478,U_15477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15478,U_15477),U_15480),U_15479)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(U_15480,sK411(U_15480,U_15479,U_15478,U_15477))))
        & hBOOL(hAPP(hAPP(c_member(U_15478),sK411(U_15480,U_15479,U_15478,U_15477)),U_15479)) )
      | ~ class_Rings_Olinordered__semidom(U_15477) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_15476,sK411(U_15480,U_15479,U_15478,U_15477))],[f_3855_2]) ).

cnf(f_3855_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15478),sK411(U_15480,U_15479,U_15478,U_15477)),U_15479))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15478,U_15477),U_15480),U_15479)))
    | ~ class_Rings_Olinordered__semidom(U_15477) ),
    inference(clausify,[status(thm)],[f_3855_3]) ).

cnf(f_3855_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(U_15480,sK411(U_15480,U_15479,U_15478,U_15477))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15477),c_Groups_Ozero__class_Ozero(U_15477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15478,U_15477),U_15480),U_15479)))
    | ~ class_Rings_Olinordered__semidom(U_15477) ),
    inference(clausify,[status(thm)],[f_3855_3]) ).

fof(f_3856_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]) ).

cnf(f_3856_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3856_1]) ).

fof(f_3857_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]) ).

cnf(f_3857_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3857_1]) ).

fof(f_3858_1,plain,
    ! [V_u_2,V_f_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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2))))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__less__ub]) ).

fof(f_3858_2,plain,
    ! [U_15483,U_15482] :
      ( 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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_15482)),U_15483))))
      | ? [U_15481] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15481),hAPP(U_15482,U_15481))) ),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

fof(f_3858_3,plain,
    ! [U_15483,U_15482] :
      ( 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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_15482)),U_15483))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK412(U_15483,U_15482)),hAPP(U_15482,sK412(U_15483,U_15482)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_15481,sK412(U_15483,U_15482))],[f_3858_2]) ).

cnf(f_3858_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),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_15482)),U_15483))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK412(U_15483,U_15482)),hAPP(U_15482,sK412(U_15483,U_15482)))) ),
    inference(clausify,[status(thm)],[f_3858_3]) ).

fof(f_3859_1,plain,
    ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__def]) ).

fof(f_3859_2,plain,
    ! [U_15485,U_15484] : c_List_Olenlex(U_15484,U_15485) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484)),tc_List_Olist(U_15484)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_15484),c_Wellfounded_Oless__than,c_List_Olex(U_15484,U_15485))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15484),tc_List_Olist(U_15484),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_15484),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484))),tc_List_Olist(U_15484)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_15484))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15484)))),c_COMBI(tc_List_Olist(U_15484)))),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

cnf(f_3859_3,plain,
    c_List_Olenlex(U_15484,U_15485) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484)),tc_List_Olist(U_15484)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_15484),c_Wellfounded_Oless__than,c_List_Olex(U_15484,U_15485))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15484),tc_List_Olist(U_15484),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_15484),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15484))),tc_List_Olist(U_15484)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_15484))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15484)))),c_COMBI(tc_List_Olist(U_15484)))),
    inference(clausify,[status(thm)],[f_3859_2]) ).

fof(f_3860_1,plain,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexn__length]) ).

fof(f_3860_2,plain,
    ! [U_15490,U_15489,U_15488,U_15487,U_15486] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15486)),U_15488) = U_15490
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15486)),U_15487) = U_15490 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15486),tc_List_Olist(U_15486))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15486),tc_List_Olist(U_15486)),U_15487),U_15488)),hAPP(c_List_Olexn(U_15486,U_15489),U_15490))) ),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

cnf(f_3860_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15486)),U_15487) = U_15490
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15486),tc_List_Olist(U_15486))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15486),tc_List_Olist(U_15486)),U_15487),U_15488)),hAPP(c_List_Olexn(U_15486,U_15489),U_15490))) ),
    inference(clausify,[status(thm)],[f_3860_2]) ).

cnf(f_3860_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15486)),U_15488) = U_15490
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15486),tc_List_Olist(U_15486))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15486),tc_List_Olist(U_15486)),U_15487),U_15488)),hAPP(c_List_Olexn(U_15486,U_15489),U_15490))) ),
    inference(clausify,[status(thm)],[f_3860_2]) ).

fof(f_3861_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_3861_2,plain,
    ! [U_15493,U_15492,U_15491] :
      ( U_15492 != U_15493
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15493) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

fof(f_3861_3,plain,
    ! [U_15493,U_15492] :
      ( ! [U_15491] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15493)
      | U_15492 != U_15493 ),
    inference(miniscope,[status(thm)],[f_3861_2]) ).

cnf(f_3861_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15491)),U_15493)
    | U_15492 != U_15493 ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

fof(f_3862_1,plain,
    ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__conv]) ).

fof(f_3862_2,plain,
    ! [U_15495,U_15494] : c_List_Olenlex(U_15494,U_15495) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15494),tc_List_Olist(U_15494),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBS(tc_List_Olist(U_15494),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_15494))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15494)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBS(tc_List_Olist(U_15494),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_15494))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15494)),c_member(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))))),c_Product__Type_OPair(tc_List_Olist(U_15494),tc_List_Olist(U_15494))))),c_List_Olex(U_15494,U_15495)))))),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

cnf(f_3862_3,plain,
    c_List_Olenlex(U_15494,U_15495) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15494),tc_List_Olist(U_15494),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBS(tc_List_Olist(U_15494),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_15494))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15494)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBS(tc_List_Olist(U_15494),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15494),tc_Nat_Onat),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_15494))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15494)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15494)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15494),tc_HOL_Obool)),tc_List_Olist(U_15494)),c_COMBC(tc_List_Olist(U_15494),tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15494),tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))),tc_fun(tc_List_Olist(U_15494),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_15494)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15494)),c_member(tc_prod(tc_List_Olist(U_15494),tc_List_Olist(U_15494))))),c_Product__Type_OPair(tc_List_Olist(U_15494),tc_List_Olist(U_15494))))),c_List_Olex(U_15494,U_15495)))))),
    inference(clausify,[status(thm)],[f_3862_2]) ).

fof(f_3863_1,plain,
    ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,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_a)),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_3863_2,plain,
    ! [U_15498,U_15497,U_15496] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15496)),c_List_Osublist(U_15496,U_15497,U_15498)) = 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_15496)),U_15497)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15498)))),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

cnf(f_3863_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15496)),c_List_Osublist(U_15496,U_15497,U_15498)) = 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_15496)),U_15497)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15498)))),
    inference(clausify,[status(thm)],[f_3863_2]) ).

fof(f_3864_1,plain,
    ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

fof(f_3864_2,plain,
    ! [U_15501,U_15500,U_15499] : hAPP(c_List_Olexn(U_15499,U_15500),hAPP(c_Nat_OSuc,U_15501)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_15499,tc_List_Olist(U_15499)),tc_prod(U_15499,tc_List_Olist(U_15499))),tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_Product__Type_Omap__pair(tc_prod(U_15499,tc_List_Olist(U_15499)),tc_List_Olist(U_15499),tc_prod(U_15499,tc_List_Olist(U_15499)),tc_List_Olist(U_15499),hAPP(c_Product__Type_Oprod_Oprod__case(U_15499,tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_List_Olist_OCons(U_15499)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15499,tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_List_Olist_OCons(U_15499)))),c_Wellfounded_Olex__prod(U_15499,tc_List_Olist(U_15499),U_15500,hAPP(c_List_Olexn(U_15499,U_15500),U_15501)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15499),tc_List_Olist(U_15499),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool)),tc_List_Olist(U_15499)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_15499))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15499)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),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_15499)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15499)))),hAPP(c_Nat_OSuc,U_15501))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),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_15499)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15499)))),hAPP(c_Nat_OSuc,U_15501)))))),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

cnf(f_3864_3,plain,
    hAPP(c_List_Olexn(U_15499,U_15500),hAPP(c_Nat_OSuc,U_15501)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_15499,tc_List_Olist(U_15499)),tc_prod(U_15499,tc_List_Olist(U_15499))),tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_Product__Type_Omap__pair(tc_prod(U_15499,tc_List_Olist(U_15499)),tc_List_Olist(U_15499),tc_prod(U_15499,tc_List_Olist(U_15499)),tc_List_Olist(U_15499),hAPP(c_Product__Type_Oprod_Oprod__case(U_15499,tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_List_Olist_OCons(U_15499)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15499,tc_List_Olist(U_15499),tc_List_Olist(U_15499)),c_List_Olist_OCons(U_15499)))),c_Wellfounded_Olex__prod(U_15499,tc_List_Olist(U_15499),U_15500,hAPP(c_List_Olexn(U_15499,U_15500),U_15501)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_15499),tc_List_Olist(U_15499))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15499),tc_List_Olist(U_15499),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15499),tc_HOL_Obool)),tc_List_Olist(U_15499)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_15499))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15499)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),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_15499)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15499)))),hAPP(c_Nat_OSuc,U_15501))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15499),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_15499)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15499)))),hAPP(c_Nat_OSuc,U_15501)))))),
    inference(clausify,[status(thm)],[f_3864_2]) ).

fof(f_3865_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_3865_2,plain,
    ! [U_15505,U_15504,U_15503,U_15502] :
      ( U_15503 != hAPP(hAPP(c_List_Olist_OCons(U_15502),U_15505),U_15504)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15502)),U_15503)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15502)),U_15504))) ),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

cnf(f_3865_3,plain,
    ( U_15503 != hAPP(hAPP(c_List_Olist_OCons(U_15502),U_15505),U_15504)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15502)),U_15503)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15502)),U_15504))) ),
    inference(clausify,[status(thm)],[f_3865_2]) ).

fof(f_3866_1,plain,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),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_a),V_a_2),V_list_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list_Oinject]) ).

fof(f_3866_2,plain,
    ! [U_15510,U_15509,U_15508,U_15507,U_15506] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_15506),U_15507),U_15508) = hAPP(hAPP(c_List_Olist_OCons(U_15506),U_15509),U_15510)
        | U_15508 != U_15510
        | U_15507 != U_15509 )
      & ( ( U_15508 = U_15510
          & U_15507 = U_15509 )
        | hAPP(hAPP(c_List_Olist_OCons(U_15506),U_15507),U_15508) != hAPP(hAPP(c_List_Olist_OCons(U_15506),U_15509),U_15510) ) ),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

fof(f_3866_3,plain,
    ( ! [U_15520,U_15518,U_15516,U_15514] :
        ( ! [U_15512] : hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15514),U_15516) = hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15518),U_15520)
        | U_15516 != U_15520
        | U_15514 != U_15518 )
    & ! [U_15519,U_15517,U_15515,U_15513] :
        ( ! [U_15511] : hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15513),U_15515) != hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15517),U_15519)
        | ( U_15515 = U_15519
          & U_15513 = U_15517 ) ) ),
    inference(miniscope,[status(thm)],[f_3866_2]) ).

cnf(f_3866_4,plain,
    ( U_15513 = U_15517
    | hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15513),U_15515) != hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15517),U_15519) ),
    inference(clausify,[status(thm)],[f_3866_3]) ).

cnf(f_3866_5,plain,
    ( U_15515 = U_15519
    | hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15513),U_15515) != hAPP(hAPP(c_List_Olist_OCons(U_15511),U_15517),U_15519) ),
    inference(clausify,[status(thm)],[f_3866_3]) ).

cnf(f_3866_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15514),U_15516) = hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15518),U_15520)
    | U_15516 != U_15520
    | U_15514 != U_15518 ),
    inference(clausify,[status(thm)],[f_3866_3]) ).

fof(f_3867_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_3867_2,plain,
    ! [U_15523,U_15522,U_15521] : hAPP(hAPP(c_List_Olist_OCons(U_15521),U_15522),U_15523) != U_15523,
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

cnf(f_3867_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_15521),U_15522),U_15523) != U_15523,
    inference(clausify,[status(thm)],[f_3867_2]) ).

fof(f_3868_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_3868_2,plain,
    ! [U_15526,U_15525,U_15524] : U_15524 != hAPP(hAPP(c_List_Olist_OCons(U_15525),U_15526),U_15524),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

cnf(f_3868_3,plain,
    U_15524 != hAPP(hAPP(c_List_Olist_OCons(U_15525),U_15526),U_15524),
    inference(clausify,[status(thm)],[f_3868_2]) ).

fof(f_3869_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_3869_2,plain,
    ! [U_15529,U_15528,U_15527] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15527)),hAPP(hAPP(c_List_Olist_OCons(U_15527),U_15528),U_15529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15527)),U_15529)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

cnf(f_3869_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15527)),hAPP(hAPP(c_List_Olist_OCons(U_15527),U_15528),U_15529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15527)),U_15529)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3869_2]) ).

fof(f_3870_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lex]) ).

fof(f_3870_2,plain,
    ! [U_15535,U_15534,U_15533,U_15532,U_15531,U_15530] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15530),tc_List_Olist(U_15530))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15530),tc_List_Olist(U_15530)),hAPP(hAPP(c_List_Olist_OCons(U_15530),U_15531),U_15532)),hAPP(hAPP(c_List_Olist_OCons(U_15530),U_15533),U_15534))),c_List_Olex(U_15530,U_15535)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15530),tc_List_Olist(U_15530))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15530),tc_List_Olist(U_15530)),U_15532),U_15534)),c_List_Olex(U_15530,U_15535)))
            | U_15531 != U_15533 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15530)),U_15532) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15530)),U_15534)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15530,U_15530)),hAPP(hAPP(c_Product__Type_OPair(U_15530,U_15530),U_15531),U_15533)),U_15535)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15530),tc_List_Olist(U_15530))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15530),tc_List_Olist(U_15530)),U_15532),U_15534)),c_List_Olex(U_15530,U_15535)))
          & U_15531 = U_15533 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15530)),U_15532) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15530)),U_15534)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15530,U_15530)),hAPP(hAPP(c_Product__Type_OPair(U_15530,U_15530),U_15531),U_15533)),U_15535)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15530),tc_List_Olist(U_15530))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15530),tc_List_Olist(U_15530)),hAPP(hAPP(c_List_Olist_OCons(U_15530),U_15531),U_15532)),hAPP(hAPP(c_List_Olist_OCons(U_15530),U_15533),U_15534))),c_List_Olex(U_15530,U_15535))) ) ),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

fof(f_3870_3,plain,
    ( ! [U_15547,U_15545,U_15543,U_15541,U_15539,U_15537] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15537),tc_List_Olist(U_15537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15537),tc_List_Olist(U_15537)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15539),U_15541)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15543),U_15545))),c_List_Olex(U_15537,U_15547)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15537),tc_List_Olist(U_15537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15537),tc_List_Olist(U_15537)),U_15541),U_15545)),c_List_Olex(U_15537,U_15547)))
            | U_15539 != U_15543 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15537)),U_15541) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15537)),U_15545)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15537,U_15537)),hAPP(hAPP(c_Product__Type_OPair(U_15537,U_15537),U_15539),U_15543)),U_15547)) ) ) )
    & ! [U_15546,U_15544,U_15542,U_15540,U_15538,U_15536] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),U_15540),U_15544)),c_List_Olex(U_15536,U_15546)))
          & U_15538 = U_15542 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15540) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15544)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15536,U_15536)),hAPP(hAPP(c_Product__Type_OPair(U_15536,U_15536),U_15538),U_15542)),U_15546)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15538),U_15540)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15542),U_15544))),c_List_Olex(U_15536,U_15546))) ) ),
    inference(miniscope,[status(thm)],[f_3870_2]) ).

cnf(f_3870_4,plain,
    ( U_15538 = U_15542
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15536,U_15536)),hAPP(hAPP(c_Product__Type_OPair(U_15536,U_15536),U_15538),U_15542)),U_15546))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15538),U_15540)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15542),U_15544))),c_List_Olex(U_15536,U_15546))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

cnf(f_3870_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),U_15540),U_15544)),c_List_Olex(U_15536,U_15546)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15536,U_15536)),hAPP(hAPP(c_Product__Type_OPair(U_15536,U_15536),U_15538),U_15542)),U_15546))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15538),U_15540)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15542),U_15544))),c_List_Olex(U_15536,U_15546))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

cnf(f_3870_6,plain,
    ( U_15538 = U_15542
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15540) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15544)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15538),U_15540)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15542),U_15544))),c_List_Olex(U_15536,U_15546))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

cnf(f_3870_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),U_15540),U_15544)),c_List_Olex(U_15536,U_15546)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15540) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15536)),U_15544)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15536),tc_List_Olist(U_15536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15536),tc_List_Olist(U_15536)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15538),U_15540)),hAPP(hAPP(c_List_Olist_OCons(U_15536),U_15542),U_15544))),c_List_Olex(U_15536,U_15546))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

cnf(f_3870_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15537)),U_15541) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15537)),U_15545)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15537,U_15537)),hAPP(hAPP(c_Product__Type_OPair(U_15537,U_15537),U_15539),U_15543)),U_15547))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15537),tc_List_Olist(U_15537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15537),tc_List_Olist(U_15537)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15539),U_15541)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15543),U_15545))),c_List_Olex(U_15537,U_15547))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

cnf(f_3870_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15537),tc_List_Olist(U_15537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15537),tc_List_Olist(U_15537)),U_15541),U_15545)),c_List_Olex(U_15537,U_15547)))
    | U_15539 != U_15543
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15537),tc_List_Olist(U_15537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15537),tc_List_Olist(U_15537)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15539),U_15541)),hAPP(hAPP(c_List_Olist_OCons(U_15537),U_15543),U_15545))),c_List_Olex(U_15537,U_15547))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

fof(f_3871_1,plain,
    ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__def]) ).

fof(f_3871_2,plain,
    ! [U_15550,U_15549,U_15548] : c_List_Oset__Cons(U_15548,U_15549,U_15550) = hAPP(c_Set_OCollect(tc_List_Olist(U_15548)),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_15548)),c_HOL_OEx(U_15548)),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_HOL_Obool),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_HOL_Obool,U_15548),c_HOL_OEx(tc_List_Olist(U_15548)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_fun(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),c_COMBS(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_15548,tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),U_15548),c_COMBS(tc_List_Olist(U_15548),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15548),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15548)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548))),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548))),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),U_15548)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_List_Olist(U_15548)),c_COMBB(tc_List_Olist(U_15548),tc_HOL_Obool,tc_List_Olist(U_15548))),c_fequal))),c_List_Olist_OCons(U_15548)))))),hAPP(hAPP(c_COMBC(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),U_15548),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_15548))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15548),c_fconj),hAPP(hAPP(c_COMBC(U_15548,tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15548)),U_15549)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_15548))),U_15550)))))),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

cnf(f_3871_3,plain,
    c_List_Oset__Cons(U_15548,U_15549,U_15550) = hAPP(c_Set_OCollect(tc_List_Olist(U_15548)),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_15548)),c_HOL_OEx(U_15548)),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_HOL_Obool),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_HOL_Obool,U_15548),c_HOL_OEx(tc_List_Olist(U_15548)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_fun(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),c_COMBS(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_15548,tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),U_15548),c_COMBS(tc_List_Olist(U_15548),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_15548)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15548),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15548)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548))),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_fun(tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548))),tc_fun(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool))),tc_List_Olist(U_15548)),c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),U_15548)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_List_Olist(U_15548)),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),tc_List_Olist(U_15548)),c_COMBB(tc_List_Olist(U_15548),tc_HOL_Obool,tc_List_Olist(U_15548))),c_fequal))),c_List_Olist_OCons(U_15548)))))),hAPP(hAPP(c_COMBC(U_15548,tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool)),U_15548),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_15548))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15548),c_fconj),hAPP(hAPP(c_COMBC(U_15548,tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15548)),U_15549)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15548),tc_fun(tc_List_Olist(U_15548),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_15548))),U_15550)))))),
    inference(clausify,[status(thm)],[f_3871_2]) ).

fof(f_3872_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_3872_2,plain,
    ! [U_15554,U_15553,U_15552,U_15551] :
      ( ( hAPP(c_Random_Opick(U_15552,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15552)),U_15553),U_15554)),U_15551) = hAPP(c_Random_Opick(U_15552,U_15554),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15551),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15552),U_15553)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15551),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15552),U_15553))) )
      & ( hAPP(c_Random_Opick(U_15552,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15552)),U_15553),U_15554)),U_15551) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_15552),U_15553)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15551),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15552),U_15553))) ) ),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

fof(f_3872_3,plain,
    ( ! [U_15562,U_15560,U_15558,U_15556] :
        ( hAPP(c_Random_Opick(U_15558,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15558)),U_15560),U_15562)),U_15556) = hAPP(c_Random_Opick(U_15558,U_15562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15556),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15558),U_15560)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15556),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15558),U_15560))) )
    & ! [U_15561,U_15559,U_15557,U_15555] :
        ( hAPP(c_Random_Opick(U_15557,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15557)),U_15559),U_15561)),U_15555) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_15557),U_15559)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15555),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15557),U_15559))) ) ),
    inference(miniscope,[status(thm)],[f_3872_2]) ).

cnf(f_3872_4,plain,
    ( hAPP(c_Random_Opick(U_15557,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15557)),U_15559),U_15561)),U_15555) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_15557),U_15559)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15555),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15557),U_15559))) ),
    inference(clausify,[status(thm)],[f_3872_3]) ).

cnf(f_3872_5,plain,
    ( hAPP(c_Random_Opick(U_15558,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15558)),U_15560),U_15562)),U_15556) = hAPP(c_Random_Opick(U_15558,U_15562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15556),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15558),U_15560)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_15556),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_15558),U_15560))) ),
    inference(clausify,[status(thm)],[f_3872_3]) ).

fof(f_3873_1,plain,
    ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(f_3873_2,plain,
    ! [U_15565,U_15564,U_15563] : c_Random_Oselect__weight(U_15563,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15563)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_15563),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_15564)),U_15565)) = c_Random_Oselect__weight(U_15563,U_15565),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

cnf(f_3873_3,plain,
    c_Random_Oselect__weight(U_15563,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_15563)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_15563),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_15564)),U_15565)) = c_Random_Oselect__weight(U_15563,U_15565),
    inference(clausify,[status(thm)],[f_3873_2]) ).

fof(f_3874_1,plain,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
            | V_a_2 != V_b_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons]) ).

fof(f_3874_2,plain,
    ! [U_15571,U_15570,U_15569,U_15568,U_15567,U_15566] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15566),tc_List_Olist(U_15566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15566),tc_List_Olist(U_15566)),hAPP(hAPP(c_List_Olist_OCons(U_15566),U_15567),U_15568)),hAPP(hAPP(c_List_Olist_OCons(U_15566),U_15569),U_15570))),c_List_Olexord(U_15566,U_15571)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15566),tc_List_Olist(U_15566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15566),tc_List_Olist(U_15566)),U_15568),U_15570)),c_List_Olexord(U_15566,U_15571)))
            | U_15567 != U_15569 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15566,U_15566)),hAPP(hAPP(c_Product__Type_OPair(U_15566,U_15566),U_15567),U_15569)),U_15571)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15566),tc_List_Olist(U_15566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15566),tc_List_Olist(U_15566)),U_15568),U_15570)),c_List_Olexord(U_15566,U_15571)))
          & U_15567 = U_15569 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15566,U_15566)),hAPP(hAPP(c_Product__Type_OPair(U_15566,U_15566),U_15567),U_15569)),U_15571))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15566),tc_List_Olist(U_15566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15566),tc_List_Olist(U_15566)),hAPP(hAPP(c_List_Olist_OCons(U_15566),U_15567),U_15568)),hAPP(hAPP(c_List_Olist_OCons(U_15566),U_15569),U_15570))),c_List_Olexord(U_15566,U_15571))) ) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

fof(f_3874_3,plain,
    ( ! [U_15583,U_15581,U_15579,U_15577,U_15575,U_15573] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15573),tc_List_Olist(U_15573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15573),tc_List_Olist(U_15573)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15575),U_15577)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15579),U_15581))),c_List_Olexord(U_15573,U_15583)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15573),tc_List_Olist(U_15573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15573),tc_List_Olist(U_15573)),U_15577),U_15581)),c_List_Olexord(U_15573,U_15583)))
            | U_15575 != U_15579 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15573,U_15573)),hAPP(hAPP(c_Product__Type_OPair(U_15573,U_15573),U_15575),U_15579)),U_15583)) ) )
    & ! [U_15582,U_15580,U_15578,U_15576,U_15574,U_15572] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15572),tc_List_Olist(U_15572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15572),tc_List_Olist(U_15572)),U_15576),U_15580)),c_List_Olexord(U_15572,U_15582)))
          & U_15574 = U_15578 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15572,U_15572)),hAPP(hAPP(c_Product__Type_OPair(U_15572,U_15572),U_15574),U_15578)),U_15582))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15572),tc_List_Olist(U_15572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15572),tc_List_Olist(U_15572)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15574),U_15576)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15578),U_15580))),c_List_Olexord(U_15572,U_15582))) ) ),
    inference(miniscope,[status(thm)],[f_3874_2]) ).

cnf(f_3874_4,plain,
    ( U_15574 = U_15578
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15572,U_15572)),hAPP(hAPP(c_Product__Type_OPair(U_15572,U_15572),U_15574),U_15578)),U_15582))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15572),tc_List_Olist(U_15572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15572),tc_List_Olist(U_15572)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15574),U_15576)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15578),U_15580))),c_List_Olexord(U_15572,U_15582))) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

cnf(f_3874_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15572),tc_List_Olist(U_15572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15572),tc_List_Olist(U_15572)),U_15576),U_15580)),c_List_Olexord(U_15572,U_15582)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15572,U_15572)),hAPP(hAPP(c_Product__Type_OPair(U_15572,U_15572),U_15574),U_15578)),U_15582))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15572),tc_List_Olist(U_15572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15572),tc_List_Olist(U_15572)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15574),U_15576)),hAPP(hAPP(c_List_Olist_OCons(U_15572),U_15578),U_15580))),c_List_Olexord(U_15572,U_15582))) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

cnf(f_3874_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15573,U_15573)),hAPP(hAPP(c_Product__Type_OPair(U_15573,U_15573),U_15575),U_15579)),U_15583))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15573),tc_List_Olist(U_15573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15573),tc_List_Olist(U_15573)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15575),U_15577)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15579),U_15581))),c_List_Olexord(U_15573,U_15583))) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

cnf(f_3874_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15573),tc_List_Olist(U_15573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15573),tc_List_Olist(U_15573)),U_15577),U_15581)),c_List_Olexord(U_15573,U_15583)))
    | U_15575 != U_15579
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15573),tc_List_Olist(U_15573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15573),tc_List_Olist(U_15573)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15575),U_15577)),hAPP(hAPP(c_List_Olist_OCons(U_15573),U_15579),U_15581))),c_List_Olexord(U_15573,U_15583))) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

fof(f_3875_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__lex]) ).

fof(f_3875_2,plain,
    ! [U_15587,U_15586,U_15585,U_15584] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15584),tc_List_Olist(U_15584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15584),tc_List_Olist(U_15584)),U_15585),U_15586)),c_List_Olex(U_15584,U_15587)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15584)),U_15585) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15584)),U_15586)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15584),tc_List_Olist(U_15584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15584),tc_List_Olist(U_15584)),U_15585),U_15586)),c_List_Olexord(U_15584,U_15587))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15584)),U_15585) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15584)),U_15586)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15584),tc_List_Olist(U_15584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15584),tc_List_Olist(U_15584)),U_15585),U_15586)),c_List_Olexord(U_15584,U_15587))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15584),tc_List_Olist(U_15584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15584),tc_List_Olist(U_15584)),U_15585),U_15586)),c_List_Olex(U_15584,U_15587))) ) ),
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

fof(f_3875_3,plain,
    ( ! [U_15595,U_15593,U_15591,U_15589] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15589),tc_List_Olist(U_15589))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15589),tc_List_Olist(U_15589)),U_15591),U_15593)),c_List_Olex(U_15589,U_15595)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15589)),U_15591) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15589)),U_15593)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15589),tc_List_Olist(U_15589))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15589),tc_List_Olist(U_15589)),U_15591),U_15593)),c_List_Olexord(U_15589,U_15595))) )
    & ! [U_15594,U_15592,U_15590,U_15588] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15588)),U_15590) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15588)),U_15592)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15588),tc_List_Olist(U_15588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15588),tc_List_Olist(U_15588)),U_15590),U_15592)),c_List_Olexord(U_15588,U_15594))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15588),tc_List_Olist(U_15588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15588),tc_List_Olist(U_15588)),U_15590),U_15592)),c_List_Olex(U_15588,U_15594))) ) ),
    inference(miniscope,[status(thm)],[f_3875_2]) ).

cnf(f_3875_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15588),tc_List_Olist(U_15588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15588),tc_List_Olist(U_15588)),U_15590),U_15592)),c_List_Olexord(U_15588,U_15594)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15588),tc_List_Olist(U_15588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15588),tc_List_Olist(U_15588)),U_15590),U_15592)),c_List_Olex(U_15588,U_15594))) ),
    inference(clausify,[status(thm)],[f_3875_3]) ).

cnf(f_3875_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15588)),U_15590) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15588)),U_15592)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15588),tc_List_Olist(U_15588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15588),tc_List_Olist(U_15588)),U_15590),U_15592)),c_List_Olex(U_15588,U_15594))) ),
    inference(clausify,[status(thm)],[f_3875_3]) ).

cnf(f_3875_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15589),tc_List_Olist(U_15589))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15589),tc_List_Olist(U_15589)),U_15591),U_15593)),c_List_Olex(U_15589,U_15595)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15589)),U_15591) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15589)),U_15593)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15589),tc_List_Olist(U_15589))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15589),tc_List_Olist(U_15589)),U_15591),U_15593)),c_List_Olexord(U_15589,U_15595))) ),
    inference(clausify,[status(thm)],[f_3875_3]) ).

fof(f_3876_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2]) ).

fof(f_3876_2,plain,
    ! [U_15601,U_15600,U_15599,U_15598,U_15597,U_15596] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15596),tc_List_Olist(U_15596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15596),tc_List_Olist(U_15596)),hAPP(hAPP(c_List_Olist_OCons(U_15596),U_15597),U_15600)),hAPP(hAPP(c_List_Olist_OCons(U_15596),U_15598),U_15601))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15596),c_List_Olistrel1(U_15596,U_15599))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15596),tc_List_Olist(U_15596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15596),tc_List_Olist(U_15596)),U_15600),U_15601)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15596),c_List_Olistrel1(U_15596,U_15599))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15596,U_15596)),hAPP(hAPP(c_Product__Type_OPair(U_15596,U_15596),U_15597),U_15598)),c_Transitive__Closure_Ortrancl(U_15596,U_15599))) ),
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

cnf(f_3876_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15596),tc_List_Olist(U_15596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15596),tc_List_Olist(U_15596)),hAPP(hAPP(c_List_Olist_OCons(U_15596),U_15597),U_15600)),hAPP(hAPP(c_List_Olist_OCons(U_15596),U_15598),U_15601))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15596),c_List_Olistrel1(U_15596,U_15599))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15596),tc_List_Olist(U_15596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15596),tc_List_Olist(U_15596)),U_15600),U_15601)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15596),c_List_Olistrel1(U_15596,U_15599))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15596,U_15596)),hAPP(hAPP(c_Product__Type_OPair(U_15596,U_15596),U_15597),U_15598)),c_Transitive__Closure_Ortrancl(U_15596,U_15599))) ),
    inference(clausify,[status(thm)],[f_3876_2]) ).

fof(f_3877_1,plain,
    ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),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_a,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_3877_2,plain,
    ! [U_15605,U_15604,U_15603,U_15602] : c_List_Olist_Olist__size(U_15602,U_15603,hAPP(hAPP(c_List_Olist_OCons(U_15602),U_15604),U_15605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15603,U_15604)),c_List_Olist_Olist__size(U_15602,U_15603,U_15605))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

cnf(f_3877_3,plain,
    c_List_Olist_Olist__size(U_15602,U_15603,hAPP(hAPP(c_List_Olist_OCons(U_15602),U_15604),U_15605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15603,U_15604)),c_List_Olist_Olist__size(U_15602,U_15603,U_15605))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3877_2]) ).

fof(f_3878_1,plain,
    ! [V_xs_2,V_r_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I]) ).

fof(f_3878_2,plain,
    ! [U_15609,U_15608,U_15607,U_15606] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15606)),hAPP(hAPP(c_List_Olist_OCons(U_15606),U_15607),U_15609)),c_Wellfounded_Oacc(tc_List_Olist(U_15606),c_List_Olistrel1(U_15606,U_15608))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15606)),U_15609),c_Wellfounded_Oacc(tc_List_Olist(U_15606),c_List_Olistrel1(U_15606,U_15608))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15606),U_15607),c_Wellfounded_Oacc(U_15606,U_15608))) ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

cnf(f_3878_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15606)),hAPP(hAPP(c_List_Olist_OCons(U_15606),U_15607),U_15609)),c_Wellfounded_Oacc(tc_List_Olist(U_15606),c_List_Olistrel1(U_15606,U_15608))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15606)),U_15609),c_Wellfounded_Oacc(tc_List_Olist(U_15606),c_List_Olistrel1(U_15606,U_15608))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15606),U_15607),c_Wellfounded_Oacc(U_15606,U_15608))) ),
    inference(clausify,[status(thm)],[f_3878_2]) ).

fof(f_3879_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__mono]) ).

fof(f_3879_2,plain,
    ! [U_15612,U_15611,U_15610] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15610),tc_List_Olist(U_15610)),tc_HOL_Obool)),c_List_Olistrel1(U_15610,U_15611)),c_List_Olistrel1(U_15610,U_15612)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15610,U_15610),tc_HOL_Obool)),U_15611),U_15612)) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

cnf(f_3879_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15610),tc_List_Olist(U_15610)),tc_HOL_Obool)),c_List_Olistrel1(U_15610,U_15611)),c_List_Olistrel1(U_15610,U_15612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15610,U_15610),tc_HOL_Obool)),U_15611),U_15612)) ),
    inference(clausify,[status(thm)],[f_3879_2]) ).

fof(f_3880_1,plain,
    ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel1__converse]) ).

fof(f_3880_2,plain,
    ! [U_15614,U_15613] : c_List_Olistrel1(U_15613,hAPP(c_Relation_Oconverse(U_15613,U_15613),U_15614)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15613),tc_List_Olist(U_15613)),c_List_Olistrel1(U_15613,U_15614)),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

cnf(f_3880_3,plain,
    c_List_Olistrel1(U_15613,hAPP(c_Relation_Oconverse(U_15613,U_15613),U_15614)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15613),tc_List_Olist(U_15613)),c_List_Olistrel1(U_15613,U_15614)),
    inference(clausify,[status(thm)],[f_3880_2]) ).

fof(f_3881_1,plain,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(f_3881_2,plain,
    ! [U_15616,U_15615] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15615),tc_List_Olist(U_15615)),tc_HOL_Obool)),c_List_Olistrel1(U_15615,c_Transitive__Closure_Ortrancl(U_15615,U_15616))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15615),c_List_Olistrel1(U_15615,U_15616)))),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

cnf(f_3881_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15615),tc_List_Olist(U_15615)),tc_HOL_Obool)),c_List_Olistrel1(U_15615,c_Transitive__Closure_Ortrancl(U_15615,U_15616))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15615),c_List_Olistrel1(U_15615,U_15616)))),
    inference(clausify,[status(thm)],[f_3881_2]) ).

fof(f_3882_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1]) ).

fof(f_3882_2,plain,
    ! [U_15621,U_15620,U_15619,U_15618,U_15617] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15617),tc_List_Olist(U_15617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15617),tc_List_Olist(U_15617)),hAPP(hAPP(c_List_Olist_OCons(U_15617),U_15621),U_15618)),hAPP(hAPP(c_List_Olist_OCons(U_15617),U_15621),U_15619))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15617),c_List_Olistrel1(U_15617,U_15620))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15617),tc_List_Olist(U_15617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15617),tc_List_Olist(U_15617)),U_15618),U_15619)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15617),c_List_Olistrel1(U_15617,U_15620)))) ),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

cnf(f_3882_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15617),tc_List_Olist(U_15617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15617),tc_List_Olist(U_15617)),hAPP(hAPP(c_List_Olist_OCons(U_15617),U_15621),U_15618)),hAPP(hAPP(c_List_Olist_OCons(U_15617),U_15621),U_15619))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15617),c_List_Olistrel1(U_15617,U_15620))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15617),tc_List_Olist(U_15617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15617),tc_List_Olist(U_15617)),U_15618),U_15619)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15617),c_List_Olistrel1(U_15617,U_15620)))) ),
    inference(clausify,[status(thm)],[f_3882_2]) ).

fof(f_3883_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I2]) ).

fof(f_3883_2,plain,
    ! [U_15626,U_15625,U_15624,U_15623,U_15622] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15622),tc_List_Olist(U_15622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15622),tc_List_Olist(U_15622)),hAPP(hAPP(c_List_Olist_OCons(U_15622),U_15626),U_15623)),hAPP(hAPP(c_List_Olist_OCons(U_15622),U_15626),U_15624))),c_List_Olistrel1(U_15622,U_15625)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15622),tc_List_Olist(U_15622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15622),tc_List_Olist(U_15622)),U_15623),U_15624)),c_List_Olistrel1(U_15622,U_15625))) ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

cnf(f_3883_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15622),tc_List_Olist(U_15622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15622),tc_List_Olist(U_15622)),hAPP(hAPP(c_List_Olist_OCons(U_15622),U_15626),U_15623)),hAPP(hAPP(c_List_Olist_OCons(U_15622),U_15626),U_15624))),c_List_Olistrel1(U_15622,U_15625)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15622),tc_List_Olist(U_15622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15622),tc_List_Olist(U_15622)),U_15623),U_15624)),c_List_Olistrel1(U_15622,U_15625))) ),
    inference(clausify,[status(thm)],[f_3883_2]) ).

fof(f_3884_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len]) ).

fof(f_3884_2,plain,
    ! [U_15630,U_15629,U_15628,U_15627] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15628) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15629)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15627),tc_List_Olist(U_15627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15627),tc_List_Olist(U_15627)),U_15628),U_15629)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15627),c_List_Olistrel1(U_15627,U_15630)))) ),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

cnf(f_3884_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15628) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15629)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15627),tc_List_Olist(U_15627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15627),tc_List_Olist(U_15627)),U_15628),U_15629)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15627),c_List_Olistrel1(U_15627,U_15630)))) ),
    inference(clausify,[status(thm)],[f_3884_2]) ).

fof(f_3885_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len]) ).

fof(f_3885_2,plain,
    ! [U_15634,U_15633,U_15632,U_15631] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15631)),U_15632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15631)),U_15633)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15631),tc_List_Olist(U_15631))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15631),tc_List_Olist(U_15631)),U_15632),U_15633)),c_List_Olistrel1(U_15631,U_15634))) ),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

cnf(f_3885_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15631)),U_15632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15631)),U_15633)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15631),tc_List_Olist(U_15631))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15631),tc_List_Olist(U_15631)),U_15632),U_15633)),c_List_Olistrel1(U_15631,U_15634))) ),
    inference(clausify,[status(thm)],[f_3885_2]) ).

fof(f_3886_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse]) ).

fof(f_3886_2,plain,
    ! [U_15638,U_15637,U_15636,U_15635] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15635),tc_List_Olist(U_15635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),U_15636),U_15637)),c_List_Olistrel1(U_15635,hAPP(c_Relation_Oconverse(U_15635,U_15635),U_15638))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15635),tc_List_Olist(U_15635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),U_15636),U_15637)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),c_List_Olistrel1(U_15635,U_15638)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15635),tc_List_Olist(U_15635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),U_15636),U_15637)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),c_List_Olistrel1(U_15635,U_15638))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15635),tc_List_Olist(U_15635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15635),tc_List_Olist(U_15635)),U_15636),U_15637)),c_List_Olistrel1(U_15635,hAPP(c_Relation_Oconverse(U_15635,U_15635),U_15638)))) ) ),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

fof(f_3886_3,plain,
    ( ! [U_15646,U_15644,U_15642,U_15640] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15640),tc_List_Olist(U_15640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),U_15642),U_15644)),c_List_Olistrel1(U_15640,hAPP(c_Relation_Oconverse(U_15640,U_15640),U_15646))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15640),tc_List_Olist(U_15640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),U_15642),U_15644)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),c_List_Olistrel1(U_15640,U_15646)))) )
    & ! [U_15645,U_15643,U_15641,U_15639] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15641),U_15643)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),c_List_Olistrel1(U_15639,U_15645))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15641),U_15643)),c_List_Olistrel1(U_15639,hAPP(c_Relation_Oconverse(U_15639,U_15639),U_15645)))) ) ),
    inference(miniscope,[status(thm)],[f_3886_2]) ).

cnf(f_3886_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15641),U_15643)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),c_List_Olistrel1(U_15639,U_15645))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15641),U_15643)),c_List_Olistrel1(U_15639,hAPP(c_Relation_Oconverse(U_15639,U_15639),U_15645)))) ),
    inference(clausify,[status(thm)],[f_3886_3]) ).

cnf(f_3886_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15640),tc_List_Olist(U_15640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),U_15642),U_15644)),c_List_Olistrel1(U_15640,hAPP(c_Relation_Oconverse(U_15640,U_15640),U_15646))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15640),tc_List_Olist(U_15640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),U_15642),U_15644)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15640),tc_List_Olist(U_15640)),c_List_Olistrel1(U_15640,U_15646)))) ),
    inference(clausify,[status(thm)],[f_3886_3]) ).

fof(f_3887_1,plain,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I1]) ).

fof(f_3887_2,plain,
    ! [U_15651,U_15650,U_15649,U_15648,U_15647] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15647),tc_List_Olist(U_15647))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15647),tc_List_Olist(U_15647)),hAPP(hAPP(c_List_Olist_OCons(U_15647),U_15648),U_15651)),hAPP(hAPP(c_List_Olist_OCons(U_15647),U_15649),U_15651))),c_List_Olistrel1(U_15647,U_15650)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15647,U_15647)),hAPP(hAPP(c_Product__Type_OPair(U_15647,U_15647),U_15648),U_15649)),U_15650)) ),
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

cnf(f_3887_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15647),tc_List_Olist(U_15647))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15647),tc_List_Olist(U_15647)),hAPP(hAPP(c_List_Olist_OCons(U_15647),U_15648),U_15651)),hAPP(hAPP(c_List_Olist_OCons(U_15647),U_15649),U_15651))),c_List_Olistrel1(U_15647,U_15650)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15647,U_15647)),hAPP(hAPP(c_Product__Type_OPair(U_15647,U_15647),U_15648),U_15649)),U_15650)) ),
    inference(clausify,[status(thm)],[f_3887_2]) ).

fof(f_3888_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( V_xs_2 != V_ys_2
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons]) ).

fof(f_3888_2,plain,
    ! [U_15657,U_15656,U_15655,U_15654,U_15653,U_15652] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15652),tc_List_Olist(U_15652))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15652),tc_List_Olist(U_15652)),hAPP(hAPP(c_List_Olist_OCons(U_15652),U_15653),U_15654)),hAPP(hAPP(c_List_Olist_OCons(U_15652),U_15655),U_15656))),c_List_Olistrel1(U_15652,U_15657)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15652),tc_List_Olist(U_15652))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15652),tc_List_Olist(U_15652)),U_15654),U_15656)),c_List_Olistrel1(U_15652,U_15657)))
            | U_15653 != U_15655 )
          & ( U_15654 != U_15656
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15652,U_15652)),hAPP(hAPP(c_Product__Type_OPair(U_15652,U_15652),U_15653),U_15655)),U_15657)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15652),tc_List_Olist(U_15652))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15652),tc_List_Olist(U_15652)),U_15654),U_15656)),c_List_Olistrel1(U_15652,U_15657)))
          & U_15653 = U_15655 )
        | ( U_15654 = U_15656
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15652,U_15652)),hAPP(hAPP(c_Product__Type_OPair(U_15652,U_15652),U_15653),U_15655)),U_15657)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15652),tc_List_Olist(U_15652))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15652),tc_List_Olist(U_15652)),hAPP(hAPP(c_List_Olist_OCons(U_15652),U_15653),U_15654)),hAPP(hAPP(c_List_Olist_OCons(U_15652),U_15655),U_15656))),c_List_Olistrel1(U_15652,U_15657))) ) ),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

fof(f_3888_3,plain,
    ( ! [U_15669,U_15667,U_15665,U_15663,U_15661,U_15659] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15659),tc_List_Olist(U_15659))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15659),tc_List_Olist(U_15659)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15661),U_15663)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15665),U_15667))),c_List_Olistrel1(U_15659,U_15669)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15659),tc_List_Olist(U_15659))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15659),tc_List_Olist(U_15659)),U_15663),U_15667)),c_List_Olistrel1(U_15659,U_15669)))
            | U_15661 != U_15665 )
          & ( U_15663 != U_15667
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15659,U_15659)),hAPP(hAPP(c_Product__Type_OPair(U_15659,U_15659),U_15661),U_15665)),U_15669)) ) ) )
    & ! [U_15668,U_15666,U_15664,U_15662,U_15660,U_15658] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),U_15662),U_15666)),c_List_Olistrel1(U_15658,U_15668)))
          & U_15660 = U_15664 )
        | ( U_15662 = U_15666
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15660),U_15664)),U_15668)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15660),U_15662)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15664),U_15666))),c_List_Olistrel1(U_15658,U_15668))) ) ),
    inference(miniscope,[status(thm)],[f_3888_2]) ).

cnf(f_3888_4,plain,
    ( U_15660 = U_15664
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15660),U_15664)),U_15668))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15660),U_15662)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15664),U_15666))),c_List_Olistrel1(U_15658,U_15668))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

cnf(f_3888_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),U_15662),U_15666)),c_List_Olistrel1(U_15658,U_15668)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15660),U_15664)),U_15668))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15660),U_15662)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15664),U_15666))),c_List_Olistrel1(U_15658,U_15668))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

cnf(f_3888_6,plain,
    ( U_15660 = U_15664
    | U_15662 = U_15666
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15660),U_15662)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15664),U_15666))),c_List_Olistrel1(U_15658,U_15668))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

cnf(f_3888_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),U_15662),U_15666)),c_List_Olistrel1(U_15658,U_15668)))
    | U_15662 = U_15666
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15658),tc_List_Olist(U_15658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15658),tc_List_Olist(U_15658)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15660),U_15662)),hAPP(hAPP(c_List_Olist_OCons(U_15658),U_15664),U_15666))),c_List_Olistrel1(U_15658,U_15668))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

cnf(f_3888_8,plain,
    ( U_15663 != U_15667
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15659,U_15659)),hAPP(hAPP(c_Product__Type_OPair(U_15659,U_15659),U_15661),U_15665)),U_15669))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15659),tc_List_Olist(U_15659))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15659),tc_List_Olist(U_15659)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15661),U_15663)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15665),U_15667))),c_List_Olistrel1(U_15659,U_15669))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

cnf(f_3888_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15659),tc_List_Olist(U_15659))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15659),tc_List_Olist(U_15659)),U_15663),U_15667)),c_List_Olistrel1(U_15659,U_15669)))
    | U_15661 != U_15665
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15659),tc_List_Olist(U_15659))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15659),tc_List_Olist(U_15659)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15661),U_15663)),hAPP(hAPP(c_List_Olist_OCons(U_15659),U_15665),U_15667))),c_List_Olistrel1(U_15659,U_15669))) ),
    inference(clausify,[status(thm)],[f_3888_3]) ).

fof(f_3889_1,plain,
    ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons]) ).

fof(f_3889_2,plain,
    ! [U_15673,U_15672,U_15671,U_15670] : hAPP(c_Relation_OImage(tc_List_Olist(U_15670),tc_List_Olist(U_15670),c_List_Olistrel(U_15670,U_15671)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15670)),hAPP(hAPP(c_List_Olist_OCons(U_15670),U_15672),U_15673)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15670),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15670,hAPP(c_Relation_OImage(U_15670,U_15670,U_15671),hAPP(hAPP(c_Set_Oinsert(U_15670),U_15672),c_Orderings_Obot__class_Obot(tc_fun(U_15670,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15670),tc_List_Olist(U_15670),c_List_Olistrel(U_15670,U_15671)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15670)),U_15673),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15670),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

cnf(f_3889_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_15670),tc_List_Olist(U_15670),c_List_Olistrel(U_15670,U_15671)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15670)),hAPP(hAPP(c_List_Olist_OCons(U_15670),U_15672),U_15673)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15670),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15670,hAPP(c_Relation_OImage(U_15670,U_15670,U_15671),hAPP(hAPP(c_Set_Oinsert(U_15670),U_15672),c_Orderings_Obot__class_Obot(tc_fun(U_15670,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15670),tc_List_Olist(U_15670),c_List_Olistrel(U_15670,U_15671)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15670)),U_15673),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15670),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3889_2]) ).

fof(f_3890_1,plain,
    ! [V_y_2,V_r_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__irreflexive]) ).

fof(f_3890_2,plain,
    ! [U_15677,U_15676,U_15675] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15675),tc_List_Olist(U_15675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15675),tc_List_Olist(U_15675)),U_15677),U_15677)),c_List_Olexord(U_15675,U_15676)))
      | ? [U_15674] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),U_15674),U_15674)),U_15676)) ),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

fof(f_3890_3,plain,
    ! [U_15677,U_15676,U_15675] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15675),tc_List_Olist(U_15675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15675),tc_List_Olist(U_15675)),U_15677),U_15677)),c_List_Olexord(U_15675,U_15676)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),sK413(U_15677,U_15676,U_15675)),sK413(U_15677,U_15676,U_15675))),U_15676)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_15674,sK413(U_15677,U_15676,U_15675))],[f_3890_2]) ).

cnf(f_3890_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15675),tc_List_Olist(U_15675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15675),tc_List_Olist(U_15675)),U_15677),U_15677)),c_List_Olexord(U_15675,U_15676)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15675,U_15675)),hAPP(hAPP(c_Product__Type_OPair(U_15675,U_15675),sK413(U_15677,U_15676,U_15675)),sK413(U_15677,U_15676,U_15675))),U_15676)) ),
    inference(clausify,[status(thm)],[f_3890_3]) ).

fof(f_3891_1,plain,
    ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__refl]) ).

fof(f_3891_2,plain,
    ! [U_15680,U_15679,U_15678] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15678),tc_List_Olist(U_15678))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15678),tc_List_Olist(U_15678)),U_15679),U_15679)),c_List_Olistrel(U_15678,c_Transitive__Closure_Ortrancl(U_15678,U_15680)))),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

cnf(f_3891_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15678),tc_List_Olist(U_15678))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15678),tc_List_Olist(U_15678)),U_15679),U_15679)),c_List_Olistrel(U_15678,c_Transitive__Closure_Ortrancl(U_15678,U_15680)))),
    inference(clausify,[status(thm)],[f_3891_2]) ).

fof(f_3892_1,plain,
    ! [V_s_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__mono]) ).

fof(f_3892_2,plain,
    ! [U_15683,U_15682,U_15681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15681),tc_List_Olist(U_15681)),tc_HOL_Obool)),c_List_Olistrel(U_15681,U_15682)),c_List_Olistrel(U_15681,U_15683)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15681,U_15681),tc_HOL_Obool)),U_15682),U_15683)) ),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

cnf(f_3892_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15681),tc_List_Olist(U_15681)),tc_HOL_Obool)),c_List_Olistrel(U_15681,U_15682)),c_List_Olistrel(U_15681,U_15683)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15681,U_15681),tc_HOL_Obool)),U_15682),U_15683)) ),
    inference(clausify,[status(thm)],[f_3892_2]) ).

fof(f_3893_1,plain,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(f_3893_2,plain,
    ! [U_15685,U_15684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15684),tc_List_Olist(U_15684)),tc_HOL_Obool)),c_List_Olistrel(U_15684,U_15685)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15684),c_List_Olistrel1(U_15684,U_15685)))),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

cnf(f_3893_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15684),tc_List_Olist(U_15684)),tc_HOL_Obool)),c_List_Olistrel(U_15684,U_15685)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15684),c_List_Olistrel1(U_15684,U_15685)))),
    inference(clausify,[status(thm)],[f_3893_2]) ).

fof(f_3894_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__eq__len]) ).

fof(f_3894_2,plain,
    ! [U_15689,U_15688,U_15687,U_15686] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15686)),U_15687) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15686)),U_15688)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15686),tc_List_Olist(U_15686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15686),tc_List_Olist(U_15686)),U_15687),U_15688)),c_List_Olistrel(U_15686,U_15689))) ),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

cnf(f_3894_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15686)),U_15687) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15686)),U_15688)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15686),tc_List_Olist(U_15686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15686),tc_List_Olist(U_15686)),U_15687),U_15688)),c_List_Olistrel(U_15686,U_15689))) ),
    inference(clausify,[status(thm)],[f_3894_2]) ).

fof(f_3895_1,plain,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans]) ).

fof(f_3895_2,plain,
    ! [U_15694,U_15693,U_15692,U_15691,U_15690] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15691),U_15694)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15692),U_15694)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15691),U_15692)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693)))) ),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

cnf(f_3895_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15691),U_15694)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15692),U_15694)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15690),tc_List_Olist(U_15690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15690),tc_List_Olist(U_15690)),U_15691),U_15692)),c_List_Olistrel(U_15690,c_Transitive__Closure_Ortrancl(U_15690,U_15693)))) ),
    inference(clausify,[status(thm)],[f_3895_2]) ).

fof(f_3896_1,plain,
    ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(f_3896_2,plain,
    ! [U_15696,U_15695] : c_List_Olistrel(U_15695,c_Transitive__Closure_Ortrancl(U_15695,U_15696)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15695),c_List_Olistrel1(U_15695,U_15696)),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

cnf(f_3896_3,plain,
    c_List_Olistrel(U_15695,c_Transitive__Closure_Ortrancl(U_15695,U_15696)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15695),c_List_Olistrel1(U_15695,U_15696)),
    inference(clausify,[status(thm)],[f_3896_2]) ).

fof(f_3897_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1]) ).

fof(f_3897_2,plain,
    ! [U_15700,U_15699,U_15698,U_15697] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15697),tc_List_Olist(U_15697))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15697),tc_List_Olist(U_15697)),U_15698),U_15699)),c_List_Olistrel(U_15697,c_Transitive__Closure_Ortrancl(U_15697,U_15700))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15697),tc_List_Olist(U_15697))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15697),tc_List_Olist(U_15697)),U_15698),U_15699)),c_List_Olistrel1(U_15697,U_15700))) ),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

cnf(f_3897_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15697),tc_List_Olist(U_15697))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15697),tc_List_Olist(U_15697)),U_15698),U_15699)),c_List_Olistrel(U_15697,c_Transitive__Closure_Ortrancl(U_15697,U_15700))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15697),tc_List_Olist(U_15697))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15697),tc_List_Olist(U_15697)),U_15698),U_15699)),c_List_Olistrel1(U_15697,U_15700))) ),
    inference(clausify,[status(thm)],[f_3897_2]) ).

fof(f_3898_1,plain,
    ! [V_r_H_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2)))
      | ~ c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel]) ).

fof(f_3898_2,plain,
    ! [U_15703,U_15702,U_15701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15701),tc_List_Olist(U_15701)),tc_HOL_Obool)),c_List_Olistrel1(U_15701,U_15702)),c_List_Olistrel(U_15701,U_15703)))
      | ~ c_Relation_Orefl__on(U_15701,c_Orderings_Otop__class_Otop(tc_fun(U_15701,tc_HOL_Obool)),U_15703)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15701,U_15701),tc_HOL_Obool)),U_15702),U_15703)) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

cnf(f_3898_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15701),tc_List_Olist(U_15701)),tc_HOL_Obool)),c_List_Olistrel1(U_15701,U_15702)),c_List_Olistrel(U_15701,U_15703)))
    | ~ c_Relation_Orefl__on(U_15701,c_Orderings_Otop__class_Otop(tc_fun(U_15701,tc_HOL_Obool)),U_15703)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15701,U_15701),tc_HOL_Obool)),U_15702),U_15703)) ),
    inference(clausify,[status(thm)],[f_3898_2]) ).

fof(f_3899_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel]) ).

fof(f_3899_2,plain,
    ! [U_15707,U_15706,U_15705,U_15704] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15704),tc_List_Olist(U_15704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15704),tc_List_Olist(U_15704)),U_15705),U_15706)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15704),c_List_Olistrel1(U_15704,U_15707))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15704),tc_List_Olist(U_15704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15704),tc_List_Olist(U_15704)),U_15705),U_15706)),c_List_Olistrel(U_15704,U_15707))) ),
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

cnf(f_3899_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15704),tc_List_Olist(U_15704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15704),tc_List_Olist(U_15704)),U_15705),U_15706)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15704),c_List_Olistrel1(U_15704,U_15707))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15704),tc_List_Olist(U_15704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15704),tc_List_Olist(U_15704)),U_15705),U_15706)),c_List_Olistrel(U_15704,U_15707))) ),
    inference(clausify,[status(thm)],[f_3899_2]) ).

fof(f_3900_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel_OCons]) ).

fof(f_3900_2,plain,
    ! [U_15713,U_15712,U_15711,U_15710,U_15709,U_15708] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15708),tc_List_Olist(U_15708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15708),tc_List_Olist(U_15708)),hAPP(hAPP(c_List_Olist_OCons(U_15708),U_15709),U_15712)),hAPP(hAPP(c_List_Olist_OCons(U_15708),U_15710),U_15713))),c_List_Olistrel(U_15708,U_15711)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15708),tc_List_Olist(U_15708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15708),tc_List_Olist(U_15708)),U_15712),U_15713)),c_List_Olistrel(U_15708,U_15711)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15708,U_15708)),hAPP(hAPP(c_Product__Type_OPair(U_15708,U_15708),U_15709),U_15710)),U_15711)) ),
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

cnf(f_3900_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15708),tc_List_Olist(U_15708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15708),tc_List_Olist(U_15708)),hAPP(hAPP(c_List_Olist_OCons(U_15708),U_15709),U_15712)),hAPP(hAPP(c_List_Olist_OCons(U_15708),U_15710),U_15713))),c_List_Olistrel(U_15708,U_15711)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15708),tc_List_Olist(U_15708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15708),tc_List_Olist(U_15708)),U_15712),U_15713)),c_List_Olistrel(U_15708,U_15711)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15708,U_15708)),hAPP(hAPP(c_Product__Type_OPair(U_15708,U_15708),U_15709),U_15710)),U_15711)) ),
    inference(clausify,[status(thm)],[f_3900_2]) ).

fof(f_3901_1,plain,
    ! [V_xa_2,V_x_2,V_r_2,T_a] :
      ( ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2)))
        | ~ c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq]) ).

fof(f_3901_2,plain,
    ! [U_15717,U_15716,U_15715,U_15714] :
      ( ( c_List_Olistrelp(U_15714,hAPP(hAPP(c_COMBC(U_15714,tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_fun(U_15714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15714,tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_fun(U_15714,tc_HOL_Obool)),U_15714),c_COMBC(U_15714,tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15714,tc_prod(U_15714,U_15714)),tc_fun(U_15714,tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),U_15714),hAPP(c_COMBB(tc_prod(U_15714,U_15714),tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool),U_15714),c_member(tc_prod(U_15714,U_15714)))),c_Product__Type_OPair(U_15714,U_15714)))),U_15715),U_15716,U_15717)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15714),tc_List_Olist(U_15714))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15714),tc_List_Olist(U_15714)),U_15716),U_15717)),c_List_Olistrel(U_15714,U_15715))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15714),tc_List_Olist(U_15714))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15714),tc_List_Olist(U_15714)),U_15716),U_15717)),c_List_Olistrel(U_15714,U_15715)))
        | ~ c_List_Olistrelp(U_15714,hAPP(hAPP(c_COMBC(U_15714,tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_fun(U_15714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15714,tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_fun(U_15714,tc_HOL_Obool)),U_15714),c_COMBC(U_15714,tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15714,tc_prod(U_15714,U_15714)),tc_fun(U_15714,tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool)),U_15714),hAPP(c_COMBB(tc_prod(U_15714,U_15714),tc_fun(tc_fun(tc_prod(U_15714,U_15714),tc_HOL_Obool),tc_HOL_Obool),U_15714),c_member(tc_prod(U_15714,U_15714)))),c_Product__Type_OPair(U_15714,U_15714)))),U_15715),U_15716,U_15717) ) ),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

fof(f_3901_3,plain,
    ( ! [U_15725,U_15723,U_15721,U_15719] :
        ( c_List_Olistrelp(U_15719,hAPP(hAPP(c_COMBC(U_15719,tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_fun(U_15719,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15719,tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_fun(U_15719,tc_HOL_Obool)),U_15719),c_COMBC(U_15719,tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15719,tc_prod(U_15719,U_15719)),tc_fun(U_15719,tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),U_15719),hAPP(c_COMBB(tc_prod(U_15719,U_15719),tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool),U_15719),c_member(tc_prod(U_15719,U_15719)))),c_Product__Type_OPair(U_15719,U_15719)))),U_15721),U_15723,U_15725)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15719),tc_List_Olist(U_15719))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15719),tc_List_Olist(U_15719)),U_15723),U_15725)),c_List_Olistrel(U_15719,U_15721))) )
    & ! [U_15724,U_15722,U_15720,U_15718] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15718),tc_List_Olist(U_15718))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15718),tc_List_Olist(U_15718)),U_15722),U_15724)),c_List_Olistrel(U_15718,U_15720)))
        | ~ c_List_Olistrelp(U_15718,hAPP(hAPP(c_COMBC(U_15718,tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_fun(U_15718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15718,tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_fun(U_15718,tc_HOL_Obool)),U_15718),c_COMBC(U_15718,tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15718,tc_prod(U_15718,U_15718)),tc_fun(U_15718,tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),U_15718),hAPP(c_COMBB(tc_prod(U_15718,U_15718),tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool),U_15718),c_member(tc_prod(U_15718,U_15718)))),c_Product__Type_OPair(U_15718,U_15718)))),U_15720),U_15722,U_15724) ) ),
    inference(miniscope,[status(thm)],[f_3901_2]) ).

cnf(f_3901_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15718),tc_List_Olist(U_15718))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15718),tc_List_Olist(U_15718)),U_15722),U_15724)),c_List_Olistrel(U_15718,U_15720)))
    | ~ c_List_Olistrelp(U_15718,hAPP(hAPP(c_COMBC(U_15718,tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_fun(U_15718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15718,tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_fun(U_15718,tc_HOL_Obool)),U_15718),c_COMBC(U_15718,tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15718,tc_prod(U_15718,U_15718)),tc_fun(U_15718,tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool)),U_15718),hAPP(c_COMBB(tc_prod(U_15718,U_15718),tc_fun(tc_fun(tc_prod(U_15718,U_15718),tc_HOL_Obool),tc_HOL_Obool),U_15718),c_member(tc_prod(U_15718,U_15718)))),c_Product__Type_OPair(U_15718,U_15718)))),U_15720),U_15722,U_15724) ),
    inference(clausify,[status(thm)],[f_3901_3]) ).

cnf(f_3901_5,plain,
    ( c_List_Olistrelp(U_15719,hAPP(hAPP(c_COMBC(U_15719,tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_fun(U_15719,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15719,tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_fun(U_15719,tc_HOL_Obool)),U_15719),c_COMBC(U_15719,tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15719,tc_prod(U_15719,U_15719)),tc_fun(U_15719,tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool)),U_15719),hAPP(c_COMBB(tc_prod(U_15719,U_15719),tc_fun(tc_fun(tc_prod(U_15719,U_15719),tc_HOL_Obool),tc_HOL_Obool),U_15719),c_member(tc_prod(U_15719,U_15719)))),c_Product__Type_OPair(U_15719,U_15719)))),U_15721),U_15723,U_15725)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15719),tc_List_Olist(U_15719))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15719),tc_List_Olist(U_15719)),U_15723),U_15725)),c_List_Olistrel(U_15719,U_15721))) ),
    inference(clausify,[status(thm)],[f_3901_3]) ).

fof(f_3902_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
      ( ? [B_x,B_xs] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons2]) ).

fof(f_3902_2,plain,
    ! [U_15732,U_15731,U_15730,U_15729,U_15728] :
      ( ? [U_15727,U_15726] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15726),U_15731)),c_List_Olistrel(U_15728,U_15732)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15728,U_15728)),hAPP(hAPP(c_Product__Type_OPair(U_15728,U_15728),U_15727),U_15730)),U_15732))
          & U_15729 = hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15727),U_15726) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

fof(f_3902_3,plain,
    ! [U_15732,U_15731,U_15730,U_15729,U_15728] :
      ( ? [U_15726] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15726),U_15731)),c_List_Olistrel(U_15728,U_15732)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15728,U_15728)),hAPP(hAPP(c_Product__Type_OPair(U_15728,U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15730)),U_15732))
          & U_15729 = hAPP(hAPP(c_List_Olist_OCons(U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15726) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_15727,sK414(U_15732,U_15731,U_15730,U_15729,U_15728))],[f_3902_2]) ).

fof(f_3902_4,plain,
    ! [U_15732,U_15731,U_15730,U_15729,U_15728] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),sK415(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15731)),c_List_Olistrel(U_15728,U_15732)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15728,U_15728)),hAPP(hAPP(c_Product__Type_OPair(U_15728,U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15730)),U_15732))
        & U_15729 = hAPP(hAPP(c_List_Olist_OCons(U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),sK415(U_15732,U_15731,U_15730,U_15729,U_15728)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_15726,sK415(U_15732,U_15731,U_15730,U_15729,U_15728))],[f_3902_3]) ).

cnf(f_3902_5,plain,
    ( U_15729 = hAPP(hAPP(c_List_Olist_OCons(U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),sK415(U_15732,U_15731,U_15730,U_15729,U_15728))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(clausify,[status(thm)],[f_3902_4]) ).

cnf(f_3902_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15728,U_15728)),hAPP(hAPP(c_Product__Type_OPair(U_15728,U_15728),sK414(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15730)),U_15732))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(clausify,[status(thm)],[f_3902_4]) ).

cnf(f_3902_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),sK415(U_15732,U_15731,U_15730,U_15729,U_15728)),U_15731)),c_List_Olistrel(U_15728,U_15732)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),hAPP(hAPP(c_List_Olist_OCons(U_15728),U_15730),U_15731))),c_List_Olistrel(U_15728,U_15732))) ),
    inference(clausify,[status(thm)],[f_3902_4]) ).

fof(f_3903_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
      ( ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2))
        | ~ c_List_Olistrelp(T_a,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_a,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_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J]) ).

fof(f_3903_2,plain,
    ! [U_15738,U_15737,U_15736,U_15735,U_15734,U_15733] :
      ( ( c_List_Olistrelp(U_15733,U_15734,hAPP(hAPP(c_List_Olist_OCons(U_15733),U_15735),U_15736),hAPP(hAPP(c_List_Olist_OCons(U_15733),U_15737),U_15738))
        | ~ c_List_Olistrelp(U_15733,U_15734,U_15736,U_15738)
        | ~ hBOOL(hAPP(hAPP(U_15734,U_15735),U_15737)) )
      & ( ( c_List_Olistrelp(U_15733,U_15734,U_15736,U_15738)
          & hBOOL(hAPP(hAPP(U_15734,U_15735),U_15737)) )
        | ~ c_List_Olistrelp(U_15733,U_15734,hAPP(hAPP(c_List_Olist_OCons(U_15733),U_15735),U_15736),hAPP(hAPP(c_List_Olist_OCons(U_15733),U_15737),U_15738)) ) ),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

fof(f_3903_3,plain,
    ( ! [U_15750,U_15748,U_15746,U_15744,U_15742,U_15740] :
        ( c_List_Olistrelp(U_15740,U_15742,hAPP(hAPP(c_List_Olist_OCons(U_15740),U_15744),U_15746),hAPP(hAPP(c_List_Olist_OCons(U_15740),U_15748),U_15750))
        | ~ c_List_Olistrelp(U_15740,U_15742,U_15746,U_15750)
        | ~ hBOOL(hAPP(hAPP(U_15742,U_15744),U_15748)) )
    & ! [U_15749,U_15747,U_15745,U_15743,U_15741,U_15739] :
        ( ( c_List_Olistrelp(U_15739,U_15741,U_15745,U_15749)
          & hBOOL(hAPP(hAPP(U_15741,U_15743),U_15747)) )
        | ~ c_List_Olistrelp(U_15739,U_15741,hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15743),U_15745),hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15747),U_15749)) ) ),
    inference(miniscope,[status(thm)],[f_3903_2]) ).

cnf(f_3903_4,plain,
    ( hBOOL(hAPP(hAPP(U_15741,U_15743),U_15747))
    | ~ c_List_Olistrelp(U_15739,U_15741,hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15743),U_15745),hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15747),U_15749)) ),
    inference(clausify,[status(thm)],[f_3903_3]) ).

cnf(f_3903_5,plain,
    ( c_List_Olistrelp(U_15739,U_15741,U_15745,U_15749)
    | ~ c_List_Olistrelp(U_15739,U_15741,hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15743),U_15745),hAPP(hAPP(c_List_Olist_OCons(U_15739),U_15747),U_15749)) ),
    inference(clausify,[status(thm)],[f_3903_3]) ).

cnf(f_3903_6,plain,
    ( c_List_Olistrelp(U_15740,U_15742,hAPP(hAPP(c_List_Olist_OCons(U_15740),U_15744),U_15746),hAPP(hAPP(c_List_Olist_OCons(U_15740),U_15748),U_15750))
    | ~ c_List_Olistrelp(U_15740,U_15742,U_15746,U_15750)
    | ~ hBOOL(hAPP(hAPP(U_15742,U_15744),U_15748)) ),
    inference(clausify,[status(thm)],[f_3903_3]) ).

fof(f_3904_1,plain,
    ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
      ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))
      | ~ c_List_Olistrelp(T_a,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_3904_2,plain,
    ! [U_15756,U_15755,U_15754,U_15753,U_15752,U_15751] :
      ( c_List_Olistrelp(U_15754,U_15751,hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15752),U_15755),hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15753),U_15756))
      | ~ c_List_Olistrelp(U_15754,U_15751,U_15755,U_15756)
      | ~ hBOOL(hAPP(hAPP(U_15751,U_15752),U_15753)) ),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

cnf(f_3904_3,plain,
    ( c_List_Olistrelp(U_15754,U_15751,hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15752),U_15755),hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15753),U_15756))
    | ~ c_List_Olistrelp(U_15754,U_15751,U_15755,U_15756)
    | ~ hBOOL(hAPP(hAPP(U_15751,U_15752),U_15753)) ),
    inference(clausify,[status(thm)],[f_3904_2]) ).

fof(f_3905_1,plain,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
      ( ? [B_y,B_ys] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons1]) ).

fof(f_3905_2,plain,
    ! [U_15763,U_15762,U_15761,U_15760,U_15759] :
      ( ? [U_15758,U_15757] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),U_15761),U_15757)),c_List_Olistrel(U_15759,U_15763)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15759,U_15759)),hAPP(hAPP(c_Product__Type_OPair(U_15759,U_15759),U_15760),U_15758)),U_15763))
          & U_15762 = hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15758),U_15757) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

fof(f_3905_3,plain,
    ! [U_15763,U_15762,U_15761,U_15760,U_15759] :
      ( ? [U_15757] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),U_15761),U_15757)),c_List_Olistrel(U_15759,U_15763)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15759,U_15759)),hAPP(hAPP(c_Product__Type_OPair(U_15759,U_15759),U_15760),sK416(U_15763,U_15762,U_15761,U_15760,U_15759))),U_15763))
          & U_15762 = hAPP(hAPP(c_List_Olist_OCons(U_15759),sK416(U_15763,U_15762,U_15761,U_15760,U_15759)),U_15757) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_15758,sK416(U_15763,U_15762,U_15761,U_15760,U_15759))],[f_3905_2]) ).

fof(f_3905_4,plain,
    ! [U_15763,U_15762,U_15761,U_15760,U_15759] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),U_15761),sK417(U_15763,U_15762,U_15761,U_15760,U_15759))),c_List_Olistrel(U_15759,U_15763)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15759,U_15759)),hAPP(hAPP(c_Product__Type_OPair(U_15759,U_15759),U_15760),sK416(U_15763,U_15762,U_15761,U_15760,U_15759))),U_15763))
        & U_15762 = hAPP(hAPP(c_List_Olist_OCons(U_15759),sK416(U_15763,U_15762,U_15761,U_15760,U_15759)),sK417(U_15763,U_15762,U_15761,U_15760,U_15759)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_15757,sK417(U_15763,U_15762,U_15761,U_15760,U_15759))],[f_3905_3]) ).

cnf(f_3905_5,plain,
    ( U_15762 = hAPP(hAPP(c_List_Olist_OCons(U_15759),sK416(U_15763,U_15762,U_15761,U_15760,U_15759)),sK417(U_15763,U_15762,U_15761,U_15760,U_15759))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(clausify,[status(thm)],[f_3905_4]) ).

cnf(f_3905_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15759,U_15759)),hAPP(hAPP(c_Product__Type_OPair(U_15759,U_15759),U_15760),sK416(U_15763,U_15762,U_15761,U_15760,U_15759))),U_15763))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(clausify,[status(thm)],[f_3905_4]) ).

cnf(f_3905_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),U_15761),sK417(U_15763,U_15762,U_15761,U_15760,U_15759))),c_List_Olistrel(U_15759,U_15763)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15759),tc_List_Olist(U_15759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15759),tc_List_Olist(U_15759)),hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15760),U_15761)),U_15762)),c_List_Olistrel(U_15759,U_15763))) ),
    inference(clausify,[status(thm)],[f_3905_4]) ).

fof(f_3906_1,plain,
    ! [V_A_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset]) ).

fof(f_3906_2,plain,
    ! [U_15766,U_15765,U_15764] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15764),tc_List_Olist(U_15764)),tc_HOL_Obool)),c_List_Olistrel(U_15764,U_15765)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15764),tc_List_Olist(U_15764)),c_List_Olists(U_15764,U_15766)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15764),tc_HOL_Obool),tc_List_Olist(U_15764)),c_List_Olists(U_15764,U_15766)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15764,U_15764),tc_HOL_Obool)),U_15765),hAPP(hAPP(c_Product__Type_OSigma(U_15764,U_15764),U_15766),hAPP(c_COMBK(tc_fun(U_15764,tc_HOL_Obool),U_15764),U_15766)))) ),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

cnf(f_3906_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15764),tc_List_Olist(U_15764)),tc_HOL_Obool)),c_List_Olistrel(U_15764,U_15765)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15764),tc_List_Olist(U_15764)),c_List_Olists(U_15764,U_15766)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15764),tc_HOL_Obool),tc_List_Olist(U_15764)),c_List_Olists(U_15764,U_15766)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15764,U_15764),tc_HOL_Obool)),U_15765),hAPP(hAPP(c_Product__Type_OSigma(U_15764,U_15764),U_15766),hAPP(c_COMBK(tc_fun(U_15764,tc_HOL_Obool),U_15764),U_15766)))) ),
    inference(clausify,[status(thm)],[f_3906_2]) ).

fof(f_3907_1,plain,
    ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lists__UNIV]) ).

fof(f_3907_2,plain,
    ! [U_15767] : c_List_Olists(U_15767,c_Orderings_Otop__class_Otop(tc_fun(U_15767,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15767),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3907_1]) ).

cnf(f_3907_3,plain,
    c_List_Olists(U_15767,c_Orderings_Otop__class_Otop(tc_fun(U_15767,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15767),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3907_2]) ).

fof(f_3908_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lists__mono]) ).

fof(f_3908_2,plain,
    ! [U_15770,U_15769,U_15768] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15768),tc_HOL_Obool)),c_List_Olists(U_15768,U_15769)),c_List_Olists(U_15768,U_15770)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15768,tc_HOL_Obool)),U_15769),U_15770)) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

cnf(f_3908_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15768),tc_HOL_Obool)),c_List_Olists(U_15768,U_15769)),c_List_Olists(U_15768,U_15770)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15768,tc_HOL_Obool)),U_15769),U_15770)) ),
    inference(clausify,[status(thm)],[f_3908_2]) ).

fof(f_3909_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__listrel]) ).

fof(f_3909_2,plain,
    ! [U_15773,U_15772,U_15771] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15771),c_List_Olists(U_15771,U_15772),c_List_Olistrel(U_15771,U_15773))
      | ~ c_Equiv__Relations_Oequiv(U_15771,U_15772,U_15773) ),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

cnf(f_3909_3,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15771),c_List_Olists(U_15771,U_15772),c_List_Olistrel(U_15771,U_15773))
    | ~ c_Equiv__Relations_Oequiv(U_15771,U_15772,U_15773) ),
    inference(clausify,[status(thm)],[f_3909_2]) ).

fof(f_3910_1,plain,
    ! [V_r_2,V_A_2,T_a] :
      ( c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2))
      | ~ c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__refl__on]) ).

fof(f_3910_2,plain,
    ! [U_15776,U_15775,U_15774] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_15774),c_List_Olists(U_15774,U_15775),c_List_Olistrel(U_15774,U_15776))
      | ~ c_Relation_Orefl__on(U_15774,U_15775,U_15776) ),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

cnf(f_3910_3,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_15774),c_List_Olists(U_15774,U_15775),c_List_Olistrel(U_15774,U_15776))
    | ~ c_Relation_Orefl__on(U_15774,U_15775,U_15776) ),
    inference(clausify,[status(thm)],[f_3910_2]) ).

fof(f_3911_1,plain,
    ! [V_A_2,V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff]) ).

fof(f_3911_2,plain,
    ! [U_15780,U_15779,U_15778,U_15777] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15777)),hAPP(hAPP(c_List_Olist_OCons(U_15777),U_15778),U_15779)),c_List_Olists(U_15777,U_15780)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15777)),U_15779),c_List_Olists(U_15777,U_15780)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15777),U_15778),U_15780)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15777)),U_15779),c_List_Olists(U_15777,U_15780)))
          & hBOOL(hAPP(hAPP(c_member(U_15777),U_15778),U_15780)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15777)),hAPP(hAPP(c_List_Olist_OCons(U_15777),U_15778),U_15779)),c_List_Olists(U_15777,U_15780))) ) ),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

fof(f_3911_3,plain,
    ( ! [U_15788,U_15786,U_15784,U_15782] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15782)),hAPP(hAPP(c_List_Olist_OCons(U_15782),U_15784),U_15786)),c_List_Olists(U_15782,U_15788)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15782)),U_15786),c_List_Olists(U_15782,U_15788)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15782),U_15784),U_15788)) )
    & ! [U_15787,U_15785,U_15783,U_15781] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15781)),U_15785),c_List_Olists(U_15781,U_15787)))
          & hBOOL(hAPP(hAPP(c_member(U_15781),U_15783),U_15787)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15781)),hAPP(hAPP(c_List_Olist_OCons(U_15781),U_15783),U_15785)),c_List_Olists(U_15781,U_15787))) ) ),
    inference(miniscope,[status(thm)],[f_3911_2]) ).

cnf(f_3911_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15781),U_15783),U_15787))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15781)),hAPP(hAPP(c_List_Olist_OCons(U_15781),U_15783),U_15785)),c_List_Olists(U_15781,U_15787))) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

cnf(f_3911_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15781)),U_15785),c_List_Olists(U_15781,U_15787)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15781)),hAPP(hAPP(c_List_Olist_OCons(U_15781),U_15783),U_15785)),c_List_Olists(U_15781,U_15787))) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

cnf(f_3911_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15782)),hAPP(hAPP(c_List_Olist_OCons(U_15782),U_15784),U_15786)),c_List_Olists(U_15782,U_15788)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15782)),U_15786),c_List_Olists(U_15782,U_15788)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15782),U_15784),U_15788)) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

fof(f_3912_1,plain,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accI]) ).

fof(f_3912_2,plain,
    ! [U_15791,U_15790,U_15789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15789)),U_15790),c_List_Olists(U_15789,c_Wellfounded_Oacc(U_15789,U_15791))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15789)),U_15790),c_Wellfounded_Oacc(tc_List_Olist(U_15789),c_List_Olistrel1(U_15789,U_15791)))) ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

cnf(f_3912_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15789)),U_15790),c_List_Olists(U_15789,c_Wellfounded_Oacc(U_15789,U_15791))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15789)),U_15790),c_Wellfounded_Oacc(tc_List_Olist(U_15789),c_List_Olistrel1(U_15789,U_15791)))) ),
    inference(clausify,[status(thm)],[f_3912_2]) ).

fof(f_3913_1,plain,
    ! [V_r_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accD]) ).

fof(f_3913_2,plain,
    ! [U_15794,U_15793,U_15792] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15792)),U_15793),c_Wellfounded_Oacc(tc_List_Olist(U_15792),c_List_Olistrel1(U_15792,U_15794))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15792)),U_15793),c_List_Olists(U_15792,c_Wellfounded_Oacc(U_15792,U_15794)))) ),
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

cnf(f_3913_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15792)),U_15793),c_Wellfounded_Oacc(tc_List_Olist(U_15792),c_List_Olistrel1(U_15792,U_15794))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15792)),U_15793),c_List_Olists(U_15792,c_Wellfounded_Oacc(U_15792,U_15794)))) ),
    inference(clausify,[status(thm)],[f_3913_2]) ).

fof(f_3914_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
        | ? [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
      & ( ( ! [B_n] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth]) ).

fof(f_3914_2,plain,
    ! [U_15800,U_15799,U_15798,U_15797] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15797),tc_List_Olist(U_15797))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15797),tc_List_Olist(U_15797)),U_15798),U_15799)),c_List_Olistrel(U_15797,U_15800)))
        | ? [U_15796] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15797,U_15797)),hAPP(hAPP(c_Product__Type_OPair(U_15797,U_15797),hAPP(hAPP(c_List_Onth(U_15797),U_15798),U_15796)),hAPP(hAPP(c_List_Onth(U_15797),U_15799),U_15796))),U_15800))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15796),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15798))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15798) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15799) )
      & ( ( ! [U_15795] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15797,U_15797)),hAPP(hAPP(c_Product__Type_OPair(U_15797,U_15797),hAPP(hAPP(c_List_Onth(U_15797),U_15798),U_15795)),hAPP(hAPP(c_List_Onth(U_15797),U_15799),U_15795))),U_15800))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15798))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15798) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15797)),U_15799) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15797),tc_List_Olist(U_15797))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15797),tc_List_Olist(U_15797)),U_15798),U_15799)),c_List_Olistrel(U_15797,U_15800))) ) ),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

fof(f_3914_3,plain,
    ( ! [U_15808,U_15806,U_15804,U_15802] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15802),tc_List_Olist(U_15802))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15802),tc_List_Olist(U_15802)),U_15804),U_15806)),c_List_Olistrel(U_15802,U_15808)))
        | ? [U_15796] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15802,U_15802)),hAPP(hAPP(c_Product__Type_OPair(U_15802,U_15802),hAPP(hAPP(c_List_Onth(U_15802),U_15804),U_15796)),hAPP(hAPP(c_List_Onth(U_15802),U_15806),U_15796))),U_15808))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15796),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15806) )
    & ! [U_15807,U_15805,U_15803,U_15801] :
        ( ( ! [U_15795] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15801,U_15801)),hAPP(hAPP(c_Product__Type_OPair(U_15801,U_15801),hAPP(hAPP(c_List_Onth(U_15801),U_15803),U_15795)),hAPP(hAPP(c_List_Onth(U_15801),U_15805),U_15795))),U_15807))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15805) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15801),tc_List_Olist(U_15801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15801),tc_List_Olist(U_15801)),U_15803),U_15805)),c_List_Olistrel(U_15801,U_15807))) ) ),
    inference(miniscope,[status(thm)],[f_3914_2]) ).

fof(f_3914_4,plain,
    ( ! [U_15808,U_15806,U_15804,U_15802] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15802),tc_List_Olist(U_15802))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15802),tc_List_Olist(U_15802)),U_15804),U_15806)),c_List_Olistrel(U_15802,U_15808)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15802,U_15802)),hAPP(hAPP(c_Product__Type_OPair(U_15802,U_15802),hAPP(hAPP(c_List_Onth(U_15802),U_15804),sK418(U_15808,U_15806,U_15804,U_15802))),hAPP(hAPP(c_List_Onth(U_15802),U_15806),sK418(U_15808,U_15806,U_15804,U_15802)))),U_15808))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK418(U_15808,U_15806,U_15804,U_15802)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15806) )
    & ! [U_15807,U_15805,U_15803,U_15801] :
        ( ( ! [U_15795] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15801,U_15801)),hAPP(hAPP(c_Product__Type_OPair(U_15801,U_15801),hAPP(hAPP(c_List_Onth(U_15801),U_15803),U_15795)),hAPP(hAPP(c_List_Onth(U_15801),U_15805),U_15795))),U_15807))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15805) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15801),tc_List_Olist(U_15801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15801),tc_List_Olist(U_15801)),U_15803),U_15805)),c_List_Olistrel(U_15801,U_15807))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_15796,sK418(U_15808,U_15806,U_15804,U_15802))],[f_3914_3]) ).

cnf(f_3914_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15805)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15801),tc_List_Olist(U_15801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15801),tc_List_Olist(U_15801)),U_15803),U_15805)),c_List_Olistrel(U_15801,U_15807))) ),
    inference(clausify,[status(thm)],[f_3914_4]) ).

cnf(f_3914_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15801,U_15801)),hAPP(hAPP(c_Product__Type_OPair(U_15801,U_15801),hAPP(hAPP(c_List_Onth(U_15801),U_15803),U_15795)),hAPP(hAPP(c_List_Onth(U_15801),U_15805),U_15795))),U_15807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15801)),U_15803)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15801),tc_List_Olist(U_15801))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15801),tc_List_Olist(U_15801)),U_15803),U_15805)),c_List_Olistrel(U_15801,U_15807))) ),
    inference(clausify,[status(thm)],[f_3914_4]) ).

cnf(f_3914_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK418(U_15808,U_15806,U_15804,U_15802)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15806)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15802),tc_List_Olist(U_15802))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15802),tc_List_Olist(U_15802)),U_15804),U_15806)),c_List_Olistrel(U_15802,U_15808))) ),
    inference(clausify,[status(thm)],[f_3914_4]) ).

cnf(f_3914_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15802,U_15802)),hAPP(hAPP(c_Product__Type_OPair(U_15802,U_15802),hAPP(hAPP(c_List_Onth(U_15802),U_15804),sK418(U_15808,U_15806,U_15804,U_15802))),hAPP(hAPP(c_List_Onth(U_15802),U_15806),sK418(U_15808,U_15806,U_15804,U_15802)))),U_15808))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15804) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15806)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15802),tc_List_Olist(U_15802))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15802),tc_List_Olist(U_15802)),U_15804),U_15806)),c_List_Olistrel(U_15802,U_15808))) ),
    inference(clausify,[status(thm)],[f_3914_4]) ).

fof(f_3915_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2)))
      | V_x_2 = V_y_2
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2))
          & B_a != B_b
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__linear]) ).

fof(f_3915_2,plain,
    ! [U_15814,U_15813,U_15812,U_15811] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
      | U_15813 = U_15814
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812)))
      | ? [U_15810,U_15809] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),U_15809),U_15810)),U_15812))
          & U_15810 != U_15809
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),U_15810),U_15809)),U_15812)) ) ),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

fof(f_3915_3,plain,
    ! [U_15814,U_15813,U_15812,U_15811] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
      | U_15813 = U_15814
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812)))
      | ? [U_15809] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),U_15809),sK419(U_15814,U_15813,U_15812,U_15811))),U_15812))
          & sK419(U_15814,U_15813,U_15812,U_15811) != U_15809
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),sK419(U_15814,U_15813,U_15812,U_15811)),U_15809)),U_15812)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_15810,sK419(U_15814,U_15813,U_15812,U_15811))],[f_3915_2]) ).

fof(f_3915_4,plain,
    ! [U_15814,U_15813,U_15812,U_15811] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
      | U_15813 = U_15814
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),sK420(U_15814,U_15813,U_15812,U_15811)),sK419(U_15814,U_15813,U_15812,U_15811))),U_15812))
        & sK419(U_15814,U_15813,U_15812,U_15811) != sK420(U_15814,U_15813,U_15812,U_15811)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),sK419(U_15814,U_15813,U_15812,U_15811)),sK420(U_15814,U_15813,U_15812,U_15811))),U_15812)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_15809,sK420(U_15814,U_15813,U_15812,U_15811))],[f_3915_3]) ).

cnf(f_3915_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),sK419(U_15814,U_15813,U_15812,U_15811)),sK420(U_15814,U_15813,U_15812,U_15811))),U_15812))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
    | U_15813 = U_15814
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812))) ),
    inference(clausify,[status(thm)],[f_3915_4]) ).

cnf(f_3915_6,plain,
    ( sK419(U_15814,U_15813,U_15812,U_15811) != sK420(U_15814,U_15813,U_15812,U_15811)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
    | U_15813 = U_15814
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812))) ),
    inference(clausify,[status(thm)],[f_3915_4]) ).

cnf(f_3915_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15811,U_15811)),hAPP(hAPP(c_Product__Type_OPair(U_15811,U_15811),sK420(U_15814,U_15813,U_15812,U_15811)),sK419(U_15814,U_15813,U_15812,U_15811))),U_15812))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15814),U_15813)),c_List_Olexord(U_15811,U_15812)))
    | U_15813 = U_15814
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15811),tc_List_Olist(U_15811))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15811),tc_List_Olist(U_15811)),U_15813),U_15814)),c_List_Olexord(U_15811,U_15812))) ),
    inference(clausify,[status(thm)],[f_3915_4]) ).

fof(f_3916_1,plain,
    ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(f_3916_2,plain,
    ! [U_15815] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15815)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15815),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

cnf(f_3916_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15815)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15815),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3916_2]) ).

fof(f_3917_1,plain,
    ! [T_a,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
      & ( ( ! [B_i] :
              ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__nth__eq]) ).

fof(f_3917_2,plain,
    ! [U_15820,U_15819,U_15818] :
      ( ( U_15818 = U_15819
        | ? [U_15817] :
            ( hAPP(hAPP(c_List_Onth(U_15820),U_15818),U_15817) != hAPP(hAPP(c_List_Onth(U_15820),U_15819),U_15817)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15817),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15818))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15818) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15819) )
      & ( ( ! [U_15816] :
              ( hAPP(hAPP(c_List_Onth(U_15820),U_15818),U_15816) = hAPP(hAPP(c_List_Onth(U_15820),U_15819),U_15816)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15818))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15818) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15820)),U_15819) )
        | U_15818 != U_15819 ) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

fof(f_3917_3,plain,
    ( ! [U_15826,U_15824,U_15822] :
        ( U_15822 = U_15824
        | ? [U_15817] :
            ( hAPP(hAPP(c_List_Onth(U_15826),U_15822),U_15817) != hAPP(hAPP(c_List_Onth(U_15826),U_15824),U_15817)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15817),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15824) )
    & ! [U_15825,U_15823,U_15821] :
        ( ( ! [U_15816] :
              ( hAPP(hAPP(c_List_Onth(U_15825),U_15821),U_15816) = hAPP(hAPP(c_List_Onth(U_15825),U_15823),U_15816)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15823) )
        | U_15821 != U_15823 ) ),
    inference(miniscope,[status(thm)],[f_3917_2]) ).

fof(f_3917_4,plain,
    ( ! [U_15826,U_15824,U_15822] :
        ( U_15822 = U_15824
        | ( hAPP(hAPP(c_List_Onth(U_15826),U_15822),sK421(U_15826,U_15824,U_15822)) != hAPP(hAPP(c_List_Onth(U_15826),U_15824),sK421(U_15826,U_15824,U_15822))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK421(U_15826,U_15824,U_15822)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15824) )
    & ! [U_15825,U_15823,U_15821] :
        ( ( ! [U_15816] :
              ( hAPP(hAPP(c_List_Onth(U_15825),U_15821),U_15816) = hAPP(hAPP(c_List_Onth(U_15825),U_15823),U_15816)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15823) )
        | U_15821 != U_15823 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_15817,sK421(U_15826,U_15824,U_15822))],[f_3917_3]) ).

cnf(f_3917_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15823)
    | U_15821 != U_15823 ),
    inference(clausify,[status(thm)],[f_3917_4]) ).

cnf(f_3917_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15825),U_15821),U_15816) = hAPP(hAPP(c_List_Onth(U_15825),U_15823),U_15816)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15825)),U_15821)))
    | U_15821 != U_15823 ),
    inference(clausify,[status(thm)],[f_3917_4]) ).

cnf(f_3917_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK421(U_15826,U_15824,U_15822)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15824)
    | U_15822 = U_15824 ),
    inference(clausify,[status(thm)],[f_3917_4]) ).

cnf(f_3917_8,plain,
    ( hAPP(hAPP(c_List_Onth(U_15826),U_15822),sK421(U_15826,U_15824,U_15822)) != hAPP(hAPP(c_List_Onth(U_15826),U_15824),sK421(U_15826,U_15824,U_15822))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15822) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15826)),U_15824)
    | U_15822 = U_15824 ),
    inference(clausify,[status(thm)],[f_3917_4]) ).

fof(f_3918_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_3918_2,plain,
    ! [U_15830,U_15829,U_15828,U_15827] : hAPP(hAPP(c_List_Onth(U_15827),hAPP(hAPP(c_List_Olist_OCons(U_15827),U_15828),U_15829)),hAPP(c_Nat_OSuc,U_15830)) = hAPP(hAPP(c_List_Onth(U_15827),U_15829),U_15830),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

cnf(f_3918_3,plain,
    hAPP(hAPP(c_List_Onth(U_15827),hAPP(hAPP(c_List_Olist_OCons(U_15827),U_15828),U_15829)),hAPP(c_Nat_OSuc,U_15830)) = hAPP(hAPP(c_List_Onth(U_15827),U_15829),U_15830),
    inference(clausify,[status(thm)],[f_3918_2]) ).

fof(f_3919_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_3919_2,plain,
    ! [U_15833,U_15832,U_15831] : hAPP(hAPP(c_List_Onth(U_15831),hAPP(hAPP(c_List_Olist_OCons(U_15831),U_15832),U_15833)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15832,
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

cnf(f_3919_3,plain,
    hAPP(hAPP(c_List_Onth(U_15831),hAPP(hAPP(c_List_Olist_OCons(U_15831),U_15832),U_15833)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15832,
    inference(clausify,[status(thm)],[f_3919_2]) ).

fof(f_3920_1,plain,
    ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_nth_Osimps]) ).

fof(f_3920_2,plain,
    ! [U_15837,U_15836,U_15835,U_15834] : hAPP(hAPP(c_List_Onth(U_15834),hAPP(hAPP(c_List_Olist_OCons(U_15834),U_15835),U_15836)),U_15837) = c_Nat_Onat_Onat__case(U_15834,U_15835,hAPP(c_List_Onth(U_15834),U_15836),U_15837),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

cnf(f_3920_3,plain,
    hAPP(hAPP(c_List_Onth(U_15834),hAPP(hAPP(c_List_Olist_OCons(U_15834),U_15835),U_15836)),U_15837) = c_Nat_Onat_Onat__case(U_15834,U_15835,hAPP(c_List_Onth(U_15834),U_15836),U_15837),
    inference(clausify,[status(thm)],[f_3920_2]) ).

fof(f_3921_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_3921_2,plain,
    ! [U_15841,U_15840,U_15839,U_15838] :
      ( ( hAPP(hAPP(c_List_Onth(U_15839),hAPP(hAPP(c_List_Olist_OCons(U_15839),U_15840),U_15841)),U_15838) = hAPP(hAPP(c_List_Onth(U_15839),U_15841),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15838),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15839),hAPP(hAPP(c_List_Olist_OCons(U_15839),U_15840),U_15841)),U_15838) = U_15840
        | U_15838 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

fof(f_3921_3,plain,
    ( ! [U_15849,U_15847,U_15845,U_15843] :
        ( hAPP(hAPP(c_List_Onth(U_15845),hAPP(hAPP(c_List_Olist_OCons(U_15845),U_15847),U_15849)),U_15843) = hAPP(hAPP(c_List_Onth(U_15845),U_15849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15843),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15848,U_15846,U_15844,U_15842] :
        ( hAPP(hAPP(c_List_Onth(U_15844),hAPP(hAPP(c_List_Olist_OCons(U_15844),U_15846),U_15848)),U_15842) = U_15846
        | U_15842 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3921_2]) ).

cnf(f_3921_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15844),hAPP(hAPP(c_List_Olist_OCons(U_15844),U_15846),U_15848)),U_15842) = U_15846
    | U_15842 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

cnf(f_3921_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15845),hAPP(hAPP(c_List_Olist_OCons(U_15845),U_15847),U_15849)),U_15843) = hAPP(hAPP(c_List_Onth(U_15845),U_15849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15843),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_15843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

fof(f_3922_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_3922_2,plain,
    ! [U_15853,U_15852,U_15851,U_15850] :
      ( ( hAPP(hAPP(c_List_Onth(U_15851),hAPP(hAPP(c_List_Olist_OCons(U_15851),U_15852),U_15853)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15850)) = hAPP(hAPP(c_List_Onth(U_15851),U_15853),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15850)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15850) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15851),hAPP(hAPP(c_List_Olist_OCons(U_15851),U_15852),U_15853)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15850)) = U_15852
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15850) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ( ! [U_15861,U_15859,U_15857,U_15855] :
        ( hAPP(hAPP(c_List_Onth(U_15857),hAPP(hAPP(c_List_Olist_OCons(U_15857),U_15859),U_15861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855)) = hAPP(hAPP(c_List_Onth(U_15857),U_15861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15860,U_15858,U_15856,U_15854] :
        ( hAPP(hAPP(c_List_Onth(U_15856),hAPP(hAPP(c_List_Olist_OCons(U_15856),U_15858),U_15860)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15854)) = U_15858
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15854) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3922_2]) ).

cnf(f_3922_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15856),hAPP(hAPP(c_List_Olist_OCons(U_15856),U_15858),U_15860)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15854)) = U_15858
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15854) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

cnf(f_3922_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15857),hAPP(hAPP(c_List_Olist_OCons(U_15857),U_15859),U_15861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855)) = hAPP(hAPP(c_List_Onth(U_15857),U_15861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15855) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
        | ( ! [B_i] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2))
              | hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) != hAPP(hAPP(c_List_Otake(T_a),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) )
          & ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) ) ) )
      & ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv]) ).

fof(f_3923_2,plain,
    ! [U_15867,U_15866,U_15865,U_15864] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15864),tc_List_Olist(U_15864))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15864),tc_List_Olist(U_15864)),U_15865),U_15866)),c_List_Olexord(U_15864,U_15867)))
        | ( ! [U_15863] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15864,U_15864)),hAPP(hAPP(c_Product__Type_OPair(U_15864,U_15864),hAPP(hAPP(c_List_Onth(U_15864),U_15865),U_15863)),hAPP(hAPP(c_List_Onth(U_15864),U_15866),U_15863))),U_15867))
              | hAPP(hAPP(c_List_Otake(U_15864),U_15863),U_15865) != hAPP(hAPP(c_List_Otake(U_15864),U_15863),U_15866)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15863),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15866)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15864),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),U_15866) != U_15865
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15866))) ) ) )
      & ( ? [U_15862] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15864,U_15864)),hAPP(hAPP(c_Product__Type_OPair(U_15864,U_15864),hAPP(hAPP(c_List_Onth(U_15864),U_15865),U_15862)),hAPP(hAPP(c_List_Onth(U_15864),U_15866),U_15862))),U_15867))
            & hAPP(hAPP(c_List_Otake(U_15864),U_15862),U_15865) = hAPP(hAPP(c_List_Otake(U_15864),U_15862),U_15866)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15862),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15866)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15864),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),U_15866) = U_15865
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15864)),U_15866))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15864),tc_List_Olist(U_15864))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15864),tc_List_Olist(U_15864)),U_15865),U_15866)),c_List_Olexord(U_15864,U_15867))) ) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

fof(f_3923_3,plain,
    ( ! [U_15875,U_15873,U_15871,U_15869] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15869),tc_List_Olist(U_15869))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15869),tc_List_Olist(U_15869)),U_15871),U_15873)),c_List_Olexord(U_15869,U_15875)))
        | ( ! [U_15863] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15869,U_15869)),hAPP(hAPP(c_Product__Type_OPair(U_15869,U_15869),hAPP(hAPP(c_List_Onth(U_15869),U_15871),U_15863)),hAPP(hAPP(c_List_Onth(U_15869),U_15873),U_15863))),U_15875))
              | hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15871) != hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15873)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15863),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15869),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),U_15873) != U_15871
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873))) ) ) )
    & ! [U_15874,U_15872,U_15870,U_15868] :
        ( ? [U_15862] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15868,U_15868)),hAPP(hAPP(c_Product__Type_OPair(U_15868,U_15868),hAPP(hAPP(c_List_Onth(U_15868),U_15870),U_15862)),hAPP(hAPP(c_List_Onth(U_15868),U_15872),U_15862))),U_15874))
            & hAPP(hAPP(c_List_Otake(U_15868),U_15862),U_15870) = hAPP(hAPP(c_List_Otake(U_15868),U_15862),U_15872)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15862),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),U_15872) = U_15870
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ) ),
    inference(miniscope,[status(thm)],[f_3923_2]) ).

fof(f_3923_4,plain,
    ( ! [U_15875,U_15873,U_15871,U_15869] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15869),tc_List_Olist(U_15869))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15869),tc_List_Olist(U_15869)),U_15871),U_15873)),c_List_Olexord(U_15869,U_15875)))
        | ( ! [U_15863] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15869,U_15869)),hAPP(hAPP(c_Product__Type_OPair(U_15869,U_15869),hAPP(hAPP(c_List_Onth(U_15869),U_15871),U_15863)),hAPP(hAPP(c_List_Onth(U_15869),U_15873),U_15863))),U_15875))
              | hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15871) != hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15873)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15863),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15869),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),U_15873) != U_15871
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873))) ) ) )
    & ! [U_15874,U_15872,U_15870,U_15868] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15868,U_15868)),hAPP(hAPP(c_Product__Type_OPair(U_15868,U_15868),hAPP(hAPP(c_List_Onth(U_15868),U_15870),sK422(U_15874,U_15872,U_15870,U_15868))),hAPP(hAPP(c_List_Onth(U_15868),U_15872),sK422(U_15874,U_15872,U_15870,U_15868)))),U_15874))
          & hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15870) = hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15872)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK422(U_15874,U_15872,U_15870,U_15868)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),U_15872) = U_15870
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_15862,sK422(U_15874,U_15872,U_15870,U_15868))],[f_3923_3]) ).

cnf(f_3923_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK422(U_15874,U_15872,U_15870,U_15868)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15870) = hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15872)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15868,U_15868)),hAPP(hAPP(c_Product__Type_OPair(U_15868,U_15868),hAPP(hAPP(c_List_Onth(U_15868),U_15870),sK422(U_15874,U_15872,U_15870,U_15868))),hAPP(hAPP(c_List_Onth(U_15868),U_15872),sK422(U_15874,U_15872,U_15870,U_15868)))),U_15874))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK422(U_15874,U_15872,U_15870,U_15868)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15872))))
    | hAPP(hAPP(c_List_Otake(U_15868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),U_15872) = U_15870
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15870) = hAPP(hAPP(c_List_Otake(U_15868),sK422(U_15874,U_15872,U_15870,U_15868)),U_15872)
    | hAPP(hAPP(c_List_Otake(U_15868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),U_15872) = U_15870
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15868,U_15868)),hAPP(hAPP(c_Product__Type_OPair(U_15868,U_15868),hAPP(hAPP(c_List_Onth(U_15868),U_15870),sK422(U_15874,U_15872,U_15870,U_15868))),hAPP(hAPP(c_List_Onth(U_15868),U_15872),sK422(U_15874,U_15872,U_15870,U_15868)))),U_15874))
    | hAPP(hAPP(c_List_Otake(U_15868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15868)),U_15870)),U_15872) = U_15870
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15868),tc_List_Olist(U_15868))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15868),tc_List_Olist(U_15868)),U_15870),U_15872)),c_List_Olexord(U_15868,U_15874))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_15869),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),U_15873) != U_15871
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15869),tc_List_Olist(U_15869))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15869),tc_List_Olist(U_15869)),U_15871),U_15873)),c_List_Olexord(U_15869,U_15875))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

cnf(f_3923_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15869,U_15869)),hAPP(hAPP(c_Product__Type_OPair(U_15869,U_15869),hAPP(hAPP(c_List_Onth(U_15869),U_15871),U_15863)),hAPP(hAPP(c_List_Onth(U_15869),U_15873),U_15863))),U_15875))
    | hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15871) != hAPP(hAPP(c_List_Otake(U_15869),U_15863),U_15873)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15863),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15869)),U_15873))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15869),tc_List_Olist(U_15869))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15869),tc_List_Olist(U_15869)),U_15871),U_15873)),c_List_Olexord(U_15869,U_15875))) ),
    inference(clausify,[status(thm)],[f_3923_4]) ).

fof(f_3924_1,plain,
    ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),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_3924_2,plain,
    ! [U_15878,U_15877,U_15876] : hAPP(c_List_Oset(U_15876),c_List_Osublist(U_15876,U_15877,U_15878)) = hAPP(c_Set_OCollect(U_15876),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15876),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15876,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_15876),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_15876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15876,tc_fun(tc_Nat_Onat,U_15876),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15876,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15876),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15876),c_COMBB(U_15876,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15876),U_15877))))),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_15876)),U_15877)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15878))))),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

cnf(f_3924_3,plain,
    hAPP(c_List_Oset(U_15876),c_List_Osublist(U_15876,U_15877,U_15878)) = hAPP(c_Set_OCollect(U_15876),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15876),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15876,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_15876),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_15876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15876,tc_fun(tc_Nat_Onat,U_15876),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15876,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15876),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15876),c_COMBB(U_15876,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15876),U_15877))))),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_15876)),U_15877)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15878))))),
    inference(clausify,[status(thm)],[f_3924_2]) ).

fof(f_3925_1,plain,
    ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__set]) ).

fof(f_3925_2,plain,
    ! [U_15880,U_15879] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),hAPP(c_List_Oset(U_15879),U_15880))),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

cnf(f_3925_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),hAPP(c_List_Oset(U_15879),U_15880))),
    inference(clausify,[status(thm)],[f_3925_2]) ).

fof(f_3926_1,plain,
    ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__subset__Cons]) ).

fof(f_3926_2,plain,
    ! [U_15883,U_15882,U_15881] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15881,tc_HOL_Obool)),hAPP(c_List_Oset(U_15881),U_15882)),hAPP(c_List_Oset(U_15881),hAPP(hAPP(c_List_Olist_OCons(U_15881),U_15883),U_15882)))),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

cnf(f_3926_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15881,tc_HOL_Obool)),hAPP(c_List_Oset(U_15881),U_15882)),hAPP(c_List_Oset(U_15881),hAPP(hAPP(c_List_Olist_OCons(U_15881),U_15883),U_15882)))),
    inference(clausify,[status(thm)],[f_3926_2]) ).

fof(f_3927_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_3927_2,plain,
    ! [U_15886,U_15885,U_15884] :
      ( hAPP(hAPP(c_List_Otake(U_15884),U_15886),U_15885) = U_15885
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15884)),U_15885)),U_15886)) ),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

cnf(f_3927_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_15884),U_15886),U_15885) = U_15885
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15884)),U_15885)),U_15886)) ),
    inference(clausify,[status(thm)],[f_3927_2]) ).

fof(f_3928_1,plain,
    ! [V_xs_2,T_a,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),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_3928_2,plain,
    ! [U_15890,U_15889,U_15888,U_15887] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15889,tc_HOL_Obool)),hAPP(c_List_Oset(U_15889),hAPP(hAPP(c_List_Otake(U_15889),U_15887),U_15890))),hAPP(c_List_Oset(U_15889),hAPP(hAPP(c_List_Otake(U_15889),U_15888),U_15890))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15887),U_15888)) ),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

cnf(f_3928_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15889,tc_HOL_Obool)),hAPP(c_List_Oset(U_15889),hAPP(hAPP(c_List_Otake(U_15889),U_15887),U_15890))),hAPP(c_List_Oset(U_15889),hAPP(hAPP(c_List_Otake(U_15889),U_15888),U_15890))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15887),U_15888)) ),
    inference(clausify,[status(thm)],[f_3928_2]) ).

fof(f_3929_1,plain,
    ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__take__subset]) ).

fof(f_3929_2,plain,
    ! [U_15893,U_15892,U_15891] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15891,tc_HOL_Obool)),hAPP(c_List_Oset(U_15891),hAPP(hAPP(c_List_Otake(U_15891),U_15892),U_15893))),hAPP(c_List_Oset(U_15891),U_15893))),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

cnf(f_3929_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15891,tc_HOL_Obool)),hAPP(c_List_Oset(U_15891),hAPP(hAPP(c_List_Otake(U_15891),U_15892),U_15893))),hAPP(c_List_Oset(U_15891),U_15893))),
    inference(clausify,[status(thm)],[f_3929_2]) ).

fof(f_3930_1,plain,
    ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__sublist__subset]) ).

fof(f_3930_2,plain,
    ! [U_15896,U_15895,U_15894] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15894,tc_HOL_Obool)),hAPP(c_List_Oset(U_15894),c_List_Osublist(U_15894,U_15895,U_15896))),hAPP(c_List_Oset(U_15894),U_15895))),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

cnf(f_3930_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15894,tc_HOL_Obool)),hAPP(c_List_Oset(U_15894),c_List_Osublist(U_15894,U_15895,U_15896))),hAPP(c_List_Oset(U_15894),U_15895))),
    inference(clausify,[status(thm)],[f_3930_2]) ).

fof(f_3931_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_3931_2,plain,
    ! [U_15900,U_15899,U_15898,U_15897] :
      ( hAPP(hAPP(c_List_Onth(U_15899),hAPP(hAPP(c_List_Otake(U_15899),U_15898),U_15900)),U_15897) = hAPP(hAPP(c_List_Onth(U_15899),U_15900),U_15897)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15897),U_15898)) ),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

cnf(f_3931_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15899),hAPP(hAPP(c_List_Otake(U_15899),U_15898),U_15900)),U_15897) = hAPP(hAPP(c_List_Onth(U_15899),U_15900),U_15897)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15897),U_15898)) ),
    inference(clausify,[status(thm)],[f_3931_2]) ).

fof(f_3932_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_3932_2,plain,
    ! [U_15904,U_15903,U_15902,U_15901] : hAPP(hAPP(c_List_Otake(U_15901),hAPP(c_Nat_OSuc,U_15902)),hAPP(hAPP(c_List_Olist_OCons(U_15901),U_15903),U_15904)) = hAPP(hAPP(c_List_Olist_OCons(U_15901),U_15903),hAPP(hAPP(c_List_Otake(U_15901),U_15902),U_15904)),
    inference(variable_rename,[status(thm)],[f_3932_1]) ).

cnf(f_3932_3,plain,
    hAPP(hAPP(c_List_Otake(U_15901),hAPP(c_Nat_OSuc,U_15902)),hAPP(hAPP(c_List_Olist_OCons(U_15901),U_15903),U_15904)) = hAPP(hAPP(c_List_Olist_OCons(U_15901),U_15903),hAPP(hAPP(c_List_Otake(U_15901),U_15902),U_15904)),
    inference(clausify,[status(thm)],[f_3932_2]) ).

fof(f_3933_1,plain,
    ! [V_xs_2,V_x_2,V_y_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | V_y_2 = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__ConsD]) ).

fof(f_3933_2,plain,
    ! [U_15908,U_15907,U_15906,U_15905] :
      ( hBOOL(hAPP(hAPP(c_member(U_15905),U_15906),hAPP(c_List_Oset(U_15905),U_15908)))
      | U_15906 = U_15907
      | ~ hBOOL(hAPP(hAPP(c_member(U_15905),U_15906),hAPP(c_List_Oset(U_15905),hAPP(hAPP(c_List_Olist_OCons(U_15905),U_15907),U_15908)))) ),
    inference(variable_rename,[status(thm)],[f_3933_1]) ).

cnf(f_3933_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15905),U_15906),hAPP(c_List_Oset(U_15905),U_15908)))
    | U_15906 = U_15907
    | ~ hBOOL(hAPP(hAPP(c_member(U_15905),U_15906),hAPP(c_List_Oset(U_15905),hAPP(hAPP(c_List_Olist_OCons(U_15905),U_15907),U_15908)))) ),
    inference(clausify,[status(thm)],[f_3933_2]) ).

fof(f_3934_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__sublistD]) ).

fof(f_3934_2,plain,
    ! [U_15912,U_15911,U_15910,U_15909] :
      ( hBOOL(hAPP(hAPP(c_member(U_15909),U_15910),hAPP(c_List_Oset(U_15909),U_15911)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15909),U_15910),hAPP(c_List_Oset(U_15909),c_List_Osublist(U_15909,U_15911,U_15912)))) ),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

cnf(f_3934_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15909),U_15910),hAPP(c_List_Oset(U_15909),U_15911)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15909),U_15910),hAPP(c_List_Oset(U_15909),c_List_Osublist(U_15909,U_15911,U_15912)))) ),
    inference(clausify,[status(thm)],[f_3934_2]) ).

fof(f_3935_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__takeD]) ).

fof(f_3935_2,plain,
    ! [U_15916,U_15915,U_15914,U_15913] :
      ( hBOOL(hAPP(hAPP(c_member(U_15913),U_15914),hAPP(c_List_Oset(U_15913),U_15916)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15913),U_15914),hAPP(c_List_Oset(U_15913),hAPP(hAPP(c_List_Otake(U_15913),U_15915),U_15916)))) ),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

cnf(f_3935_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15913),U_15914),hAPP(c_List_Oset(U_15913),U_15916)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15913),U_15914),hAPP(c_List_Oset(U_15913),hAPP(hAPP(c_List_Otake(U_15913),U_15915),U_15916)))) ),
    inference(clausify,[status(thm)],[f_3935_2]) ).

fof(f_3936_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__sublistI]) ).

fof(f_3936_2,plain,
    ! [U_15920,U_15919,U_15918,U_15917] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15917),U_15918),hAPP(c_List_Oset(U_15917),c_List_Osublist(U_15917,U_15919,U_15920))))
      | hBOOL(hAPP(hAPP(c_member(U_15917),U_15918),hAPP(c_List_Oset(U_15917),U_15919))) ),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

cnf(f_3936_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15917),U_15918),hAPP(c_List_Oset(U_15917),c_List_Osublist(U_15917,U_15919,U_15920))))
    | hBOOL(hAPP(hAPP(c_member(U_15917),U_15918),hAPP(c_List_Oset(U_15917),U_15919))) ),
    inference(clausify,[status(thm)],[f_3936_2]) ).

fof(f_3937_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_3937_2,plain,
    ! [U_15923,U_15922,U_15921] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15921)),hAPP(hAPP(c_List_Otake(U_15921),U_15922),U_15923)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15921)),U_15923)),U_15922),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

cnf(f_3937_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15921)),hAPP(hAPP(c_List_Otake(U_15921),U_15922),U_15923)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15921)),U_15923)),U_15922),
    inference(clausify,[status(thm)],[f_3937_2]) ).

fof(f_3938_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_3938_2,plain,
    ! [U_15927,U_15926,U_15925,U_15924] : hAPP(hAPP(c_List_Otake(U_15924),U_15925),hAPP(hAPP(c_List_Otake(U_15924),U_15926),U_15927)) = hAPP(hAPP(c_List_Otake(U_15924),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15925),U_15926)),U_15927),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

cnf(f_3938_3,plain,
    hAPP(hAPP(c_List_Otake(U_15924),U_15925),hAPP(hAPP(c_List_Otake(U_15924),U_15926),U_15927)) = hAPP(hAPP(c_List_Otake(U_15924),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15925),U_15926)),U_15927),
    inference(clausify,[status(thm)],[f_3938_2]) ).

fof(f_3939_1,plain,
    ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(f_3939_2,plain,
    ! [U_15930,U_15929,U_15928] : c_List_Osublist(U_15928,U_15929,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15930)) = hAPP(hAPP(c_List_Otake(U_15928),U_15930),U_15929),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

cnf(f_3939_3,plain,
    c_List_Osublist(U_15928,U_15929,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15930)) = hAPP(hAPP(c_List_Otake(U_15928),U_15930),U_15929),
    inference(clausify,[status(thm)],[f_3939_2]) ).

fof(f_3940_1,plain,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(f_3940_2,plain,
    ! [U_15933,U_15932,U_15931] : hAPP(c_List_Oset(U_15931),hAPP(hAPP(c_List_Olist_OCons(U_15931),U_15932),U_15933)) = hAPP(hAPP(c_Set_Oinsert(U_15931),U_15932),hAPP(c_List_Oset(U_15931),U_15933)),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

cnf(f_3940_3,plain,
    hAPP(c_List_Oset(U_15931),hAPP(hAPP(c_List_Olist_OCons(U_15931),U_15932),U_15933)) = hAPP(hAPP(c_Set_Oinsert(U_15931),U_15932),hAPP(c_List_Oset(U_15931),U_15933)),
    inference(clausify,[status(thm)],[f_3940_2]) ).

fof(f_3941_1,plain,
    ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_card__length]) ).

fof(f_3941_2,plain,
    ! [U_15935,U_15934] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15934),hAPP(c_List_Oset(U_15934),U_15935))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15934)),U_15935))),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

cnf(f_3941_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15934),hAPP(c_List_Oset(U_15934),U_15935))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15934)),U_15935))),
    inference(clausify,[status(thm)],[f_3941_2]) ).

fof(f_3942_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ? [B_i] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__set__conv__all__nth]) ).

fof(f_3942_2,plain,
    ! [U_15942,U_15941,U_15940] :
      ( ( ! [U_15939] :
            ( hBOOL(hAPP(U_15942,U_15939))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15940),U_15939),hAPP(c_List_Oset(U_15940),U_15941))) )
        | ? [U_15938] :
            ( ~ hBOOL(hAPP(U_15942,hAPP(hAPP(c_List_Onth(U_15940),U_15941),U_15938)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15940)),U_15941))) ) )
      & ( ! [U_15937] :
            ( hBOOL(hAPP(U_15942,hAPP(hAPP(c_List_Onth(U_15940),U_15941),U_15937)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15940)),U_15941))) )
        | ? [U_15936] :
            ( ~ hBOOL(hAPP(U_15942,U_15936))
            & hBOOL(hAPP(hAPP(c_member(U_15940),U_15936),hAPP(c_List_Oset(U_15940),U_15941))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

fof(f_3942_3,plain,
    ( ! [U_15948,U_15946,U_15944] :
        ( ! [U_15939] :
            ( hBOOL(hAPP(U_15948,U_15939))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15944),U_15939),hAPP(c_List_Oset(U_15944),U_15946))) )
        | ? [U_15938] :
            ( ~ hBOOL(hAPP(U_15948,hAPP(hAPP(c_List_Onth(U_15944),U_15946),U_15938)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15944)),U_15946))) ) )
    & ! [U_15947,U_15945,U_15943] :
        ( ! [U_15937] :
            ( hBOOL(hAPP(U_15947,hAPP(hAPP(c_List_Onth(U_15943),U_15945),U_15937)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15943)),U_15945))) )
        | ? [U_15936] :
            ( ~ hBOOL(hAPP(U_15947,U_15936))
            & hBOOL(hAPP(hAPP(c_member(U_15943),U_15936),hAPP(c_List_Oset(U_15943),U_15945))) ) ) ),
    inference(miniscope,[status(thm)],[f_3942_2]) ).

fof(f_3942_4,plain,
    ( ! [U_15948,U_15946,U_15944] :
        ( ! [U_15939] :
            ( hBOOL(hAPP(U_15948,U_15939))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15944),U_15939),hAPP(c_List_Oset(U_15944),U_15946))) )
        | ? [U_15938] :
            ( ~ hBOOL(hAPP(U_15948,hAPP(hAPP(c_List_Onth(U_15944),U_15946),U_15938)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15944)),U_15946))) ) )
    & ! [U_15947,U_15945,U_15943] :
        ( ! [U_15937] :
            ( hBOOL(hAPP(U_15947,hAPP(hAPP(c_List_Onth(U_15943),U_15945),U_15937)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15943)),U_15945))) )
        | ( ~ hBOOL(hAPP(U_15947,sK423(U_15947,U_15945,U_15943)))
          & hBOOL(hAPP(hAPP(c_member(U_15943),sK423(U_15947,U_15945,U_15943)),hAPP(c_List_Oset(U_15943),U_15945))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_15936,sK423(U_15947,U_15945,U_15943))],[f_3942_3]) ).

fof(f_3942_5,plain,
    ( ! [U_15948,U_15946,U_15944] :
        ( ! [U_15939] :
            ( hBOOL(hAPP(U_15948,U_15939))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15944),U_15939),hAPP(c_List_Oset(U_15944),U_15946))) )
        | ( ~ hBOOL(hAPP(U_15948,hAPP(hAPP(c_List_Onth(U_15944),U_15946),sK424(U_15948,U_15946,U_15944))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK424(U_15948,U_15946,U_15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15944)),U_15946))) ) )
    & ! [U_15947,U_15945,U_15943] :
        ( ! [U_15937] :
            ( hBOOL(hAPP(U_15947,hAPP(hAPP(c_List_Onth(U_15943),U_15945),U_15937)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15943)),U_15945))) )
        | ( ~ hBOOL(hAPP(U_15947,sK423(U_15947,U_15945,U_15943)))
          & hBOOL(hAPP(hAPP(c_member(U_15943),sK423(U_15947,U_15945,U_15943)),hAPP(c_List_Oset(U_15943),U_15945))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_15938,sK424(U_15948,U_15946,U_15944))],[f_3942_4]) ).

cnf(f_3942_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15943),sK423(U_15947,U_15945,U_15943)),hAPP(c_List_Oset(U_15943),U_15945)))
    | hBOOL(hAPP(U_15947,hAPP(hAPP(c_List_Onth(U_15943),U_15945),U_15937)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15943)),U_15945))) ),
    inference(clausify,[status(thm)],[f_3942_5]) ).

cnf(f_3942_7,plain,
    ( ~ hBOOL(hAPP(U_15947,sK423(U_15947,U_15945,U_15943)))
    | hBOOL(hAPP(U_15947,hAPP(hAPP(c_List_Onth(U_15943),U_15945),U_15937)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15937),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15943)),U_15945))) ),
    inference(clausify,[status(thm)],[f_3942_5]) ).

cnf(f_3942_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK424(U_15948,U_15946,U_15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15944)),U_15946)))
    | hBOOL(hAPP(U_15948,U_15939))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15944),U_15939),hAPP(c_List_Oset(U_15944),U_15946))) ),
    inference(clausify,[status(thm)],[f_3942_5]) ).

cnf(f_3942_9,plain,
    ( ~ hBOOL(hAPP(U_15948,hAPP(hAPP(c_List_Onth(U_15944),U_15946),sK424(U_15948,U_15946,U_15944))))
    | hBOOL(hAPP(U_15948,U_15939))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15944),U_15939),hAPP(c_List_Oset(U_15944),U_15946))) ),
    inference(clausify,[status(thm)],[f_3942_5]) ).

fof(f_3943_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,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_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation]) ).

fof(f_3943_2,plain,
    ! [U_15953,U_15952,U_15951,U_15950,U_15949] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15952),c_List_Olist_Olist__size(U_15949,U_15953,U_15951)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15952),hAPP(U_15953,U_15950)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15949),U_15950),hAPP(c_List_Oset(U_15949),U_15951))) ),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

cnf(f_3943_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15952),c_List_Olist_Olist__size(U_15949,U_15953,U_15951)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15952),hAPP(U_15953,U_15950)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15949),U_15950),hAPP(c_List_Oset(U_15949),U_15951))) ),
    inference(clausify,[status(thm)],[f_3943_2]) ).

fof(f_3944_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,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_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H]) ).

fof(f_3944_2,plain,
    ! [U_15958,U_15957,U_15956,U_15955,U_15954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15957),c_List_Olist_Olist__size(U_15954,U_15958,U_15956)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15957),hAPP(U_15958,U_15955)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15954),U_15955),hAPP(c_List_Oset(U_15954),U_15956))) ),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

cnf(f_3944_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15957),c_List_Olist_Olist__size(U_15954,U_15958,U_15956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15957),hAPP(U_15958,U_15955)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15954),U_15955),hAPP(c_List_Oset(U_15954),U_15956))) ),
    inference(clausify,[status(thm)],[f_3944_2]) ).

fof(f_3945_1,plain,
    ! [V_A_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lists__conv__set]) ).

fof(f_3945_2,plain,
    ! [U_15963,U_15962,U_15961] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15961)),U_15962),c_List_Olists(U_15961,U_15963)))
        | ? [U_15960] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15961),U_15960),U_15963))
            & hBOOL(hAPP(hAPP(c_member(U_15961),U_15960),hAPP(c_List_Oset(U_15961),U_15962))) ) )
      & ( ! [U_15959] :
            ( hBOOL(hAPP(hAPP(c_member(U_15961),U_15959),U_15963))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15961),U_15959),hAPP(c_List_Oset(U_15961),U_15962))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15961)),U_15962),c_List_Olists(U_15961,U_15963))) ) ),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

fof(f_3945_3,plain,
    ( ! [U_15969,U_15967,U_15965] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15965)),U_15967),c_List_Olists(U_15965,U_15969)))
        | ? [U_15960] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15965),U_15960),U_15969))
            & hBOOL(hAPP(hAPP(c_member(U_15965),U_15960),hAPP(c_List_Oset(U_15965),U_15967))) ) )
    & ! [U_15968,U_15966,U_15964] :
        ( ! [U_15959] :
            ( hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),U_15968))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),hAPP(c_List_Oset(U_15964),U_15966))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15964)),U_15966),c_List_Olists(U_15964,U_15968))) ) ),
    inference(miniscope,[status(thm)],[f_3945_2]) ).

fof(f_3945_4,plain,
    ( ! [U_15969,U_15967,U_15965] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15965)),U_15967),c_List_Olists(U_15965,U_15969)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_15965),sK425(U_15969,U_15967,U_15965)),U_15969))
          & hBOOL(hAPP(hAPP(c_member(U_15965),sK425(U_15969,U_15967,U_15965)),hAPP(c_List_Oset(U_15965),U_15967))) ) )
    & ! [U_15968,U_15966,U_15964] :
        ( ! [U_15959] :
            ( hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),U_15968))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),hAPP(c_List_Oset(U_15964),U_15966))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15964)),U_15966),c_List_Olists(U_15964,U_15968))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_15960,sK425(U_15969,U_15967,U_15965))],[f_3945_3]) ).

cnf(f_3945_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),U_15968))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15964),U_15959),hAPP(c_List_Oset(U_15964),U_15966)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15964)),U_15966),c_List_Olists(U_15964,U_15968))) ),
    inference(clausify,[status(thm)],[f_3945_4]) ).

cnf(f_3945_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15965),sK425(U_15969,U_15967,U_15965)),hAPP(c_List_Oset(U_15965),U_15967)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15965)),U_15967),c_List_Olists(U_15965,U_15969))) ),
    inference(clausify,[status(thm)],[f_3945_4]) ).

cnf(f_3945_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15965),sK425(U_15969,U_15967,U_15965)),U_15969))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15965)),U_15967),c_List_Olists(U_15965,U_15969))) ),
    inference(clausify,[status(thm)],[f_3945_4]) ).

fof(f_3946_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( 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_a)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set]) ).

fof(f_3946_2,plain,
    ! [U_15972,U_15971,U_15970] :
      ( 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_15970)),U_15972)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15970),U_15971),hAPP(c_List_Oset(U_15970),U_15972))) ),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

cnf(f_3946_3,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_15970)),U_15972)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15970),U_15971),hAPP(c_List_Oset(U_15970),U_15972))) ),
    inference(clausify,[status(thm)],[f_3946_2]) ).

fof(f_3947_1,plain,
    ! [V_xs_2,T_a,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__mem]) ).

fof(f_3947_2,plain,
    ! [U_15975,U_15974,U_15973] :
      ( hBOOL(hAPP(hAPP(c_member(U_15974),hAPP(hAPP(c_List_Onth(U_15974),U_15975),U_15973)),hAPP(c_List_Oset(U_15974),U_15975)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15973),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15974)),U_15975))) ),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

cnf(f_3947_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15974),hAPP(hAPP(c_List_Onth(U_15974),U_15975),U_15973)),hAPP(c_List_Oset(U_15974),U_15975)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15973),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15974)),U_15975))) ),
    inference(clausify,[status(thm)],[f_3947_2]) ).

fof(f_3948_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
        | ! [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) )
      & ( ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth]) ).

fof(f_3948_2,plain,
    ! [U_15980,U_15979,U_15978] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15978),U_15979),hAPP(c_List_Oset(U_15978),U_15980)))
        | ! [U_15977] :
            ( hAPP(hAPP(c_List_Onth(U_15978),U_15980),U_15977) != U_15979
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15978)),U_15980))) ) )
      & ( ? [U_15976] :
            ( hAPP(hAPP(c_List_Onth(U_15978),U_15980),U_15976) = U_15979
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15976),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15978)),U_15980))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15978),U_15979),hAPP(c_List_Oset(U_15978),U_15980))) ) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

fof(f_3948_3,plain,
    ( ! [U_15986,U_15984,U_15982] :
        ( hBOOL(hAPP(hAPP(c_member(U_15982),U_15984),hAPP(c_List_Oset(U_15982),U_15986)))
        | ! [U_15977] :
            ( hAPP(hAPP(c_List_Onth(U_15982),U_15986),U_15977) != U_15984
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15982)),U_15986))) ) )
    & ! [U_15985,U_15983,U_15981] :
        ( ? [U_15976] :
            ( hAPP(hAPP(c_List_Onth(U_15981),U_15985),U_15976) = U_15983
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15976),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15981)),U_15985))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15981),U_15983),hAPP(c_List_Oset(U_15981),U_15985))) ) ),
    inference(miniscope,[status(thm)],[f_3948_2]) ).

fof(f_3948_4,plain,
    ( ! [U_15986,U_15984,U_15982] :
        ( hBOOL(hAPP(hAPP(c_member(U_15982),U_15984),hAPP(c_List_Oset(U_15982),U_15986)))
        | ! [U_15977] :
            ( hAPP(hAPP(c_List_Onth(U_15982),U_15986),U_15977) != U_15984
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15982)),U_15986))) ) )
    & ! [U_15985,U_15983,U_15981] :
        ( ( hAPP(hAPP(c_List_Onth(U_15981),U_15985),sK426(U_15985,U_15983,U_15981)) = U_15983
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK426(U_15985,U_15983,U_15981)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15981)),U_15985))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15981),U_15983),hAPP(c_List_Oset(U_15981),U_15985))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_15976,sK426(U_15985,U_15983,U_15981))],[f_3948_3]) ).

cnf(f_3948_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK426(U_15985,U_15983,U_15981)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15981)),U_15985)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15981),U_15983),hAPP(c_List_Oset(U_15981),U_15985))) ),
    inference(clausify,[status(thm)],[f_3948_4]) ).

cnf(f_3948_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15981),U_15985),sK426(U_15985,U_15983,U_15981)) = U_15983
    | ~ hBOOL(hAPP(hAPP(c_member(U_15981),U_15983),hAPP(c_List_Oset(U_15981),U_15985))) ),
    inference(clausify,[status(thm)],[f_3948_4]) ).

cnf(f_3948_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15982),U_15984),hAPP(c_List_Oset(U_15982),U_15986)))
    | hAPP(hAPP(c_List_Onth(U_15982),U_15986),U_15977) != U_15984
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15982)),U_15986))) ),
    inference(clausify,[status(thm)],[f_3948_4]) ).

fof(f_3949_1,plain,
    ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_lists__eq__set]) ).

fof(f_3949_2,plain,
    ! [U_15988,U_15987] : c_List_Olists(U_15987,U_15988) = hAPP(c_Set_OCollect(tc_List_Olist(U_15987)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15987),tc_fun(U_15987,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15987,tc_HOL_Obool),tc_fun(tc_fun(U_15987,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15987)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15987,tc_HOL_Obool))),c_List_Oset(U_15987))),U_15988)),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

cnf(f_3949_3,plain,
    c_List_Olists(U_15987,U_15988) = hAPP(c_Set_OCollect(tc_List_Olist(U_15987)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15987),tc_fun(U_15987,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15987,tc_HOL_Obool),tc_fun(tc_fun(U_15987,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15987)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15987,tc_HOL_Obool))),c_List_Oset(U_15987))),U_15988)),
    inference(clausify,[status(thm)],[f_3949_2]) ).

fof(f_3950_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_set__conv__nth]) ).

fof(f_3950_2,plain,
    ! [U_15990,U_15989] : hAPP(c_List_Oset(U_15989),U_15990) = hAPP(c_Set_OCollect(U_15989),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15989),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15989,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_15989),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_15989),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15989,tc_fun(tc_Nat_Onat,U_15989),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15989,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15989),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15989),c_COMBB(U_15989,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15989),U_15990))))),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_15989)),U_15990))))),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

cnf(f_3950_3,plain,
    hAPP(c_List_Oset(U_15989),U_15990) = hAPP(c_Set_OCollect(U_15989),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15989),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15989,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(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_15989),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(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_15989),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15989,tc_fun(tc_Nat_Onat,U_15989),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15989,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15989),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15989),c_COMBB(U_15989,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15989),U_15990))))),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_15989)),U_15990))))),
    inference(clausify,[status(thm)],[f_3950_2]) ).

fof(f_3951_1,plain,
    ! [V_n_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq]) ).

fof(f_3951_2,plain,
    ! [U_15993,U_15992,U_15991] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15991)),hAPP(c_Set_OCollect(tc_List_Olist(U_15991)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15991),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_15991)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15991),tc_fun(U_15991,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15991,tc_HOL_Obool),tc_fun(tc_fun(U_15991,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15991)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15991,tc_HOL_Obool))),c_List_Oset(U_15991))),U_15992))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15991),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_15991)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15991)))),U_15993)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15991),U_15992)) ),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

cnf(f_3951_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15991)),hAPP(c_Set_OCollect(tc_List_Olist(U_15991)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15991),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_15991)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15991),tc_fun(U_15991,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15991,tc_HOL_Obool),tc_fun(tc_fun(U_15991,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15991)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15991,tc_HOL_Obool))),c_List_Oset(U_15991))),U_15992))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15991),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_15991)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15991)))),U_15993)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15991),U_15992)) ),
    inference(clausify,[status(thm)],[f_3951_2]) ).

fof(f_3952_1,plain,
    ! [V_n_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le]) ).

fof(f_3952_2,plain,
    ! [U_15996,U_15995,U_15994] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15994)),hAPP(c_Set_OCollect(tc_List_Olist(U_15994)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15994),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_15994)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15994),tc_fun(U_15994,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15994,tc_HOL_Obool),tc_fun(tc_fun(U_15994,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15994)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15994,tc_HOL_Obool))),c_List_Oset(U_15994))),U_15995))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15994),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_15994)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15994)))),U_15996)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15994),U_15995)) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

cnf(f_3952_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15994)),hAPP(c_Set_OCollect(tc_List_Olist(U_15994)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15994),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_15994)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15994),tc_fun(U_15994,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15994,tc_HOL_Obool),tc_fun(tc_fun(U_15994,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15994)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15994,tc_HOL_Obool))),c_List_Oset(U_15994))),U_15995))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15994),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_15994)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15994)))),U_15996)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15994),U_15995)) ),
    inference(clausify,[status(thm)],[f_3952_2]) ).

fof(f_3953_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_3953_2,plain,
    ( ( c_Com_OWT__bodies
      | ? [U_15998] :
          ( ~ 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_15998))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_15998),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_15997] :
          ( 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_15997))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_15997),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_3953_1]) ).

fof(f_3953_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)),sK427))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK427),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_15997] :
          ( 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_15997))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_15997),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,[sK427]),skolemize(U_15998,sK427)],[f_3953_2]) ).

cnf(f_3953_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)),U_15997))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_15997),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

cnf(f_3953_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK427),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

cnf(f_3953_6,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)),sK427))
    | c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

fof(f_3954_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip]) ).

fof(f_3954_2,plain,
    ! [U_16004,U_16003,U_16002,U_16001] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16001),tc_List_Olist(U_16001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16001),tc_List_Olist(U_16001)),U_16002),U_16003)),c_List_Olistrel(U_16001,U_16004)))
        | ? [U_16000] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16001,U_16001,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16001,tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_fun(U_16001,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16001,tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_fun(U_16001,tc_HOL_Obool)),U_16001),c_COMBC(U_16001,tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16001,tc_prod(U_16001,U_16001)),tc_fun(U_16001,tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),U_16001),hAPP(c_COMBB(tc_prod(U_16001,U_16001),tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool),U_16001),c_member(tc_prod(U_16001,U_16001)))),c_Product__Type_OPair(U_16001,U_16001)))),U_16004)),U_16000))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16001,U_16001)),U_16000),hAPP(c_List_Oset(tc_prod(U_16001,U_16001)),hAPP(hAPP(c_List_Ozip(U_16001,U_16001),U_16002),U_16003)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16001)),U_16002) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16001)),U_16003) )
      & ( ( ! [U_15999] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16001,U_16001,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16001,tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_fun(U_16001,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16001,tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_fun(U_16001,tc_HOL_Obool)),U_16001),c_COMBC(U_16001,tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16001,tc_prod(U_16001,U_16001)),tc_fun(U_16001,tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool)),U_16001),hAPP(c_COMBB(tc_prod(U_16001,U_16001),tc_fun(tc_fun(tc_prod(U_16001,U_16001),tc_HOL_Obool),tc_HOL_Obool),U_16001),c_member(tc_prod(U_16001,U_16001)))),c_Product__Type_OPair(U_16001,U_16001)))),U_16004)),U_15999))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16001,U_16001)),U_15999),hAPP(c_List_Oset(tc_prod(U_16001,U_16001)),hAPP(hAPP(c_List_Ozip(U_16001,U_16001),U_16002),U_16003)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16001)),U_16002) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16001)),U_16003) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16001),tc_List_Olist(U_16001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16001),tc_List_Olist(U_16001)),U_16002),U_16003)),c_List_Olistrel(U_16001,U_16004))) ) ),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

fof(f_3954_3,plain,
    ( ! [U_16012,U_16010,U_16008,U_16006] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16006),tc_List_Olist(U_16006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16006),tc_List_Olist(U_16006)),U_16008),U_16010)),c_List_Olistrel(U_16006,U_16012)))
        | ? [U_16000] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16006,U_16006,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),U_16006),c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_prod(U_16006,U_16006)),tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),U_16006),hAPP(c_COMBB(tc_prod(U_16006,U_16006),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool),U_16006),c_member(tc_prod(U_16006,U_16006)))),c_Product__Type_OPair(U_16006,U_16006)))),U_16012)),U_16000))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16006,U_16006)),U_16000),hAPP(c_List_Oset(tc_prod(U_16006,U_16006)),hAPP(hAPP(c_List_Ozip(U_16006,U_16006),U_16008),U_16010)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16008) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16010) )
    & ! [U_16011,U_16009,U_16007,U_16005] :
        ( ( ! [U_15999] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16005,U_16005,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),U_16005),c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_prod(U_16005,U_16005)),tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),U_16005),hAPP(c_COMBB(tc_prod(U_16005,U_16005),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool),U_16005),c_member(tc_prod(U_16005,U_16005)))),c_Product__Type_OPair(U_16005,U_16005)))),U_16011)),U_15999))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16005,U_16005)),U_15999),hAPP(c_List_Oset(tc_prod(U_16005,U_16005)),hAPP(hAPP(c_List_Ozip(U_16005,U_16005),U_16007),U_16009)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16007) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16009) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16005),tc_List_Olist(U_16005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16005),tc_List_Olist(U_16005)),U_16007),U_16009)),c_List_Olistrel(U_16005,U_16011))) ) ),
    inference(miniscope,[status(thm)],[f_3954_2]) ).

fof(f_3954_4,plain,
    ( ! [U_16012,U_16010,U_16008,U_16006] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16006),tc_List_Olist(U_16006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16006),tc_List_Olist(U_16006)),U_16008),U_16010)),c_List_Olistrel(U_16006,U_16012)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16006,U_16006,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),U_16006),c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_prod(U_16006,U_16006)),tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),U_16006),hAPP(c_COMBB(tc_prod(U_16006,U_16006),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool),U_16006),c_member(tc_prod(U_16006,U_16006)))),c_Product__Type_OPair(U_16006,U_16006)))),U_16012)),sK428(U_16012,U_16010,U_16008,U_16006)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16006,U_16006)),sK428(U_16012,U_16010,U_16008,U_16006)),hAPP(c_List_Oset(tc_prod(U_16006,U_16006)),hAPP(hAPP(c_List_Ozip(U_16006,U_16006),U_16008),U_16010)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16008) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16010) )
    & ! [U_16011,U_16009,U_16007,U_16005] :
        ( ( ! [U_15999] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16005,U_16005,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),U_16005),c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_prod(U_16005,U_16005)),tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),U_16005),hAPP(c_COMBB(tc_prod(U_16005,U_16005),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool),U_16005),c_member(tc_prod(U_16005,U_16005)))),c_Product__Type_OPair(U_16005,U_16005)))),U_16011)),U_15999))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16005,U_16005)),U_15999),hAPP(c_List_Oset(tc_prod(U_16005,U_16005)),hAPP(hAPP(c_List_Ozip(U_16005,U_16005),U_16007),U_16009)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16007) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16009) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16005),tc_List_Olist(U_16005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16005),tc_List_Olist(U_16005)),U_16007),U_16009)),c_List_Olistrel(U_16005,U_16011))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_16000,sK428(U_16012,U_16010,U_16008,U_16006))],[f_3954_3]) ).

cnf(f_3954_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16007) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16005)),U_16009)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16005),tc_List_Olist(U_16005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16005),tc_List_Olist(U_16005)),U_16007),U_16009)),c_List_Olistrel(U_16005,U_16011))) ),
    inference(clausify,[status(thm)],[f_3954_4]) ).

cnf(f_3954_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16005,U_16005,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_fun(U_16005,tc_HOL_Obool)),U_16005),c_COMBC(U_16005,tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16005,tc_prod(U_16005,U_16005)),tc_fun(U_16005,tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool)),U_16005),hAPP(c_COMBB(tc_prod(U_16005,U_16005),tc_fun(tc_fun(tc_prod(U_16005,U_16005),tc_HOL_Obool),tc_HOL_Obool),U_16005),c_member(tc_prod(U_16005,U_16005)))),c_Product__Type_OPair(U_16005,U_16005)))),U_16011)),U_15999))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16005,U_16005)),U_15999),hAPP(c_List_Oset(tc_prod(U_16005,U_16005)),hAPP(hAPP(c_List_Ozip(U_16005,U_16005),U_16007),U_16009))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16005),tc_List_Olist(U_16005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16005),tc_List_Olist(U_16005)),U_16007),U_16009)),c_List_Olistrel(U_16005,U_16011))) ),
    inference(clausify,[status(thm)],[f_3954_4]) ).

cnf(f_3954_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16006,U_16006)),sK428(U_16012,U_16010,U_16008,U_16006)),hAPP(c_List_Oset(tc_prod(U_16006,U_16006)),hAPP(hAPP(c_List_Ozip(U_16006,U_16006),U_16008),U_16010))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16008) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16010)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16006),tc_List_Olist(U_16006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16006),tc_List_Olist(U_16006)),U_16008),U_16010)),c_List_Olistrel(U_16006,U_16012))) ),
    inference(clausify,[status(thm)],[f_3954_4]) ).

cnf(f_3954_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16006,U_16006,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_fun(U_16006,tc_HOL_Obool)),U_16006),c_COMBC(U_16006,tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16006,tc_prod(U_16006,U_16006)),tc_fun(U_16006,tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool)),U_16006),hAPP(c_COMBB(tc_prod(U_16006,U_16006),tc_fun(tc_fun(tc_prod(U_16006,U_16006),tc_HOL_Obool),tc_HOL_Obool),U_16006),c_member(tc_prod(U_16006,U_16006)))),c_Product__Type_OPair(U_16006,U_16006)))),U_16012)),sK428(U_16012,U_16010,U_16008,U_16006)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16008) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16006)),U_16010)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16006),tc_List_Olist(U_16006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16006),tc_List_Olist(U_16006)),U_16008),U_16010)),c_List_Olistrel(U_16006,U_16012))) ),
    inference(clausify,[status(thm)],[f_3954_4]) ).

fof(f_3955_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_3955_2,plain,
    ! [U_16017,U_16016,U_16015,U_16014,U_16013] : hAPP(hAPP(c_List_Otake(tc_prod(U_16013,U_16014)),U_16015),hAPP(hAPP(c_List_Ozip(U_16013,U_16014),U_16016),U_16017)) = hAPP(hAPP(c_List_Ozip(U_16013,U_16014),hAPP(hAPP(c_List_Otake(U_16013),U_16015),U_16016)),hAPP(hAPP(c_List_Otake(U_16014),U_16015),U_16017)),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

cnf(f_3955_3,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_16013,U_16014)),U_16015),hAPP(hAPP(c_List_Ozip(U_16013,U_16014),U_16016),U_16017)) = hAPP(hAPP(c_List_Ozip(U_16013,U_16014),hAPP(hAPP(c_List_Otake(U_16013),U_16015),U_16016)),hAPP(hAPP(c_List_Otake(U_16014),U_16015),U_16017)),
    inference(clausify,[status(thm)],[f_3955_2]) ).

fof(f_3956_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_3956_2,plain,
    ! [U_16021,U_16020,U_16019,U_16018] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_16018,U_16019))),hAPP(hAPP(c_List_Ozip(U_16018,U_16019),U_16020),U_16021)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16018)),U_16020)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16019)),U_16021)),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

cnf(f_3956_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_16018,U_16019))),hAPP(hAPP(c_List_Ozip(U_16018,U_16019),U_16020),U_16021)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16018)),U_16020)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16019)),U_16021)),
    inference(clausify,[status(thm)],[f_3956_2]) ).

fof(f_3957_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_3957_2,plain,
    ! [U_16027,U_16026,U_16025,U_16024,U_16023,U_16022] : hAPP(hAPP(c_List_Ozip(U_16022,U_16023),hAPP(hAPP(c_List_Olist_OCons(U_16022),U_16024),U_16025)),hAPP(hAPP(c_List_Olist_OCons(U_16023),U_16026),U_16027)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_16022,U_16023)),hAPP(hAPP(c_Product__Type_OPair(U_16022,U_16023),U_16024),U_16026)),hAPP(hAPP(c_List_Ozip(U_16022,U_16023),U_16025),U_16027)),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

cnf(f_3957_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16022,U_16023),hAPP(hAPP(c_List_Olist_OCons(U_16022),U_16024),U_16025)),hAPP(hAPP(c_List_Olist_OCons(U_16023),U_16026),U_16027)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_16022,U_16023)),hAPP(hAPP(c_Product__Type_OPair(U_16022,U_16023),U_16024),U_16026)),hAPP(hAPP(c_List_Ozip(U_16022,U_16023),U_16025),U_16027)),
    inference(clausify,[status(thm)],[f_3957_2]) ).

fof(f_3958_1,plain,
    ! [T_a,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__zip__eq]) ).

fof(f_3958_2,plain,
    ! [U_16032,U_16031,U_16030] :
      ( ( U_16030 = U_16031
        | ? [U_16029] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16032,U_16032,tc_HOL_Obool),c_fequal),U_16029))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16032,U_16032)),U_16029),hAPP(c_List_Oset(tc_prod(U_16032,U_16032)),hAPP(hAPP(c_List_Ozip(U_16032,U_16032),U_16030),U_16031)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16032)),U_16030) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16032)),U_16031) )
      & ( ( ! [U_16028] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16032,U_16032,tc_HOL_Obool),c_fequal),U_16028))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16032,U_16032)),U_16028),hAPP(c_List_Oset(tc_prod(U_16032,U_16032)),hAPP(hAPP(c_List_Ozip(U_16032,U_16032),U_16030),U_16031)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16032)),U_16030) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16032)),U_16031) )
        | U_16030 != U_16031 ) ),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

fof(f_3958_3,plain,
    ( ! [U_16038,U_16036,U_16034] :
        ( U_16034 = U_16036
        | ? [U_16029] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16038,U_16038,tc_HOL_Obool),c_fequal),U_16029))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16038,U_16038)),U_16029),hAPP(c_List_Oset(tc_prod(U_16038,U_16038)),hAPP(hAPP(c_List_Ozip(U_16038,U_16038),U_16034),U_16036)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16034) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16036) )
    & ! [U_16037,U_16035,U_16033] :
        ( ( ! [U_16028] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16037,U_16037,tc_HOL_Obool),c_fequal),U_16028))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16037,U_16037)),U_16028),hAPP(c_List_Oset(tc_prod(U_16037,U_16037)),hAPP(hAPP(c_List_Ozip(U_16037,U_16037),U_16033),U_16035)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16033) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16035) )
        | U_16033 != U_16035 ) ),
    inference(miniscope,[status(thm)],[f_3958_2]) ).

fof(f_3958_4,plain,
    ( ! [U_16038,U_16036,U_16034] :
        ( U_16034 = U_16036
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16038,U_16038,tc_HOL_Obool),c_fequal),sK429(U_16038,U_16036,U_16034)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16038,U_16038)),sK429(U_16038,U_16036,U_16034)),hAPP(c_List_Oset(tc_prod(U_16038,U_16038)),hAPP(hAPP(c_List_Ozip(U_16038,U_16038),U_16034),U_16036)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16034) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16036) )
    & ! [U_16037,U_16035,U_16033] :
        ( ( ! [U_16028] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16037,U_16037,tc_HOL_Obool),c_fequal),U_16028))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16037,U_16037)),U_16028),hAPP(c_List_Oset(tc_prod(U_16037,U_16037)),hAPP(hAPP(c_List_Ozip(U_16037,U_16037),U_16033),U_16035)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16033) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16035) )
        | U_16033 != U_16035 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_16029,sK429(U_16038,U_16036,U_16034))],[f_3958_3]) ).

cnf(f_3958_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16033) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16037)),U_16035)
    | U_16033 != U_16035 ),
    inference(clausify,[status(thm)],[f_3958_4]) ).

cnf(f_3958_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16037,U_16037,tc_HOL_Obool),c_fequal),U_16028))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16037,U_16037)),U_16028),hAPP(c_List_Oset(tc_prod(U_16037,U_16037)),hAPP(hAPP(c_List_Ozip(U_16037,U_16037),U_16033),U_16035))))
    | U_16033 != U_16035 ),
    inference(clausify,[status(thm)],[f_3958_4]) ).

cnf(f_3958_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16038,U_16038)),sK429(U_16038,U_16036,U_16034)),hAPP(c_List_Oset(tc_prod(U_16038,U_16038)),hAPP(hAPP(c_List_Ozip(U_16038,U_16038),U_16034),U_16036))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16034) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16036)
    | U_16034 = U_16036 ),
    inference(clausify,[status(thm)],[f_3958_4]) ).

cnf(f_3958_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_16038,U_16038,tc_HOL_Obool),c_fequal),sK429(U_16038,U_16036,U_16034)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16034) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16038)),U_16036)
    | U_16034 = U_16036 ),
    inference(clausify,[status(thm)],[f_3958_4]) ).

fof(f_3959_1,plain,
    ! [V_xs_2,V_b_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2))))
        | V_a_2 != V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( ( V_a_2 = V_b_2
          & hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zip__same]) ).

fof(f_3959_2,plain,
    ! [U_16042,U_16041,U_16040,U_16039] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16039,U_16039)),hAPP(hAPP(c_Product__Type_OPair(U_16039,U_16039),U_16040),U_16041)),hAPP(c_List_Oset(tc_prod(U_16039,U_16039)),hAPP(hAPP(c_List_Ozip(U_16039,U_16039),U_16042),U_16042))))
        | U_16040 != U_16041
        | ~ hBOOL(hAPP(hAPP(c_member(U_16039),U_16040),hAPP(c_List_Oset(U_16039),U_16042))) )
      & ( ( U_16040 = U_16041
          & hBOOL(hAPP(hAPP(c_member(U_16039),U_16040),hAPP(c_List_Oset(U_16039),U_16042))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16039,U_16039)),hAPP(hAPP(c_Product__Type_OPair(U_16039,U_16039),U_16040),U_16041)),hAPP(c_List_Oset(tc_prod(U_16039,U_16039)),hAPP(hAPP(c_List_Ozip(U_16039,U_16039),U_16042),U_16042)))) ) ),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

fof(f_3959_3,plain,
    ( ! [U_16050,U_16048,U_16046,U_16044] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16044,U_16044)),hAPP(hAPP(c_Product__Type_OPair(U_16044,U_16044),U_16046),U_16048)),hAPP(c_List_Oset(tc_prod(U_16044,U_16044)),hAPP(hAPP(c_List_Ozip(U_16044,U_16044),U_16050),U_16050))))
        | U_16046 != U_16048
        | ~ hBOOL(hAPP(hAPP(c_member(U_16044),U_16046),hAPP(c_List_Oset(U_16044),U_16050))) )
    & ! [U_16049,U_16047,U_16045,U_16043] :
        ( ( U_16045 = U_16047
          & hBOOL(hAPP(hAPP(c_member(U_16043),U_16045),hAPP(c_List_Oset(U_16043),U_16049))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_Product__Type_OPair(U_16043,U_16043),U_16045),U_16047)),hAPP(c_List_Oset(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_List_Ozip(U_16043,U_16043),U_16049),U_16049)))) ) ),
    inference(miniscope,[status(thm)],[f_3959_2]) ).

cnf(f_3959_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16043),U_16045),hAPP(c_List_Oset(U_16043),U_16049)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_Product__Type_OPair(U_16043,U_16043),U_16045),U_16047)),hAPP(c_List_Oset(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_List_Ozip(U_16043,U_16043),U_16049),U_16049)))) ),
    inference(clausify,[status(thm)],[f_3959_3]) ).

cnf(f_3959_5,plain,
    ( U_16045 = U_16047
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_Product__Type_OPair(U_16043,U_16043),U_16045),U_16047)),hAPP(c_List_Oset(tc_prod(U_16043,U_16043)),hAPP(hAPP(c_List_Ozip(U_16043,U_16043),U_16049),U_16049)))) ),
    inference(clausify,[status(thm)],[f_3959_3]) ).

cnf(f_3959_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16044,U_16044)),hAPP(hAPP(c_Product__Type_OPair(U_16044,U_16044),U_16046),U_16048)),hAPP(c_List_Oset(tc_prod(U_16044,U_16044)),hAPP(hAPP(c_List_Ozip(U_16044,U_16044),U_16050),U_16050))))
    | U_16046 != U_16048
    | ~ hBOOL(hAPP(hAPP(c_member(U_16044),U_16046),hAPP(c_List_Oset(U_16044),U_16050))) ),
    inference(clausify,[status(thm)],[f_3959_3]) ).

fof(f_3960_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__leftD]) ).

fof(f_3960_2,plain,
    ! [U_16056,U_16055,U_16054,U_16053,U_16052,U_16051] :
      ( hBOOL(hAPP(hAPP(c_member(U_16051),U_16053),hAPP(c_List_Oset(U_16051),U_16055)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16051,U_16052)),hAPP(hAPP(c_Product__Type_OPair(U_16051,U_16052),U_16053),U_16054)),hAPP(c_List_Oset(tc_prod(U_16051,U_16052)),hAPP(hAPP(c_List_Ozip(U_16051,U_16052),U_16055),U_16056)))) ),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

cnf(f_3960_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16051),U_16053),hAPP(c_List_Oset(U_16051),U_16055)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16051,U_16052)),hAPP(hAPP(c_Product__Type_OPair(U_16051,U_16052),U_16053),U_16054)),hAPP(c_List_Oset(tc_prod(U_16051,U_16052)),hAPP(hAPP(c_List_Ozip(U_16051,U_16052),U_16055),U_16056)))) ),
    inference(clausify,[status(thm)],[f_3960_2]) ).

fof(f_3961_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__rightD]) ).

fof(f_3961_2,plain,
    ! [U_16062,U_16061,U_16060,U_16059,U_16058,U_16057] :
      ( hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),hAPP(c_List_Oset(U_16058),U_16062)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16057,U_16058),U_16059),U_16060)),hAPP(c_List_Oset(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_List_Ozip(U_16057,U_16058),U_16061),U_16062)))) ),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

fof(f_3961_3,plain,
    ! [U_16062,U_16061,U_16060,U_16059,U_16058] :
      ( ! [U_16057] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16057,U_16058),U_16059),U_16060)),hAPP(c_List_Oset(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_List_Ozip(U_16057,U_16058),U_16061),U_16062))))
      | hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),hAPP(c_List_Oset(U_16058),U_16062))) ),
    inference(miniscope,[status(thm)],[f_3961_2]) ).

cnf(f_3961_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16057,U_16058),U_16059),U_16060)),hAPP(c_List_Oset(tc_prod(U_16057,U_16058)),hAPP(hAPP(c_List_Ozip(U_16057,U_16058),U_16061),U_16062))))
    | hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),hAPP(c_List_Oset(U_16058),U_16062))) ),
    inference(clausify,[status(thm)],[f_3961_3]) ).

fof(f_3962_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2)))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__zipE]) ).

fof(f_3962_2,plain,
    ! [U_16068,U_16067,U_16066,U_16065,U_16064,U_16063] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_16064),U_16066),hAPP(c_List_Oset(U_16064),U_16068)))
        & hBOOL(hAPP(hAPP(c_member(U_16063),U_16065),hAPP(c_List_Oset(U_16063),U_16067))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_Product__Type_OPair(U_16063,U_16064),U_16065),U_16066)),hAPP(c_List_Oset(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_List_Ozip(U_16063,U_16064),U_16067),U_16068)))) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

cnf(f_3962_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16063),U_16065),hAPP(c_List_Oset(U_16063),U_16067)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_Product__Type_OPair(U_16063,U_16064),U_16065),U_16066)),hAPP(c_List_Oset(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_List_Ozip(U_16063,U_16064),U_16067),U_16068)))) ),
    inference(clausify,[status(thm)],[f_3962_2]) ).

cnf(f_3962_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16064),U_16066),hAPP(c_List_Oset(U_16064),U_16068)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_Product__Type_OPair(U_16063,U_16064),U_16065),U_16066)),hAPP(c_List_Oset(tc_prod(U_16063,U_16064)),hAPP(hAPP(c_List_Ozip(U_16063,U_16064),U_16067),U_16068)))) ),
    inference(clausify,[status(thm)],[f_3962_2]) ).

fof(f_3963_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_3963_2,plain,
    ! [U_16073,U_16072,U_16071,U_16070,U_16069] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_16070,U_16072)),hAPP(hAPP(c_List_Ozip(U_16070,U_16072),U_16071),U_16073)),U_16069) = hAPP(hAPP(c_Product__Type_OPair(U_16070,U_16072),hAPP(hAPP(c_List_Onth(U_16070),U_16071),U_16069)),hAPP(hAPP(c_List_Onth(U_16072),U_16073),U_16069))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16069),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16072)),U_16073)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16069),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16070)),U_16071))) ),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

cnf(f_3963_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_16070,U_16072)),hAPP(hAPP(c_List_Ozip(U_16070,U_16072),U_16071),U_16073)),U_16069) = hAPP(hAPP(c_Product__Type_OPair(U_16070,U_16072),hAPP(hAPP(c_List_Onth(U_16070),U_16071),U_16069)),hAPP(hAPP(c_List_Onth(U_16072),U_16073),U_16069))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16069),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16072)),U_16073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16069),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16070)),U_16071))) ),
    inference(clausify,[status(thm)],[f_3963_2]) ).

fof(f_3964_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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)),tc_prod(T_a,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)),tc_prod(T_a,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(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__zip]) ).

fof(f_3964_2,plain,
    ! [U_16077,U_16076,U_16075,U_16074] : hAPP(c_List_Oset(tc_prod(U_16074,U_16075)),hAPP(hAPP(c_List_Ozip(U_16074,U_16075),U_16076),U_16077)) = hAPP(c_Set_OCollect(tc_prod(U_16074,U_16075)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16074,U_16075)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_16074,U_16075),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_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_16074,U_16075)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(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_16074,U_16075)),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_16074,U_16075),tc_fun(tc_Nat_Onat,tc_prod(U_16074,U_16075)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16074,U_16075),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_16074,U_16075)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_16074,U_16075)),c_COMBB(tc_prod(U_16074,U_16075),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_16075,tc_prod(U_16074,U_16075)),hAPP(hAPP(c_COMBB(U_16074,tc_fun(U_16075,tc_prod(U_16074,U_16075)),tc_Nat_Onat),c_Product__Type_OPair(U_16074,U_16075)),hAPP(c_List_Onth(U_16074),U_16076))),hAPP(c_List_Onth(U_16075),U_16077)))))),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_16074)),U_16076)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16075)),U_16077)))))),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

cnf(f_3964_3,plain,
    hAPP(c_List_Oset(tc_prod(U_16074,U_16075)),hAPP(hAPP(c_List_Ozip(U_16074,U_16075),U_16076),U_16077)) = hAPP(c_Set_OCollect(tc_prod(U_16074,U_16075)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16074,U_16075)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_16074,U_16075),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_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_16074,U_16075)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(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_16074,U_16075)),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_16074,U_16075),tc_fun(tc_Nat_Onat,tc_prod(U_16074,U_16075)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16074,U_16075),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_16074,U_16075)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_16074,U_16075)),c_COMBB(tc_prod(U_16074,U_16075),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_16075,tc_prod(U_16074,U_16075)),hAPP(hAPP(c_COMBB(U_16074,tc_fun(U_16075,tc_prod(U_16074,U_16075)),tc_Nat_Onat),c_Product__Type_OPair(U_16074,U_16075)),hAPP(c_List_Onth(U_16074),U_16076))),hAPP(c_List_Onth(U_16075),U_16077)))))),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_16074)),U_16076)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16075)),U_16077)))))),
    inference(clausify,[status(thm)],[f_3964_2]) ).

fof(f_3965_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_3965_2,plain,
    ! [U_16079,U_16078] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_16078,U_16079) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16078),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_16079),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

cnf(f_3965_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_16078,U_16079) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16078),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_16079),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3965_2]) ).

fof(f_3966_1,plain,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),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_a)),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth]) ).

fof(f_3966_2,plain,
    ! [U_16081,U_16080] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16080),U_16081) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_16080),hAPP(c_List_Onth(U_16080),U_16081)),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_16080)),U_16081)))
      | ~ class_Groups_Ocomm__monoid__add(U_16080) ),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

cnf(f_3966_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16080),U_16081) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_16080),hAPP(c_List_Onth(U_16080),U_16081)),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_16080)),U_16081)))
    | ~ class_Groups_Ocomm__monoid__add(U_16080) ),
    inference(clausify,[status(thm)],[f_3966_2]) ).

fof(f_3967_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_3967_2,plain,
    ! [U_16084] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16084) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16083] :
            ( U_16083 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16083),hAPP(c_List_Oset(tc_Nat_Onat),U_16084))) ) )
      & ( ! [U_16082] :
            ( U_16082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16082),hAPP(c_List_Oset(tc_Nat_Onat),U_16084))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16084) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

fof(f_3967_3,plain,
    ( ! [U_16086] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16083] :
            ( U_16083 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16083),hAPP(c_List_Oset(tc_Nat_Onat),U_16086))) ) )
    & ! [U_16085] :
        ( ! [U_16082] :
            ( U_16082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16082),hAPP(c_List_Oset(tc_Nat_Onat),U_16085))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16085) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3967_2]) ).

fof(f_3967_4,plain,
    ( ! [U_16086] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK430(U_16086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK430(U_16086)),hAPP(c_List_Oset(tc_Nat_Onat),U_16086))) ) )
    & ! [U_16085] :
        ( ! [U_16082] :
            ( U_16082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16082),hAPP(c_List_Oset(tc_Nat_Onat),U_16085))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16085) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_16083,sK430(U_16086))],[f_3967_3]) ).

cnf(f_3967_5,plain,
    ( U_16082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16082),hAPP(c_List_Oset(tc_Nat_Onat),U_16085)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16085) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3967_4]) ).

cnf(f_3967_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK430(U_16086)),hAPP(c_List_Oset(tc_Nat_Onat),U_16086)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3967_4]) ).

cnf(f_3967_7,plain,
    ( sK430(U_16086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3967_4]) ).

fof(f_3968_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_3968_2,plain,
    ! [U_16088,U_16087] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16087,U_16088)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_16087,U_16088),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

cnf(f_3968_3,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16087,U_16088)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_16087,U_16088),
    inference(clausify,[status(thm)],[f_3968_2]) ).

fof(f_3969_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_3969_2,plain,
    ! [U_16090,U_16089] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_16089,U_16090) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16089,U_16090)),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

cnf(f_3969_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_16089,U_16090) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16089,U_16090)),
    inference(clausify,[status(thm)],[f_3969_2]) ).

fof(f_3970_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_3970_2,plain,
    ! [U_16092,U_16091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_16092),U_16091)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16092)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16091),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_16092))) ),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

cnf(f_3970_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_16092),U_16091)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_16092)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16091),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_16092))) ),
    inference(clausify,[status(thm)],[f_3970_2]) ).

fof(f_3971_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_3971_2,plain,
    ! [U_16095,U_16094,U_16093] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16093),hAPP(hAPP(c_List_Olist_OCons(U_16093),U_16094),U_16095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16093),U_16094),hAPP(c_List_Omonoid__add__class_Olistsum(U_16093),U_16095))
      | ~ class_Groups_Omonoid__add(U_16093) ),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

cnf(f_3971_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16093),hAPP(hAPP(c_List_Olist_OCons(U_16093),U_16094),U_16095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16093),U_16094),hAPP(c_List_Omonoid__add__class_Olistsum(U_16093),U_16095))
    | ~ class_Groups_Omonoid__add(U_16093) ),
    inference(clausify,[status(thm)],[f_3971_2]) ).

fof(f_3972_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_3972_2,plain,
    ! [U_16097,U_16096] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_16096),U_16097) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_16097),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

cnf(f_3972_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_16096),U_16097) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_16096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_16097),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3972_2]) ).

fof(f_3973_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_3973_2,plain,
    ! [U_16099,U_16098] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_16098,U_16099) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16098),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16099)),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

cnf(f_3973_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_16098,U_16099) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16098),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16099)),
    inference(clausify,[status(thm)],[f_3973_2]) ).

fof(f_3974_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_3974_2,plain,
    ! [U_16100] :
      ( ( c_List_Onat__list(U_16100)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16100)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16100))
        | ~ c_List_Onat__list(U_16100) ) ),
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

fof(f_3974_3,plain,
    ( ! [U_16102] :
        ( c_List_Onat__list(U_16102)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16102)) )
    & ! [U_16101] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16101))
        | ~ c_List_Onat__list(U_16101) ) ),
    inference(miniscope,[status(thm)],[f_3974_2]) ).

cnf(f_3974_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16101))
    | ~ c_List_Onat__list(U_16101) ),
    inference(clausify,[status(thm)],[f_3974_3]) ).

cnf(f_3974_5,plain,
    ( c_List_Onat__list(U_16102)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_16102)) ),
    inference(clausify,[status(thm)],[f_3974_3]) ).

fof(f_3975_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,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_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__pointwise]) ).

fof(f_3975_2,plain,
    ! [U_16107,U_16106,U_16105,U_16104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_16104,U_16106,U_16105)),c_List_Olist_Olist__size(U_16104,U_16107,U_16105)))
      | ? [U_16103] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_16106,U_16103)),hAPP(U_16107,U_16103)))
          & hBOOL(hAPP(hAPP(c_member(U_16104),U_16103),hAPP(c_List_Oset(U_16104),U_16105))) ) ),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

fof(f_3975_3,plain,
    ! [U_16107,U_16106,U_16105,U_16104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_16104,U_16106,U_16105)),c_List_Olist_Olist__size(U_16104,U_16107,U_16105)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_16106,sK431(U_16107,U_16106,U_16105,U_16104))),hAPP(U_16107,sK431(U_16107,U_16106,U_16105,U_16104))))
        & hBOOL(hAPP(hAPP(c_member(U_16104),sK431(U_16107,U_16106,U_16105,U_16104)),hAPP(c_List_Oset(U_16104),U_16105))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_16103,sK431(U_16107,U_16106,U_16105,U_16104))],[f_3975_2]) ).

cnf(f_3975_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16104),sK431(U_16107,U_16106,U_16105,U_16104)),hAPP(c_List_Oset(U_16104),U_16105)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_16104,U_16106,U_16105)),c_List_Olist_Olist__size(U_16104,U_16107,U_16105))) ),
    inference(clausify,[status(thm)],[f_3975_3]) ).

cnf(f_3975_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_16106,sK431(U_16107,U_16106,U_16105,U_16104))),hAPP(U_16107,sK431(U_16107,U_16106,U_16105,U_16104))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_16104,U_16106,U_16105)),c_List_Olist_Olist__size(U_16104,U_16107,U_16105))) ),
    inference(clausify,[status(thm)],[f_3975_3]) ).

fof(f_3976_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_3976_2,plain,
    ! [U_16110,U_16109,U_16108] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_16109),U_16108),U_16110)) = 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_16109)),U_16110)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_16109),U_16108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16108),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_16109))) ),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

cnf(f_3976_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_16109),U_16108),U_16110)) = 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_16109)),U_16110)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_16109),U_16108))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16108),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_16109))) ),
    inference(clausify,[status(thm)],[f_3976_2]) ).

fof(f_3977_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_3977_2,plain,
    ! [U_16113,U_16112,U_16111] :
      ( c_List_Obutlast(U_16112,hAPP(hAPP(c_List_Otake(U_16112),U_16111),U_16113)) = hAPP(hAPP(c_List_Otake(U_16112),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16111),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16113)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16112)),U_16113))) ),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

cnf(f_3977_3,plain,
    ( c_List_Obutlast(U_16112,hAPP(hAPP(c_List_Otake(U_16112),U_16111),U_16113)) = hAPP(hAPP(c_List_Otake(U_16112),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16111),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16113)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16112)),U_16113))) ),
    inference(clausify,[status(thm)],[f_3977_2]) ).

fof(f_3978_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_3978_2,plain,
    ! [U_16117,U_16116,U_16115,U_16114] :
      ( hAPP(hAPP(c_List_Olist__update(U_16114,U_16115),U_16116),U_16117) = U_16115
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16114)),U_16115)),U_16116)) ),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

cnf(f_3978_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16114,U_16115),U_16116),U_16117) = U_16115
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16114)),U_16115)),U_16116)) ),
    inference(clausify,[status(thm)],[f_3978_2]) ).

fof(f_3979_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_3979_2,plain,
    ! [U_16120,U_16119,U_16118] : hAPP(hAPP(c_List_Olist__update(U_16118,U_16119),U_16120),hAPP(hAPP(c_List_Onth(U_16118),U_16119),U_16120)) = U_16119,
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

cnf(f_3979_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16118,U_16119),U_16120),hAPP(hAPP(c_List_Onth(U_16118),U_16119),U_16120)) = U_16119,
    inference(clausify,[status(thm)],[f_3979_2]) ).

fof(f_3980_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_3980_2,plain,
    ! [U_16125,U_16124,U_16123,U_16122,U_16121] :
      ( hAPP(hAPP(c_List_Onth(U_16123),hAPP(hAPP(c_List_Olist__update(U_16123,U_16124),U_16121),U_16125)),U_16122) = hAPP(hAPP(c_List_Onth(U_16123),U_16124),U_16122)
      | U_16121 = U_16122 ),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

cnf(f_3980_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16123),hAPP(hAPP(c_List_Olist__update(U_16123,U_16124),U_16121),U_16125)),U_16122) = hAPP(hAPP(c_List_Onth(U_16123),U_16124),U_16122)
    | U_16121 = U_16122 ),
    inference(clausify,[status(thm)],[f_3980_2]) ).

fof(f_3981_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_3981_2,plain,
    ! [U_16129,U_16128,U_16127,U_16126] :
      ( ( c_List_Obutlast(U_16127,hAPP(hAPP(c_List_Olist__update(U_16127,U_16128),U_16126),U_16129)) = hAPP(hAPP(c_List_Olist__update(U_16127,c_List_Obutlast(U_16127,U_16128)),U_16126),U_16129)
        | U_16126 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16127)),U_16128)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_16127,hAPP(hAPP(c_List_Olist__update(U_16127,U_16128),U_16126),U_16129)) = c_List_Obutlast(U_16127,U_16128)
        | U_16126 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16127)),U_16128)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

fof(f_3981_3,plain,
    ( ! [U_16137,U_16135,U_16133,U_16131] :
        ( c_List_Obutlast(U_16133,hAPP(hAPP(c_List_Olist__update(U_16133,U_16135),U_16131),U_16137)) = hAPP(hAPP(c_List_Olist__update(U_16133,c_List_Obutlast(U_16133,U_16135)),U_16131),U_16137)
        | U_16131 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16133)),U_16135)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_16136,U_16134,U_16132,U_16130] :
        ( c_List_Obutlast(U_16132,hAPP(hAPP(c_List_Olist__update(U_16132,U_16134),U_16130),U_16136)) = c_List_Obutlast(U_16132,U_16134)
        | U_16130 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16132)),U_16134)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_3981_2]) ).

cnf(f_3981_4,plain,
    ( c_List_Obutlast(U_16132,hAPP(hAPP(c_List_Olist__update(U_16132,U_16134),U_16130),U_16136)) = c_List_Obutlast(U_16132,U_16134)
    | U_16130 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16132)),U_16134)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3981_3]) ).

cnf(f_3981_5,plain,
    ( c_List_Obutlast(U_16133,hAPP(hAPP(c_List_Olist__update(U_16133,U_16135),U_16131),U_16137)) = hAPP(hAPP(c_List_Olist__update(U_16133,c_List_Obutlast(U_16133,U_16135)),U_16131),U_16137)
    | U_16131 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16133)),U_16135)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3981_3]) ).

fof(f_3982_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_3982_2,plain,
    ! [U_16141,U_16140,U_16139,U_16138] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16138)),hAPP(hAPP(c_List_Olist__update(U_16138,U_16139),U_16140),U_16141)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16138)),U_16139),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

cnf(f_3982_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16138)),hAPP(hAPP(c_List_Olist__update(U_16138,U_16139),U_16140),U_16141)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16138)),U_16139),
    inference(clausify,[status(thm)],[f_3982_2]) ).

fof(f_3983_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_3983_2,plain,
    ! [U_16148,U_16147,U_16146,U_16145,U_16144,U_16143,U_16142] : hAPP(hAPP(c_List_Ozip(U_16142,U_16143),hAPP(hAPP(c_List_Olist__update(U_16142,U_16144),U_16145),U_16146)),hAPP(hAPP(c_List_Olist__update(U_16143,U_16147),U_16145),U_16148)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_16142,U_16143),hAPP(hAPP(c_List_Ozip(U_16142,U_16143),U_16144),U_16147)),U_16145),hAPP(hAPP(c_Product__Type_OPair(U_16142,U_16143),U_16146),U_16148)),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

cnf(f_3983_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16142,U_16143),hAPP(hAPP(c_List_Olist__update(U_16142,U_16144),U_16145),U_16146)),hAPP(hAPP(c_List_Olist__update(U_16143,U_16147),U_16145),U_16148)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_16142,U_16143),hAPP(hAPP(c_List_Ozip(U_16142,U_16143),U_16144),U_16147)),U_16145),hAPP(hAPP(c_Product__Type_OPair(U_16142,U_16143),U_16146),U_16148)),
    inference(clausify,[status(thm)],[f_3983_2]) ).

fof(f_3984_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_3984_2,plain,
    ! [U_16154,U_16153,U_16152,U_16151,U_16150,U_16149] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_16149,U_16150),hAPP(hAPP(c_List_Ozip(U_16149,U_16150),U_16151),U_16152)),U_16153),U_16154) = hAPP(hAPP(c_List_Ozip(U_16149,U_16150),hAPP(hAPP(c_List_Olist__update(U_16149,U_16151),U_16153),hAPP(c_Product__Type_Ofst(U_16149,U_16150),U_16154))),hAPP(hAPP(c_List_Olist__update(U_16150,U_16152),U_16153),hAPP(c_Product__Type_Osnd(U_16149,U_16150),U_16154))),
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

cnf(f_3984_3,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_16149,U_16150),hAPP(hAPP(c_List_Ozip(U_16149,U_16150),U_16151),U_16152)),U_16153),U_16154) = hAPP(hAPP(c_List_Ozip(U_16149,U_16150),hAPP(hAPP(c_List_Olist__update(U_16149,U_16151),U_16153),hAPP(c_Product__Type_Ofst(U_16149,U_16150),U_16154))),hAPP(hAPP(c_List_Olist__update(U_16150,U_16152),U_16153),hAPP(c_Product__Type_Osnd(U_16149,U_16150),U_16154))),
    inference(clausify,[status(thm)],[f_3984_2]) ).

fof(f_3985_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_3985_2,plain,
    ! [U_16160,U_16159,U_16158,U_16157,U_16156,U_16155] :
      ( hAPP(hAPP(c_List_Olist__update(U_16157,hAPP(hAPP(c_List_Olist__update(U_16157,U_16158),U_16155),U_16159)),U_16156),U_16160) = hAPP(hAPP(c_List_Olist__update(U_16157,hAPP(hAPP(c_List_Olist__update(U_16157,U_16158),U_16156),U_16160)),U_16155),U_16159)
      | U_16155 = U_16156 ),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

cnf(f_3985_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16157,hAPP(hAPP(c_List_Olist__update(U_16157,U_16158),U_16155),U_16159)),U_16156),U_16160) = hAPP(hAPP(c_List_Olist__update(U_16157,hAPP(hAPP(c_List_Olist__update(U_16157,U_16158),U_16156),U_16160)),U_16155),U_16159)
    | U_16155 = U_16156 ),
    inference(clausify,[status(thm)],[f_3985_2]) ).

fof(f_3986_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_3986_2,plain,
    ! [U_16165,U_16164,U_16163,U_16162,U_16161] : hAPP(hAPP(c_List_Olist__update(U_16161,hAPP(hAPP(c_List_Olist__update(U_16161,U_16162),U_16163),U_16164)),U_16163),U_16165) = hAPP(hAPP(c_List_Olist__update(U_16161,U_16162),U_16163),U_16165),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

cnf(f_3986_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16161,hAPP(hAPP(c_List_Olist__update(U_16161,U_16162),U_16163),U_16164)),U_16163),U_16165) = hAPP(hAPP(c_List_Olist__update(U_16161,U_16162),U_16163),U_16165),
    inference(clausify,[status(thm)],[f_3986_2]) ).

fof(f_3987_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_3987_2,plain,
    ! [U_16170,U_16169,U_16168,U_16167,U_16166] : hAPP(hAPP(c_List_Olist__update(U_16166,hAPP(hAPP(c_List_Olist_OCons(U_16166),U_16167),U_16168)),hAPP(c_Nat_OSuc,U_16169)),U_16170) = hAPP(hAPP(c_List_Olist_OCons(U_16166),U_16167),hAPP(hAPP(c_List_Olist__update(U_16166,U_16168),U_16169),U_16170)),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

cnf(f_3987_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16166,hAPP(hAPP(c_List_Olist_OCons(U_16166),U_16167),U_16168)),hAPP(c_Nat_OSuc,U_16169)),U_16170) = hAPP(hAPP(c_List_Olist_OCons(U_16166),U_16167),hAPP(hAPP(c_List_Olist__update(U_16166,U_16168),U_16169),U_16170)),
    inference(clausify,[status(thm)],[f_3987_2]) ).

fof(f_3988_1,plain,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2),
    inference(fof_nnf,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(f_3988_2,plain,
    ! [U_16175,U_16174,U_16173,U_16172,U_16171] : hAPP(hAPP(c_List_Olist__update(U_16171,hAPP(hAPP(c_List_Olist_OCons(U_16171),U_16172),U_16173)),U_16174),U_16175) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16171),hAPP(hAPP(c_List_Olist_OCons(U_16171),U_16175),U_16173),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16171),tc_List_Olist(U_16171),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_16171),U_16172)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_16171,tc_List_Olist(U_16171)),c_List_Olist__update(U_16171,U_16173)),U_16175)),U_16174),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

cnf(f_3988_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16171,hAPP(hAPP(c_List_Olist_OCons(U_16171),U_16172),U_16173)),U_16174),U_16175) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16171),hAPP(hAPP(c_List_Olist_OCons(U_16171),U_16175),U_16173),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16171),tc_List_Olist(U_16171),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_16171),U_16172)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_16171,tc_List_Olist(U_16171)),c_List_Olist__update(U_16171,U_16173)),U_16175)),U_16174),
    inference(clausify,[status(thm)],[f_3988_2]) ).

fof(f_3989_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_3989_2,plain,
    ! [U_16179,U_16178,U_16177,U_16176] : hAPP(hAPP(c_List_Olist__update(U_16176,hAPP(hAPP(c_List_Olist_OCons(U_16176),U_16177),U_16178)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16179) = hAPP(hAPP(c_List_Olist_OCons(U_16176),U_16179),U_16178),
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

cnf(f_3989_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16176,hAPP(hAPP(c_List_Olist_OCons(U_16176),U_16177),U_16178)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16179) = hAPP(hAPP(c_List_Olist_OCons(U_16176),U_16179),U_16178),
    inference(clausify,[status(thm)],[f_3989_2]) ).

fof(f_3990_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlastD]) ).

fof(f_3990_2,plain,
    ! [U_16182,U_16181,U_16180] :
      ( hBOOL(hAPP(hAPP(c_member(U_16180),U_16181),hAPP(c_List_Oset(U_16180),U_16182)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16180),U_16181),hAPP(c_List_Oset(U_16180),c_List_Obutlast(U_16180,U_16182)))) ),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

cnf(f_3990_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16180),U_16181),hAPP(c_List_Oset(U_16180),U_16182)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16180),U_16181),hAPP(c_List_Oset(U_16180),c_List_Obutlast(U_16180,U_16182)))) ),
    inference(clausify,[status(thm)],[f_3990_2]) ).

fof(f_3991_1,plain,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__subsetI]) ).

fof(f_3991_2,plain,
    ! [U_16187,U_16186,U_16185,U_16184,U_16183] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16183,tc_HOL_Obool)),hAPP(c_List_Oset(U_16183),hAPP(hAPP(c_List_Olist__update(U_16183,U_16184),U_16187),U_16186))),U_16185))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16183),U_16186),U_16185))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16183,tc_HOL_Obool)),hAPP(c_List_Oset(U_16183),U_16184)),U_16185)) ),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

cnf(f_3991_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16183,tc_HOL_Obool)),hAPP(c_List_Oset(U_16183),hAPP(hAPP(c_List_Olist__update(U_16183,U_16184),U_16187),U_16186))),U_16185))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16183),U_16186),U_16185))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16183,tc_HOL_Obool)),hAPP(c_List_Oset(U_16183),U_16184)),U_16185)) ),
    inference(clausify,[status(thm)],[f_3991_2]) ).

fof(f_3992_1,plain,
    ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__update__subset__insert]) ).

fof(f_3992_2,plain,
    ! [U_16191,U_16190,U_16189,U_16188] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16188,tc_HOL_Obool)),hAPP(c_List_Oset(U_16188),hAPP(hAPP(c_List_Olist__update(U_16188,U_16189),U_16190),U_16191))),hAPP(hAPP(c_Set_Oinsert(U_16188),U_16191),hAPP(c_List_Oset(U_16188),U_16189)))),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

cnf(f_3992_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16188,tc_HOL_Obool)),hAPP(c_List_Oset(U_16188),hAPP(hAPP(c_List_Olist__update(U_16188,U_16189),U_16190),U_16191))),hAPP(hAPP(c_Set_Oinsert(U_16188),U_16191),hAPP(c_List_Oset(U_16188),U_16189)))),
    inference(clausify,[status(thm)],[f_3992_2]) ).

fof(f_3993_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_3993_2,plain,
    ! [U_16195,U_16194,U_16193,U_16192] :
      ( hAPP(hAPP(c_List_Onth(U_16193),hAPP(hAPP(c_List_Olist__update(U_16193,U_16194),U_16192),U_16195)),U_16192) = U_16195
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16193)),U_16194))) ),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

cnf(f_3993_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16193),hAPP(hAPP(c_List_Olist__update(U_16193,U_16194),U_16192),U_16195)),U_16192) = U_16195
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16193)),U_16194))) ),
    inference(clausify,[status(thm)],[f_3993_2]) ).

fof(f_3994_1,plain,
    ! [V_x_2,V_xs_2,T_a,V_i_2] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
          | hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) != V_x_2 )
        & ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2
          | hAPP(hAPP(c_List_Olist__update(T_a,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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__same__conv]) ).

fof(f_3994_2,plain,
    ! [U_16199,U_16198,U_16197,U_16196] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_16197,U_16198),U_16196),U_16199) = U_16198
          | hAPP(hAPP(c_List_Onth(U_16197),U_16198),U_16196) != U_16199 )
        & ( hAPP(hAPP(c_List_Onth(U_16197),U_16198),U_16196) = U_16199
          | hAPP(hAPP(c_List_Olist__update(U_16197,U_16198),U_16196),U_16199) != U_16198 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16196),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16197)),U_16198))) ),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

cnf(f_3994_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16197),U_16198),U_16196) = U_16199
    | hAPP(hAPP(c_List_Olist__update(U_16197,U_16198),U_16196),U_16199) != U_16198
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16196),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16197)),U_16198))) ),
    inference(clausify,[status(thm)],[f_3994_2]) ).

cnf(f_3994_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16197,U_16198),U_16196),U_16199) = U_16198
    | hAPP(hAPP(c_List_Onth(U_16197),U_16198),U_16196) != U_16199
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16196),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16197)),U_16198))) ),
    inference(clausify,[status(thm)],[f_3994_2]) ).

fof(f_3995_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_3995_2,plain,
    ! [U_16204,U_16203,U_16202,U_16201,U_16200] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_16201),hAPP(hAPP(c_List_Olist__update(U_16201,U_16202),U_16200),U_16204)),U_16203) = hAPP(hAPP(c_List_Onth(U_16201),U_16202),U_16203)
          | U_16200 = U_16203 )
        & ( hAPP(hAPP(c_List_Onth(U_16201),hAPP(hAPP(c_List_Olist__update(U_16201,U_16202),U_16200),U_16204)),U_16203) = U_16204
          | U_16200 != U_16203 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16200),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16201)),U_16202))) ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

cnf(f_3995_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16201),hAPP(hAPP(c_List_Olist__update(U_16201,U_16202),U_16200),U_16204)),U_16203) = U_16204
    | U_16200 != U_16203
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16200),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16201)),U_16202))) ),
    inference(clausify,[status(thm)],[f_3995_2]) ).

cnf(f_3995_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_16201),hAPP(hAPP(c_List_Olist__update(U_16201,U_16202),U_16200),U_16204)),U_16203) = hAPP(hAPP(c_List_Onth(U_16201),U_16202),U_16203)
    | U_16200 = U_16203
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16200),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16201)),U_16202))) ),
    inference(clausify,[status(thm)],[f_3995_2]) ).

fof(f_3996_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_3996_2,plain,
    ! [U_16207,U_16206,U_16205] :
      ( hAPP(hAPP(c_List_Otake(U_16206),U_16205),c_List_Obutlast(U_16206,U_16207)) = hAPP(hAPP(c_List_Otake(U_16206),U_16205),U_16207)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16206)),U_16207))) ),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

cnf(f_3996_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16206),U_16205),c_List_Obutlast(U_16206,U_16207)) = hAPP(hAPP(c_List_Otake(U_16206),U_16205),U_16207)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16206)),U_16207))) ),
    inference(clausify,[status(thm)],[f_3996_2]) ).

fof(f_3997_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_3997_2,plain,
    ! [U_16209,U_16208] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16208)),c_List_Obutlast(U_16208,U_16209)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16208)),U_16209)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

cnf(f_3997_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16208)),c_List_Obutlast(U_16208,U_16209)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16208)),U_16209)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_3997_2]) ).

fof(f_3998_1,plain,
    ! [V_x_2,V_xs_2,T_a,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__memI]) ).

fof(f_3998_2,plain,
    ! [U_16213,U_16212,U_16211,U_16210] :
      ( hBOOL(hAPP(hAPP(c_member(U_16211),U_16213),hAPP(c_List_Oset(U_16211),hAPP(hAPP(c_List_Olist__update(U_16211,U_16212),U_16210),U_16213))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16211)),U_16212))) ),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

cnf(f_3998_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16211),U_16213),hAPP(c_List_Oset(U_16211),hAPP(hAPP(c_List_Olist__update(U_16211,U_16212),U_16210),U_16213))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16211)),U_16212))) ),
    inference(clausify,[status(thm)],[f_3998_2]) ).

fof(f_3999_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_3999_2,plain,
    ! [U_16215,U_16214] : c_List_Obutlast(U_16214,U_16215) = hAPP(hAPP(c_List_Otake(U_16214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16214)),U_16215)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16215),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

cnf(f_3999_3,plain,
    c_List_Obutlast(U_16214,U_16215) = hAPP(hAPP(c_List_Otake(U_16214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16214)),U_16215)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16215),
    inference(clausify,[status(thm)],[f_3999_2]) ).

fof(f_4000_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
        | ! [B_y,B_n] :
            ( V_ys_2 != hAPP(hAPP(c_List_Olist__update(T_a,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_a)),V_xs_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) ) )
      & ( ? [B_y,B_n] :
            ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,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_a)),V_xs_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update]) ).

fof(f_4000_2,plain,
    ! [U_16223,U_16222,U_16221,U_16220] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16220),tc_List_Olist(U_16220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16220),tc_List_Olist(U_16220)),U_16221),U_16222)),c_List_Olistrel1(U_16220,U_16223)))
        | ! [U_16219,U_16218] :
            ( U_16222 != hAPP(hAPP(c_List_Olist__update(U_16220,U_16221),U_16218),U_16219)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16220)),U_16221)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16220,U_16220)),hAPP(hAPP(c_Product__Type_OPair(U_16220,U_16220),hAPP(hAPP(c_List_Onth(U_16220),U_16221),U_16218)),U_16219)),U_16223)) ) )
      & ( ? [U_16217,U_16216] :
            ( U_16222 = hAPP(hAPP(c_List_Olist__update(U_16220,U_16221),U_16216),U_16217)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16220)),U_16221)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16220,U_16220)),hAPP(hAPP(c_Product__Type_OPair(U_16220,U_16220),hAPP(hAPP(c_List_Onth(U_16220),U_16221),U_16216)),U_16217)),U_16223)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16220),tc_List_Olist(U_16220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16220),tc_List_Olist(U_16220)),U_16221),U_16222)),c_List_Olistrel1(U_16220,U_16223))) ) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ( ! [U_16231,U_16229,U_16227,U_16225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16225),tc_List_Olist(U_16225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16225),tc_List_Olist(U_16225)),U_16227),U_16229)),c_List_Olistrel1(U_16225,U_16231)))
        | ! [U_16219,U_16218] :
            ( U_16229 != hAPP(hAPP(c_List_Olist__update(U_16225,U_16227),U_16218),U_16219)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16225)),U_16227)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16225,U_16225)),hAPP(hAPP(c_Product__Type_OPair(U_16225,U_16225),hAPP(hAPP(c_List_Onth(U_16225),U_16227),U_16218)),U_16219)),U_16231)) ) )
    & ! [U_16230,U_16228,U_16226,U_16224] :
        ( ? [U_16217,U_16216] :
            ( U_16228 = hAPP(hAPP(c_List_Olist__update(U_16224,U_16226),U_16216),U_16217)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16224)),U_16226)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16224,U_16224)),hAPP(hAPP(c_Product__Type_OPair(U_16224,U_16224),hAPP(hAPP(c_List_Onth(U_16224),U_16226),U_16216)),U_16217)),U_16230)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ) ),
    inference(miniscope,[status(thm)],[f_4000_2]) ).

fof(f_4000_4,plain,
    ( ! [U_16231,U_16229,U_16227,U_16225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16225),tc_List_Olist(U_16225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16225),tc_List_Olist(U_16225)),U_16227),U_16229)),c_List_Olistrel1(U_16225,U_16231)))
        | ! [U_16219,U_16218] :
            ( U_16229 != hAPP(hAPP(c_List_Olist__update(U_16225,U_16227),U_16218),U_16219)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16225)),U_16227)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16225,U_16225)),hAPP(hAPP(c_Product__Type_OPair(U_16225,U_16225),hAPP(hAPP(c_List_Onth(U_16225),U_16227),U_16218)),U_16219)),U_16231)) ) )
    & ! [U_16230,U_16228,U_16226,U_16224] :
        ( ? [U_16216] :
            ( U_16228 = hAPP(hAPP(c_List_Olist__update(U_16224,U_16226),U_16216),sK432(U_16230,U_16228,U_16226,U_16224))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16224)),U_16226)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16224,U_16224)),hAPP(hAPP(c_Product__Type_OPair(U_16224,U_16224),hAPP(hAPP(c_List_Onth(U_16224),U_16226),U_16216)),sK432(U_16230,U_16228,U_16226,U_16224))),U_16230)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_16217,sK432(U_16230,U_16228,U_16226,U_16224))],[f_4000_3]) ).

fof(f_4000_5,plain,
    ( ! [U_16231,U_16229,U_16227,U_16225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16225),tc_List_Olist(U_16225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16225),tc_List_Olist(U_16225)),U_16227),U_16229)),c_List_Olistrel1(U_16225,U_16231)))
        | ! [U_16219,U_16218] :
            ( U_16229 != hAPP(hAPP(c_List_Olist__update(U_16225,U_16227),U_16218),U_16219)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16225)),U_16227)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16225,U_16225)),hAPP(hAPP(c_Product__Type_OPair(U_16225,U_16225),hAPP(hAPP(c_List_Onth(U_16225),U_16227),U_16218)),U_16219)),U_16231)) ) )
    & ! [U_16230,U_16228,U_16226,U_16224] :
        ( ( U_16228 = hAPP(hAPP(c_List_Olist__update(U_16224,U_16226),sK433(U_16230,U_16228,U_16226,U_16224)),sK432(U_16230,U_16228,U_16226,U_16224))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK433(U_16230,U_16228,U_16226,U_16224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16224)),U_16226)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16224,U_16224)),hAPP(hAPP(c_Product__Type_OPair(U_16224,U_16224),hAPP(hAPP(c_List_Onth(U_16224),U_16226),sK433(U_16230,U_16228,U_16226,U_16224))),sK432(U_16230,U_16228,U_16226,U_16224))),U_16230)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_16216,sK433(U_16230,U_16228,U_16226,U_16224))],[f_4000_4]) ).

cnf(f_4000_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16224,U_16224)),hAPP(hAPP(c_Product__Type_OPair(U_16224,U_16224),hAPP(hAPP(c_List_Onth(U_16224),U_16226),sK433(U_16230,U_16228,U_16226,U_16224))),sK432(U_16230,U_16228,U_16226,U_16224))),U_16230))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ),
    inference(clausify,[status(thm)],[f_4000_5]) ).

cnf(f_4000_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK433(U_16230,U_16228,U_16226,U_16224)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16224)),U_16226)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ),
    inference(clausify,[status(thm)],[f_4000_5]) ).

cnf(f_4000_8,plain,
    ( U_16228 = hAPP(hAPP(c_List_Olist__update(U_16224,U_16226),sK433(U_16230,U_16228,U_16226,U_16224)),sK432(U_16230,U_16228,U_16226,U_16224))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16224),tc_List_Olist(U_16224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16224),tc_List_Olist(U_16224)),U_16226),U_16228)),c_List_Olistrel1(U_16224,U_16230))) ),
    inference(clausify,[status(thm)],[f_4000_5]) ).

cnf(f_4000_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16225),tc_List_Olist(U_16225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16225),tc_List_Olist(U_16225)),U_16227),U_16229)),c_List_Olistrel1(U_16225,U_16231)))
    | U_16229 != hAPP(hAPP(c_List_Olist__update(U_16225,U_16227),U_16218),U_16219)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16225)),U_16227)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16225,U_16225)),hAPP(hAPP(c_Product__Type_OPair(U_16225,U_16225),hAPP(hAPP(c_List_Onth(U_16225),U_16227),U_16218)),U_16219)),U_16231)) ),
    inference(clausify,[status(thm)],[f_4000_5]) ).

fof(f_4001_1,plain,
    ! [V_i_2,V_a_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2)))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__list__update]) ).

fof(f_4001_2,plain,
    ! [U_16235,U_16234,U_16233,U_16232] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16232),hAPP(hAPP(c_List_Olist__update(U_16232,U_16233),U_16235),U_16234)))
      | hBOOL(hAPP(hAPP(c_member(U_16232),U_16234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16232,tc_HOL_Obool)),hAPP(c_List_Oset(U_16232),U_16233)),hAPP(hAPP(c_Set_Oinsert(U_16232),hAPP(hAPP(c_List_Onth(U_16232),U_16233),U_16235)),c_Orderings_Obot__class_Obot(tc_fun(U_16232,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16232),U_16233)) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

cnf(f_4001_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16232),hAPP(hAPP(c_List_Olist__update(U_16232,U_16233),U_16235),U_16234)))
    | hBOOL(hAPP(hAPP(c_member(U_16232),U_16234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16232,tc_HOL_Obool)),hAPP(c_List_Oset(U_16232),U_16233)),hAPP(hAPP(c_Set_Oinsert(U_16232),hAPP(hAPP(c_List_Onth(U_16232),U_16233),U_16235)),c_Orderings_Obot__class_Obot(tc_fun(U_16232,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16232),U_16233)) ),
    inference(clausify,[status(thm)],[f_4001_2]) ).

fof(f_4002_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_4002_2,plain,
    ! [U_16237,U_16236] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_16236,U_16237))),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

cnf(f_4002_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_16236,U_16237))),
    inference(clausify,[status(thm)],[f_4002_2]) ).

fof(f_4003_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_4003_2,plain,
    ! [U_16240,U_16239,U_16238] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16238),hAPP(hAPP(c_List_Otake(U_16238),U_16240),U_16239)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16238),U_16239)) ),
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

cnf(f_4003_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16238),hAPP(hAPP(c_List_Otake(U_16238),U_16240),U_16239)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16238),U_16239)) ),
    inference(clausify,[status(thm)],[f_4003_2]) ).

fof(f_4004_1,plain,
    ! [V_I_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__sublistI]) ).

fof(f_4004_2,plain,
    ! [U_16243,U_16242,U_16241] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16241),c_List_Osublist(U_16241,U_16242,U_16243)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16241),U_16242)) ),
    inference(variable_rename,[status(thm)],[f_4004_1]) ).

cnf(f_4004_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16241),c_List_Osublist(U_16241,U_16242,U_16243)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16241),U_16242)) ),
    inference(clausify,[status(thm)],[f_4004_2]) ).

fof(f_4005_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_4005_2,plain,
    ! [U_16247,U_16246,U_16245,U_16244] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_16246,U_16244)),hAPP(hAPP(c_List_Ozip(U_16246,U_16244),U_16247),U_16245)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16244),U_16245)) ),
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

cnf(f_4005_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_16246,U_16244)),hAPP(hAPP(c_List_Ozip(U_16246,U_16244),U_16247),U_16245)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16244),U_16245)) ),
    inference(clausify,[status(thm)],[f_4005_2]) ).

fof(f_4006_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_4006_2,plain,
    ! [U_16251,U_16250,U_16249,U_16248] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_16248,U_16250)),hAPP(hAPP(c_List_Ozip(U_16248,U_16250),U_16249),U_16251)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16249)) ),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

cnf(f_4006_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_16248,U_16250)),hAPP(hAPP(c_List_Ozip(U_16248,U_16250),U_16249),U_16251)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16249)) ),
    inference(clausify,[status(thm)],[f_4006_2]) ).

fof(f_4007_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(f_4007_2,plain,
    ! [U_16254,U_16253,U_16252] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16252),hAPP(hAPP(c_List_Olist_OCons(U_16252),U_16253),U_16254)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16252),U_16254))
        | hBOOL(hAPP(hAPP(c_member(U_16252),U_16253),hAPP(c_List_Oset(U_16252),U_16254))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_16252),U_16254))
          & ~ hBOOL(hAPP(hAPP(c_member(U_16252),U_16253),hAPP(c_List_Oset(U_16252),U_16254))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16252),hAPP(hAPP(c_List_Olist_OCons(U_16252),U_16253),U_16254))) ) ),
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

fof(f_4007_3,plain,
    ( ! [U_16260,U_16258,U_16256] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16256),hAPP(hAPP(c_List_Olist_OCons(U_16256),U_16258),U_16260)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16256),U_16260))
        | hBOOL(hAPP(hAPP(c_member(U_16256),U_16258),hAPP(c_List_Oset(U_16256),U_16260))) )
    & ! [U_16259,U_16257,U_16255] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_16255),U_16259))
          & ~ hBOOL(hAPP(hAPP(c_member(U_16255),U_16257),hAPP(c_List_Oset(U_16255),U_16259))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),hAPP(hAPP(c_List_Olist_OCons(U_16255),U_16257),U_16259))) ) ),
    inference(miniscope,[status(thm)],[f_4007_2]) ).

cnf(f_4007_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16255),U_16257),hAPP(c_List_Oset(U_16255),U_16259)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),hAPP(hAPP(c_List_Olist_OCons(U_16255),U_16257),U_16259))) ),
    inference(clausify,[status(thm)],[f_4007_3]) ).

cnf(f_4007_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16255),U_16259))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),hAPP(hAPP(c_List_Olist_OCons(U_16255),U_16257),U_16259))) ),
    inference(clausify,[status(thm)],[f_4007_3]) ).

cnf(f_4007_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16256),hAPP(hAPP(c_List_Olist_OCons(U_16256),U_16258),U_16260)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16256),U_16260))
    | hBOOL(hAPP(hAPP(c_member(U_16256),U_16258),hAPP(c_List_Oset(U_16256),U_16260))) ),
    inference(clausify,[status(thm)],[f_4007_3]) ).

fof(f_4008_1,plain,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__distinct]) ).

fof(f_4008_2,plain,
    ! [U_16262,U_16261] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16261),U_16262))
      | hAPP(c_Finite__Set_Ocard(U_16261),hAPP(c_List_Oset(U_16261),U_16262)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16261)),U_16262) ),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

cnf(f_4008_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16261),U_16262))
    | hAPP(c_Finite__Set_Ocard(U_16261),hAPP(c_List_Oset(U_16261),U_16262)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16261)),U_16262) ),
    inference(clausify,[status(thm)],[f_4008_2]) ).

fof(f_4009_1,plain,
    ! [V_xs_2,T_a] :
      ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__card]) ).

fof(f_4009_2,plain,
    ! [U_16264,U_16263] :
      ( hAPP(c_Finite__Set_Ocard(U_16263),hAPP(c_List_Oset(U_16263),U_16264)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16263)),U_16264)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16263),U_16264)) ),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

cnf(f_4009_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_16263),hAPP(c_List_Oset(U_16263),U_16264)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16263)),U_16264)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16263),U_16264)) ),
    inference(clausify,[status(thm)],[f_4009_2]) ).

fof(f_4010_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_a] :
      ( ( ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2)
          | V_i_2 != V_j_2 )
        & ( V_i_2 = V_j_2
          | hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) != hAPP(hAPP(c_List_Onth(T_a),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_a)),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_a)),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq]) ).

fof(f_4010_2,plain,
    ! [U_16268,U_16267,U_16266,U_16265] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16267) = hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16268)
          | U_16267 != U_16268 )
        & ( U_16267 = U_16268
          | hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16267) != hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16268) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16268),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16267),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16265),U_16266)) ),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

cnf(f_4010_3,plain,
    ( U_16267 = U_16268
    | hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16267) != hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16268),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16267),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16265),U_16266)) ),
    inference(clausify,[status(thm)],[f_4010_2]) ).

cnf(f_4010_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16267) = hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16268)
    | U_16267 != U_16268
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16268),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16267),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16265),U_16266)) ),
    inference(clausify,[status(thm)],[f_4010_2]) ).

fof(f_4011_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | ? [B_i] :
            ( ? [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),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_a)),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_a)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( ! [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),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_a)),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_a)),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__conv__nth]) ).

fof(f_4011_2,plain,
    ! [U_16274,U_16273] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16273),U_16274))
        | ? [U_16272] :
            ( ? [U_16271] :
                ( hAPP(hAPP(c_List_Onth(U_16273),U_16274),U_16272) = hAPP(hAPP(c_List_Onth(U_16273),U_16274),U_16271)
                & U_16272 != U_16271
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16274))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16272),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16274))) ) )
      & ( ! [U_16270] :
            ( ! [U_16269] :
                ( hAPP(hAPP(c_List_Onth(U_16273),U_16274),U_16270) != hAPP(hAPP(c_List_Onth(U_16273),U_16274),U_16269)
                | U_16270 = U_16269
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16274))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16274))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16273),U_16274)) ) ),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

fof(f_4011_3,plain,
    ( ! [U_16278,U_16276] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278))
        | ? [U_16272] :
            ( ? [U_16271] :
                ( hAPP(hAPP(c_List_Onth(U_16276),U_16278),U_16272) = hAPP(hAPP(c_List_Onth(U_16276),U_16278),U_16271)
                & U_16272 != U_16271
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16272),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278))) ) )
    & ! [U_16277,U_16275] :
        ( ! [U_16270] :
            ( ! [U_16269] :
                ( hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16270) != hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16269)
                | U_16270 = U_16269
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16275),U_16277)) ) ),
    inference(miniscope,[status(thm)],[f_4011_2]) ).

fof(f_4011_4,plain,
    ( ! [U_16278,U_16276] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278))
        | ( ? [U_16271] :
              ( hAPP(hAPP(c_List_Onth(U_16276),U_16278),sK434(U_16278,U_16276)) = hAPP(hAPP(c_List_Onth(U_16276),U_16278),U_16271)
              & sK434(U_16278,U_16276) != U_16271
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK434(U_16278,U_16276)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278))) ) )
    & ! [U_16277,U_16275] :
        ( ! [U_16270] :
            ( ! [U_16269] :
                ( hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16270) != hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16269)
                | U_16270 = U_16269
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16275),U_16277)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_16272,sK434(U_16278,U_16276))],[f_4011_3]) ).

fof(f_4011_5,plain,
    ( ! [U_16278,U_16276] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278))
        | ( hAPP(hAPP(c_List_Onth(U_16276),U_16278),sK434(U_16278,U_16276)) = hAPP(hAPP(c_List_Onth(U_16276),U_16278),sK435(U_16278,U_16276))
          & sK434(U_16278,U_16276) != sK435(U_16278,U_16276)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK435(U_16278,U_16276)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK434(U_16278,U_16276)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278))) ) )
    & ! [U_16277,U_16275] :
        ( ! [U_16270] :
            ( ! [U_16269] :
                ( hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16270) != hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16269)
                | U_16270 = U_16269
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16275),U_16277)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_16271,sK435(U_16278,U_16276))],[f_4011_4]) ).

cnf(f_4011_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16270) != hAPP(hAPP(c_List_Onth(U_16275),U_16277),U_16269)
    | U_16270 = U_16269
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16275)),U_16277)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16275),U_16277)) ),
    inference(clausify,[status(thm)],[f_4011_5]) ).

cnf(f_4011_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK434(U_16278,U_16276)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278)))
    | hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278)) ),
    inference(clausify,[status(thm)],[f_4011_5]) ).

cnf(f_4011_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK435(U_16278,U_16276)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16276)),U_16278)))
    | hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278)) ),
    inference(clausify,[status(thm)],[f_4011_5]) ).

cnf(f_4011_9,plain,
    ( sK434(U_16278,U_16276) != sK435(U_16278,U_16276)
    | hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278)) ),
    inference(clausify,[status(thm)],[f_4011_5]) ).

cnf(f_4011_10,plain,
    ( hAPP(hAPP(c_List_Onth(U_16276),U_16278),sK434(U_16278,U_16276)) = hAPP(hAPP(c_List_Onth(U_16276),U_16278),sK435(U_16278,U_16276))
    | hBOOL(hAPP(c_List_Odistinct(U_16276),U_16278)) ),
    inference(clausify,[status(thm)],[f_4011_5]) ).

fof(f_4012_1,plain,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum]) ).

fof(f_4012_2,plain,
    ! [U_16280,U_16279] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16279),U_16280) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_16279,U_16279),c_COMBI(U_16279)),hAPP(c_List_Oset(U_16279),U_16280))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16279),U_16280))
      | ~ class_Groups_Ocomm__monoid__add(U_16279) ),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

cnf(f_4012_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16279),U_16280) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_16279,U_16279),c_COMBI(U_16279)),hAPP(c_List_Oset(U_16279),U_16280))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16279),U_16280))
    | ~ class_Groups_Ocomm__monoid__add(U_16279) ),
    inference(clausify,[status(thm)],[f_4012_2]) ).

fof(f_4013_1,plain,
    ! [V_A_2,T_a] :
      ( ( c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
      & ( c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(f_4013_2,plain,
    ! [U_16282,U_16281] :
      ( ( c_Nitpick_Ocard_H(U_16281,U_16282) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_16281),U_16282)) )
      & ( c_Nitpick_Ocard_H(U_16281,U_16282) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16281)),c_Hilbert__Choice_OEps(tc_List_Olist(U_16281),hAPP(hAPP(c_COMBS(tc_List_Olist(U_16281),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_16281)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16281),tc_fun(U_16281,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16281,tc_HOL_Obool),tc_fun(tc_fun(U_16281,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_16281)),c_fequal),c_List_Oset(U_16281))),U_16282))),c_List_Odistinct(U_16281))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16281),U_16282)) ) ),
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

fof(f_4013_3,plain,
    ( ! [U_16286,U_16284] :
        ( c_Nitpick_Ocard_H(U_16284,U_16286) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_16284),U_16286)) )
    & ! [U_16285,U_16283] :
        ( c_Nitpick_Ocard_H(U_16283,U_16285) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16283)),c_Hilbert__Choice_OEps(tc_List_Olist(U_16283),hAPP(hAPP(c_COMBS(tc_List_Olist(U_16283),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_16283)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16283),tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16283,tc_HOL_Obool),tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_16283)),c_fequal),c_List_Oset(U_16283))),U_16285))),c_List_Odistinct(U_16283))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16283),U_16285)) ) ),
    inference(miniscope,[status(thm)],[f_4013_2]) ).

cnf(f_4013_4,plain,
    ( c_Nitpick_Ocard_H(U_16283,U_16285) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16283)),c_Hilbert__Choice_OEps(tc_List_Olist(U_16283),hAPP(hAPP(c_COMBS(tc_List_Olist(U_16283),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_16283)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16283),tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16283,tc_HOL_Obool),tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_16283)),c_fequal),c_List_Oset(U_16283))),U_16285))),c_List_Odistinct(U_16283))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16283),U_16285)) ),
    inference(clausify,[status(thm)],[f_4013_3]) ).

cnf(f_4013_5,plain,
    ( c_Nitpick_Ocard_H(U_16284,U_16286) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_16284),U_16286)) ),
    inference(clausify,[status(thm)],[f_4013_3]) ).

fof(f_4014_1,plain,
    ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__upds]) ).

fof(f_4014_2,plain,
    ! [U_16291,U_16290,U_16289,U_16288,U_16287] : c_Map_Odom(U_16287,U_16288,c_Map_Omap__upds(U_16287,U_16288,U_16289,U_16290,U_16291)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16287,tc_HOL_Obool)),hAPP(c_List_Oset(U_16287),hAPP(hAPP(c_List_Otake(U_16287),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16288)),U_16291)),U_16290))),c_Map_Odom(U_16287,U_16288,U_16289)),
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

cnf(f_4014_3,plain,
    c_Map_Odom(U_16287,U_16288,c_Map_Omap__upds(U_16287,U_16288,U_16289,U_16290,U_16291)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16287,tc_HOL_Obool)),hAPP(c_List_Oset(U_16287),hAPP(hAPP(c_List_Otake(U_16287),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16288)),U_16291)),U_16290))),c_Map_Odom(U_16287,U_16288,U_16289)),
    inference(clausify,[status(thm)],[f_4014_2]) ).

fof(f_4015_1,plain,
    ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
      ( hAPP(c_Map_Omap__upds(T_a,T_b,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_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__apply__nontin]) ).

fof(f_4015_2,plain,
    ! [U_16297,U_16296,U_16295,U_16294,U_16293,U_16292] :
      ( hAPP(c_Map_Omap__upds(U_16292,U_16295,U_16296,U_16294,U_16297),U_16293) = hAPP(U_16296,U_16293)
      | hBOOL(hAPP(hAPP(c_member(U_16292),U_16293),hAPP(c_List_Oset(U_16292),U_16294))) ),
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

cnf(f_4015_3,plain,
    ( hAPP(c_Map_Omap__upds(U_16292,U_16295,U_16296,U_16294,U_16297),U_16293) = hAPP(U_16296,U_16293)
    | hBOOL(hAPP(hAPP(c_member(U_16292),U_16293),hAPP(c_List_Oset(U_16292),U_16294))) ),
    inference(clausify,[status(thm)],[f_4015_2]) ).

fof(f_4016_1,plain,
    ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
      ( c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,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_b)),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_a)),V_xs_2)),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__list__update2__drop]) ).

fof(f_4016_2,plain,
    ! [U_16304,U_16303,U_16302,U_16301,U_16300,U_16299,U_16298] :
      ( c_Map_Omap__upds(U_16298,U_16301,U_16303,U_16299,hAPP(hAPP(c_List_Olist__update(U_16301,U_16302),U_16300),U_16304)) = c_Map_Omap__upds(U_16298,U_16301,U_16303,U_16299,U_16302)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16300),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16301)),U_16302)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16298)),U_16299)),U_16300)) ),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

cnf(f_4016_3,plain,
    ( c_Map_Omap__upds(U_16298,U_16301,U_16303,U_16299,hAPP(hAPP(c_List_Olist__update(U_16301,U_16302),U_16300),U_16304)) = c_Map_Omap__upds(U_16298,U_16301,U_16303,U_16299,U_16302)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16300),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16301)),U_16302)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16298)),U_16299)),U_16300)) ),
    inference(clausify,[status(thm)],[f_4016_2]) ).

fof(f_4017_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_4017_2,plain,
    ! [U_16309,U_16308,U_16307,U_16306] :
      ( hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16308) = hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16309)
      | ? [U_16305] :
          ( hAPP(hAPP(c_List_Onth(U_16307),U_16308),U_16305) != hAPP(hAPP(c_List_Onth(U_16307),U_16309),U_16305)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16305),U_16306)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16308))) ),
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

fof(f_4017_3,plain,
    ! [U_16309,U_16308,U_16307,U_16306] :
      ( hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16308) = hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16309)
      | ( hAPP(hAPP(c_List_Onth(U_16307),U_16308),sK436(U_16309,U_16308,U_16307,U_16306)) != hAPP(hAPP(c_List_Onth(U_16307),U_16309),sK436(U_16309,U_16308,U_16307,U_16306))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK436(U_16309,U_16308,U_16307,U_16306)),U_16306)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16308))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_16305,sK436(U_16309,U_16308,U_16307,U_16306))],[f_4017_2]) ).

cnf(f_4017_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK436(U_16309,U_16308,U_16307,U_16306)),U_16306))
    | hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16308) = hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16309)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16308))) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

cnf(f_4017_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_16307),U_16308),sK436(U_16309,U_16308,U_16307,U_16306)) != hAPP(hAPP(c_List_Onth(U_16307),U_16309),sK436(U_16309,U_16308,U_16307,U_16306))
    | hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16308) = hAPP(hAPP(c_List_Otake(U_16307),U_16306),U_16309)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16307)),U_16308))) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

fof(f_4018_1,plain,
    ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__upds]) ).

fof(f_4018_2,plain,
    ! [U_16315,U_16314,U_16313,U_16312,U_16311,U_16310] :
      ( c_Map_Orestrict__map(U_16310,U_16312,c_Map_Omap__upds(U_16310,U_16312,U_16315,U_16311,U_16313),U_16314) = c_Map_Omap__upds(U_16310,U_16312,c_Map_Orestrict__map(U_16310,U_16312,U_16315,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16310,tc_HOL_Obool)),U_16314),hAPP(c_List_Oset(U_16310),U_16311))),U_16311,U_16313)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16310,tc_HOL_Obool)),hAPP(c_List_Oset(U_16310),U_16311)),U_16314))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16310)),U_16311) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16312)),U_16313) ),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

cnf(f_4018_3,plain,
    ( c_Map_Orestrict__map(U_16310,U_16312,c_Map_Omap__upds(U_16310,U_16312,U_16315,U_16311,U_16313),U_16314) = c_Map_Omap__upds(U_16310,U_16312,c_Map_Orestrict__map(U_16310,U_16312,U_16315,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16310,tc_HOL_Obool)),U_16314),hAPP(c_List_Oset(U_16310),U_16311))),U_16311,U_16313)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16310,tc_HOL_Obool)),hAPP(c_List_Oset(U_16310),U_16311)),U_16314))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16310)),U_16311) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16312)),U_16313) ),
    inference(clausify,[status(thm)],[f_4018_2]) ).

fof(f_4019_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,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_4019_2,plain,
    ! [U_16320,U_16319,U_16318,U_16317,U_16316] : c_Map_Orestrict__map(U_16316,U_16317,U_16318,hAPP(hAPP(c_Set_Oinsert(U_16316),U_16319),U_16320)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16316,tc_Option_Ooption(U_16317)),c_Map_Orestrict__map(U_16316,U_16317,U_16318,U_16320)),U_16319),hAPP(U_16318,U_16319)),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

cnf(f_4019_3,plain,
    c_Map_Orestrict__map(U_16316,U_16317,U_16318,hAPP(hAPP(c_Set_Oinsert(U_16316),U_16319),U_16320)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16316,tc_Option_Ooption(U_16317)),c_Map_Orestrict__map(U_16316,U_16317,U_16318,U_16320)),U_16319),hAPP(U_16318,U_16319)),
    inference(clausify,[status(thm)],[f_4019_2]) ).

fof(f_4020_1,plain,
    ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_restrict__restrict]) ).

fof(f_4020_2,plain,
    ! [U_16325,U_16324,U_16323,U_16322,U_16321] : c_Map_Orestrict__map(U_16321,U_16322,c_Map_Orestrict__map(U_16321,U_16322,U_16323,U_16324),U_16325) = c_Map_Orestrict__map(U_16321,U_16322,U_16323,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16321,tc_HOL_Obool)),U_16324),U_16325)),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

cnf(f_4020_3,plain,
    c_Map_Orestrict__map(U_16321,U_16322,c_Map_Orestrict__map(U_16321,U_16322,U_16323,U_16324),U_16325) = c_Map_Orestrict__map(U_16321,U_16322,U_16323,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16321,tc_HOL_Obool)),U_16324),U_16325)),
    inference(clausify,[status(thm)],[f_4020_2]) ).

fof(f_4021_1,plain,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__in]) ).

fof(f_4021_2,plain,
    ! [U_16330,U_16329,U_16328,U_16327,U_16326] :
      ( hAPP(c_Map_Orestrict__map(U_16326,U_16329,U_16330,U_16328),U_16327) = hAPP(U_16330,U_16327)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16326),U_16327),U_16328)) ),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

cnf(f_4021_3,plain,
    ( hAPP(c_Map_Orestrict__map(U_16326,U_16329,U_16330,U_16328),U_16327) = hAPP(U_16330,U_16327)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16326),U_16327),U_16328)) ),
    inference(clausify,[status(thm)],[f_4021_2]) ).

fof(f_4022_1,plain,
    ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_dom__restrict]) ).

fof(f_4022_2,plain,
    ! [U_16334,U_16333,U_16332,U_16331] : c_Map_Odom(U_16331,U_16332,c_Map_Orestrict__map(U_16331,U_16332,U_16333,U_16334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16331,tc_HOL_Obool)),c_Map_Odom(U_16331,U_16332,U_16333)),U_16334),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

cnf(f_4022_3,plain,
    c_Map_Odom(U_16331,U_16332,c_Map_Orestrict__map(U_16331,U_16332,U_16333,U_16334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16331,tc_HOL_Obool)),c_Map_Odom(U_16331,U_16332,U_16333)),U_16334),
    inference(clausify,[status(thm)],[f_4022_2]) ).

fof(f_4023_1,plain,
    ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict]) ).

fof(f_4023_2,plain,
    ! [U_16340,U_16339,U_16338,U_16337,U_16336,U_16335] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16335,tc_Option_Ooption(U_16336)),c_Map_Orestrict__map(U_16335,U_16336,U_16337,U_16338)),U_16339),U_16340) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16335,tc_Option_Ooption(U_16336)),c_Map_Orestrict__map(U_16335,U_16336,U_16337,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16335,tc_HOL_Obool)),U_16338),hAPP(hAPP(c_Set_Oinsert(U_16335),U_16339),c_Orderings_Obot__class_Obot(tc_fun(U_16335,tc_HOL_Obool)))))),U_16339),U_16340),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

cnf(f_4023_3,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16335,tc_Option_Ooption(U_16336)),c_Map_Orestrict__map(U_16335,U_16336,U_16337,U_16338)),U_16339),U_16340) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16335,tc_Option_Ooption(U_16336)),c_Map_Orestrict__map(U_16335,U_16336,U_16337,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16335,tc_HOL_Obool)),U_16338),hAPP(hAPP(c_Set_Oinsert(U_16335),U_16339),c_Orderings_Obot__class_Obot(tc_fun(U_16335,tc_HOL_Obool)))))),U_16339),U_16340),
    inference(clausify,[status(thm)],[f_4023_2]) ).

fof(f_4024_1,plain,
    ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict__conv]) ).

fof(f_4024_2,plain,
    ! [U_16346,U_16345,U_16344,U_16343,U_16342,U_16341] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16341,tc_Option_Ooption(U_16344)),c_Map_Orestrict__map(U_16341,U_16344,U_16345,U_16343)),U_16342),U_16346) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16341,tc_Option_Ooption(U_16344)),c_Map_Orestrict__map(U_16341,U_16344,U_16345,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16341,tc_HOL_Obool)),U_16343),hAPP(hAPP(c_Set_Oinsert(U_16341),U_16342),c_Orderings_Obot__class_Obot(tc_fun(U_16341,tc_HOL_Obool)))))),U_16342),U_16346)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16342),U_16343)) ),
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

cnf(f_4024_3,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16341,tc_Option_Ooption(U_16344)),c_Map_Orestrict__map(U_16341,U_16344,U_16345,U_16343)),U_16342),U_16346) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16341,tc_Option_Ooption(U_16344)),c_Map_Orestrict__map(U_16341,U_16344,U_16345,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16341,tc_HOL_Obool)),U_16343),hAPP(hAPP(c_Set_Oinsert(U_16341),U_16342),c_Orderings_Obot__class_Obot(tc_fun(U_16341,tc_HOL_Obool)))))),U_16342),U_16346)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16342),U_16343)) ),
    inference(clausify,[status(thm)],[f_4024_2]) ).

fof(f_4025_1,plain,
    ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( ( c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) )
      & ( c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__fun__upd]) ).

fof(f_4025_2,plain,
    ! [U_16352,U_16351,U_16350,U_16349,U_16348,U_16347] :
      ( ( c_Map_Orestrict__map(U_16347,U_16350,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16347,tc_Option_Ooption(U_16350)),U_16351),U_16348),U_16352),U_16349) = c_Map_Orestrict__map(U_16347,U_16350,U_16351,U_16349)
        | hBOOL(hAPP(hAPP(c_member(U_16347),U_16348),U_16349)) )
      & ( c_Map_Orestrict__map(U_16347,U_16350,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16347,tc_Option_Ooption(U_16350)),U_16351),U_16348),U_16352),U_16349) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16347,tc_Option_Ooption(U_16350)),c_Map_Orestrict__map(U_16347,U_16350,U_16351,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16347,tc_HOL_Obool)),U_16349),hAPP(hAPP(c_Set_Oinsert(U_16347),U_16348),c_Orderings_Obot__class_Obot(tc_fun(U_16347,tc_HOL_Obool)))))),U_16348),U_16352)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16347),U_16348),U_16349)) ) ),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

fof(f_4025_3,plain,
    ( ! [U_16364,U_16362,U_16360,U_16358,U_16356,U_16354] :
        ( c_Map_Orestrict__map(U_16354,U_16360,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16354,tc_Option_Ooption(U_16360)),U_16362),U_16356),U_16364),U_16358) = c_Map_Orestrict__map(U_16354,U_16360,U_16362,U_16358)
        | hBOOL(hAPP(hAPP(c_member(U_16354),U_16356),U_16358)) )
    & ! [U_16363,U_16361,U_16359,U_16357,U_16355,U_16353] :
        ( c_Map_Orestrict__map(U_16353,U_16359,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16353,tc_Option_Ooption(U_16359)),U_16361),U_16355),U_16363),U_16357) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16353,tc_Option_Ooption(U_16359)),c_Map_Orestrict__map(U_16353,U_16359,U_16361,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16353,tc_HOL_Obool)),U_16357),hAPP(hAPP(c_Set_Oinsert(U_16353),U_16355),c_Orderings_Obot__class_Obot(tc_fun(U_16353,tc_HOL_Obool)))))),U_16355),U_16363)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16353),U_16355),U_16357)) ) ),
    inference(miniscope,[status(thm)],[f_4025_2]) ).

cnf(f_4025_4,plain,
    ( c_Map_Orestrict__map(U_16353,U_16359,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16353,tc_Option_Ooption(U_16359)),U_16361),U_16355),U_16363),U_16357) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16353,tc_Option_Ooption(U_16359)),c_Map_Orestrict__map(U_16353,U_16359,U_16361,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16353,tc_HOL_Obool)),U_16357),hAPP(hAPP(c_Set_Oinsert(U_16353),U_16355),c_Orderings_Obot__class_Obot(tc_fun(U_16353,tc_HOL_Obool)))))),U_16355),U_16363)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16353),U_16355),U_16357)) ),
    inference(clausify,[status(thm)],[f_4025_3]) ).

cnf(f_4025_5,plain,
    ( c_Map_Orestrict__map(U_16354,U_16360,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16354,tc_Option_Ooption(U_16360)),U_16362),U_16356),U_16364),U_16358) = c_Map_Orestrict__map(U_16354,U_16360,U_16362,U_16358)
    | hBOOL(hAPP(hAPP(c_member(U_16354),U_16356),U_16358)) ),
    inference(clausify,[status(thm)],[f_4025_3]) ).

fof(f_4026_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__eq]) ).

fof(f_4026_2,plain,
    ! [U_16367,U_16366,U_16365] :
      ( hAPP(c_List_Oset(U_16365),c_List_Oremove1(U_16365,U_16367,U_16366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16365,tc_HOL_Obool)),hAPP(c_List_Oset(U_16365),U_16366)),hAPP(hAPP(c_Set_Oinsert(U_16365),U_16367),c_Orderings_Obot__class_Obot(tc_fun(U_16365,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16365),U_16366)) ),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

cnf(f_4026_3,plain,
    ( hAPP(c_List_Oset(U_16365),c_List_Oremove1(U_16365,U_16367,U_16366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16365,tc_HOL_Obool)),hAPP(c_List_Oset(U_16365),U_16366)),hAPP(hAPP(c_Set_Oinsert(U_16365),U_16367),c_Orderings_Obot__class_Obot(tc_fun(U_16365,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16365),U_16366)) ),
    inference(clausify,[status(thm)],[f_4026_2]) ).

fof(f_4027_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_4027_2,plain,
    ! [U_16371,U_16370,U_16369,U_16368] :
      ( ( hAPP(hAPP(c_List_Otake(U_16369),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16368)),hAPP(hAPP(c_List_Olist_OCons(U_16369),U_16370),U_16371)) = hAPP(hAPP(c_List_Olist_OCons(U_16369),U_16370),hAPP(hAPP(c_List_Otake(U_16369),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16368)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16371))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16368) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_16369),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16368)),hAPP(hAPP(c_List_Olist_OCons(U_16369),U_16370),U_16371)) = c_List_Olist_ONil(U_16369)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16368) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

fof(f_4027_3,plain,
    ( ! [U_16379,U_16377,U_16375,U_16373] :
        ( hAPP(hAPP(c_List_Otake(U_16375),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373)),hAPP(hAPP(c_List_Olist_OCons(U_16375),U_16377),U_16379)) = hAPP(hAPP(c_List_Olist_OCons(U_16375),U_16377),hAPP(hAPP(c_List_Otake(U_16375),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16379))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16378,U_16376,U_16374,U_16372] :
        ( hAPP(hAPP(c_List_Otake(U_16374),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16372)),hAPP(hAPP(c_List_Olist_OCons(U_16374),U_16376),U_16378)) = c_List_Olist_ONil(U_16374)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16372) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4027_2]) ).

cnf(f_4027_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_16374),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16372)),hAPP(hAPP(c_List_Olist_OCons(U_16374),U_16376),U_16378)) = c_List_Olist_ONil(U_16374)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16372) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

cnf(f_4027_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_16375),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373)),hAPP(hAPP(c_List_Olist_OCons(U_16375),U_16377),U_16379)) = hAPP(hAPP(c_List_Olist_OCons(U_16375),U_16377),hAPP(hAPP(c_List_Otake(U_16375),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16379))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

fof(f_4028_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_lists_ONil]) ).

fof(f_4028_2,plain,
    ! [U_16381,U_16380] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16380)),c_List_Olist_ONil(U_16380)),c_List_Olists(U_16380,U_16381))),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

cnf(f_4028_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16380)),c_List_Olist_ONil(U_16380)),c_List_Olists(U_16380,U_16381))),
    inference(clausify,[status(thm)],[f_4028_2]) ).

fof(f_4029_1,plain,
    ! [V_r_2,V_xs_2,T_a] :
      ( V_xs_2 = c_List_Olist_ONil(T_a)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil2]) ).

fof(f_4029_2,plain,
    ! [U_16384,U_16383,U_16382] :
      ( U_16383 = c_List_Olist_ONil(U_16382)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16382),tc_List_Olist(U_16382))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16382),tc_List_Olist(U_16382)),U_16383),c_List_Olist_ONil(U_16382))),c_List_Olistrel(U_16382,U_16384))) ),
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

cnf(f_4029_3,plain,
    ( U_16383 = c_List_Olist_ONil(U_16382)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16382),tc_List_Olist(U_16382))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16382),tc_List_Olist(U_16382)),U_16383),c_List_Olist_ONil(U_16382))),c_List_Olistrel(U_16382,U_16384))) ),
    inference(clausify,[status(thm)],[f_4029_2]) ).

fof(f_4030_1,plain,
    ! [V_r_2,V_xs_2,T_a] :
      ( V_xs_2 = c_List_Olist_ONil(T_a)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil1]) ).

fof(f_4030_2,plain,
    ! [U_16387,U_16386,U_16385] :
      ( U_16386 = c_List_Olist_ONil(U_16385)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16385),tc_List_Olist(U_16385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16385),tc_List_Olist(U_16385)),c_List_Olist_ONil(U_16385)),U_16386)),c_List_Olistrel(U_16385,U_16387))) ),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

cnf(f_4030_3,plain,
    ( U_16386 = c_List_Olist_ONil(U_16385)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16385),tc_List_Olist(U_16385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16385),tc_List_Olist(U_16385)),c_List_Olist_ONil(U_16385)),U_16386)),c_List_Olistrel(U_16385,U_16387))) ),
    inference(clausify,[status(thm)],[f_4030_2]) ).

fof(f_4031_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_4031_2,plain,
    ! [U_16390,U_16389,U_16388] : hAPP(hAPP(c_List_Olist__update(U_16388,c_List_Olist_ONil(U_16388)),U_16389),U_16390) = c_List_Olist_ONil(U_16388),
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

cnf(f_4031_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16388,c_List_Olist_ONil(U_16388)),U_16389),U_16390) = c_List_Olist_ONil(U_16388),
    inference(clausify,[status(thm)],[f_4031_2]) ).

fof(f_4032_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_4032_2,plain,
    ! [U_16393,U_16392,U_16391] : hAPP(hAPP(c_List_Olist__update(U_16391,c_List_Olist_ONil(U_16391)),U_16392),U_16393) = c_List_Olist_ONil(U_16391),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

cnf(f_4032_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16391,c_List_Olist_ONil(U_16391)),U_16392),U_16393) = c_List_Olist_ONil(U_16391),
    inference(clausify,[status(thm)],[f_4032_2]) ).

fof(f_4033_1,plain,
    ! [V_x_2,V_k_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__nonempty]) ).

fof(f_4033_2,plain,
    ! [U_16397,U_16396,U_16395,U_16394] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_16394,U_16395),U_16396),U_16397) = c_List_Olist_ONil(U_16394)
        | U_16395 != c_List_Olist_ONil(U_16394) )
      & ( U_16395 = c_List_Olist_ONil(U_16394)
        | hAPP(hAPP(c_List_Olist__update(U_16394,U_16395),U_16396),U_16397) != c_List_Olist_ONil(U_16394) ) ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

fof(f_4033_3,plain,
    ( ! [U_16405,U_16403,U_16401,U_16399] :
        ( hAPP(hAPP(c_List_Olist__update(U_16399,U_16401),U_16403),U_16405) = c_List_Olist_ONil(U_16399)
        | U_16401 != c_List_Olist_ONil(U_16399) )
    & ! [U_16404,U_16402,U_16400,U_16398] :
        ( U_16400 = c_List_Olist_ONil(U_16398)
        | hAPP(hAPP(c_List_Olist__update(U_16398,U_16400),U_16402),U_16404) != c_List_Olist_ONil(U_16398) ) ),
    inference(miniscope,[status(thm)],[f_4033_2]) ).

cnf(f_4033_4,plain,
    ( U_16400 = c_List_Olist_ONil(U_16398)
    | hAPP(hAPP(c_List_Olist__update(U_16398,U_16400),U_16402),U_16404) != c_List_Olist_ONil(U_16398) ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

cnf(f_4033_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16399,U_16401),U_16403),U_16405) = c_List_Olist_ONil(U_16399)
    | U_16401 != c_List_Olist_ONil(U_16399) ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

fof(f_4034_1,plain,
    ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(f_4034_2,plain,
    ! [U_16406] : hAPP(c_List_Oset(U_16406),c_List_Olist_ONil(U_16406)) = c_Orderings_Obot__class_Obot(tc_fun(U_16406,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

cnf(f_4034_3,plain,
    hAPP(c_List_Oset(U_16406),c_List_Olist_ONil(U_16406)) = c_Orderings_Obot__class_Obot(tc_fun(U_16406,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4034_2]) ).

fof(f_4035_1,plain,
    ! [V_xs_2,T_a] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(c_List_Oset(T_a),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty2]) ).

fof(f_4035_2,plain,
    ! [U_16408,U_16407] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_16407,tc_HOL_Obool)) = hAPP(c_List_Oset(U_16407),U_16408)
        | U_16408 != c_List_Olist_ONil(U_16407) )
      & ( U_16408 = c_List_Olist_ONil(U_16407)
        | c_Orderings_Obot__class_Obot(tc_fun(U_16407,tc_HOL_Obool)) != hAPP(c_List_Oset(U_16407),U_16408) ) ),
    inference(variable_rename,[status(thm)],[f_4035_1]) ).

fof(f_4035_3,plain,
    ( ! [U_16412,U_16410] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_16410,tc_HOL_Obool)) = hAPP(c_List_Oset(U_16410),U_16412)
        | U_16412 != c_List_Olist_ONil(U_16410) )
    & ! [U_16411,U_16409] :
        ( U_16411 = c_List_Olist_ONil(U_16409)
        | c_Orderings_Obot__class_Obot(tc_fun(U_16409,tc_HOL_Obool)) != hAPP(c_List_Oset(U_16409),U_16411) ) ),
    inference(miniscope,[status(thm)],[f_4035_2]) ).

cnf(f_4035_4,plain,
    ( U_16411 = c_List_Olist_ONil(U_16409)
    | c_Orderings_Obot__class_Obot(tc_fun(U_16409,tc_HOL_Obool)) != hAPP(c_List_Oset(U_16409),U_16411) ),
    inference(clausify,[status(thm)],[f_4035_3]) ).

cnf(f_4035_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_16410,tc_HOL_Obool)) = hAPP(c_List_Oset(U_16410),U_16412)
    | U_16412 != c_List_Olist_ONil(U_16410) ),
    inference(clausify,[status(thm)],[f_4035_3]) ).

fof(f_4036_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(c_List_Oset(T_a),V_xs_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty]) ).

fof(f_4036_2,plain,
    ! [U_16414,U_16413] :
      ( ( hAPP(c_List_Oset(U_16413),U_16414) = c_Orderings_Obot__class_Obot(tc_fun(U_16413,tc_HOL_Obool))
        | U_16414 != c_List_Olist_ONil(U_16413) )
      & ( U_16414 = c_List_Olist_ONil(U_16413)
        | hAPP(c_List_Oset(U_16413),U_16414) != c_Orderings_Obot__class_Obot(tc_fun(U_16413,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

fof(f_4036_3,plain,
    ( ! [U_16418,U_16416] :
        ( hAPP(c_List_Oset(U_16416),U_16418) = c_Orderings_Obot__class_Obot(tc_fun(U_16416,tc_HOL_Obool))
        | U_16418 != c_List_Olist_ONil(U_16416) )
    & ! [U_16417,U_16415] :
        ( U_16417 = c_List_Olist_ONil(U_16415)
        | hAPP(c_List_Oset(U_16415),U_16417) != c_Orderings_Obot__class_Obot(tc_fun(U_16415,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4036_2]) ).

cnf(f_4036_4,plain,
    ( U_16417 = c_List_Olist_ONil(U_16415)
    | hAPP(c_List_Oset(U_16415),U_16417) != c_Orderings_Obot__class_Obot(tc_fun(U_16415,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4036_3]) ).

cnf(f_4036_5,plain,
    ( hAPP(c_List_Oset(U_16416),U_16418) = c_Orderings_Obot__class_Obot(tc_fun(U_16416,tc_HOL_Obool))
    | U_16418 != c_List_Olist_ONil(U_16416) ),
    inference(clausify,[status(thm)],[f_4036_3]) ).

fof(f_4037_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__0__conv]) ).

fof(f_4037_2,plain,
    ! [U_16420,U_16419] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16419)),U_16420) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_16420 != c_List_Olist_ONil(U_16419) )
      & ( U_16420 = c_List_Olist_ONil(U_16419)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16419)),U_16420) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

fof(f_4037_3,plain,
    ( ! [U_16424,U_16422] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16422)),U_16424) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_16424 != c_List_Olist_ONil(U_16422) )
    & ! [U_16423,U_16421] :
        ( U_16423 = c_List_Olist_ONil(U_16421)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16421)),U_16423) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4037_2]) ).

cnf(f_4037_4,plain,
    ( U_16423 = c_List_Olist_ONil(U_16421)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16421)),U_16423) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4037_3]) ).

cnf(f_4037_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16422)),U_16424) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_16424 != c_List_Olist_ONil(U_16422) ),
    inference(clausify,[status(thm)],[f_4037_3]) ).

fof(f_4038_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_4038_2,plain,
    ! [U_16425] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16425)),c_List_Olist_ONil(U_16425)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

cnf(f_4038_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16425)),c_List_Olist_ONil(U_16425)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4038_2]) ).

fof(f_4039_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_4039_2,plain,
    ! [U_16426] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16426),c_List_Olist_ONil(U_16426)) = c_Groups_Ozero__class_Ozero(U_16426)
      | ~ class_Groups_Omonoid__add(U_16426) ),
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

cnf(f_4039_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16426),c_List_Olist_ONil(U_16426)) = c_Groups_Ozero__class_Ozero(U_16426)
    | ~ class_Groups_Omonoid__add(U_16426) ),
    inference(clausify,[status(thm)],[f_4039_2]) ).

fof(f_4040_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_4040_2,plain,
    ! [U_16429,U_16428,U_16427] : hAPP(hAPP(c_List_Ozip(U_16427,U_16428),c_List_Olist_ONil(U_16427)),U_16429) = c_List_Olist_ONil(tc_prod(U_16427,U_16428)),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

cnf(f_4040_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16427,U_16428),c_List_Olist_ONil(U_16427)),U_16429) = c_List_Olist_ONil(tc_prod(U_16427,U_16428)),
    inference(clausify,[status(thm)],[f_4040_2]) ).

fof(f_4041_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_4041_2,plain,
    ! [U_16432,U_16431,U_16430] : hAPP(hAPP(c_List_Ozip(U_16430,U_16431),U_16432),c_List_Olist_ONil(U_16431)) = c_List_Olist_ONil(tc_prod(U_16430,U_16431)),
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

cnf(f_4041_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16430,U_16431),U_16432),c_List_Olist_ONil(U_16431)) = c_List_Olist_ONil(tc_prod(U_16430,U_16431)),
    inference(clausify,[status(thm)],[f_4041_2]) ).

fof(f_4042_1,plain,
    ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(f_4042_2,plain,
    ! [U_16434,U_16433] : c_List_Olistrelp(U_16433,U_16434,c_List_Olist_ONil(U_16433),c_List_Olist_ONil(U_16433)),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

cnf(f_4042_3,plain,
    c_List_Olistrelp(U_16433,U_16434,c_List_Olist_ONil(U_16433),c_List_Olist_ONil(U_16433)),
    inference(clausify,[status(thm)],[f_4042_2]) ).

fof(f_4043_1,plain,
    ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_ONil]) ).

fof(f_4043_2,plain,
    ! [U_16436,U_16435] : c_List_Olistrelp(U_16435,U_16436,c_List_Olist_ONil(U_16435),c_List_Olist_ONil(U_16435)),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

cnf(f_4043_3,plain,
    c_List_Olistrelp(U_16435,U_16436,c_List_Olist_ONil(U_16435),c_List_Olist_ONil(U_16435)),
    inference(clausify,[status(thm)],[f_4043_2]) ).

fof(f_4044_1,plain,
    ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(f_4044_2,plain,
    ! [U_16438,U_16437] : c_List_Olist_Olist__size(U_16437,U_16438,c_List_Olist_ONil(U_16437)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

cnf(f_4044_3,plain,
    c_List_Olist_Olist__size(U_16437,U_16438,c_List_Olist_ONil(U_16437)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4044_2]) ).

fof(f_4045_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_4045_2,plain,
    ! [U_16442,U_16441,U_16440,U_16439] : c_List_Oremove1(U_16439,U_16440,c_List_Oremove1(U_16439,U_16441,U_16442)) = c_List_Oremove1(U_16439,U_16441,c_List_Oremove1(U_16439,U_16440,U_16442)),
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

cnf(f_4045_3,plain,
    c_List_Oremove1(U_16439,U_16440,c_List_Oremove1(U_16439,U_16441,U_16442)) = c_List_Oremove1(U_16439,U_16441,c_List_Oremove1(U_16439,U_16440,U_16442)),
    inference(clausify,[status(thm)],[f_4045_2]) ).

fof(f_4046_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_4046_2,plain,
    ! [U_16444,U_16443] : c_List_Oremove1(U_16443,U_16444,c_List_Olist_ONil(U_16443)) = c_List_Olist_ONil(U_16443),
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

cnf(f_4046_3,plain,
    c_List_Oremove1(U_16443,U_16444,c_List_Olist_ONil(U_16443)) = c_List_Olist_ONil(U_16443),
    inference(clausify,[status(thm)],[f_4046_2]) ).

fof(f_4047_1,plain,
    ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_sublist__nil]) ).

fof(f_4047_2,plain,
    ! [U_16446,U_16445] : c_List_Osublist(U_16445,c_List_Olist_ONil(U_16445),U_16446) = c_List_Olist_ONil(U_16445),
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

cnf(f_4047_3,plain,
    c_List_Osublist(U_16445,c_List_Olist_ONil(U_16445),U_16446) = c_List_Olist_ONil(U_16445),
    inference(clausify,[status(thm)],[f_4047_2]) ).

fof(f_4048_1,plain,
    ! [V_xs_2,V_n_2,T_a] :
      ( ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
        | ( V_xs_2 != c_List_Olist_ONil(T_a)
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__eq__Nil]) ).

fof(f_4048_2,plain,
    ! [U_16449,U_16448,U_16447] :
      ( ( hAPP(hAPP(c_List_Otake(U_16447),U_16448),U_16449) = c_List_Olist_ONil(U_16447)
        | ( U_16449 != c_List_Olist_ONil(U_16447)
          & U_16448 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_16449 = c_List_Olist_ONil(U_16447)
        | U_16448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_16447),U_16448),U_16449) != c_List_Olist_ONil(U_16447) ) ),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

fof(f_4048_3,plain,
    ( ! [U_16455,U_16453,U_16451] :
        ( hAPP(hAPP(c_List_Otake(U_16451),U_16453),U_16455) = c_List_Olist_ONil(U_16451)
        | ( U_16455 != c_List_Olist_ONil(U_16451)
          & U_16453 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_16454,U_16452,U_16450] :
        ( U_16454 = c_List_Olist_ONil(U_16450)
        | U_16452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_16450),U_16452),U_16454) != c_List_Olist_ONil(U_16450) ) ),
    inference(miniscope,[status(thm)],[f_4048_2]) ).

cnf(f_4048_4,plain,
    ( U_16454 = c_List_Olist_ONil(U_16450)
    | U_16452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_16450),U_16452),U_16454) != c_List_Olist_ONil(U_16450) ),
    inference(clausify,[status(thm)],[f_4048_3]) ).

cnf(f_4048_5,plain,
    ( U_16453 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_16451),U_16453),U_16455) = c_List_Olist_ONil(U_16451) ),
    inference(clausify,[status(thm)],[f_4048_3]) ).

cnf(f_4048_6,plain,
    ( U_16455 != c_List_Olist_ONil(U_16451)
    | hAPP(hAPP(c_List_Otake(U_16451),U_16453),U_16455) = c_List_Olist_ONil(U_16451) ),
    inference(clausify,[status(thm)],[f_4048_3]) ).

fof(f_4049_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_4049_2,plain,
    ! [U_16457,U_16456] : hAPP(hAPP(c_List_Otake(U_16456),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16457) = c_List_Olist_ONil(U_16456),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

cnf(f_4049_3,plain,
    hAPP(hAPP(c_List_Otake(U_16456),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16457) = c_List_Olist_ONil(U_16456),
    inference(clausify,[status(thm)],[f_4049_2]) ).

fof(f_4050_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_4050_2,plain,
    ! [U_16459,U_16458] : hAPP(hAPP(c_List_Otake(U_16458),U_16459),c_List_Olist_ONil(U_16458)) = c_List_Olist_ONil(U_16458),
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

cnf(f_4050_3,plain,
    hAPP(hAPP(c_List_Otake(U_16458),U_16459),c_List_Olist_ONil(U_16458)) = c_List_Olist_ONil(U_16458),
    inference(clausify,[status(thm)],[f_4050_2]) ).

fof(f_4051_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_4051_2,plain,
    ! [U_16461,U_16460] :
      ( c_List_Oupto(U_16461,U_16460) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_16460),U_16461)) ),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

cnf(f_4051_3,plain,
    ( c_List_Oupto(U_16461,U_16460) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_16460),U_16461)) ),
    inference(clausify,[status(thm)],[f_4051_2]) ).

fof(f_4052_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_4052_2,plain,
    ! [U_16464,U_16463,U_16462] : c_List_Olist_ONil(U_16462) != hAPP(hAPP(c_List_Olist_OCons(U_16462),U_16463),U_16464),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

cnf(f_4052_3,plain,
    c_List_Olist_ONil(U_16462) != hAPP(hAPP(c_List_Olist_OCons(U_16462),U_16463),U_16464),
    inference(clausify,[status(thm)],[f_4052_2]) ).

fof(f_4053_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_4053_2,plain,
    ! [U_16467,U_16466,U_16465] : hAPP(hAPP(c_List_Olist_OCons(U_16465),U_16466),U_16467) != c_List_Olist_ONil(U_16465),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

cnf(f_4053_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_16465),U_16466),U_16467) != c_List_Olist_ONil(U_16465),
    inference(clausify,[status(thm)],[f_4053_2]) ).

fof(f_4054_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_4054_2,plain,
    ! [U_16471,U_16470,U_16469,U_16468] :
      ( ( c_List_Oremove1(U_16470,U_16468,hAPP(hAPP(c_List_Olist_OCons(U_16470),U_16469),U_16471)) = hAPP(hAPP(c_List_Olist_OCons(U_16470),U_16469),c_List_Oremove1(U_16470,U_16468,U_16471))
        | U_16468 = U_16469 )
      & ( c_List_Oremove1(U_16470,U_16468,hAPP(hAPP(c_List_Olist_OCons(U_16470),U_16469),U_16471)) = U_16471
        | U_16468 != U_16469 ) ),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

fof(f_4054_3,plain,
    ( ! [U_16479,U_16477,U_16475,U_16473] :
        ( c_List_Oremove1(U_16477,U_16473,hAPP(hAPP(c_List_Olist_OCons(U_16477),U_16475),U_16479)) = hAPP(hAPP(c_List_Olist_OCons(U_16477),U_16475),c_List_Oremove1(U_16477,U_16473,U_16479))
        | U_16473 = U_16475 )
    & ! [U_16478,U_16476,U_16474,U_16472] :
        ( c_List_Oremove1(U_16476,U_16472,hAPP(hAPP(c_List_Olist_OCons(U_16476),U_16474),U_16478)) = U_16478
        | U_16472 != U_16474 ) ),
    inference(miniscope,[status(thm)],[f_4054_2]) ).

cnf(f_4054_4,plain,
    ( c_List_Oremove1(U_16476,U_16472,hAPP(hAPP(c_List_Olist_OCons(U_16476),U_16474),U_16478)) = U_16478
    | U_16472 != U_16474 ),
    inference(clausify,[status(thm)],[f_4054_3]) ).

cnf(f_4054_5,plain,
    ( c_List_Oremove1(U_16477,U_16473,hAPP(hAPP(c_List_Olist_OCons(U_16477),U_16475),U_16479)) = hAPP(hAPP(c_List_Olist_OCons(U_16477),U_16475),c_List_Oremove1(U_16477,U_16473,U_16479))
    | U_16473 = U_16475 ),
    inference(clausify,[status(thm)],[f_4054_3]) ).

fof(f_4055_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_4055_2,plain,
    ! [U_16482,U_16481,U_16480] :
      ( ( c_List_Obutlast(U_16481,hAPP(hAPP(c_List_Olist_OCons(U_16481),U_16482),U_16480)) = hAPP(hAPP(c_List_Olist_OCons(U_16481),U_16482),c_List_Obutlast(U_16481,U_16480))
        | U_16480 = c_List_Olist_ONil(U_16481) )
      & ( c_List_Obutlast(U_16481,hAPP(hAPP(c_List_Olist_OCons(U_16481),U_16482),U_16480)) = c_List_Olist_ONil(U_16481)
        | U_16480 != c_List_Olist_ONil(U_16481) ) ),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

fof(f_4055_3,plain,
    ( ! [U_16488,U_16486,U_16484] :
        ( c_List_Obutlast(U_16486,hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16488),U_16484)) = hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16488),c_List_Obutlast(U_16486,U_16484))
        | U_16484 = c_List_Olist_ONil(U_16486) )
    & ! [U_16487,U_16485,U_16483] :
        ( c_List_Obutlast(U_16485,hAPP(hAPP(c_List_Olist_OCons(U_16485),U_16487),U_16483)) = c_List_Olist_ONil(U_16485)
        | U_16483 != c_List_Olist_ONil(U_16485) ) ),
    inference(miniscope,[status(thm)],[f_4055_2]) ).

cnf(f_4055_4,plain,
    ( c_List_Obutlast(U_16485,hAPP(hAPP(c_List_Olist_OCons(U_16485),U_16487),U_16483)) = c_List_Olist_ONil(U_16485)
    | U_16483 != c_List_Olist_ONil(U_16485) ),
    inference(clausify,[status(thm)],[f_4055_3]) ).

cnf(f_4055_5,plain,
    ( c_List_Obutlast(U_16486,hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16488),U_16484)) = hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16488),c_List_Obutlast(U_16486,U_16484))
    | U_16484 = c_List_Olist_ONil(U_16486) ),
    inference(clausify,[status(thm)],[f_4055_3]) ).

fof(f_4056_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_4056_2,plain,
    ! [U_16489] : c_List_Obutlast(U_16489,c_List_Olist_ONil(U_16489)) = c_List_Olist_ONil(U_16489),
    inference(variable_rename,[status(thm)],[f_4056_1]) ).

cnf(f_4056_3,plain,
    c_List_Obutlast(U_16489,c_List_Olist_ONil(U_16489)) = c_List_Olist_ONil(U_16489),
    inference(clausify,[status(thm)],[f_4056_2]) ).

fof(f_4057_1,plain,
    ! [V_xs_2,T_a,V_b_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) ) )
      | V_a_2 = V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_in__set__remove1]) ).

fof(f_4057_2,plain,
    ! [U_16493,U_16492,U_16491,U_16490] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),c_List_Oremove1(U_16492,U_16491,U_16493))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),U_16493))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),U_16493)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),c_List_Oremove1(U_16492,U_16491,U_16493)))) ) )
      | U_16490 = U_16491 ),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

cnf(f_4057_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),U_16493)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),c_List_Oremove1(U_16492,U_16491,U_16493))))
    | U_16490 = U_16491 ),
    inference(clausify,[status(thm)],[f_4057_2]) ).

cnf(f_4057_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),c_List_Oremove1(U_16492,U_16491,U_16493))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16492),U_16490),hAPP(c_List_Oset(U_16492),U_16493)))
    | U_16490 = U_16491 ),
    inference(clausify,[status(thm)],[f_4057_2]) ).

fof(f_4058_1,plain,
    ! [V_y_2,V_xs_2,V_x_2,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2))))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__remove1]) ).

fof(f_4058_2,plain,
    ! [U_16497,U_16496,U_16495,U_16494] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16494),U_16495),hAPP(c_List_Oset(U_16494),c_List_Oremove1(U_16494,U_16497,U_16496))))
      | hBOOL(hAPP(hAPP(c_member(U_16494),U_16495),hAPP(c_List_Oset(U_16494),U_16496))) ),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

cnf(f_4058_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16494),U_16495),hAPP(c_List_Oset(U_16494),c_List_Oremove1(U_16494,U_16497,U_16496))))
    | hBOOL(hAPP(hAPP(c_member(U_16494),U_16495),hAPP(c_List_Oset(U_16494),U_16496))) ),
    inference(clausify,[status(thm)],[f_4058_2]) ).

fof(f_4059_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__idem]) ).

fof(f_4059_2,plain,
    ! [U_16500,U_16499,U_16498] :
      ( c_List_Oremove1(U_16498,U_16499,U_16500) = U_16500
      | hBOOL(hAPP(hAPP(c_member(U_16498),U_16499),hAPP(c_List_Oset(U_16498),U_16500))) ),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

cnf(f_4059_3,plain,
    ( c_List_Oremove1(U_16498,U_16499,U_16500) = U_16500
    | hBOOL(hAPP(hAPP(c_member(U_16498),U_16499),hAPP(c_List_Oset(U_16498),U_16500))) ),
    inference(clausify,[status(thm)],[f_4059_2]) ).

fof(f_4060_1,plain,
    ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__upds__Nil1]) ).

fof(f_4060_2,plain,
    ! [U_16504,U_16503,U_16502,U_16501] : c_Map_Omap__upds(U_16501,U_16502,U_16503,c_List_Olist_ONil(U_16501),U_16504) = U_16503,
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

cnf(f_4060_3,plain,
    c_Map_Omap__upds(U_16501,U_16502,U_16503,c_List_Olist_ONil(U_16501),U_16504) = U_16503,
    inference(clausify,[status(thm)],[f_4060_2]) ).

fof(f_4061_1,plain,
    ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__upds__Nil2]) ).

fof(f_4061_2,plain,
    ! [U_16508,U_16507,U_16506,U_16505] : c_Map_Omap__upds(U_16505,U_16506,U_16507,U_16508,c_List_Olist_ONil(U_16506)) = U_16507,
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

cnf(f_4061_3,plain,
    c_Map_Omap__upds(U_16505,U_16506,U_16507,U_16508,c_List_Olist_ONil(U_16506)) = U_16507,
    inference(clausify,[status(thm)],[f_4061_2]) ).

fof(f_4062_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_4062_2,plain,
    ! [U_16511,U_16510,U_16509] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16509),c_List_Oremove1(U_16509,U_16511,U_16510)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16509),U_16510)) ),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

cnf(f_4062_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16509),c_List_Oremove1(U_16509,U_16511,U_16510)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16509),U_16510)) ),
    inference(clausify,[status(thm)],[f_4062_2]) ).

fof(f_4063_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_4063_2,plain,
    ! [U_16512] : hBOOL(hAPP(c_List_Odistinct(U_16512),c_List_Olist_ONil(U_16512))),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

cnf(f_4063_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_16512),c_List_Olist_ONil(U_16512))),
    inference(clausify,[status(thm)],[f_4063_2]) ).

fof(f_4064_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_4064_2,plain,
    ! [U_16514,U_16513] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16514),c_List_Obutlast(U_16514,U_16513)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16514),U_16513))
      | U_16513 = c_List_Olist_ONil(U_16514) ),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

cnf(f_4064_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16514),c_List_Obutlast(U_16514,U_16513)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16514),U_16513))
    | U_16513 = c_List_Olist_ONil(U_16514) ),
    inference(clausify,[status(thm)],[f_4064_2]) ).

fof(f_4065_1,plain,
    ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_sublist__empty]) ).

fof(f_4065_2,plain,
    ! [U_16516,U_16515] : c_List_Osublist(U_16515,U_16516,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_16515),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

cnf(f_4065_3,plain,
    c_List_Osublist(U_16515,U_16516,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_16515),
    inference(clausify,[status(thm)],[f_4065_2]) ).

fof(f_4066_1,plain,
    ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__subset]) ).

fof(f_4066_2,plain,
    ! [U_16519,U_16518,U_16517] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16517,tc_HOL_Obool)),hAPP(c_List_Oset(U_16517),c_List_Oremove1(U_16517,U_16518,U_16519))),hAPP(c_List_Oset(U_16517),U_16519))),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

cnf(f_4066_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16517,tc_HOL_Obool)),hAPP(c_List_Oset(U_16517),c_List_Oremove1(U_16517,U_16518,U_16519))),hAPP(c_List_Oset(U_16517),U_16519))),
    inference(clausify,[status(thm)],[f_4066_2]) ).

fof(f_4067_1,plain,
    ! [V_xs_2,T_a] :
      ( ( 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_a)),V_xs_2)))
        | V_xs_2 = c_List_Olist_ONil(T_a) )
      & ( V_xs_2 != c_List_Olist_ONil(T_a)
        | ~ 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_a)),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv]) ).

fof(f_4067_2,plain,
    ! [U_16521,U_16520] :
      ( ( 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_16520)),U_16521)))
        | U_16521 = c_List_Olist_ONil(U_16520) )
      & ( U_16521 != c_List_Olist_ONil(U_16520)
        | ~ 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_16520)),U_16521))) ) ),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

fof(f_4067_3,plain,
    ( ! [U_16525,U_16523] :
        ( 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_16523)),U_16525)))
        | U_16525 = c_List_Olist_ONil(U_16523) )
    & ! [U_16524,U_16522] :
        ( U_16524 != c_List_Olist_ONil(U_16522)
        | ~ 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_16522)),U_16524))) ) ),
    inference(miniscope,[status(thm)],[f_4067_2]) ).

cnf(f_4067_4,plain,
    ( U_16524 != c_List_Olist_ONil(U_16522)
    | ~ 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_16522)),U_16524))) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_5,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_16523)),U_16525)))
    | U_16525 = c_List_Olist_ONil(U_16523) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

fof(f_4068_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_4068_2,plain,
    ! [U_16528,U_16527,U_16526] : hAPP(hAPP(c_List_Otake(U_16526),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16526),U_16527),U_16528)) = hAPP(hAPP(c_List_Olist_OCons(U_16526),U_16527),c_List_Olist_ONil(U_16526)),
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

cnf(f_4068_3,plain,
    hAPP(hAPP(c_List_Otake(U_16526),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16526),U_16527),U_16528)) = hAPP(hAPP(c_List_Olist_OCons(U_16526),U_16527),c_List_Olist_ONil(U_16526)),
    inference(clausify,[status(thm)],[f_4068_2]) ).

fof(f_4069_1,plain,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(f_4069_2,plain,
    ! [U_16531,U_16530,U_16529] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16529),tc_List_Olist(U_16529))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16529),tc_List_Olist(U_16529)),U_16530),c_List_Olist_ONil(U_16529))),c_List_Olistrel1(U_16529,U_16531))),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

cnf(f_4069_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16529),tc_List_Olist(U_16529))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16529),tc_List_Olist(U_16529)),U_16530),c_List_Olist_ONil(U_16529))),c_List_Olistrel1(U_16529,U_16531))),
    inference(clausify,[status(thm)],[f_4069_2]) ).

fof(f_4070_1,plain,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(f_4070_2,plain,
    ! [U_16534,U_16533,U_16532] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16532),tc_List_Olist(U_16532))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16532),tc_List_Olist(U_16532)),c_List_Olist_ONil(U_16532)),U_16533)),c_List_Olistrel1(U_16532,U_16534))),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

cnf(f_4070_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16532),tc_List_Olist(U_16532))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16532),tc_List_Olist(U_16532)),c_List_Olist_ONil(U_16532)),U_16533)),c_List_Olistrel1(U_16532,U_16534))),
    inference(clausify,[status(thm)],[f_4070_2]) ).

fof(f_4071_1,plain,
    ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_listrel_ONil]) ).

fof(f_4071_2,plain,
    ! [U_16536,U_16535] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16535),tc_List_Olist(U_16535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16535),tc_List_Olist(U_16535)),c_List_Olist_ONil(U_16535)),c_List_Olist_ONil(U_16535))),c_List_Olistrel(U_16535,U_16536))),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

cnf(f_4071_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16535),tc_List_Olist(U_16535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16535),tc_List_Olist(U_16535)),c_List_Olist_ONil(U_16535)),c_List_Olist_ONil(U_16535))),c_List_Olistrel(U_16535,U_16536))),
    inference(clausify,[status(thm)],[f_4071_2]) ).

fof(f_4072_1,plain,
    ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__right]) ).

fof(f_4072_2,plain,
    ! [U_16539,U_16538,U_16537] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16537),tc_List_Olist(U_16537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16537),tc_List_Olist(U_16537)),U_16538),c_List_Olist_ONil(U_16537))),c_List_Olexord(U_16537,U_16539))),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

cnf(f_4072_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16537),tc_List_Olist(U_16537))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16537),tc_List_Olist(U_16537)),U_16538),c_List_Olist_ONil(U_16537))),c_List_Olexord(U_16537,U_16539))),
    inference(clausify,[status(thm)],[f_4072_2]) ).

fof(f_4073_1,plain,
    ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(f_4073_2,plain,
    ! [U_16542,U_16541,U_16540] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16540),tc_List_Olist(U_16540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16540),tc_List_Olist(U_16540)),U_16541),c_List_Olist_ONil(U_16540))),c_List_Olex(U_16540,U_16542))),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

cnf(f_4073_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16540),tc_List_Olist(U_16540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16540),tc_List_Olist(U_16540)),U_16541),c_List_Olist_ONil(U_16540))),c_List_Olex(U_16540,U_16542))),
    inference(clausify,[status(thm)],[f_4073_2]) ).

fof(f_4074_1,plain,
    ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil__notin__lex]) ).

fof(f_4074_2,plain,
    ! [U_16545,U_16544,U_16543] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16543),tc_List_Olist(U_16543))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16543),tc_List_Olist(U_16543)),c_List_Olist_ONil(U_16543)),U_16544)),c_List_Olex(U_16543,U_16545))),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

cnf(f_4074_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16543),tc_List_Olist(U_16543))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16543),tc_List_Olist(U_16543)),c_List_Olist_ONil(U_16543)),U_16544)),c_List_Olex(U_16543,U_16545))),
    inference(clausify,[status(thm)],[f_4074_2]) ).

fof(f_4075_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_take__Cons]) ).

fof(f_4075_2,plain,
    ! [U_16549,U_16548,U_16547,U_16546] : hAPP(hAPP(c_List_Otake(U_16546),U_16547),hAPP(hAPP(c_List_Olist_OCons(U_16546),U_16548),U_16549)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16546),c_List_Olist_ONil(U_16546),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16546),tc_List_Olist(U_16546),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_16546),U_16548)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16546),tc_List_Olist(U_16546)),c_List_Otake(U_16546)),U_16549)),U_16547),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

cnf(f_4075_3,plain,
    hAPP(hAPP(c_List_Otake(U_16546),U_16547),hAPP(hAPP(c_List_Olist_OCons(U_16546),U_16548),U_16549)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16546),c_List_Olist_ONil(U_16546),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16546),tc_List_Olist(U_16546),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_16546),U_16548)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16546),tc_List_Olist(U_16546)),c_List_Otake(U_16546)),U_16549)),U_16547),
    inference(clausify,[status(thm)],[f_4075_2]) ).

fof(f_4076_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_4076_2,plain,
    ! [U_16551,U_16550] :
      ( ( c_List_Oupto(U_16550,U_16551) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16550),U_16551)) )
      & ( c_List_Oupto(U_16550,U_16551) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_16550),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16550),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16551))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16550),U_16551)) ) ),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

fof(f_4076_3,plain,
    ( ! [U_16555,U_16553] :
        ( c_List_Oupto(U_16553,U_16555) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16553),U_16555)) )
    & ! [U_16554,U_16552] :
        ( c_List_Oupto(U_16552,U_16554) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_16552),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16552),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16552),U_16554)) ) ),
    inference(miniscope,[status(thm)],[f_4076_2]) ).

cnf(f_4076_4,plain,
    ( c_List_Oupto(U_16552,U_16554) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_16552),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16552),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16552),U_16554)) ),
    inference(clausify,[status(thm)],[f_4076_3]) ).

cnf(f_4076_5,plain,
    ( c_List_Oupto(U_16553,U_16555) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16553),U_16555)) ),
    inference(clausify,[status(thm)],[f_4076_3]) ).

fof(f_4077_1,plain,
    ! [V_x_2,T_a,V_A_2] :
      ( ( c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) )
      & ( c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
        | ~ 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_4077_2,plain,
    ! [U_16558,U_16557,U_16556] :
      ( ( c_List_Osublist(U_16557,hAPP(hAPP(c_List_Olist_OCons(U_16557),U_16558),c_List_Olist_ONil(U_16557)),U_16556) = c_List_Olist_ONil(U_16557)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16556)) )
      & ( c_List_Osublist(U_16557,hAPP(hAPP(c_List_Olist_OCons(U_16557),U_16558),c_List_Olist_ONil(U_16557)),U_16556) = hAPP(hAPP(c_List_Olist_OCons(U_16557),U_16558),c_List_Olist_ONil(U_16557))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16556)) ) ),
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

fof(f_4077_3,plain,
    ( ! [U_16564,U_16562,U_16560] :
        ( c_List_Osublist(U_16562,hAPP(hAPP(c_List_Olist_OCons(U_16562),U_16564),c_List_Olist_ONil(U_16562)),U_16560) = c_List_Olist_ONil(U_16562)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16560)) )
    & ! [U_16563,U_16561,U_16559] :
        ( c_List_Osublist(U_16561,hAPP(hAPP(c_List_Olist_OCons(U_16561),U_16563),c_List_Olist_ONil(U_16561)),U_16559) = hAPP(hAPP(c_List_Olist_OCons(U_16561),U_16563),c_List_Olist_ONil(U_16561))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16559)) ) ),
    inference(miniscope,[status(thm)],[f_4077_2]) ).

cnf(f_4077_4,plain,
    ( c_List_Osublist(U_16561,hAPP(hAPP(c_List_Olist_OCons(U_16561),U_16563),c_List_Olist_ONil(U_16561)),U_16559) = hAPP(hAPP(c_List_Olist_OCons(U_16561),U_16563),c_List_Olist_ONil(U_16561))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16559)) ),
    inference(clausify,[status(thm)],[f_4077_3]) ).

cnf(f_4077_5,plain,
    ( c_List_Osublist(U_16562,hAPP(hAPP(c_List_Olist_OCons(U_16562),U_16564),c_List_Olist_ONil(U_16562)),U_16560) = c_List_Olist_ONil(U_16562)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16560)) ),
    inference(clausify,[status(thm)],[f_4077_3]) ).

fof(f_4078_1,plain,
    ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_lists__empty]) ).

fof(f_4078_2,plain,
    ! [U_16565] : c_List_Olists(U_16565,c_Orderings_Obot__class_Obot(tc_fun(U_16565,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16565)),c_List_Olist_ONil(U_16565)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16565),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

cnf(f_4078_3,plain,
    c_List_Olists(U_16565,c_Orderings_Obot__class_Obot(tc_fun(U_16565,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16565)),c_List_Olist_ONil(U_16565)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16565),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4078_2]) ).

fof(f_4079_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_4079_2,plain,
    ! [U_16569,U_16568,U_16567,U_16566] :
      ( ( hAPP(hAPP(c_List_Otake(U_16567),U_16566),hAPP(hAPP(c_List_Olist_OCons(U_16567),U_16568),U_16569)) = hAPP(hAPP(c_List_Olist_OCons(U_16567),U_16568),hAPP(hAPP(c_List_Otake(U_16567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16566),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16569))
        | U_16566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_16567),U_16566),hAPP(hAPP(c_List_Olist_OCons(U_16567),U_16568),U_16569)) = c_List_Olist_ONil(U_16567)
        | U_16566 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

fof(f_4079_3,plain,
    ( ! [U_16577,U_16575,U_16573,U_16571] :
        ( hAPP(hAPP(c_List_Otake(U_16573),U_16571),hAPP(hAPP(c_List_Olist_OCons(U_16573),U_16575),U_16577)) = hAPP(hAPP(c_List_Olist_OCons(U_16573),U_16575),hAPP(hAPP(c_List_Otake(U_16573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16571),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16577))
        | U_16571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16576,U_16574,U_16572,U_16570] :
        ( hAPP(hAPP(c_List_Otake(U_16572),U_16570),hAPP(hAPP(c_List_Olist_OCons(U_16572),U_16574),U_16576)) = c_List_Olist_ONil(U_16572)
        | U_16570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4079_2]) ).

cnf(f_4079_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_16572),U_16570),hAPP(hAPP(c_List_Olist_OCons(U_16572),U_16574),U_16576)) = c_List_Olist_ONil(U_16572)
    | U_16570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4079_3]) ).

cnf(f_4079_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_16573),U_16571),hAPP(hAPP(c_List_Olist_OCons(U_16573),U_16575),U_16577)) = hAPP(hAPP(c_List_Olist_OCons(U_16573),U_16575),hAPP(hAPP(c_List_Otake(U_16573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16571),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16577))
    | U_16571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4079_3]) ).

fof(f_4080_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_4080_2,plain,
    ! [U_16579,U_16578] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16578),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16579)) = 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_16578)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16579))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16578),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16579)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16578)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16578)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16578)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16579))) ) ),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

fof(f_4080_3,plain,
    ( ! [U_16583,U_16581] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16581),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16583)) = 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_16581)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16583))) )
    & ! [U_16582,U_16580] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582))) ) ),
    inference(miniscope,[status(thm)],[f_4080_2]) ).

cnf(f_4080_4,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16580)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16582))) ),
    inference(clausify,[status(thm)],[f_4080_3]) ).

cnf(f_4080_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16581),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16583)) = 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_16581)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_16583))) ),
    inference(clausify,[status(thm)],[f_4080_3]) ).

fof(f_4081_1,plain,
    ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil]) ).

fof(f_4081_2,plain,
    ! [U_16585,U_16584] : hAPP(c_Relation_OImage(tc_List_Olist(U_16584),tc_List_Olist(U_16584),c_List_Olistrel(U_16584,U_16585)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16584)),c_List_Olist_ONil(U_16584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16584),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16584)),c_List_Olist_ONil(U_16584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16584),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

cnf(f_4081_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_16584),tc_List_Olist(U_16584),c_List_Olistrel(U_16584,U_16585)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16584)),c_List_Olist_ONil(U_16584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16584),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16584)),c_List_Olist_ONil(U_16584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16584),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4081_2]) ).

fof(f_4082_1,plain,
    ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(f_4082_2,plain,
    ! [U_16587,U_16586] : c_List_Oset__Cons(U_16586,U_16587,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16586)),c_List_Olist_ONil(U_16586)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16586),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_16586,tc_List_Olist(U_16586),hAPP(hAPP(c_COMBC(U_16586,tc_List_Olist(U_16586),tc_List_Olist(U_16586)),c_List_Olist_OCons(U_16586)),c_List_Olist_ONil(U_16586))),U_16587),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

cnf(f_4082_3,plain,
    c_List_Oset__Cons(U_16586,U_16587,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16586)),c_List_Olist_ONil(U_16586)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16586),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_16586,tc_List_Olist(U_16586),hAPP(hAPP(c_COMBC(U_16586,tc_List_Olist(U_16586),tc_List_Olist(U_16586)),c_List_Olist_OCons(U_16586)),c_List_Olist_ONil(U_16586))),U_16587),
    inference(clausify,[status(thm)],[f_4082_2]) ).

fof(f_4083_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,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_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remove1]) ).

fof(f_4083_2,plain,
    ! [U_16590,U_16589,U_16588] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16588)),c_List_Oremove1(U_16588,U_16589,U_16590)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16588)),U_16590)
        | hBOOL(hAPP(hAPP(c_member(U_16588),U_16589),hAPP(c_List_Oset(U_16588),U_16590))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16588)),c_List_Oremove1(U_16588,U_16589,U_16590)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16588)),U_16590)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16588),U_16589),hAPP(c_List_Oset(U_16588),U_16590))) ) ),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

fof(f_4083_3,plain,
    ( ! [U_16596,U_16594,U_16592] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16592)),c_List_Oremove1(U_16592,U_16594,U_16596)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16592)),U_16596)
        | hBOOL(hAPP(hAPP(c_member(U_16592),U_16594),hAPP(c_List_Oset(U_16592),U_16596))) )
    & ! [U_16595,U_16593,U_16591] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16591)),c_List_Oremove1(U_16591,U_16593,U_16595)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16591)),U_16595)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16591),U_16593),hAPP(c_List_Oset(U_16591),U_16595))) ) ),
    inference(miniscope,[status(thm)],[f_4083_2]) ).

cnf(f_4083_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16591)),c_List_Oremove1(U_16591,U_16593,U_16595)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16591)),U_16595)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16591),U_16593),hAPP(c_List_Oset(U_16591),U_16595))) ),
    inference(clausify,[status(thm)],[f_4083_3]) ).

cnf(f_4083_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16592)),c_List_Oremove1(U_16592,U_16594,U_16596)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16592)),U_16596)
    | hBOOL(hAPP(hAPP(c_member(U_16592),U_16594),hAPP(c_List_Oset(U_16592),U_16596))) ),
    inference(clausify,[status(thm)],[f_4083_3]) ).

fof(f_4084_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_4084_2,plain,
    ! [U_16598,U_16597] :
      ( ( ( c_List_Oupto(U_16597,U_16598) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16597),U_16598)) )
        & ( c_List_Oupto(U_16597,U_16598) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_16597),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16597),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16598))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16597),U_16598)) ) )
      | ~ 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_16597),U_16598))) ),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

cnf(f_4084_3,plain,
    ( c_List_Oupto(U_16597,U_16598) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_16597),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16597),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_16598))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16597),U_16598))
    | ~ 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_16597),U_16598))) ),
    inference(clausify,[status(thm)],[f_4084_2]) ).

cnf(f_4084_4,plain,
    ( c_List_Oupto(U_16597,U_16598) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16597),U_16598))
    | ~ 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_16597),U_16598))) ),
    inference(clausify,[status(thm)],[f_4084_2]) ).

fof(f_4085_1,plain,
    ! [V_s_2,T_a,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_select]) ).

fof(f_4085_2,plain,
    ! [U_16601,U_16600,U_16599] :
      ( hBOOL(hAPP(hAPP(c_member(U_16600),hAPP(c_Product__Type_Ofst(U_16600,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_16600,U_16599),U_16601))),hAPP(c_List_Oset(U_16600),U_16599)))
      | U_16599 = c_List_Olist_ONil(U_16600) ),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

cnf(f_4085_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16600),hAPP(c_Product__Type_Ofst(U_16600,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_16600,U_16599),U_16601))),hAPP(c_List_Oset(U_16600),U_16599)))
    | U_16599 = c_List_Olist_ONil(U_16600) ),
    inference(clausify,[status(thm)],[f_4085_2]) ).

fof(f_4086_1,plain,
    ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(f_4086_2,plain,
    ! [U_16602] : c_List_Olistset(U_16602,c_List_Olist_ONil(tc_fun(U_16602,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16602)),c_List_Olist_ONil(U_16602)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16602),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

cnf(f_4086_3,plain,
    c_List_Olistset(U_16602,c_List_Olist_ONil(tc_fun(U_16602,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_16602)),c_List_Olist_ONil(U_16602)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_16602),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4086_2]) ).

fof(f_4087_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons]) ).

fof(f_4087_2,plain,
    ! [U_16607,U_16606,U_16605,U_16604,U_16603] : hAPP(hAPP(c_List_Ozip(U_16603,U_16604),U_16605),hAPP(hAPP(c_List_Olist_OCons(U_16604),U_16606),U_16607)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_16603,U_16604)),U_16603,c_List_Olist_ONil(tc_prod(U_16603,U_16604)),hAPP(hAPP(c_COMBC(U_16603,tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604)))),U_16603),c_COMBB(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(U_16603))),hAPP(hAPP(c_COMBB(tc_prod(U_16603,U_16604),tc_fun(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604))),U_16603),c_List_Olist_OCons(tc_prod(U_16603,U_16604))),hAPP(hAPP(c_COMBC(U_16603,U_16604,tc_prod(U_16603,U_16604)),c_Product__Type_OPair(U_16603,U_16604)),U_16606)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16603),tc_List_Olist(U_16604),tc_List_Olist(tc_prod(U_16603,U_16604))),c_List_Ozip(U_16603,U_16604)),U_16607))),U_16605),
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

cnf(f_4087_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16603,U_16604),U_16605),hAPP(hAPP(c_List_Olist_OCons(U_16604),U_16606),U_16607)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_16603,U_16604)),U_16603,c_List_Olist_ONil(tc_prod(U_16603,U_16604)),hAPP(hAPP(c_COMBC(U_16603,tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604))),tc_fun(tc_List_Olist(U_16603),tc_List_Olist(tc_prod(U_16603,U_16604)))),U_16603),c_COMBB(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(U_16603))),hAPP(hAPP(c_COMBB(tc_prod(U_16603,U_16604),tc_fun(tc_List_Olist(tc_prod(U_16603,U_16604)),tc_List_Olist(tc_prod(U_16603,U_16604))),U_16603),c_List_Olist_OCons(tc_prod(U_16603,U_16604))),hAPP(hAPP(c_COMBC(U_16603,U_16604,tc_prod(U_16603,U_16604)),c_Product__Type_OPair(U_16603,U_16604)),U_16606)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16603),tc_List_Olist(U_16604),tc_List_Olist(tc_prod(U_16603,U_16604))),c_List_Ozip(U_16603,U_16604)),U_16607))),U_16605),
    inference(clausify,[status(thm)],[f_4087_2]) ).

fof(f_4088_1,plain,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),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_4088_2,plain,
    ! [U_16613,U_16612,U_16611,U_16610,U_16609,U_16608] : hAPP(c_List_Olist_Olist__case(U_16608,U_16609,U_16610,U_16611),hAPP(hAPP(c_List_Olist_OCons(U_16609),U_16612),U_16613)) = hAPP(hAPP(U_16611,U_16612),U_16613),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

cnf(f_4088_3,plain,
    hAPP(c_List_Olist_Olist__case(U_16608,U_16609,U_16610,U_16611),hAPP(hAPP(c_List_Olist_OCons(U_16609),U_16612),U_16613)) = hAPP(hAPP(U_16611,U_16612),U_16613),
    inference(clausify,[status(thm)],[f_4088_2]) ).

fof(f_4089_1,plain,
    ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(f_4089_2,plain,
    ! [U_16617,U_16616,U_16615,U_16614] : hAPP(c_List_Olist_Olist__case(U_16614,U_16615,U_16616,U_16617),c_List_Olist_ONil(U_16615)) = U_16616,
    inference(variable_rename,[status(thm)],[f_4089_1]) ).

cnf(f_4089_3,plain,
    hAPP(c_List_Olist_Olist__case(U_16614,U_16615,U_16616,U_16617),c_List_Olist_ONil(U_16615)) = U_16616,
    inference(clausify,[status(thm)],[f_4089_2]) ).

fof(f_4090_1,plain,
    ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(f_4090_2,plain,
    ! [U_16620,U_16619,U_16618] : c_List_Olistset(U_16618,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_16618,tc_HOL_Obool)),U_16619),U_16620)) = c_List_Oset__Cons(U_16618,U_16619,c_List_Olistset(U_16618,U_16620)),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

cnf(f_4090_3,plain,
    c_List_Olistset(U_16618,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_16618,tc_HOL_Obool)),U_16619),U_16620)) = c_List_Oset__Cons(U_16618,U_16619,c_List_Olistset(U_16618,U_16620)),
    inference(clausify,[status(thm)],[f_4090_2]) ).

fof(f_4091_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons1]) ).

fof(f_4091_2,plain,
    ! [U_16625,U_16624,U_16623,U_16622,U_16621] : hAPP(hAPP(c_List_Ozip(U_16621,U_16622),hAPP(hAPP(c_List_Olist_OCons(U_16621),U_16623),U_16624)),U_16625) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_16621,U_16622)),U_16622,c_List_Olist_ONil(tc_prod(U_16621,U_16622)),hAPP(hAPP(c_COMBC(U_16622,tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622)))),U_16622),c_COMBB(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(U_16622))),hAPP(hAPP(c_COMBB(tc_prod(U_16621,U_16622),tc_fun(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622))),U_16622),c_List_Olist_OCons(tc_prod(U_16621,U_16622))),hAPP(c_Product__Type_OPair(U_16621,U_16622),U_16623)))),hAPP(c_List_Ozip(U_16621,U_16622),U_16624))),U_16625),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

cnf(f_4091_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16621,U_16622),hAPP(hAPP(c_List_Olist_OCons(U_16621),U_16623),U_16624)),U_16625) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_16621,U_16622)),U_16622,c_List_Olist_ONil(tc_prod(U_16621,U_16622)),hAPP(hAPP(c_COMBC(U_16622,tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622))),tc_fun(tc_List_Olist(U_16622),tc_List_Olist(tc_prod(U_16621,U_16622)))),U_16622),c_COMBB(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(U_16622))),hAPP(hAPP(c_COMBB(tc_prod(U_16621,U_16622),tc_fun(tc_List_Olist(tc_prod(U_16621,U_16622)),tc_List_Olist(tc_prod(U_16621,U_16622))),U_16622),c_List_Olist_OCons(tc_prod(U_16621,U_16622))),hAPP(c_Product__Type_OPair(U_16621,U_16622),U_16623)))),hAPP(c_List_Ozip(U_16621,U_16622),U_16624))),U_16625),
    inference(clausify,[status(thm)],[f_4091_2]) ).

fof(f_4092_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove]) ).

fof(f_4092_2,plain,
    ! [U_16628,U_16627,U_16626] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_16626,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16626,tc_HOL_Obool)),U_16627),hAPP(hAPP(c_Set_Oinsert(U_16626),U_16628),c_Orderings_Obot__class_Obot(tc_fun(U_16626,tc_HOL_Obool))))) = c_List_Oremove1(U_16626,U_16628,c_List_Olinorder__class_Osorted__list__of__set(U_16626,U_16627))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16626),U_16627))
      | ~ class_Orderings_Olinorder(U_16626) ),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

cnf(f_4092_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_16626,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16626,tc_HOL_Obool)),U_16627),hAPP(hAPP(c_Set_Oinsert(U_16626),U_16628),c_Orderings_Obot__class_Obot(tc_fun(U_16626,tc_HOL_Obool))))) = c_List_Oremove1(U_16626,U_16628,c_List_Olinorder__class_Osorted__list__of__set(U_16626,U_16627))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16626),U_16627))
    | ~ class_Orderings_Olinorder(U_16626) ),
    inference(clausify,[status(thm)],[f_4092_2]) ).

fof(f_4093_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Opinduct]) ).

fof(f_4093_2,plain,
    ! [U_16633,U_16632,U_16631] :
      ( hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
      | ? [U_16630,U_16629] :
          ( ~ hBOOL(hAPP(hAPP(U_16633,U_16630),U_16629))
          & ( hBOOL(hAPP(hAPP(U_16633,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_16630),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_16629))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_16630),U_16629)) )
          & 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_16630),U_16629))) )
      | ~ 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_16631),U_16632))) ),
    inference(variable_rename,[status(thm)],[f_4093_1]) ).

fof(f_4093_3,plain,
    ! [U_16633,U_16632,U_16631] :
      ( hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
      | ? [U_16629] :
          ( ~ hBOOL(hAPP(hAPP(U_16633,sK437(U_16633,U_16632,U_16631)),U_16629))
          & ( hBOOL(hAPP(hAPP(U_16633,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_16629))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),U_16629)) )
          & 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),sK437(U_16633,U_16632,U_16631)),U_16629))) )
      | ~ 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_16631),U_16632))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_16630,sK437(U_16633,U_16632,U_16631))],[f_4093_2]) ).

fof(f_4093_4,plain,
    ! [U_16633,U_16632,U_16631] :
      ( hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
      | ( ~ hBOOL(hAPP(hAPP(U_16633,sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631)))
        & ( hBOOL(hAPP(hAPP(U_16633,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK438(U_16633,U_16632,U_16631)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631))) )
        & 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),sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631)))) )
      | ~ 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_16631),U_16632))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_16629,sK438(U_16633,U_16632,U_16631))],[f_4093_3]) ).

cnf(f_4093_5,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),sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631))))
    | hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
    | ~ 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_16631),U_16632))) ),
    inference(clausify,[status(thm)],[f_4093_4]) ).

cnf(f_4093_6,plain,
    ( hBOOL(hAPP(hAPP(U_16633,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK438(U_16633,U_16632,U_16631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631)))
    | hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
    | ~ 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_16631),U_16632))) ),
    inference(clausify,[status(thm)],[f_4093_4]) ).

cnf(f_4093_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_16633,sK437(U_16633,U_16632,U_16631)),sK438(U_16633,U_16632,U_16631)))
    | hBOOL(hAPP(hAPP(U_16633,U_16631),U_16632))
    | ~ 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_16631),U_16632))) ),
    inference(clausify,[status(thm)],[f_4093_4]) ).

fof(f_4094_1,plain,
    ! [T_a] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty]) ).

fof(f_4094_2,plain,
    ! [U_16634] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_16634,c_Orderings_Obot__class_Obot(tc_fun(U_16634,tc_HOL_Obool))) = c_List_Olist_ONil(U_16634)
      | ~ class_Orderings_Olinorder(U_16634) ),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

cnf(f_4094_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_16634,c_Orderings_Obot__class_Obot(tc_fun(U_16634,tc_HOL_Obool))) = c_List_Olist_ONil(U_16634)
    | ~ class_Orderings_Olinorder(U_16634) ),
    inference(clausify,[status(thm)],[f_4094_2]) ).

fof(f_4095_1,plain,
    ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
      ( ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,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(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),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_4095_2,plain,
    ! [U_16639,U_16638,U_16637,U_16636,U_16635] :
      ( ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16636,U_16637,U_16638),U_16635),U_16639) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_16637),U_16636),tc_prod(U_16637,U_16636),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16637),U_16636),c_List_Olist_ONil(U_16637)),U_16639),hAPP(c_Product__Type_Oprod_Oprod__case(U_16637,U_16636,tc_prod(tc_List_Olist(U_16637),U_16636)),hAPP(hAPP(c_COMBC(U_16637,tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636)),tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_16637),U_16636),tc_prod(tc_List_Olist(U_16637),U_16636)),tc_fun(tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636)),tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636))),U_16637),c_COMBB(tc_prod(tc_List_Olist(U_16637),U_16636),tc_prod(tc_List_Olist(U_16637),U_16636),U_16636)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16637),tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636))),tc_fun(tc_prod(tc_List_Olist(U_16637),U_16636),tc_prod(tc_List_Olist(U_16637),U_16636)),U_16637),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_16637),U_16636,tc_prod(tc_List_Olist(U_16637),U_16636))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16637),tc_List_Olist(U_16637)),tc_fun(tc_List_Olist(U_16637),tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636))),U_16637),hAPP(c_COMBB(tc_List_Olist(U_16637),tc_fun(U_16636,tc_prod(tc_List_Olist(U_16637),U_16636)),tc_List_Olist(U_16637)),c_Product__Type_OPair(tc_List_Olist(U_16637),U_16636))),c_List_Olist_OCons(U_16637))))),hAPP(c_Lazy__Sequence_Oanamorph(U_16636,U_16637,U_16638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_16635),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_16638,U_16639))
        | U_16635 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16636,U_16637,U_16638),U_16635),U_16639) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16637),U_16636),c_List_Olist_ONil(U_16637)),U_16639)
        | U_16635 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

fof(f_4095_3,plain,
    ( ! [U_16649,U_16647,U_16645,U_16643,U_16641] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16643,U_16645,U_16647),U_16641),U_16649) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(U_16645,U_16643),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16645),U_16643),c_List_Olist_ONil(U_16645)),U_16649),hAPP(c_Product__Type_Oprod_Oprod__case(U_16645,U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),hAPP(hAPP(c_COMBC(U_16645,tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),U_16645),c_COMBB(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643),U_16643)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),tc_fun(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643)),U_16645),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_16645),U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16645),tc_List_Olist(U_16645)),tc_fun(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),U_16645),hAPP(c_COMBB(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_List_Olist(U_16645)),c_Product__Type_OPair(tc_List_Olist(U_16645),U_16643))),c_List_Olist_OCons(U_16645))))),hAPP(c_Lazy__Sequence_Oanamorph(U_16643,U_16645,U_16647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_16641),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_16647,U_16649))
        | U_16641 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_16648,U_16646,U_16644,U_16642,U_16640] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16642,U_16644,U_16646),U_16640),U_16648) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16644),U_16642),c_List_Olist_ONil(U_16644)),U_16648)
        | U_16640 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4095_2]) ).

cnf(f_4095_4,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16642,U_16644,U_16646),U_16640),U_16648) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16644),U_16642),c_List_Olist_ONil(U_16644)),U_16648)
    | U_16640 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4095_3]) ).

cnf(f_4095_5,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_16643,U_16645,U_16647),U_16641),U_16649) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(U_16645,U_16643),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16645),U_16643),c_List_Olist_ONil(U_16645)),U_16649),hAPP(c_Product__Type_Oprod_Oprod__case(U_16645,U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),hAPP(hAPP(c_COMBC(U_16645,tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),U_16645),c_COMBB(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643),U_16643)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),tc_fun(tc_prod(tc_List_Olist(U_16645),U_16643),tc_prod(tc_List_Olist(U_16645),U_16643)),U_16645),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_16645),U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_16645),tc_List_Olist(U_16645)),tc_fun(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643))),U_16645),hAPP(c_COMBB(tc_List_Olist(U_16645),tc_fun(U_16643,tc_prod(tc_List_Olist(U_16645),U_16643)),tc_List_Olist(U_16645)),c_Product__Type_OPair(tc_List_Olist(U_16645),U_16643))),c_List_Olist_OCons(U_16645))))),hAPP(c_Lazy__Sequence_Oanamorph(U_16643,U_16645,U_16647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_16641),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_16647,U_16649))
    | U_16641 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4095_3]) ).

fof(f_4096_1,plain,
    ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),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_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,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_4096_2,plain,
    ! [U_16653,U_16652,U_16651,U_16650] : c_List_Osublist(U_16650,hAPP(hAPP(c_List_Olist_OCons(U_16650),U_16651),U_16652),U_16653) = hAPP(hAPP(c_List_Oappend(U_16650),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_16650)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16653)),hAPP(hAPP(c_List_Olist_OCons(U_16650),U_16651),c_List_Olist_ONil(U_16650))),c_List_Olist_ONil(U_16650))),c_List_Osublist(U_16650,U_16652,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_16653)))),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

cnf(f_4096_3,plain,
    c_List_Osublist(U_16650,hAPP(hAPP(c_List_Olist_OCons(U_16650),U_16651),U_16652),U_16653) = hAPP(hAPP(c_List_Oappend(U_16650),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_16650)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16653)),hAPP(hAPP(c_List_Olist_OCons(U_16650),U_16651),c_List_Olist_ONil(U_16650))),c_List_Olist_ONil(U_16650))),c_List_Osublist(U_16650,U_16652,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_16653)))),
    inference(clausify,[status(thm)],[f_4096_2]) ).

fof(f_4097_1,plain,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
        | ( ! [B_ys_H] :
              ( hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) != V_xs_2
              | V_ys_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) )
          & ( V_zs_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
            | V_ys_2 != c_List_Olist_ONil(T_a) ) ) )
      & ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_a) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv]) ).

fof(f_4097_2,plain,
    ! [U_16660,U_16659,U_16658,U_16657,U_16656] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16656),U_16657),U_16658) = hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16660)
        | ( ! [U_16655] :
              ( hAPP(hAPP(c_List_Oappend(U_16656),U_16655),U_16658) != U_16660
              | U_16657 != hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16655) )
          & ( U_16658 != hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16660)
            | U_16657 != c_List_Olist_ONil(U_16656) ) ) )
      & ( ? [U_16654] :
            ( hAPP(hAPP(c_List_Oappend(U_16656),U_16654),U_16658) = U_16660
            & U_16657 = hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16654) )
        | ( U_16658 = hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16660)
          & U_16657 = c_List_Olist_ONil(U_16656) )
        | hAPP(hAPP(c_List_Oappend(U_16656),U_16657),U_16658) != hAPP(hAPP(c_List_Olist_OCons(U_16656),U_16659),U_16660) ) ),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

fof(f_4097_3,plain,
    ( ! [U_16670,U_16668,U_16666,U_16664,U_16662] :
        ( hAPP(hAPP(c_List_Oappend(U_16662),U_16664),U_16666) = hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670)
        | ( ! [U_16655] :
              ( hAPP(hAPP(c_List_Oappend(U_16662),U_16655),U_16666) != U_16670
              | U_16664 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16655) )
          & ( U_16666 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670)
            | U_16664 != c_List_Olist_ONil(U_16662) ) ) )
    & ! [U_16669,U_16667,U_16665,U_16663,U_16661] :
        ( ? [U_16654] :
            ( hAPP(hAPP(c_List_Oappend(U_16661),U_16654),U_16665) = U_16669
            & U_16663 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16654) )
        | ( U_16665 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669)
          & U_16663 = c_List_Olist_ONil(U_16661) )
        | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ) ),
    inference(miniscope,[status(thm)],[f_4097_2]) ).

fof(f_4097_4,plain,
    ( ! [U_16670,U_16668,U_16666,U_16664,U_16662] :
        ( hAPP(hAPP(c_List_Oappend(U_16662),U_16664),U_16666) = hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670)
        | ( ! [U_16655] :
              ( hAPP(hAPP(c_List_Oappend(U_16662),U_16655),U_16666) != U_16670
              | U_16664 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16655) )
          & ( U_16666 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670)
            | U_16664 != c_List_Olist_ONil(U_16662) ) ) )
    & ! [U_16669,U_16667,U_16665,U_16663,U_16661] :
        ( ( hAPP(hAPP(c_List_Oappend(U_16661),sK439(U_16669,U_16667,U_16665,U_16663,U_16661)),U_16665) = U_16669
          & U_16663 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),sK439(U_16669,U_16667,U_16665,U_16663,U_16661)) )
        | ( U_16665 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669)
          & U_16663 = c_List_Olist_ONil(U_16661) )
        | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_16654,sK439(U_16669,U_16667,U_16665,U_16663,U_16661))],[f_4097_3]) ).

cnf(f_4097_5,plain,
    ( U_16663 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),sK439(U_16669,U_16667,U_16665,U_16663,U_16661))
    | U_16663 = c_List_Olist_ONil(U_16661)
    | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

cnf(f_4097_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16661),sK439(U_16669,U_16667,U_16665,U_16663,U_16661)),U_16665) = U_16669
    | U_16663 = c_List_Olist_ONil(U_16661)
    | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

cnf(f_4097_7,plain,
    ( U_16663 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),sK439(U_16669,U_16667,U_16665,U_16663,U_16661))
    | U_16665 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669)
    | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

cnf(f_4097_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16661),sK439(U_16669,U_16667,U_16665,U_16663,U_16661)),U_16665) = U_16669
    | U_16665 = hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669)
    | hAPP(hAPP(c_List_Oappend(U_16661),U_16663),U_16665) != hAPP(hAPP(c_List_Olist_OCons(U_16661),U_16667),U_16669) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

cnf(f_4097_9,plain,
    ( U_16666 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670)
    | U_16664 != c_List_Olist_ONil(U_16662)
    | hAPP(hAPP(c_List_Oappend(U_16662),U_16664),U_16666) = hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

cnf(f_4097_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16662),U_16655),U_16666) != U_16670
    | U_16664 != hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16655)
    | hAPP(hAPP(c_List_Oappend(U_16662),U_16664),U_16666) = hAPP(hAPP(c_List_Olist_OCons(U_16662),U_16668),U_16670) ),
    inference(clausify,[status(thm)],[f_4097_4]) ).

fof(f_4098_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)
        | ( ! [B_ys_H] :
              ( V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)
              | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) != V_ys_2 )
          & ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) != V_zs_2
            | V_ys_2 != c_List_Olist_ONil(T_a) ) ) )
      & ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_a) )
        | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv]) ).

fof(f_4098_2,plain,
    ! [U_16677,U_16676,U_16675,U_16674,U_16673] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16675) = hAPP(hAPP(c_List_Oappend(U_16673),U_16676),U_16677)
        | ( ! [U_16672] :
              ( U_16675 != hAPP(hAPP(c_List_Oappend(U_16673),U_16672),U_16677)
              | hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16672) != U_16676 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16675) != U_16677
            | U_16676 != c_List_Olist_ONil(U_16673) ) ) )
      & ( ? [U_16671] :
            ( U_16675 = hAPP(hAPP(c_List_Oappend(U_16673),U_16671),U_16677)
            & hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16671) = U_16676 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16675) = U_16677
          & U_16676 = c_List_Olist_ONil(U_16673) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16673),U_16674),U_16675) != hAPP(hAPP(c_List_Oappend(U_16673),U_16676),U_16677) ) ),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

fof(f_4098_3,plain,
    ( ! [U_16687,U_16685,U_16683,U_16681,U_16679] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) = hAPP(hAPP(c_List_Oappend(U_16679),U_16685),U_16687)
        | ( ! [U_16672] :
              ( U_16683 != hAPP(hAPP(c_List_Oappend(U_16679),U_16672),U_16687)
              | hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16672) != U_16685 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) != U_16687
            | U_16685 != c_List_Olist_ONil(U_16679) ) ) )
    & ! [U_16686,U_16684,U_16682,U_16680,U_16678] :
        ( ? [U_16671] :
            ( U_16682 = hAPP(hAPP(c_List_Oappend(U_16678),U_16671),U_16686)
            & hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16671) = U_16684 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) = U_16686
          & U_16684 = c_List_Olist_ONil(U_16678) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ) ),
    inference(miniscope,[status(thm)],[f_4098_2]) ).

fof(f_4098_4,plain,
    ( ! [U_16687,U_16685,U_16683,U_16681,U_16679] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) = hAPP(hAPP(c_List_Oappend(U_16679),U_16685),U_16687)
        | ( ! [U_16672] :
              ( U_16683 != hAPP(hAPP(c_List_Oappend(U_16679),U_16672),U_16687)
              | hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16672) != U_16685 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) != U_16687
            | U_16685 != c_List_Olist_ONil(U_16679) ) ) )
    & ! [U_16686,U_16684,U_16682,U_16680,U_16678] :
        ( ( U_16682 = hAPP(hAPP(c_List_Oappend(U_16678),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)),U_16686)
          & hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)) = U_16684 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) = U_16686
          & U_16684 = c_List_Olist_ONil(U_16678) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_16671,sK440(U_16686,U_16684,U_16682,U_16680,U_16678))],[f_4098_3]) ).

cnf(f_4098_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)) = U_16684
    | U_16684 = c_List_Olist_ONil(U_16678)
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

cnf(f_4098_6,plain,
    ( U_16682 = hAPP(hAPP(c_List_Oappend(U_16678),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)),U_16686)
    | U_16684 = c_List_Olist_ONil(U_16678)
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

cnf(f_4098_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)) = U_16684
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) = U_16686
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

cnf(f_4098_8,plain,
    ( U_16682 = hAPP(hAPP(c_List_Oappend(U_16678),sK440(U_16686,U_16684,U_16682,U_16680,U_16678)),U_16686)
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) = U_16686
    | hAPP(hAPP(c_List_Olist_OCons(U_16678),U_16680),U_16682) != hAPP(hAPP(c_List_Oappend(U_16678),U_16684),U_16686) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

cnf(f_4098_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) != U_16687
    | U_16685 != c_List_Olist_ONil(U_16679)
    | hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) = hAPP(hAPP(c_List_Oappend(U_16679),U_16685),U_16687) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

cnf(f_4098_10,plain,
    ( U_16683 != hAPP(hAPP(c_List_Oappend(U_16679),U_16672),U_16687)
    | hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16672) != U_16685
    | hAPP(hAPP(c_List_Olist_OCons(U_16679),U_16681),U_16683) = hAPP(hAPP(c_List_Oappend(U_16679),U_16685),U_16687) ),
    inference(clausify,[status(thm)],[f_4098_4]) ).

fof(f_4099_1,plain,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))
        | 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_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) != hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append1__eq__conv]) ).

fof(f_4099_2,plain,
    ! [U_16692,U_16691,U_16690,U_16689,U_16688] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16688),U_16689),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16690),c_List_Olist_ONil(U_16688))) = hAPP(hAPP(c_List_Oappend(U_16688),U_16691),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16692),c_List_Olist_ONil(U_16688)))
        | U_16690 != U_16692
        | U_16689 != U_16691 )
      & ( ( U_16690 = U_16692
          & U_16689 = U_16691 )
        | hAPP(hAPP(c_List_Oappend(U_16688),U_16689),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16690),c_List_Olist_ONil(U_16688))) != hAPP(hAPP(c_List_Oappend(U_16688),U_16691),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16692),c_List_Olist_ONil(U_16688))) ) ),
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

fof(f_4099_3,plain,
    ( ! [U_16702,U_16700,U_16698,U_16696] :
        ( ! [U_16694] : hAPP(hAPP(c_List_Oappend(U_16694),U_16696),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16698),c_List_Olist_ONil(U_16694))) = hAPP(hAPP(c_List_Oappend(U_16694),U_16700),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16702),c_List_Olist_ONil(U_16694)))
        | U_16698 != U_16702
        | U_16696 != U_16700 )
    & ! [U_16701,U_16699,U_16697,U_16695] :
        ( ! [U_16693] : hAPP(hAPP(c_List_Oappend(U_16693),U_16695),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16697),c_List_Olist_ONil(U_16693))) != hAPP(hAPP(c_List_Oappend(U_16693),U_16699),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16701),c_List_Olist_ONil(U_16693)))
        | ( U_16697 = U_16701
          & U_16695 = U_16699 ) ) ),
    inference(miniscope,[status(thm)],[f_4099_2]) ).

cnf(f_4099_4,plain,
    ( U_16695 = U_16699
    | hAPP(hAPP(c_List_Oappend(U_16693),U_16695),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16697),c_List_Olist_ONil(U_16693))) != hAPP(hAPP(c_List_Oappend(U_16693),U_16699),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16701),c_List_Olist_ONil(U_16693))) ),
    inference(clausify,[status(thm)],[f_4099_3]) ).

cnf(f_4099_5,plain,
    ( U_16697 = U_16701
    | hAPP(hAPP(c_List_Oappend(U_16693),U_16695),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16697),c_List_Olist_ONil(U_16693))) != hAPP(hAPP(c_List_Oappend(U_16693),U_16699),hAPP(hAPP(c_List_Olist_OCons(U_16693),U_16701),c_List_Olist_ONil(U_16693))) ),
    inference(clausify,[status(thm)],[f_4099_3]) ).

cnf(f_4099_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16694),U_16696),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16698),c_List_Olist_ONil(U_16694))) = hAPP(hAPP(c_List_Oappend(U_16694),U_16700),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16702),c_List_Olist_ONil(U_16694)))
    | U_16698 != U_16702
    | U_16696 != U_16700 ),
    inference(clausify,[status(thm)],[f_4099_3]) ).

fof(f_4100_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_4100_2,plain,
    ! [U_16706,U_16705,U_16704,U_16703] : hAPP(hAPP(c_List_Oappend(U_16703),hAPP(hAPP(c_List_Olist_OCons(U_16703),U_16704),U_16705)),U_16706) = hAPP(hAPP(c_List_Olist_OCons(U_16703),U_16704),hAPP(hAPP(c_List_Oappend(U_16703),U_16705),U_16706)),
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

cnf(f_4100_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16703),hAPP(hAPP(c_List_Olist_OCons(U_16703),U_16704),U_16705)),U_16706) = hAPP(hAPP(c_List_Olist_OCons(U_16703),U_16704),hAPP(hAPP(c_List_Oappend(U_16703),U_16705),U_16706)),
    inference(clausify,[status(thm)],[f_4100_2]) ).

fof(f_4101_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_4101_2,plain,
    ! [U_16712,U_16711,U_16710,U_16709,U_16708,U_16707] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_16707),U_16708),U_16711) = hAPP(hAPP(c_List_Oappend(U_16707),U_16710),U_16712)
      | U_16711 != hAPP(hAPP(c_List_Oappend(U_16707),U_16709),U_16712)
      | hAPP(hAPP(c_List_Olist_OCons(U_16707),U_16708),U_16709) != U_16710 ),
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

cnf(f_4101_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16707),U_16708),U_16711) = hAPP(hAPP(c_List_Oappend(U_16707),U_16710),U_16712)
    | U_16711 != hAPP(hAPP(c_List_Oappend(U_16707),U_16709),U_16712)
    | hAPP(hAPP(c_List_Olist_OCons(U_16707),U_16708),U_16709) != U_16710 ),
    inference(clausify,[status(thm)],[f_4101_2]) ).

fof(f_4102_1,plain,
    ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_set__append]) ).

fof(f_4102_2,plain,
    ! [U_16715,U_16714,U_16713] : hAPP(c_List_Oset(U_16713),hAPP(hAPP(c_List_Oappend(U_16713),U_16714),U_16715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16713,tc_HOL_Obool)),hAPP(c_List_Oset(U_16713),U_16714)),hAPP(c_List_Oset(U_16713),U_16715)),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

cnf(f_4102_3,plain,
    hAPP(c_List_Oset(U_16713),hAPP(hAPP(c_List_Oappend(U_16713),U_16714),U_16715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16713,tc_HOL_Obool)),hAPP(c_List_Oset(U_16713),U_16714)),hAPP(c_List_Oset(U_16713),U_16715)),
    inference(clausify,[status(thm)],[f_4102_2]) ).

fof(f_4103_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_4103_2,plain,
    ! [U_16721,U_16720,U_16719,U_16718,U_16717,U_16716] :
      ( hAPP(hAPP(c_List_Ozip(U_16716,U_16718),hAPP(hAPP(c_List_Oappend(U_16716),U_16717),U_16720)),hAPP(hAPP(c_List_Oappend(U_16718),U_16719),U_16721)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16716,U_16718)),hAPP(hAPP(c_List_Ozip(U_16716,U_16718),U_16717),U_16719)),hAPP(hAPP(c_List_Ozip(U_16716,U_16718),U_16720),U_16721))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16716)),U_16720) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16718)),U_16721)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16716)),U_16717) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16718)),U_16719) ),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

cnf(f_4103_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_16716,U_16718),hAPP(hAPP(c_List_Oappend(U_16716),U_16717),U_16720)),hAPP(hAPP(c_List_Oappend(U_16718),U_16719),U_16721)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16716,U_16718)),hAPP(hAPP(c_List_Ozip(U_16716,U_16718),U_16717),U_16719)),hAPP(hAPP(c_List_Ozip(U_16716,U_16718),U_16720),U_16721))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16716)),U_16720) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16718)),U_16721)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16716)),U_16717) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16718)),U_16719) ),
    inference(clausify,[status(thm)],[f_4103_2]) ).

fof(f_4104_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_4104_2,plain,
    ! [U_16724,U_16723,U_16722] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),hAPP(hAPP(c_List_Oappend(U_16722),U_16723),U_16724)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),U_16723)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),U_16724)),
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

cnf(f_4104_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),hAPP(hAPP(c_List_Oappend(U_16722),U_16723),U_16724)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),U_16723)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16722)),U_16724)),
    inference(clausify,[status(thm)],[f_4104_2]) ).

fof(f_4105_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_4105_2,plain,
    ! [U_16727,U_16726,U_16725] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),hAPP(hAPP(c_List_Oappend(U_16725),U_16726),U_16727)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16725),hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),U_16726)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),U_16727))
      | ~ class_Groups_Omonoid__add(U_16725) ),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

cnf(f_4105_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),hAPP(hAPP(c_List_Oappend(U_16725),U_16726),U_16727)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16725),hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),U_16726)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16725),U_16727))
    | ~ class_Groups_Omonoid__add(U_16725) ),
    inference(clausify,[status(thm)],[f_4105_2]) ).

fof(f_4106_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_4106_2,plain,
    ! [U_16733,U_16732,U_16731,U_16730,U_16729,U_16728] :
      ( hAPP(hAPP(c_List_Oappend(U_16728),U_16729),U_16732) = hAPP(hAPP(c_List_Oappend(U_16728),U_16731),U_16733)
      | U_16732 != hAPP(hAPP(c_List_Oappend(U_16728),U_16730),U_16733)
      | hAPP(hAPP(c_List_Oappend(U_16728),U_16729),U_16730) != U_16731 ),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

cnf(f_4106_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16728),U_16729),U_16732) = hAPP(hAPP(c_List_Oappend(U_16728),U_16731),U_16733)
    | U_16732 != hAPP(hAPP(c_List_Oappend(U_16728),U_16730),U_16733)
    | hAPP(hAPP(c_List_Oappend(U_16728),U_16729),U_16730) != U_16731 ),
    inference(clausify,[status(thm)],[f_4106_2]) ).

fof(f_4107_1,plain,
    ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__same__eq]) ).

fof(f_4107_2,plain,
    ! [U_16737,U_16736,U_16735,U_16734] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16734),U_16735),U_16736) = hAPP(hAPP(c_List_Oappend(U_16734),U_16737),U_16736)
        | U_16735 != U_16737 )
      & ( U_16735 = U_16737
        | hAPP(hAPP(c_List_Oappend(U_16734),U_16735),U_16736) != hAPP(hAPP(c_List_Oappend(U_16734),U_16737),U_16736) ) ),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

fof(f_4107_3,plain,
    ( ! [U_16745,U_16743,U_16741] :
        ( ! [U_16739] : hAPP(hAPP(c_List_Oappend(U_16739),U_16741),U_16743) = hAPP(hAPP(c_List_Oappend(U_16739),U_16745),U_16743)
        | U_16741 != U_16745 )
    & ! [U_16744,U_16742,U_16740] :
        ( ! [U_16738] : hAPP(hAPP(c_List_Oappend(U_16738),U_16740),U_16742) != hAPP(hAPP(c_List_Oappend(U_16738),U_16744),U_16742)
        | U_16740 = U_16744 ) ),
    inference(miniscope,[status(thm)],[f_4107_2]) ).

cnf(f_4107_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16738),U_16740),U_16742) != hAPP(hAPP(c_List_Oappend(U_16738),U_16744),U_16742)
    | U_16740 = U_16744 ),
    inference(clausify,[status(thm)],[f_4107_3]) ).

cnf(f_4107_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16739),U_16741),U_16743) = hAPP(hAPP(c_List_Oappend(U_16739),U_16745),U_16743)
    | U_16741 != U_16745 ),
    inference(clausify,[status(thm)],[f_4107_3]) ).

fof(f_4108_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_same__append__eq]) ).

fof(f_4108_2,plain,
    ! [U_16749,U_16748,U_16747,U_16746] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16746),U_16747),U_16748) = hAPP(hAPP(c_List_Oappend(U_16746),U_16747),U_16749)
        | U_16748 != U_16749 )
      & ( U_16748 = U_16749
        | hAPP(hAPP(c_List_Oappend(U_16746),U_16747),U_16748) != hAPP(hAPP(c_List_Oappend(U_16746),U_16747),U_16749) ) ),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

fof(f_4108_3,plain,
    ( ! [U_16757,U_16755] :
        ( ! [U_16753,U_16751] : hAPP(hAPP(c_List_Oappend(U_16751),U_16753),U_16755) = hAPP(hAPP(c_List_Oappend(U_16751),U_16753),U_16757)
        | U_16755 != U_16757 )
    & ! [U_16756,U_16754] :
        ( ! [U_16752,U_16750] : hAPP(hAPP(c_List_Oappend(U_16750),U_16752),U_16754) != hAPP(hAPP(c_List_Oappend(U_16750),U_16752),U_16756)
        | U_16754 = U_16756 ) ),
    inference(miniscope,[status(thm)],[f_4108_2]) ).

cnf(f_4108_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16750),U_16752),U_16754) != hAPP(hAPP(c_List_Oappend(U_16750),U_16752),U_16756)
    | U_16754 = U_16756 ),
    inference(clausify,[status(thm)],[f_4108_3]) ).

cnf(f_4108_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16751),U_16753),U_16755) = hAPP(hAPP(c_List_Oappend(U_16751),U_16753),U_16757)
    | U_16755 != U_16757 ),
    inference(clausify,[status(thm)],[f_4108_3]) ).

fof(f_4109_1,plain,
    ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)
        | ! [B_us] :
            ( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2)
              | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) != V_zs_2 )
            & ( hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) != V_ts_2
              | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) ) ) )
      & ( ? [B_us] :
            ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2)
              & hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 )
            | ( hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) ) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).

fof(f_4109_2,plain,
    ! [U_16764,U_16763,U_16762,U_16761,U_16760] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16760),U_16761),U_16762) = hAPP(hAPP(c_List_Oappend(U_16760),U_16763),U_16764)
        | ! [U_16759] :
            ( ( U_16762 != hAPP(hAPP(c_List_Oappend(U_16760),U_16759),U_16764)
              | hAPP(hAPP(c_List_Oappend(U_16760),U_16761),U_16759) != U_16763 )
            & ( hAPP(hAPP(c_List_Oappend(U_16760),U_16759),U_16762) != U_16764
              | U_16761 != hAPP(hAPP(c_List_Oappend(U_16760),U_16763),U_16759) ) ) )
      & ( ? [U_16758] :
            ( ( U_16762 = hAPP(hAPP(c_List_Oappend(U_16760),U_16758),U_16764)
              & hAPP(hAPP(c_List_Oappend(U_16760),U_16761),U_16758) = U_16763 )
            | ( hAPP(hAPP(c_List_Oappend(U_16760),U_16758),U_16762) = U_16764
              & U_16761 = hAPP(hAPP(c_List_Oappend(U_16760),U_16763),U_16758) ) )
        | hAPP(hAPP(c_List_Oappend(U_16760),U_16761),U_16762) != hAPP(hAPP(c_List_Oappend(U_16760),U_16763),U_16764) ) ),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

fof(f_4109_3,plain,
    ( ! [U_16778,U_16776,U_16774,U_16772,U_16770] :
        ( hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16774) = hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16778)
        | ( ! [U_16768] :
              ( U_16774 != hAPP(hAPP(c_List_Oappend(U_16770),U_16768),U_16778)
              | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16768) != U_16776 )
          & ! [U_16767] :
              ( hAPP(hAPP(c_List_Oappend(U_16770),U_16767),U_16774) != U_16778
              | U_16772 != hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16767) ) ) )
    & ! [U_16777,U_16775,U_16773,U_16771,U_16769] :
        ( ? [U_16766] :
            ( U_16773 = hAPP(hAPP(c_List_Oappend(U_16769),U_16766),U_16777)
            & hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16766) = U_16775 )
        | ? [U_16765] :
            ( hAPP(hAPP(c_List_Oappend(U_16769),U_16765),U_16773) = U_16777
            & U_16771 = hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16765) )
        | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ) ),
    inference(miniscope,[status(thm)],[f_4109_2]) ).

fof(f_4109_4,plain,
    ( ! [U_16778,U_16776,U_16774,U_16772,U_16770] :
        ( hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16774) = hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16778)
        | ( ! [U_16768] :
              ( U_16774 != hAPP(hAPP(c_List_Oappend(U_16770),U_16768),U_16778)
              | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16768) != U_16776 )
          & ! [U_16767] :
              ( hAPP(hAPP(c_List_Oappend(U_16770),U_16767),U_16774) != U_16778
              | U_16772 != hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16767) ) ) )
    & ! [U_16777,U_16775,U_16773,U_16771,U_16769] :
        ( ? [U_16766] :
            ( U_16773 = hAPP(hAPP(c_List_Oappend(U_16769),U_16766),U_16777)
            & hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16766) = U_16775 )
        | ( hAPP(hAPP(c_List_Oappend(U_16769),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16773) = U_16777
          & U_16771 = hAPP(hAPP(c_List_Oappend(U_16769),U_16775),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)) )
        | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_16765,sK441(U_16777,U_16775,U_16773,U_16771,U_16769))],[f_4109_3]) ).

fof(f_4109_5,plain,
    ( ! [U_16778,U_16776,U_16774,U_16772,U_16770] :
        ( hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16774) = hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16778)
        | ( ! [U_16768] :
              ( U_16774 != hAPP(hAPP(c_List_Oappend(U_16770),U_16768),U_16778)
              | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16768) != U_16776 )
          & ! [U_16767] :
              ( hAPP(hAPP(c_List_Oappend(U_16770),U_16767),U_16774) != U_16778
              | U_16772 != hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16767) ) ) )
    & ! [U_16777,U_16775,U_16773,U_16771,U_16769] :
        ( ( U_16773 = hAPP(hAPP(c_List_Oappend(U_16769),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16777)
          & hAPP(hAPP(c_List_Oappend(U_16769),U_16771),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)) = U_16775 )
        | ( hAPP(hAPP(c_List_Oappend(U_16769),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16773) = U_16777
          & U_16771 = hAPP(hAPP(c_List_Oappend(U_16769),U_16775),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)) )
        | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_16766,sK442(U_16777,U_16775,U_16773,U_16771,U_16769))],[f_4109_4]) ).

cnf(f_4109_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16769),U_16771),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)) = U_16775
    | U_16771 = hAPP(hAPP(c_List_Oappend(U_16769),U_16775),sK441(U_16777,U_16775,U_16773,U_16771,U_16769))
    | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

cnf(f_4109_7,plain,
    ( U_16773 = hAPP(hAPP(c_List_Oappend(U_16769),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16777)
    | U_16771 = hAPP(hAPP(c_List_Oappend(U_16769),U_16775),sK441(U_16777,U_16775,U_16773,U_16771,U_16769))
    | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

cnf(f_4109_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16769),U_16771),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)) = U_16775
    | hAPP(hAPP(c_List_Oappend(U_16769),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16773) = U_16777
    | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

cnf(f_4109_9,plain,
    ( U_16773 = hAPP(hAPP(c_List_Oappend(U_16769),sK442(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16777)
    | hAPP(hAPP(c_List_Oappend(U_16769),sK441(U_16777,U_16775,U_16773,U_16771,U_16769)),U_16773) = U_16777
    | hAPP(hAPP(c_List_Oappend(U_16769),U_16771),U_16773) != hAPP(hAPP(c_List_Oappend(U_16769),U_16775),U_16777) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

cnf(f_4109_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16770),U_16767),U_16774) != U_16778
    | U_16772 != hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16767)
    | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16774) = hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16778) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

cnf(f_4109_11,plain,
    ( U_16774 != hAPP(hAPP(c_List_Oappend(U_16770),U_16768),U_16778)
    | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16768) != U_16776
    | hAPP(hAPP(c_List_Oappend(U_16770),U_16772),U_16774) = hAPP(hAPP(c_List_Oappend(U_16770),U_16776),U_16778) ),
    inference(clausify,[status(thm)],[f_4109_5]) ).

fof(f_4110_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_4110_2,plain,
    ! [U_16782,U_16781,U_16780,U_16779] : hAPP(hAPP(c_List_Oappend(U_16779),hAPP(hAPP(c_List_Oappend(U_16779),U_16780),U_16781)),U_16782) = hAPP(hAPP(c_List_Oappend(U_16779),U_16780),hAPP(hAPP(c_List_Oappend(U_16779),U_16781),U_16782)),
    inference(variable_rename,[status(thm)],[f_4110_1]) ).

cnf(f_4110_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16779),hAPP(hAPP(c_List_Oappend(U_16779),U_16780),U_16781)),U_16782) = hAPP(hAPP(c_List_Oappend(U_16779),U_16780),hAPP(hAPP(c_List_Oappend(U_16779),U_16781),U_16782)),
    inference(clausify,[status(thm)],[f_4110_2]) ).

fof(f_4111_1,plain,
    ! [V_A_2,V_ys_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv]) ).

fof(f_4111_2,plain,
    ! [U_16786,U_16785,U_16784,U_16783] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),hAPP(hAPP(c_List_Oappend(U_16783),U_16784),U_16785)),c_List_Olists(U_16783,U_16786)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),U_16785),c_List_Olists(U_16783,U_16786)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),U_16784),c_List_Olists(U_16783,U_16786))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),U_16785),c_List_Olists(U_16783,U_16786)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),U_16784),c_List_Olists(U_16783,U_16786))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16783)),hAPP(hAPP(c_List_Oappend(U_16783),U_16784),U_16785)),c_List_Olists(U_16783,U_16786))) ) ),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

fof(f_4111_3,plain,
    ( ! [U_16794,U_16792,U_16790,U_16788] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),hAPP(hAPP(c_List_Oappend(U_16788),U_16790),U_16792)),c_List_Olists(U_16788,U_16794)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),U_16792),c_List_Olists(U_16788,U_16794)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),U_16790),c_List_Olists(U_16788,U_16794))) )
    & ! [U_16793,U_16791,U_16789,U_16787] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),U_16791),c_List_Olists(U_16787,U_16793)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),U_16789),c_List_Olists(U_16787,U_16793))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),hAPP(hAPP(c_List_Oappend(U_16787),U_16789),U_16791)),c_List_Olists(U_16787,U_16793))) ) ),
    inference(miniscope,[status(thm)],[f_4111_2]) ).

cnf(f_4111_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),U_16789),c_List_Olists(U_16787,U_16793)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),hAPP(hAPP(c_List_Oappend(U_16787),U_16789),U_16791)),c_List_Olists(U_16787,U_16793))) ),
    inference(clausify,[status(thm)],[f_4111_3]) ).

cnf(f_4111_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),U_16791),c_List_Olists(U_16787,U_16793)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16787)),hAPP(hAPP(c_List_Oappend(U_16787),U_16789),U_16791)),c_List_Olists(U_16787,U_16793))) ),
    inference(clausify,[status(thm)],[f_4111_3]) ).

cnf(f_4111_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),hAPP(hAPP(c_List_Oappend(U_16788),U_16790),U_16792)),c_List_Olists(U_16788,U_16794)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),U_16792),c_List_Olists(U_16788,U_16794)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16788)),U_16790),c_List_Olists(U_16788,U_16794))) ),
    inference(clausify,[status(thm)],[f_4111_3]) ).

fof(f_4112_1,plain,
    ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop]) ).

fof(f_4112_2,plain,
    ! [U_16800,U_16799,U_16798,U_16797,U_16796,U_16795] :
      ( c_Map_Omap__upds(U_16795,U_16797,U_16799,U_16796,hAPP(hAPP(c_List_Oappend(U_16797),U_16798),U_16800)) = c_Map_Omap__upds(U_16795,U_16797,U_16799,U_16796,U_16798)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16797)),U_16798) ),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

cnf(f_4112_3,plain,
    ( c_Map_Omap__upds(U_16795,U_16797,U_16799,U_16796,hAPP(hAPP(c_List_Oappend(U_16797),U_16798),U_16800)) = c_Map_Omap__upds(U_16795,U_16797,U_16799,U_16796,U_16798)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16797)),U_16798) ),
    inference(clausify,[status(thm)],[f_4112_2]) ).

fof(f_4113_1,plain,
    ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop]) ).

fof(f_4113_2,plain,
    ! [U_16806,U_16805,U_16804,U_16803,U_16802,U_16801] :
      ( c_Map_Omap__upds(U_16801,U_16803,U_16805,hAPP(hAPP(c_List_Oappend(U_16801),U_16802),U_16806),U_16804) = c_Map_Omap__upds(U_16801,U_16803,U_16805,U_16802,U_16804)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16801)),U_16802) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16803)),U_16804) ),
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

cnf(f_4113_3,plain,
    ( c_Map_Omap__upds(U_16801,U_16803,U_16805,hAPP(hAPP(c_List_Oappend(U_16801),U_16802),U_16806),U_16804) = c_Map_Omap__upds(U_16801,U_16803,U_16805,U_16802,U_16804)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16801)),U_16802) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16803)),U_16804) ),
    inference(clausify,[status(thm)],[f_4113_2]) ).

fof(f_4114_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_4114_2,plain,
    ! [U_16809,U_16808,U_16807] :
      ( ( c_List_Obutlast(U_16808,hAPP(hAPP(c_List_Oappend(U_16808),U_16809),U_16807)) = hAPP(hAPP(c_List_Oappend(U_16808),U_16809),c_List_Obutlast(U_16808,U_16807))
        | U_16807 = c_List_Olist_ONil(U_16808) )
      & ( c_List_Obutlast(U_16808,hAPP(hAPP(c_List_Oappend(U_16808),U_16809),U_16807)) = c_List_Obutlast(U_16808,U_16809)
        | U_16807 != c_List_Olist_ONil(U_16808) ) ),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

fof(f_4114_3,plain,
    ( ! [U_16815,U_16813,U_16811] :
        ( c_List_Obutlast(U_16813,hAPP(hAPP(c_List_Oappend(U_16813),U_16815),U_16811)) = hAPP(hAPP(c_List_Oappend(U_16813),U_16815),c_List_Obutlast(U_16813,U_16811))
        | U_16811 = c_List_Olist_ONil(U_16813) )
    & ! [U_16814,U_16812,U_16810] :
        ( c_List_Obutlast(U_16812,hAPP(hAPP(c_List_Oappend(U_16812),U_16814),U_16810)) = c_List_Obutlast(U_16812,U_16814)
        | U_16810 != c_List_Olist_ONil(U_16812) ) ),
    inference(miniscope,[status(thm)],[f_4114_2]) ).

cnf(f_4114_4,plain,
    ( c_List_Obutlast(U_16812,hAPP(hAPP(c_List_Oappend(U_16812),U_16814),U_16810)) = c_List_Obutlast(U_16812,U_16814)
    | U_16810 != c_List_Olist_ONil(U_16812) ),
    inference(clausify,[status(thm)],[f_4114_3]) ).

cnf(f_4114_5,plain,
    ( c_List_Obutlast(U_16813,hAPP(hAPP(c_List_Oappend(U_16813),U_16815),U_16811)) = hAPP(hAPP(c_List_Oappend(U_16813),U_16815),c_List_Obutlast(U_16813,U_16811))
    | U_16811 = c_List_Olist_ONil(U_16813) ),
    inference(clausify,[status(thm)],[f_4114_3]) ).

fof(f_4115_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_4115_2,plain,
    ! [U_16817,U_16816] : hAPP(hAPP(c_List_Oappend(U_16816),c_List_Olist_ONil(U_16816)),U_16817) = U_16817,
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

cnf(f_4115_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16816),c_List_Olist_ONil(U_16816)),U_16817) = U_16817,
    inference(clausify,[status(thm)],[f_4115_2]) ).

fof(f_4116_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_a)
          & V_xs_2 = c_List_Olist_ONil(T_a) )
        | c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv]) ).

fof(f_4116_2,plain,
    ! [U_16820,U_16819,U_16818] :
      ( ( c_List_Olist_ONil(U_16818) = hAPP(hAPP(c_List_Oappend(U_16818),U_16819),U_16820)
        | U_16820 != c_List_Olist_ONil(U_16818)
        | U_16819 != c_List_Olist_ONil(U_16818) )
      & ( ( U_16820 = c_List_Olist_ONil(U_16818)
          & U_16819 = c_List_Olist_ONil(U_16818) )
        | c_List_Olist_ONil(U_16818) != hAPP(hAPP(c_List_Oappend(U_16818),U_16819),U_16820) ) ),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

fof(f_4116_3,plain,
    ( ! [U_16826,U_16824,U_16822] :
        ( c_List_Olist_ONil(U_16822) = hAPP(hAPP(c_List_Oappend(U_16822),U_16824),U_16826)
        | U_16826 != c_List_Olist_ONil(U_16822)
        | U_16824 != c_List_Olist_ONil(U_16822) )
    & ! [U_16825,U_16823,U_16821] :
        ( ( U_16825 = c_List_Olist_ONil(U_16821)
          & U_16823 = c_List_Olist_ONil(U_16821) )
        | c_List_Olist_ONil(U_16821) != hAPP(hAPP(c_List_Oappend(U_16821),U_16823),U_16825) ) ),
    inference(miniscope,[status(thm)],[f_4116_2]) ).

cnf(f_4116_4,plain,
    ( U_16823 = c_List_Olist_ONil(U_16821)
    | c_List_Olist_ONil(U_16821) != hAPP(hAPP(c_List_Oappend(U_16821),U_16823),U_16825) ),
    inference(clausify,[status(thm)],[f_4116_3]) ).

cnf(f_4116_5,plain,
    ( U_16825 = c_List_Olist_ONil(U_16821)
    | c_List_Olist_ONil(U_16821) != hAPP(hAPP(c_List_Oappend(U_16821),U_16823),U_16825) ),
    inference(clausify,[status(thm)],[f_4116_3]) ).

cnf(f_4116_6,plain,
    ( c_List_Olist_ONil(U_16822) = hAPP(hAPP(c_List_Oappend(U_16822),U_16824),U_16826)
    | U_16826 != c_List_Olist_ONil(U_16822)
    | U_16824 != c_List_Olist_ONil(U_16822) ),
    inference(clausify,[status(thm)],[f_4116_3]) ).

fof(f_4117_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_4117_2,plain,
    ! [U_16828,U_16827] : hAPP(hAPP(c_List_Oappend(U_16827),U_16828),c_List_Olist_ONil(U_16827)) = U_16828,
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

cnf(f_4117_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16827),U_16828),c_List_Olist_ONil(U_16827)) = U_16828,
    inference(clausify,[status(thm)],[f_4117_2]) ).

fof(f_4118_1,plain,
    ! [V_ys_2,T_a,V_xs_2] :
      ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_a) )
      & ( V_ys_2 = c_List_Olist_ONil(T_a)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv]) ).

fof(f_4118_2,plain,
    ! [U_16831,U_16830,U_16829] :
      ( ( U_16829 = hAPP(hAPP(c_List_Oappend(U_16830),U_16829),U_16831)
        | U_16831 != c_List_Olist_ONil(U_16830) )
      & ( U_16831 = c_List_Olist_ONil(U_16830)
        | U_16829 != hAPP(hAPP(c_List_Oappend(U_16830),U_16829),U_16831) ) ),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

fof(f_4118_3,plain,
    ( ! [U_16837,U_16835] :
        ( ! [U_16833] : U_16833 = hAPP(hAPP(c_List_Oappend(U_16835),U_16833),U_16837)
        | U_16837 != c_List_Olist_ONil(U_16835) )
    & ! [U_16836,U_16834] :
        ( ! [U_16832] : U_16832 != hAPP(hAPP(c_List_Oappend(U_16834),U_16832),U_16836)
        | U_16836 = c_List_Olist_ONil(U_16834) ) ),
    inference(miniscope,[status(thm)],[f_4118_2]) ).

cnf(f_4118_4,plain,
    ( U_16832 != hAPP(hAPP(c_List_Oappend(U_16834),U_16832),U_16836)
    | U_16836 = c_List_Olist_ONil(U_16834) ),
    inference(clausify,[status(thm)],[f_4118_3]) ).

cnf(f_4118_5,plain,
    ( U_16833 = hAPP(hAPP(c_List_Oappend(U_16835),U_16833),U_16837)
    | U_16837 != c_List_Olist_ONil(U_16835) ),
    inference(clausify,[status(thm)],[f_4118_3]) ).

fof(f_4119_1,plain,
    ! [V_xs_2,T_a,V_ys_2] :
      ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv2]) ).

fof(f_4119_2,plain,
    ! [U_16840,U_16839,U_16838] :
      ( ( U_16838 = hAPP(hAPP(c_List_Oappend(U_16839),U_16840),U_16838)
        | U_16840 != c_List_Olist_ONil(U_16839) )
      & ( U_16840 = c_List_Olist_ONil(U_16839)
        | U_16838 != hAPP(hAPP(c_List_Oappend(U_16839),U_16840),U_16838) ) ),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

fof(f_4119_3,plain,
    ( ! [U_16846,U_16844] :
        ( ! [U_16842] : U_16842 = hAPP(hAPP(c_List_Oappend(U_16844),U_16846),U_16842)
        | U_16846 != c_List_Olist_ONil(U_16844) )
    & ! [U_16845,U_16843] :
        ( ! [U_16841] : U_16841 != hAPP(hAPP(c_List_Oappend(U_16843),U_16845),U_16841)
        | U_16845 = c_List_Olist_ONil(U_16843) ) ),
    inference(miniscope,[status(thm)],[f_4119_2]) ).

cnf(f_4119_4,plain,
    ( U_16841 != hAPP(hAPP(c_List_Oappend(U_16843),U_16845),U_16841)
    | U_16845 = c_List_Olist_ONil(U_16843) ),
    inference(clausify,[status(thm)],[f_4119_3]) ).

cnf(f_4119_5,plain,
    ( U_16842 = hAPP(hAPP(c_List_Oappend(U_16844),U_16846),U_16842)
    | U_16846 != c_List_Olist_ONil(U_16844) ),
    inference(clausify,[status(thm)],[f_4119_3]) ).

fof(f_4120_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
        | V_ys_2 != c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_a)
          & V_xs_2 = c_List_Olist_ONil(T_a) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv]) ).

fof(f_4120_2,plain,
    ! [U_16849,U_16848,U_16847] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16847),U_16848),U_16849) = c_List_Olist_ONil(U_16847)
        | U_16849 != c_List_Olist_ONil(U_16847)
        | U_16848 != c_List_Olist_ONil(U_16847) )
      & ( ( U_16849 = c_List_Olist_ONil(U_16847)
          & U_16848 = c_List_Olist_ONil(U_16847) )
        | hAPP(hAPP(c_List_Oappend(U_16847),U_16848),U_16849) != c_List_Olist_ONil(U_16847) ) ),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

fof(f_4120_3,plain,
    ( ! [U_16855,U_16853,U_16851] :
        ( hAPP(hAPP(c_List_Oappend(U_16851),U_16853),U_16855) = c_List_Olist_ONil(U_16851)
        | U_16855 != c_List_Olist_ONil(U_16851)
        | U_16853 != c_List_Olist_ONil(U_16851) )
    & ! [U_16854,U_16852,U_16850] :
        ( ( U_16854 = c_List_Olist_ONil(U_16850)
          & U_16852 = c_List_Olist_ONil(U_16850) )
        | hAPP(hAPP(c_List_Oappend(U_16850),U_16852),U_16854) != c_List_Olist_ONil(U_16850) ) ),
    inference(miniscope,[status(thm)],[f_4120_2]) ).

cnf(f_4120_4,plain,
    ( U_16852 = c_List_Olist_ONil(U_16850)
    | hAPP(hAPP(c_List_Oappend(U_16850),U_16852),U_16854) != c_List_Olist_ONil(U_16850) ),
    inference(clausify,[status(thm)],[f_4120_3]) ).

cnf(f_4120_5,plain,
    ( U_16854 = c_List_Olist_ONil(U_16850)
    | hAPP(hAPP(c_List_Oappend(U_16850),U_16852),U_16854) != c_List_Olist_ONil(U_16850) ),
    inference(clausify,[status(thm)],[f_4120_3]) ).

cnf(f_4120_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16851),U_16853),U_16855) = c_List_Olist_ONil(U_16851)
    | U_16855 != c_List_Olist_ONil(U_16851)
    | U_16853 != c_List_Olist_ONil(U_16851) ),
    inference(clausify,[status(thm)],[f_4120_3]) ).

fof(f_4121_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
        | V_ys_2 != c_List_Olist_ONil(T_a) )
      & ( V_ys_2 = c_List_Olist_ONil(T_a)
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv]) ).

fof(f_4121_2,plain,
    ! [U_16858,U_16857,U_16856] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16856),U_16857),U_16858) = U_16857
        | U_16858 != c_List_Olist_ONil(U_16856) )
      & ( U_16858 = c_List_Olist_ONil(U_16856)
        | hAPP(hAPP(c_List_Oappend(U_16856),U_16857),U_16858) != U_16857 ) ),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

fof(f_4121_3,plain,
    ( ! [U_16864,U_16862,U_16860] :
        ( hAPP(hAPP(c_List_Oappend(U_16860),U_16862),U_16864) = U_16862
        | U_16864 != c_List_Olist_ONil(U_16860) )
    & ! [U_16863,U_16861,U_16859] :
        ( U_16863 = c_List_Olist_ONil(U_16859)
        | hAPP(hAPP(c_List_Oappend(U_16859),U_16861),U_16863) != U_16861 ) ),
    inference(miniscope,[status(thm)],[f_4121_2]) ).

cnf(f_4121_4,plain,
    ( U_16863 = c_List_Olist_ONil(U_16859)
    | hAPP(hAPP(c_List_Oappend(U_16859),U_16861),U_16863) != U_16861 ),
    inference(clausify,[status(thm)],[f_4121_3]) ).

cnf(f_4121_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16860),U_16862),U_16864) = U_16862
    | U_16864 != c_List_Olist_ONil(U_16860) ),
    inference(clausify,[status(thm)],[f_4121_3]) ).

fof(f_4122_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv2]) ).

fof(f_4122_2,plain,
    ! [U_16867,U_16866,U_16865] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16865),U_16866),U_16867) = U_16867
        | U_16866 != c_List_Olist_ONil(U_16865) )
      & ( U_16866 = c_List_Olist_ONil(U_16865)
        | hAPP(hAPP(c_List_Oappend(U_16865),U_16866),U_16867) != U_16867 ) ),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

fof(f_4122_3,plain,
    ( ! [U_16873,U_16871,U_16869] :
        ( hAPP(hAPP(c_List_Oappend(U_16869),U_16871),U_16873) = U_16873
        | U_16871 != c_List_Olist_ONil(U_16869) )
    & ! [U_16872,U_16870,U_16868] :
        ( U_16870 = c_List_Olist_ONil(U_16868)
        | hAPP(hAPP(c_List_Oappend(U_16868),U_16870),U_16872) != U_16872 ) ),
    inference(miniscope,[status(thm)],[f_4122_2]) ).

cnf(f_4122_4,plain,
    ( U_16870 = c_List_Olist_ONil(U_16868)
    | hAPP(hAPP(c_List_Oappend(U_16868),U_16870),U_16872) != U_16872 ),
    inference(clausify,[status(thm)],[f_4122_3]) ).

cnf(f_4122_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16869),U_16871),U_16873) = U_16873
    | U_16871 != c_List_Olist_ONil(U_16869) ),
    inference(clausify,[status(thm)],[f_4122_3]) ).

fof(f_4123_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_4123_2,plain,
    ! [U_16876,U_16875,U_16874] :
      ( U_16874 = hAPP(hAPP(c_List_Oappend(U_16876),c_List_Olist_ONil(U_16876)),U_16875)
      | U_16874 != U_16875 ),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

cnf(f_4123_3,plain,
    ( U_16874 = hAPP(hAPP(c_List_Oappend(U_16876),c_List_Olist_ONil(U_16876)),U_16875)
    | U_16874 != U_16875 ),
    inference(clausify,[status(thm)],[f_4123_2]) ).

fof(f_4124_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_4124_2,plain,
    ! [U_16880,U_16879,U_16878,U_16877] : hAPP(hAPP(c_List_Onth(U_16877),hAPP(hAPP(c_List_Oappend(U_16877),U_16878),hAPP(hAPP(c_List_Olist_OCons(U_16877),U_16879),U_16880))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16877)),U_16878)) = U_16879,
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

cnf(f_4124_3,plain,
    hAPP(hAPP(c_List_Onth(U_16877),hAPP(hAPP(c_List_Oappend(U_16877),U_16878),hAPP(hAPP(c_List_Olist_OCons(U_16877),U_16879),U_16880))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16877)),U_16878)) = U_16879,
    inference(clausify,[status(thm)],[f_4124_2]) ).

fof(f_4125_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_4125_2,plain,
    ! [U_16884,U_16883,U_16882,U_16881] : hAPP(hAPP(c_List_Onth(U_16881),hAPP(hAPP(c_List_Oappend(U_16881),U_16882),U_16883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16881)),U_16882)),U_16884)) = hAPP(hAPP(c_List_Onth(U_16881),U_16883),U_16884),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

cnf(f_4125_3,plain,
    hAPP(hAPP(c_List_Onth(U_16881),hAPP(hAPP(c_List_Oappend(U_16881),U_16882),U_16883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16881)),U_16882)),U_16884)) = hAPP(hAPP(c_List_Onth(U_16881),U_16883),U_16884),
    inference(clausify,[status(thm)],[f_4125_2]) ).

fof(f_4126_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_4126_2,plain,
    ! [U_16888,U_16887,U_16886,U_16885] : hAPP(hAPP(c_List_Otake(U_16885),U_16886),hAPP(hAPP(c_List_Oappend(U_16885),U_16887),U_16888)) = hAPP(hAPP(c_List_Oappend(U_16885),hAPP(hAPP(c_List_Otake(U_16885),U_16886),U_16887)),hAPP(hAPP(c_List_Otake(U_16885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16886),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16885)),U_16887))),U_16888)),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

cnf(f_4126_3,plain,
    hAPP(hAPP(c_List_Otake(U_16885),U_16886),hAPP(hAPP(c_List_Oappend(U_16885),U_16887),U_16888)) = hAPP(hAPP(c_List_Oappend(U_16885),hAPP(hAPP(c_List_Otake(U_16885),U_16886),U_16887)),hAPP(hAPP(c_List_Otake(U_16885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16886),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16885)),U_16887))),U_16888)),
    inference(clausify,[status(thm)],[f_4126_2]) ).

fof(f_4127_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_4127_2,plain,
    ! [U_16893,U_16892,U_16891,U_16890,U_16889] :
      ( hAPP(hAPP(c_List_Olist__update(U_16890,hAPP(hAPP(c_List_Oappend(U_16890),U_16891),U_16892)),U_16889),U_16893) = hAPP(hAPP(c_List_Oappend(U_16890),hAPP(hAPP(c_List_Olist__update(U_16890,U_16891),U_16889),U_16893)),U_16892)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16889),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16890)),U_16891))) ),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

cnf(f_4127_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16890,hAPP(hAPP(c_List_Oappend(U_16890),U_16891),U_16892)),U_16889),U_16893) = hAPP(hAPP(c_List_Oappend(U_16890),hAPP(hAPP(c_List_Olist__update(U_16890,U_16891),U_16889),U_16893)),U_16892)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16889),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16890)),U_16891))) ),
    inference(clausify,[status(thm)],[f_4127_2]) ).

fof(f_4128_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_4128_2,plain,
    ! [U_16898,U_16897,U_16896,U_16895,U_16894] : hAPP(hAPP(c_List_Olist__update(U_16894,hAPP(hAPP(c_List_Oappend(U_16894),U_16895),hAPP(hAPP(c_List_Olist_OCons(U_16894),U_16896),U_16897))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16894)),U_16895)),U_16898) = hAPP(hAPP(c_List_Oappend(U_16894),U_16895),hAPP(hAPP(c_List_Olist_OCons(U_16894),U_16898),U_16897)),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

cnf(f_4128_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16894,hAPP(hAPP(c_List_Oappend(U_16894),U_16895),hAPP(hAPP(c_List_Olist_OCons(U_16894),U_16896),U_16897))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16894)),U_16895)),U_16898) = hAPP(hAPP(c_List_Oappend(U_16894),U_16895),hAPP(hAPP(c_List_Olist_OCons(U_16894),U_16898),U_16897)),
    inference(clausify,[status(thm)],[f_4128_2]) ).

fof(f_4129_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_a] :
      ( ( c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__append]) ).

fof(f_4129_2,plain,
    ! [U_16902,U_16901,U_16900,U_16899] :
      ( ( c_List_Oremove1(U_16899,U_16900,hAPP(hAPP(c_List_Oappend(U_16899),U_16901),U_16902)) = hAPP(hAPP(c_List_Oappend(U_16899),U_16901),c_List_Oremove1(U_16899,U_16900,U_16902))
        | hBOOL(hAPP(hAPP(c_member(U_16899),U_16900),hAPP(c_List_Oset(U_16899),U_16901))) )
      & ( c_List_Oremove1(U_16899,U_16900,hAPP(hAPP(c_List_Oappend(U_16899),U_16901),U_16902)) = hAPP(hAPP(c_List_Oappend(U_16899),c_List_Oremove1(U_16899,U_16900,U_16901)),U_16902)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16899),U_16900),hAPP(c_List_Oset(U_16899),U_16901))) ) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

fof(f_4129_3,plain,
    ( ! [U_16910,U_16908,U_16906,U_16904] :
        ( c_List_Oremove1(U_16904,U_16906,hAPP(hAPP(c_List_Oappend(U_16904),U_16908),U_16910)) = hAPP(hAPP(c_List_Oappend(U_16904),U_16908),c_List_Oremove1(U_16904,U_16906,U_16910))
        | hBOOL(hAPP(hAPP(c_member(U_16904),U_16906),hAPP(c_List_Oset(U_16904),U_16908))) )
    & ! [U_16909,U_16907,U_16905,U_16903] :
        ( c_List_Oremove1(U_16903,U_16905,hAPP(hAPP(c_List_Oappend(U_16903),U_16907),U_16909)) = hAPP(hAPP(c_List_Oappend(U_16903),c_List_Oremove1(U_16903,U_16905,U_16907)),U_16909)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16903),U_16905),hAPP(c_List_Oset(U_16903),U_16907))) ) ),
    inference(miniscope,[status(thm)],[f_4129_2]) ).

cnf(f_4129_4,plain,
    ( c_List_Oremove1(U_16903,U_16905,hAPP(hAPP(c_List_Oappend(U_16903),U_16907),U_16909)) = hAPP(hAPP(c_List_Oappend(U_16903),c_List_Oremove1(U_16903,U_16905,U_16907)),U_16909)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16903),U_16905),hAPP(c_List_Oset(U_16903),U_16907))) ),
    inference(clausify,[status(thm)],[f_4129_3]) ).

cnf(f_4129_5,plain,
    ( c_List_Oremove1(U_16904,U_16906,hAPP(hAPP(c_List_Oappend(U_16904),U_16908),U_16910)) = hAPP(hAPP(c_List_Oappend(U_16904),U_16908),c_List_Oremove1(U_16904,U_16906,U_16910))
    | hBOOL(hAPP(hAPP(c_member(U_16904),U_16906),hAPP(c_List_Oset(U_16904),U_16908))) ),
    inference(clausify,[status(thm)],[f_4129_3]) ).

fof(f_4130_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2))))
        & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI]) ).

fof(f_4130_2,plain,
    ! [U_16914,U_16913,U_16912,U_16911] :
      ( hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,hAPP(hAPP(c_List_Oappend(U_16911),U_16913),U_16914)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,U_16914))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,U_16913)))) ) ),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

cnf(f_4130_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,U_16913))))
    | hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,hAPP(hAPP(c_List_Oappend(U_16911),U_16913),U_16914))))) ),
    inference(clausify,[status(thm)],[f_4130_2]) ).

cnf(f_4130_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,U_16914))))
    | hBOOL(hAPP(hAPP(c_member(U_16911),U_16912),hAPP(c_List_Oset(U_16911),c_List_Obutlast(U_16911,hAPP(hAPP(c_List_Oappend(U_16911),U_16913),U_16914))))) ),
    inference(clausify,[status(thm)],[f_4130_2]) ).

fof(f_4131_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_4131_2,plain,
    ! [U_16917,U_16916,U_16915] : c_List_Obutlast(U_16915,hAPP(hAPP(c_List_Oappend(U_16915),U_16916),hAPP(hAPP(c_List_Olist_OCons(U_16915),U_16917),c_List_Olist_ONil(U_16915)))) = U_16916,
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

cnf(f_4131_3,plain,
    c_List_Obutlast(U_16915,hAPP(hAPP(c_List_Oappend(U_16915),U_16916),hAPP(hAPP(c_List_Olist_OCons(U_16915),U_16917),c_List_Olist_ONil(U_16915)))) = U_16916,
    inference(clausify,[status(thm)],[f_4131_2]) ).

fof(f_4132_1,plain,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,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_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__listrel1I]) ).

fof(f_4132_2,plain,
    ! [U_16923,U_16922,U_16921,U_16920,U_16919,U_16918] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),hAPP(hAPP(c_List_Oappend(U_16918),U_16919),U_16922)),hAPP(hAPP(c_List_Oappend(U_16918),U_16920),U_16923))),c_List_Olistrel1(U_16918,U_16921)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),U_16922),U_16923)),c_List_Olistrel1(U_16918,U_16921)))
          | U_16919 != U_16920 )
        & ( U_16922 != U_16923
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),U_16919),U_16920)),c_List_Olistrel1(U_16918,U_16921))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4132_1]) ).

cnf(f_4132_3,plain,
    ( U_16922 != U_16923
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),U_16919),U_16920)),c_List_Olistrel1(U_16918,U_16921)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),hAPP(hAPP(c_List_Oappend(U_16918),U_16919),U_16922)),hAPP(hAPP(c_List_Oappend(U_16918),U_16920),U_16923))),c_List_Olistrel1(U_16918,U_16921))) ),
    inference(clausify,[status(thm)],[f_4132_2]) ).

cnf(f_4132_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),U_16922),U_16923)),c_List_Olistrel1(U_16918,U_16921)))
    | U_16919 != U_16920
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16918),tc_List_Olist(U_16918))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16918),tc_List_Olist(U_16918)),hAPP(hAPP(c_List_Oappend(U_16918),U_16919),U_16922)),hAPP(hAPP(c_List_Oappend(U_16918),U_16920),U_16923))),c_List_Olistrel1(U_16918,U_16921))) ),
    inference(clausify,[status(thm)],[f_4132_2]) ).

fof(f_4133_1,plain,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI]) ).

fof(f_4133_2,plain,
    ! [U_16928,U_16927,U_16926,U_16925,U_16924] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16924),tc_List_Olist(U_16924))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16924),tc_List_Olist(U_16924)),hAPP(hAPP(c_List_Oappend(U_16924),U_16928),U_16925)),hAPP(hAPP(c_List_Oappend(U_16924),U_16928),U_16926))),c_List_Olexord(U_16924,U_16927)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16924),tc_List_Olist(U_16924))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16924),tc_List_Olist(U_16924)),U_16925),U_16926)),c_List_Olexord(U_16924,U_16927))) ),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

cnf(f_4133_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16924),tc_List_Olist(U_16924))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16924),tc_List_Olist(U_16924)),hAPP(hAPP(c_List_Oappend(U_16924),U_16928),U_16925)),hAPP(hAPP(c_List_Oappend(U_16924),U_16928),U_16926))),c_List_Olexord(U_16924,U_16927)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16924),tc_List_Olist(U_16924))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16924),tc_List_Olist(U_16924)),U_16925),U_16926)),c_List_Olexord(U_16924,U_16927))) ),
    inference(clausify,[status(thm)],[f_4133_2]) ).

fof(f_4134_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
          & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__append]) ).

fof(f_4134_2,plain,
    ! [U_16931,U_16930,U_16929] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16929),hAPP(hAPP(c_List_Oappend(U_16929),U_16930),U_16931)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16929,tc_HOL_Obool)),hAPP(c_List_Oset(U_16929),U_16930)),hAPP(c_List_Oset(U_16929),U_16931)) != c_Orderings_Obot__class_Obot(tc_fun(U_16929,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16929),U_16931))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16929),U_16930)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16929,tc_HOL_Obool)),hAPP(c_List_Oset(U_16929),U_16930)),hAPP(c_List_Oset(U_16929),U_16931)) = c_Orderings_Obot__class_Obot(tc_fun(U_16929,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16929),U_16931))
          & hBOOL(hAPP(c_List_Odistinct(U_16929),U_16930)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16929),hAPP(hAPP(c_List_Oappend(U_16929),U_16930),U_16931))) ) ),
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

fof(f_4134_3,plain,
    ( ! [U_16937,U_16935,U_16933] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16933),hAPP(hAPP(c_List_Oappend(U_16933),U_16935),U_16937)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16933,tc_HOL_Obool)),hAPP(c_List_Oset(U_16933),U_16935)),hAPP(c_List_Oset(U_16933),U_16937)) != c_Orderings_Obot__class_Obot(tc_fun(U_16933,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16933),U_16937))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16933),U_16935)) )
    & ! [U_16936,U_16934,U_16932] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16932,tc_HOL_Obool)),hAPP(c_List_Oset(U_16932),U_16934)),hAPP(c_List_Oset(U_16932),U_16936)) = c_Orderings_Obot__class_Obot(tc_fun(U_16932,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16932),U_16936))
          & hBOOL(hAPP(c_List_Odistinct(U_16932),U_16934)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16932),hAPP(hAPP(c_List_Oappend(U_16932),U_16934),U_16936))) ) ),
    inference(miniscope,[status(thm)],[f_4134_2]) ).

cnf(f_4134_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16932),U_16934))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16932),hAPP(hAPP(c_List_Oappend(U_16932),U_16934),U_16936))) ),
    inference(clausify,[status(thm)],[f_4134_3]) ).

cnf(f_4134_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16932),U_16936))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16932),hAPP(hAPP(c_List_Oappend(U_16932),U_16934),U_16936))) ),
    inference(clausify,[status(thm)],[f_4134_3]) ).

cnf(f_4134_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16932,tc_HOL_Obool)),hAPP(c_List_Oset(U_16932),U_16934)),hAPP(c_List_Oset(U_16932),U_16936)) = c_Orderings_Obot__class_Obot(tc_fun(U_16932,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16932),hAPP(hAPP(c_List_Oappend(U_16932),U_16934),U_16936))) ),
    inference(clausify,[status(thm)],[f_4134_3]) ).

cnf(f_4134_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16933),hAPP(hAPP(c_List_Oappend(U_16933),U_16935),U_16937)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16933,tc_HOL_Obool)),hAPP(c_List_Oset(U_16933),U_16935)),hAPP(c_List_Oset(U_16933),U_16937)) != c_Orderings_Obot__class_Obot(tc_fun(U_16933,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16933),U_16937))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16933),U_16935)) ),
    inference(clausify,[status(thm)],[f_4134_3]) ).

fof(f_4135_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_4135_2,plain,
    ! [U_16941,U_16940,U_16939,U_16938] :
      ( ( hAPP(hAPP(c_List_Onth(U_16939),hAPP(hAPP(c_List_Oappend(U_16939),U_16940),U_16941)),U_16938) = hAPP(hAPP(c_List_Onth(U_16939),U_16941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16939)),U_16940)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16939)),U_16940))) )
      & ( hAPP(hAPP(c_List_Onth(U_16939),hAPP(hAPP(c_List_Oappend(U_16939),U_16940),U_16941)),U_16938) = hAPP(hAPP(c_List_Onth(U_16939),U_16940),U_16938)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16938),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16939)),U_16940))) ) ),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

fof(f_4135_3,plain,
    ( ! [U_16949,U_16947,U_16945,U_16943] :
        ( hAPP(hAPP(c_List_Onth(U_16945),hAPP(hAPP(c_List_Oappend(U_16945),U_16947),U_16949)),U_16943) = hAPP(hAPP(c_List_Onth(U_16945),U_16949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16943),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16945)),U_16947)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16943),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16945)),U_16947))) )
    & ! [U_16948,U_16946,U_16944,U_16942] :
        ( hAPP(hAPP(c_List_Onth(U_16944),hAPP(hAPP(c_List_Oappend(U_16944),U_16946),U_16948)),U_16942) = hAPP(hAPP(c_List_Onth(U_16944),U_16946),U_16942)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16942),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16944)),U_16946))) ) ),
    inference(miniscope,[status(thm)],[f_4135_2]) ).

cnf(f_4135_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_16944),hAPP(hAPP(c_List_Oappend(U_16944),U_16946),U_16948)),U_16942) = hAPP(hAPP(c_List_Onth(U_16944),U_16946),U_16942)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16942),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16944)),U_16946))) ),
    inference(clausify,[status(thm)],[f_4135_3]) ).

cnf(f_4135_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_16945),hAPP(hAPP(c_List_Oappend(U_16945),U_16947),U_16949)),U_16943) = hAPP(hAPP(c_List_Onth(U_16945),U_16949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16943),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16945)),U_16947)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16943),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16945)),U_16947))) ),
    inference(clausify,[status(thm)],[f_4135_3]) ).

fof(f_4136_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_4136_2,plain,
    ! [U_16954,U_16953,U_16952,U_16951,U_16950] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_16951,hAPP(hAPP(c_List_Oappend(U_16951),U_16952),U_16953)),U_16950),U_16954) = hAPP(hAPP(c_List_Oappend(U_16951),U_16952),hAPP(hAPP(c_List_Olist__update(U_16951,U_16953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16950),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16951)),U_16952))),U_16954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16950),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16951)),U_16952))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_16951,hAPP(hAPP(c_List_Oappend(U_16951),U_16952),U_16953)),U_16950),U_16954) = hAPP(hAPP(c_List_Oappend(U_16951),hAPP(hAPP(c_List_Olist__update(U_16951,U_16952),U_16950),U_16954)),U_16953)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16950),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16951)),U_16952))) ) ),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

fof(f_4136_3,plain,
    ( ! [U_16964,U_16962,U_16960,U_16958,U_16956] :
        ( hAPP(hAPP(c_List_Olist__update(U_16958,hAPP(hAPP(c_List_Oappend(U_16958),U_16960),U_16962)),U_16956),U_16964) = hAPP(hAPP(c_List_Oappend(U_16958),U_16960),hAPP(hAPP(c_List_Olist__update(U_16958,U_16962),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16956),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16958)),U_16960))),U_16964))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16956),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16958)),U_16960))) )
    & ! [U_16963,U_16961,U_16959,U_16957,U_16955] :
        ( hAPP(hAPP(c_List_Olist__update(U_16957,hAPP(hAPP(c_List_Oappend(U_16957),U_16959),U_16961)),U_16955),U_16963) = hAPP(hAPP(c_List_Oappend(U_16957),hAPP(hAPP(c_List_Olist__update(U_16957,U_16959),U_16955),U_16963)),U_16961)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16955),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16957)),U_16959))) ) ),
    inference(miniscope,[status(thm)],[f_4136_2]) ).

cnf(f_4136_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16957,hAPP(hAPP(c_List_Oappend(U_16957),U_16959),U_16961)),U_16955),U_16963) = hAPP(hAPP(c_List_Oappend(U_16957),hAPP(hAPP(c_List_Olist__update(U_16957,U_16959),U_16955),U_16963)),U_16961)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16955),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16957)),U_16959))) ),
    inference(clausify,[status(thm)],[f_4136_3]) ).

cnf(f_4136_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16958,hAPP(hAPP(c_List_Oappend(U_16958),U_16960),U_16962)),U_16956),U_16964) = hAPP(hAPP(c_List_Oappend(U_16958),U_16960),hAPP(hAPP(c_List_Olist__update(U_16958,U_16962),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16956),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16958)),U_16960))),U_16964))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16956),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16958)),U_16960))) ),
    inference(clausify,[status(thm)],[f_4136_3]) ).

fof(f_4137_1,plain,
    ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,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_a)),V_l_2)))),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__append]) ).

fof(f_4137_2,plain,
    ! [U_16968,U_16967,U_16966,U_16965] : c_List_Osublist(U_16965,hAPP(hAPP(c_List_Oappend(U_16965),U_16966),U_16967),U_16968) = hAPP(hAPP(c_List_Oappend(U_16965),c_List_Osublist(U_16965,U_16966,U_16968)),c_List_Osublist(U_16965,U_16967,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_16965)),U_16966)))),U_16968)))),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

cnf(f_4137_3,plain,
    c_List_Osublist(U_16965,hAPP(hAPP(c_List_Oappend(U_16965),U_16966),U_16967),U_16968) = hAPP(hAPP(c_List_Oappend(U_16965),c_List_Osublist(U_16965,U_16966,U_16968)),c_List_Osublist(U_16965,U_16967,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_16965)),U_16966)))),U_16968)))),
    inference(clausify,[status(thm)],[f_4137_2]) ).

fof(f_4138_1,plain,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
      | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2))
      | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I]) ).

fof(f_4138_2,plain,
    ! [U_16976,U_16975,U_16974,U_16973,U_16972,U_16971,U_16970,U_16969] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16969),tc_List_Olist(U_16969))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16969),tc_List_Olist(U_16969)),U_16973),U_16976)),c_List_Olistrel1(U_16969,U_16972)))
      | U_16976 != hAPP(hAPP(c_List_Oappend(U_16969),U_16974),hAPP(hAPP(c_List_Olist_OCons(U_16969),U_16971),U_16975))
      | U_16973 != hAPP(hAPP(c_List_Oappend(U_16969),U_16974),hAPP(hAPP(c_List_Olist_OCons(U_16969),U_16970),U_16975))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16969,U_16969)),hAPP(hAPP(c_Product__Type_OPair(U_16969,U_16969),U_16970),U_16971)),U_16972)) ),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

cnf(f_4138_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16969),tc_List_Olist(U_16969))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16969),tc_List_Olist(U_16969)),U_16973),U_16976)),c_List_Olistrel1(U_16969,U_16972)))
    | U_16976 != hAPP(hAPP(c_List_Oappend(U_16969),U_16974),hAPP(hAPP(c_List_Olist_OCons(U_16969),U_16971),U_16975))
    | U_16973 != hAPP(hAPP(c_List_Oappend(U_16969),U_16974),hAPP(hAPP(c_List_Olist_OCons(U_16969),U_16970),U_16975))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16969,U_16969)),hAPP(hAPP(c_Product__Type_OPair(U_16969,U_16969),U_16970),U_16971)),U_16972)) ),
    inference(clausify,[status(thm)],[f_4138_2]) ).

fof(f_4139_1,plain,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI]) ).

fof(f_4139_2,plain,
    ! [U_16983,U_16982,U_16981,U_16980,U_16979,U_16978,U_16977] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16977),tc_List_Olist(U_16977))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16977),tc_List_Olist(U_16977)),hAPP(hAPP(c_List_Oappend(U_16977),U_16981),hAPP(hAPP(c_List_Olist_OCons(U_16977),U_16978),U_16982))),hAPP(hAPP(c_List_Oappend(U_16977),U_16981),hAPP(hAPP(c_List_Olist_OCons(U_16977),U_16979),U_16983)))),c_List_Olexord(U_16977,U_16980)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16978),U_16979)),U_16980)) ),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

cnf(f_4139_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16977),tc_List_Olist(U_16977))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16977),tc_List_Olist(U_16977)),hAPP(hAPP(c_List_Oappend(U_16977),U_16981),hAPP(hAPP(c_List_Olist_OCons(U_16977),U_16978),U_16982))),hAPP(hAPP(c_List_Oappend(U_16977),U_16981),hAPP(hAPP(c_List_Olist_OCons(U_16977),U_16979),U_16983)))),c_List_Olexord(U_16977,U_16980)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16978),U_16979)),U_16980)) ),
    inference(clausify,[status(thm)],[f_4139_2]) ).

fof(f_4140_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_4140_2,plain,
    ! [U_16986,U_16985,U_16984] :
      ( hAPP(hAPP(c_List_Otake(U_16985),hAPP(c_Nat_OSuc,U_16984)),U_16986) = hAPP(hAPP(c_List_Oappend(U_16985),hAPP(hAPP(c_List_Otake(U_16985),U_16984),U_16986)),hAPP(hAPP(c_List_Olist_OCons(U_16985),hAPP(hAPP(c_List_Onth(U_16985),U_16986),U_16984)),c_List_Olist_ONil(U_16985)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16984),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),U_16986))) ),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

cnf(f_4140_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16985),hAPP(c_Nat_OSuc,U_16984)),U_16986) = hAPP(hAPP(c_List_Oappend(U_16985),hAPP(hAPP(c_List_Otake(U_16985),U_16984),U_16986)),hAPP(hAPP(c_List_Olist_OCons(U_16985),hAPP(hAPP(c_List_Onth(U_16985),U_16986),U_16984)),c_List_Olist_ONil(U_16985)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16984),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),U_16986))) ),
    inference(clausify,[status(thm)],[f_4140_2]) ).

fof(f_4141_1,plain,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff]) ).

fof(f_4141_2,plain,
    ! [U_16992,U_16991,U_16990,U_16989,U_16988,U_16987] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16987),tc_List_Olist(U_16987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16987),tc_List_Olist(U_16987)),hAPP(hAPP(c_List_Oappend(U_16987),U_16988),hAPP(hAPP(c_List_Olist_OCons(U_16987),U_16989),c_List_Olist_ONil(U_16987)))),hAPP(hAPP(c_List_Oappend(U_16987),U_16990),hAPP(hAPP(c_List_Olist_OCons(U_16987),U_16991),c_List_Olist_ONil(U_16987))))),c_List_Olistrel1(U_16987,U_16992)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16987,U_16987)),hAPP(hAPP(c_Product__Type_OPair(U_16987,U_16987),U_16989),U_16991)),U_16992))
            | U_16988 != U_16990 )
          & ( U_16989 != U_16991
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16987),tc_List_Olist(U_16987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16987),tc_List_Olist(U_16987)),U_16988),U_16990)),c_List_Olistrel1(U_16987,U_16992))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16987,U_16987)),hAPP(hAPP(c_Product__Type_OPair(U_16987,U_16987),U_16989),U_16991)),U_16992))
          & U_16988 = U_16990 )
        | ( U_16989 = U_16991
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16987),tc_List_Olist(U_16987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16987),tc_List_Olist(U_16987)),U_16988),U_16990)),c_List_Olistrel1(U_16987,U_16992))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16987),tc_List_Olist(U_16987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16987),tc_List_Olist(U_16987)),hAPP(hAPP(c_List_Oappend(U_16987),U_16988),hAPP(hAPP(c_List_Olist_OCons(U_16987),U_16989),c_List_Olist_ONil(U_16987)))),hAPP(hAPP(c_List_Oappend(U_16987),U_16990),hAPP(hAPP(c_List_Olist_OCons(U_16987),U_16991),c_List_Olist_ONil(U_16987))))),c_List_Olistrel1(U_16987,U_16992))) ) ),
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

fof(f_4141_3,plain,
    ( ! [U_17004,U_17002,U_17000,U_16998,U_16996,U_16994] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16994),tc_List_Olist(U_16994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16994),tc_List_Olist(U_16994)),hAPP(hAPP(c_List_Oappend(U_16994),U_16996),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_16998),c_List_Olist_ONil(U_16994)))),hAPP(hAPP(c_List_Oappend(U_16994),U_17000),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_17002),c_List_Olist_ONil(U_16994))))),c_List_Olistrel1(U_16994,U_17004)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16994,U_16994)),hAPP(hAPP(c_Product__Type_OPair(U_16994,U_16994),U_16998),U_17002)),U_17004))
            | U_16996 != U_17000 )
          & ( U_16998 != U_17002
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16994),tc_List_Olist(U_16994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16994),tc_List_Olist(U_16994)),U_16996),U_17000)),c_List_Olistrel1(U_16994,U_17004))) ) ) )
    & ! [U_17003,U_17001,U_16999,U_16997,U_16995,U_16993] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16993,U_16993)),hAPP(hAPP(c_Product__Type_OPair(U_16993,U_16993),U_16997),U_17001)),U_17003))
          & U_16995 = U_16999 )
        | ( U_16997 = U_17001
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),U_16995),U_16999)),c_List_Olistrel1(U_16993,U_17003))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),hAPP(hAPP(c_List_Oappend(U_16993),U_16995),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_16997),c_List_Olist_ONil(U_16993)))),hAPP(hAPP(c_List_Oappend(U_16993),U_16999),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_17001),c_List_Olist_ONil(U_16993))))),c_List_Olistrel1(U_16993,U_17003))) ) ),
    inference(miniscope,[status(thm)],[f_4141_2]) ).

cnf(f_4141_4,plain,
    ( U_16995 = U_16999
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),U_16995),U_16999)),c_List_Olistrel1(U_16993,U_17003)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),hAPP(hAPP(c_List_Oappend(U_16993),U_16995),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_16997),c_List_Olist_ONil(U_16993)))),hAPP(hAPP(c_List_Oappend(U_16993),U_16999),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_17001),c_List_Olist_ONil(U_16993))))),c_List_Olistrel1(U_16993,U_17003))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

cnf(f_4141_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16993,U_16993)),hAPP(hAPP(c_Product__Type_OPair(U_16993,U_16993),U_16997),U_17001)),U_17003))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),U_16995),U_16999)),c_List_Olistrel1(U_16993,U_17003)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),hAPP(hAPP(c_List_Oappend(U_16993),U_16995),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_16997),c_List_Olist_ONil(U_16993)))),hAPP(hAPP(c_List_Oappend(U_16993),U_16999),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_17001),c_List_Olist_ONil(U_16993))))),c_List_Olistrel1(U_16993,U_17003))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

cnf(f_4141_6,plain,
    ( U_16995 = U_16999
    | U_16997 = U_17001
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),hAPP(hAPP(c_List_Oappend(U_16993),U_16995),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_16997),c_List_Olist_ONil(U_16993)))),hAPP(hAPP(c_List_Oappend(U_16993),U_16999),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_17001),c_List_Olist_ONil(U_16993))))),c_List_Olistrel1(U_16993,U_17003))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

cnf(f_4141_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16993,U_16993)),hAPP(hAPP(c_Product__Type_OPair(U_16993,U_16993),U_16997),U_17001)),U_17003))
    | U_16997 = U_17001
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16993),tc_List_Olist(U_16993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16993),tc_List_Olist(U_16993)),hAPP(hAPP(c_List_Oappend(U_16993),U_16995),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_16997),c_List_Olist_ONil(U_16993)))),hAPP(hAPP(c_List_Oappend(U_16993),U_16999),hAPP(hAPP(c_List_Olist_OCons(U_16993),U_17001),c_List_Olist_ONil(U_16993))))),c_List_Olistrel1(U_16993,U_17003))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

cnf(f_4141_8,plain,
    ( U_16998 != U_17002
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16994),tc_List_Olist(U_16994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16994),tc_List_Olist(U_16994)),U_16996),U_17000)),c_List_Olistrel1(U_16994,U_17004)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16994),tc_List_Olist(U_16994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16994),tc_List_Olist(U_16994)),hAPP(hAPP(c_List_Oappend(U_16994),U_16996),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_16998),c_List_Olist_ONil(U_16994)))),hAPP(hAPP(c_List_Oappend(U_16994),U_17000),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_17002),c_List_Olist_ONil(U_16994))))),c_List_Olistrel1(U_16994,U_17004))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

cnf(f_4141_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16994,U_16994)),hAPP(hAPP(c_Product__Type_OPair(U_16994,U_16994),U_16998),U_17002)),U_17004))
    | U_16996 != U_17000
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16994),tc_List_Olist(U_16994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16994),tc_List_Olist(U_16994)),hAPP(hAPP(c_List_Oappend(U_16994),U_16996),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_16998),c_List_Olist_ONil(U_16994)))),hAPP(hAPP(c_List_Oappend(U_16994),U_17000),hAPP(hAPP(c_List_Olist_OCons(U_16994),U_17002),c_List_Olist_ONil(U_16994))))),c_List_Olistrel1(U_16994,U_17004))) ),
    inference(clausify,[status(thm)],[f_4141_3]) ).

fof(f_4142_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_a] :
      ( ? [B_x,B_y] :
          ( ? [B_us,B_vs] :
              ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs))
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1E]) ).

fof(f_4142_2,plain,
    ! [U_17012,U_17011,U_17010,U_17009] :
      ( ? [U_17008,U_17007] :
          ( ? [U_17006,U_17005] :
              ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),U_17007),U_17005))
              & U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),U_17008),U_17005)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),U_17008),U_17007)),U_17012)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

fof(f_4142_3,plain,
    ! [U_17012,U_17011,U_17010,U_17009] :
      ( ? [U_17007] :
          ( ? [U_17006,U_17005] :
              ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),U_17007),U_17005))
              & U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),U_17005)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),U_17007)),U_17012)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_17008,sK443(U_17012,U_17011,U_17010,U_17009))],[f_4142_2]) ).

fof(f_4142_4,plain,
    ! [U_17012,U_17011,U_17010,U_17009] :
      ( ( ? [U_17006,U_17005] :
            ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK444(U_17012,U_17011,U_17010,U_17009)),U_17005))
            & U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),U_17006),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),U_17005)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK444(U_17012,U_17011,U_17010,U_17009))),U_17012)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_17007,sK444(U_17012,U_17011,U_17010,U_17009))],[f_4142_3]) ).

fof(f_4142_5,plain,
    ! [U_17012,U_17011,U_17010,U_17009] :
      ( ( ? [U_17005] :
            ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK444(U_17012,U_17011,U_17010,U_17009)),U_17005))
            & U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),U_17005)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK444(U_17012,U_17011,U_17010,U_17009))),U_17012)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_17006,sK445(U_17012,U_17011,U_17010,U_17009))],[f_4142_4]) ).

fof(f_4142_6,plain,
    ! [U_17012,U_17011,U_17010,U_17009] :
      ( ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK444(U_17012,U_17011,U_17010,U_17009)),sK446(U_17012,U_17011,U_17010,U_17009)))
        & U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK446(U_17012,U_17011,U_17010,U_17009)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK444(U_17012,U_17011,U_17010,U_17009))),U_17012)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_17005,sK446(U_17012,U_17011,U_17010,U_17009))],[f_4142_5]) ).

cnf(f_4142_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17009,U_17009)),hAPP(hAPP(c_Product__Type_OPair(U_17009,U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK444(U_17012,U_17011,U_17010,U_17009))),U_17012))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(clausify,[status(thm)],[f_4142_6]) ).

cnf(f_4142_8,plain,
    ( U_17010 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK443(U_17012,U_17011,U_17010,U_17009)),sK446(U_17012,U_17011,U_17010,U_17009)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(clausify,[status(thm)],[f_4142_6]) ).

cnf(f_4142_9,plain,
    ( U_17011 = hAPP(hAPP(c_List_Oappend(U_17009),sK445(U_17012,U_17011,U_17010,U_17009)),hAPP(hAPP(c_List_Olist_OCons(U_17009),sK444(U_17012,U_17011,U_17010,U_17009)),sK446(U_17012,U_17011,U_17010,U_17009)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17009),tc_List_Olist(U_17009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17009),tc_List_Olist(U_17009)),U_17010),U_17011)),c_List_Olistrel1(U_17009,U_17012))) ),
    inference(clausify,[status(thm)],[f_4142_6]) ).

fof(f_4143_1,plain,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2)))
      | ? [B_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftD]) ).

fof(f_4143_2,plain,
    ! [U_17018,U_17017,U_17016,U_17015,U_17014] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),U_17016),U_17017)),c_List_Olexord(U_17014,U_17018)))
      | ? [U_17013] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_17014,U_17014)),hAPP(hAPP(c_Product__Type_OPair(U_17014,U_17014),U_17013),U_17013)),U_17018))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17016)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17017))),c_List_Olexord(U_17014,U_17018))) ),
    inference(variable_rename,[status(thm)],[f_4143_1]) ).

fof(f_4143_3,plain,
    ! [U_17018,U_17017,U_17016,U_17015,U_17014] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),U_17016),U_17017)),c_List_Olexord(U_17014,U_17018)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_17014,U_17014)),hAPP(hAPP(c_Product__Type_OPair(U_17014,U_17014),sK447(U_17018,U_17017,U_17016,U_17015,U_17014)),sK447(U_17018,U_17017,U_17016,U_17015,U_17014))),U_17018))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17016)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17017))),c_List_Olexord(U_17014,U_17018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_17013,sK447(U_17018,U_17017,U_17016,U_17015,U_17014))],[f_4143_2]) ).

cnf(f_4143_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),U_17016),U_17017)),c_List_Olexord(U_17014,U_17018)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_17014,U_17014)),hAPP(hAPP(c_Product__Type_OPair(U_17014,U_17014),sK447(U_17018,U_17017,U_17016,U_17015,U_17014)),sK447(U_17018,U_17017,U_17016,U_17015,U_17014))),U_17018))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17014),tc_List_Olist(U_17014))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17014),tc_List_Olist(U_17014)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17016)),hAPP(hAPP(c_List_Oappend(U_17014),U_17015),U_17017))),c_List_Olexord(U_17014,U_17018))) ),
    inference(clausify,[status(thm)],[f_4143_3]) ).

fof(f_4144_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rotate1__def]) ).

fof(f_4144_2,plain,
    ! [U_17020,U_17019] : hAPP(c_List_Orotate1(U_17019),U_17020) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_17019),U_17019,c_List_Olist_ONil(U_17019),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17019),tc_fun(tc_List_Olist(U_17019),tc_List_Olist(U_17019)),U_17019),hAPP(c_COMBC(tc_List_Olist(U_17019),tc_List_Olist(U_17019),tc_List_Olist(U_17019)),c_List_Oappend(U_17019))),hAPP(hAPP(c_COMBC(U_17019,tc_List_Olist(U_17019),tc_List_Olist(U_17019)),c_List_Olist_OCons(U_17019)),c_List_Olist_ONil(U_17019)))),U_17020),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

cnf(f_4144_3,plain,
    hAPP(c_List_Orotate1(U_17019),U_17020) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_17019),U_17019,c_List_Olist_ONil(U_17019),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17019),tc_fun(tc_List_Olist(U_17019),tc_List_Olist(U_17019)),U_17019),hAPP(c_COMBC(tc_List_Olist(U_17019),tc_List_Olist(U_17019),tc_List_Olist(U_17019)),c_List_Oappend(U_17019))),hAPP(hAPP(c_COMBC(U_17019,tc_List_Olist(U_17019),tc_List_Olist(U_17019)),c_List_Olist_OCons(U_17019)),c_List_Olist_ONil(U_17019)))),U_17020),
    inference(clausify,[status(thm)],[f_4144_2]) ).

fof(f_4145_1,plain,
    ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__append1]) ).

fof(f_4145_2,plain,
    ! [U_17026,U_17025,U_17024,U_17023,U_17022,U_17021] :
      ( c_Map_Omap__upds(U_17021,U_17023,U_17025,hAPP(hAPP(c_List_Oappend(U_17021),U_17022),hAPP(hAPP(c_List_Olist_OCons(U_17021),U_17026),c_List_Olist_ONil(U_17021))),U_17024) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17021,tc_Option_Ooption(U_17023)),c_Map_Omap__upds(U_17021,U_17023,U_17025,U_17022,U_17024)),U_17026),hAPP(c_Option_Ooption_OSome(U_17023),hAPP(hAPP(c_List_Onth(U_17023),U_17024),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17021)),U_17022))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17021)),U_17022)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17023)),U_17024))) ),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

cnf(f_4145_3,plain,
    ( c_Map_Omap__upds(U_17021,U_17023,U_17025,hAPP(hAPP(c_List_Oappend(U_17021),U_17022),hAPP(hAPP(c_List_Olist_OCons(U_17021),U_17026),c_List_Olist_ONil(U_17021))),U_17024) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17021,tc_Option_Ooption(U_17023)),c_Map_Omap__upds(U_17021,U_17023,U_17025,U_17022,U_17024)),U_17026),hAPP(c_Option_Ooption_OSome(U_17023),hAPP(hAPP(c_List_Onth(U_17023),U_17024),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17021)),U_17022))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17021)),U_17022)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17023)),U_17024))) ),
    inference(clausify,[status(thm)],[f_4145_2]) ).

fof(f_4146_1,plain,
    ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__map__upd]) ).

fof(f_4146_2,plain,
    ! [U_17032,U_17031,U_17030,U_17029,U_17028,U_17027] :
      ( hAPP(c_Set_Oimage(U_17027,tc_Option_Ooption(U_17030),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17027,tc_Option_Ooption(U_17030)),U_17031),U_17028),hAPP(c_Option_Ooption_OSome(U_17030),U_17032))),U_17029) = hAPP(c_Set_Oimage(U_17027,tc_Option_Ooption(U_17030),U_17031),U_17029)
      | hBOOL(hAPP(hAPP(c_member(U_17027),U_17028),U_17029)) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

cnf(f_4146_3,plain,
    ( hAPP(c_Set_Oimage(U_17027,tc_Option_Ooption(U_17030),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17027,tc_Option_Ooption(U_17030)),U_17031),U_17028),hAPP(c_Option_Ooption_OSome(U_17030),U_17032))),U_17029) = hAPP(c_Set_Oimage(U_17027,tc_Option_Ooption(U_17030),U_17031),U_17029)
    | hBOOL(hAPP(hAPP(c_member(U_17027),U_17028),U_17029)) ),
    inference(clausify,[status(thm)],[f_4146_2]) ).

fof(f_4147_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate1]) ).

fof(f_4147_2,plain,
    ! [U_17034,U_17033] : hAPP(c_List_Oset(U_17033),hAPP(c_List_Orotate1(U_17033),U_17034)) = hAPP(c_List_Oset(U_17033),U_17034),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

cnf(f_4147_3,plain,
    hAPP(c_List_Oset(U_17033),hAPP(c_List_Orotate1(U_17033),U_17034)) = hAPP(c_List_Oset(U_17033),U_17034),
    inference(clausify,[status(thm)],[f_4147_2]) ).

fof(f_4148_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_4148_2,plain,
    ! [U_17036,U_17035] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17035)),hAPP(c_List_Orotate1(U_17035),U_17036)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17035)),U_17036),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

cnf(f_4148_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17035)),hAPP(c_List_Orotate1(U_17035),U_17036)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17035)),U_17036),
    inference(clausify,[status(thm)],[f_4148_2]) ).

fof(f_4149_1,plain,
    ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_dom__const]) ).

fof(f_4149_2,plain,
    ! [U_17039,U_17038,U_17037] : c_Map_Odom(U_17037,U_17038,hAPP(hAPP(c_COMBB(U_17038,tc_Option_Ooption(U_17038),U_17037),c_Option_Ooption_OSome(U_17038)),U_17039)) = c_Orderings_Otop__class_Otop(tc_fun(U_17037,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

cnf(f_4149_3,plain,
    c_Map_Odom(U_17037,U_17038,hAPP(hAPP(c_COMBB(U_17038,tc_Option_Ooption(U_17038),U_17037),c_Option_Ooption_OSome(U_17038)),U_17039)) = c_Orderings_Otop__class_Otop(tc_fun(U_17037,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4149_2]) ).

fof(f_4150_1,plain,
    ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2)))
      | hAPP(V_m_2,V_a_2) != hAPP(c_Option_Ooption_OSome(T_a),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_domI]) ).

fof(f_4150_2,plain,
    ! [U_17044,U_17043,U_17042,U_17041,U_17040] :
      ( hBOOL(hAPP(hAPP(c_member(U_17044),U_17041),c_Map_Odom(U_17044,U_17042,U_17040)))
      | hAPP(U_17040,U_17041) != hAPP(c_Option_Ooption_OSome(U_17042),U_17043) ),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

cnf(f_4150_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17044),U_17041),c_Map_Odom(U_17044,U_17042,U_17040)))
    | hAPP(U_17040,U_17041) != hAPP(c_Option_Ooption_OSome(U_17042),U_17043) ),
    inference(clausify,[status(thm)],[f_4150_2]) ).

fof(f_4151_1,plain,
    ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2)
      | hAPP(V_f_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_insert__dom]) ).

fof(f_4151_2,plain,
    ! [U_17049,U_17048,U_17047,U_17046,U_17045] :
      ( hAPP(hAPP(c_Set_Oinsert(U_17049),U_17046),c_Map_Odom(U_17049,U_17047,U_17045)) = c_Map_Odom(U_17049,U_17047,U_17045)
      | hAPP(U_17045,U_17046) != hAPP(c_Option_Ooption_OSome(U_17047),U_17048) ),
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

cnf(f_4151_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_17049),U_17046),c_Map_Odom(U_17049,U_17047,U_17045)) = c_Map_Odom(U_17049,U_17047,U_17045)
    | hAPP(U_17045,U_17046) != hAPP(c_Option_Ooption_OSome(U_17047),U_17048) ),
    inference(clausify,[status(thm)],[f_4151_2]) ).

fof(f_4152_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct1__rotate]) ).

fof(f_4152_2,plain,
    ! [U_17051,U_17050] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17050),hAPP(c_List_Orotate1(U_17050),U_17051)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17050),U_17051)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_17050),U_17051))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17050),hAPP(c_List_Orotate1(U_17050),U_17051))) ) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

fof(f_4152_3,plain,
    ( ! [U_17055,U_17053] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17053),hAPP(c_List_Orotate1(U_17053),U_17055)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17053),U_17055)) )
    & ! [U_17054,U_17052] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17052),U_17054))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17052),hAPP(c_List_Orotate1(U_17052),U_17054))) ) ),
    inference(miniscope,[status(thm)],[f_4152_2]) ).

cnf(f_4152_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17052),U_17054))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17052),hAPP(c_List_Orotate1(U_17052),U_17054))) ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

cnf(f_4152_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17053),hAPP(c_List_Orotate1(U_17053),U_17055)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17053),U_17055)) ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

fof(f_4153_1,plain,
    ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
      ( V_x_2 = V_y_2
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__eqD1]) ).

fof(f_4153_2,plain,
    ! [U_17062,U_17061,U_17060,U_17059,U_17058,U_17057,U_17056] :
      ( U_17060 = U_17062
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17058),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17060)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17061),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17062)) ),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

fof(f_4153_3,plain,
    ! [U_17062,U_17061,U_17060] :
      ( ! [U_17059,U_17058,U_17057,U_17056] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17058),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17060)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17061),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17062))
      | U_17060 = U_17062 ),
    inference(miniscope,[status(thm)],[f_4153_2]) ).

cnf(f_4153_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17058),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17060)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17056,tc_Option_Ooption(U_17057)),U_17061),U_17059),hAPP(c_Option_Ooption_OSome(U_17057),U_17062))
    | U_17060 = U_17062 ),
    inference(clausify,[status(thm)],[f_4153_3]) ).

fof(f_4154_1,plain,
    ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2
      | hAPP(V_t_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__triv]) ).

fof(f_4154_2,plain,
    ! [U_17067,U_17066,U_17065,U_17064,U_17063] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17067,tc_Option_Ooption(U_17065)),U_17063),U_17064),hAPP(c_Option_Ooption_OSome(U_17065),U_17066)) = U_17063
      | hAPP(U_17063,U_17064) != hAPP(c_Option_Ooption_OSome(U_17065),U_17066) ),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

cnf(f_4154_3,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17067,tc_Option_Ooption(U_17065)),U_17063),U_17064),hAPP(c_Option_Ooption_OSome(U_17065),U_17066)) = U_17063
    | hAPP(U_17063,U_17064) != hAPP(c_Option_Ooption_OSome(U_17065),U_17066) ),
    inference(clausify,[status(thm)],[f_4154_2]) ).

fof(f_4155_1,plain,
    ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
        | ( ( hAPP(V_m_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),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_a),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_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold]) ).

fof(f_4155_2,plain,
    ! [U_17074,U_17073,U_17072,U_17071,U_17070,U_17069,U_17068] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17068,tc_Option_Ooption(U_17069)),U_17070),U_17071),hAPP(c_Option_Ooption_OSome(U_17069),U_17072)),U_17073) = hAPP(c_Option_Ooption_OSome(U_17069),U_17074)
        | ( ( hAPP(U_17070,U_17073) != hAPP(c_Option_Ooption_OSome(U_17069),U_17074)
            | U_17073 = U_17071 )
          & ( U_17072 != U_17074
            | U_17073 != U_17071 ) ) )
      & ( ( hAPP(U_17070,U_17073) = hAPP(c_Option_Ooption_OSome(U_17069),U_17074)
          & U_17073 != U_17071 )
        | ( U_17072 = U_17074
          & U_17073 = U_17071 )
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17068,tc_Option_Ooption(U_17069)),U_17070),U_17071),hAPP(c_Option_Ooption_OSome(U_17069),U_17072)),U_17073) != hAPP(c_Option_Ooption_OSome(U_17069),U_17074) ) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

fof(f_4155_3,plain,
    ( ! [U_17088,U_17086,U_17084,U_17082,U_17080,U_17078] :
        ( ! [U_17076] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17076,tc_Option_Ooption(U_17078)),U_17080),U_17082),hAPP(c_Option_Ooption_OSome(U_17078),U_17084)),U_17086) = hAPP(c_Option_Ooption_OSome(U_17078),U_17088)
        | ( ( hAPP(U_17080,U_17086) != hAPP(c_Option_Ooption_OSome(U_17078),U_17088)
            | U_17086 = U_17082 )
          & ( U_17084 != U_17088
            | U_17086 != U_17082 ) ) )
    & ! [U_17087,U_17085,U_17083,U_17081,U_17079,U_17077] :
        ( ! [U_17075] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17075,tc_Option_Ooption(U_17077)),U_17079),U_17081),hAPP(c_Option_Ooption_OSome(U_17077),U_17083)),U_17085) != hAPP(c_Option_Ooption_OSome(U_17077),U_17087)
        | ( hAPP(U_17079,U_17085) = hAPP(c_Option_Ooption_OSome(U_17077),U_17087)
          & U_17085 != U_17081 )
        | ( U_17083 = U_17087
          & U_17085 = U_17081 ) ) ),
    inference(miniscope,[status(thm)],[f_4155_2]) ).

cnf(f_4155_4,plain,
    ( U_17085 != U_17081
    | U_17085 = U_17081
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17075,tc_Option_Ooption(U_17077)),U_17079),U_17081),hAPP(c_Option_Ooption_OSome(U_17077),U_17083)),U_17085) != hAPP(c_Option_Ooption_OSome(U_17077),U_17087) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_5,plain,
    ( hAPP(U_17079,U_17085) = hAPP(c_Option_Ooption_OSome(U_17077),U_17087)
    | U_17085 = U_17081
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17075,tc_Option_Ooption(U_17077)),U_17079),U_17081),hAPP(c_Option_Ooption_OSome(U_17077),U_17083)),U_17085) != hAPP(c_Option_Ooption_OSome(U_17077),U_17087) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_6,plain,
    ( U_17085 != U_17081
    | U_17083 = U_17087
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17075,tc_Option_Ooption(U_17077)),U_17079),U_17081),hAPP(c_Option_Ooption_OSome(U_17077),U_17083)),U_17085) != hAPP(c_Option_Ooption_OSome(U_17077),U_17087) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_7,plain,
    ( hAPP(U_17079,U_17085) = hAPP(c_Option_Ooption_OSome(U_17077),U_17087)
    | U_17083 = U_17087
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17075,tc_Option_Ooption(U_17077)),U_17079),U_17081),hAPP(c_Option_Ooption_OSome(U_17077),U_17083)),U_17085) != hAPP(c_Option_Ooption_OSome(U_17077),U_17087) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_8,plain,
    ( U_17084 != U_17088
    | U_17086 != U_17082
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17076,tc_Option_Ooption(U_17078)),U_17080),U_17082),hAPP(c_Option_Ooption_OSome(U_17078),U_17084)),U_17086) = hAPP(c_Option_Ooption_OSome(U_17078),U_17088) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_9,plain,
    ( hAPP(U_17080,U_17086) != hAPP(c_Option_Ooption_OSome(U_17078),U_17088)
    | U_17086 = U_17082
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17076,tc_Option_Ooption(U_17078)),U_17080),U_17082),hAPP(c_Option_Ooption_OSome(U_17078),U_17084)),U_17086) = hAPP(c_Option_Ooption_OSome(U_17078),U_17088) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

fof(f_4156_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(c_List_Orotate1(T_a),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv]) ).

fof(f_4156_2,plain,
    ! [U_17090,U_17089] :
      ( ( hAPP(c_List_Orotate1(U_17089),U_17090) = c_List_Olist_ONil(U_17089)
        | U_17090 != c_List_Olist_ONil(U_17089) )
      & ( U_17090 = c_List_Olist_ONil(U_17089)
        | hAPP(c_List_Orotate1(U_17089),U_17090) != c_List_Olist_ONil(U_17089) ) ),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

fof(f_4156_3,plain,
    ( ! [U_17094,U_17092] :
        ( hAPP(c_List_Orotate1(U_17092),U_17094) = c_List_Olist_ONil(U_17092)
        | U_17094 != c_List_Olist_ONil(U_17092) )
    & ! [U_17093,U_17091] :
        ( U_17093 = c_List_Olist_ONil(U_17091)
        | hAPP(c_List_Orotate1(U_17091),U_17093) != c_List_Olist_ONil(U_17091) ) ),
    inference(miniscope,[status(thm)],[f_4156_2]) ).

cnf(f_4156_4,plain,
    ( U_17093 = c_List_Olist_ONil(U_17091)
    | hAPP(c_List_Orotate1(U_17091),U_17093) != c_List_Olist_ONil(U_17091) ),
    inference(clausify,[status(thm)],[f_4156_3]) ).

cnf(f_4156_5,plain,
    ( hAPP(c_List_Orotate1(U_17092),U_17094) = c_List_Olist_ONil(U_17092)
    | U_17094 != c_List_Olist_ONil(U_17092) ),
    inference(clausify,[status(thm)],[f_4156_3]) ).

fof(f_4157_1,plain,
    ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2),
    inference(fof_nnf,[status(thm)],[fact_map__upds__Cons]) ).

fof(f_4157_2,plain,
    ! [U_17101,U_17100,U_17099,U_17098,U_17097,U_17096,U_17095] : c_Map_Omap__upds(U_17095,U_17096,U_17097,hAPP(hAPP(c_List_Olist_OCons(U_17095),U_17098),U_17099),hAPP(hAPP(c_List_Olist_OCons(U_17096),U_17100),U_17101)) = c_Map_Omap__upds(U_17095,U_17096,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17095,tc_Option_Ooption(U_17096)),U_17097),U_17098),hAPP(c_Option_Ooption_OSome(U_17096),U_17100)),U_17099,U_17101),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

cnf(f_4157_3,plain,
    c_Map_Omap__upds(U_17095,U_17096,U_17097,hAPP(hAPP(c_List_Olist_OCons(U_17095),U_17098),U_17099),hAPP(hAPP(c_List_Olist_OCons(U_17096),U_17100),U_17101)) = c_Map_Omap__upds(U_17095,U_17096,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17095,tc_Option_Ooption(U_17096)),U_17097),U_17098),hAPP(c_Option_Ooption_OSome(U_17096),U_17100)),U_17099,U_17101),
    inference(clausify,[status(thm)],[f_4157_2]) ).

fof(f_4158_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_4158_2,plain,
    ! [U_17104] :
      ( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17104)))
        | ! [U_17103] : hAPP(c_Com_Obody,U_17104) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17103) )
      & ( ? [U_17102] : hAPP(c_Com_Obody,U_17104) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17102)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17104))) ) ),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

fof(f_4158_3,plain,
    ( ! [U_17106] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17106)))
        | ! [U_17103] : hAPP(c_Com_Obody,U_17106) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17103) )
    & ! [U_17105] :
        ( ? [U_17102] : hAPP(c_Com_Obody,U_17105) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17102)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17105))) ) ),
    inference(miniscope,[status(thm)],[f_4158_2]) ).

fof(f_4158_4,plain,
    ( ! [U_17106] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17106)))
        | ! [U_17103] : hAPP(c_Com_Obody,U_17106) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17103) )
    & ! [U_17105] :
        ( hAPP(c_Com_Obody,U_17105) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK448(U_17105))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17105))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_17102,sK448(U_17105))],[f_4158_3]) ).

cnf(f_4158_5,plain,
    ( hAPP(c_Com_Obody,U_17105) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK448(U_17105))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17105))) ),
    inference(clausify,[status(thm)],[f_4158_4]) ).

cnf(f_4158_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17106)))
    | hAPP(c_Com_Obody,U_17106) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17103) ),
    inference(clausify,[status(thm)],[f_4158_4]) ).

fof(f_4159_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__updI]) ).

fof(f_4159_2,plain,
    ! [U_17111,U_17110,U_17109,U_17108,U_17107] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17107)),hAPP(c_Set_Oimage(U_17108,tc_Option_Ooption(U_17107),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17108,tc_Option_Ooption(U_17107)),U_17109),U_17110),hAPP(c_Option_Ooption_OSome(U_17107),U_17111))),c_Orderings_Otop__class_Otop(tc_fun(U_17108,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17107)),hAPP(c_Set_Oimage(U_17108,tc_Option_Ooption(U_17107),U_17109),c_Orderings_Otop__class_Otop(tc_fun(U_17108,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

cnf(f_4159_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17107)),hAPP(c_Set_Oimage(U_17108,tc_Option_Ooption(U_17107),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17108,tc_Option_Ooption(U_17107)),U_17109),U_17110),hAPP(c_Option_Ooption_OSome(U_17107),U_17111))),c_Orderings_Otop__class_Otop(tc_fun(U_17108,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17107)),hAPP(c_Set_Oimage(U_17108,tc_Option_Ooption(U_17107),U_17109),c_Orderings_Otop__class_Otop(tc_fun(U_17108,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_4159_2]) ).

fof(f_4160_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_4160_2,plain,
    ! [U_17113,U_17112] :
      ( hBOOL(hAPP(c_Com_OWT,U_17113))
      | hAPP(c_Com_Obody,U_17112) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17113)
      | ~ c_Com_OWT__bodies ),
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

fof(f_4160_3,plain,
    ( ! [U_17113] :
        ( ! [U_17112] : hAPP(c_Com_Obody,U_17112) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17113)
        | hBOOL(hAPP(c_Com_OWT,U_17113)) )
    | ~ c_Com_OWT__bodies ),
    inference(miniscope,[status(thm)],[f_4160_2]) ).

cnf(f_4160_4,plain,
    ( hAPP(c_Com_Obody,U_17112) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17113)
    | hBOOL(hAPP(c_Com_OWT,U_17113))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_4160_3]) ).

fof(f_4161_1,plain,
    ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
      ( c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__upds__twist]) ).

fof(f_4161_2,plain,
    ! [U_17120,U_17119,U_17118,U_17117,U_17116,U_17115,U_17114] :
      ( c_Map_Omap__upds(U_17114,U_17117,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17114,tc_Option_Ooption(U_17117)),U_17118),U_17115),hAPP(c_Option_Ooption_OSome(U_17117),U_17119)),U_17116,U_17120) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17114,tc_Option_Ooption(U_17117)),c_Map_Omap__upds(U_17114,U_17117,U_17118,U_17116,U_17120)),U_17115),hAPP(c_Option_Ooption_OSome(U_17117),U_17119))
      | hBOOL(hAPP(hAPP(c_member(U_17114),U_17115),hAPP(c_List_Oset(U_17114),U_17116))) ),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

cnf(f_4161_3,plain,
    ( c_Map_Omap__upds(U_17114,U_17117,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17114,tc_Option_Ooption(U_17117)),U_17118),U_17115),hAPP(c_Option_Ooption_OSome(U_17117),U_17119)),U_17116,U_17120) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17114,tc_Option_Ooption(U_17117)),c_Map_Omap__upds(U_17114,U_17117,U_17118,U_17116,U_17120)),U_17115),hAPP(c_Option_Ooption_OSome(U_17117),U_17119))
    | hBOOL(hAPP(hAPP(c_member(U_17114),U_17115),hAPP(c_List_Oset(U_17114),U_17116))) ),
    inference(clausify,[status(thm)],[f_4161_2]) ).

fof(f_4162_1,plain,
    ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_restrict__upd__same]) ).

fof(f_4162_2,plain,
    ! [U_17125,U_17124,U_17123,U_17122,U_17121] : c_Map_Orestrict__map(U_17121,U_17122,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17121,tc_Option_Ooption(U_17122)),U_17123),U_17124),hAPP(c_Option_Ooption_OSome(U_17122),U_17125)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_17121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_17121),U_17124),c_Orderings_Obot__class_Obot(tc_fun(U_17121,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_17121,U_17122,U_17123,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_17121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_17121),U_17124),c_Orderings_Obot__class_Obot(tc_fun(U_17121,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

cnf(f_4162_3,plain,
    c_Map_Orestrict__map(U_17121,U_17122,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17121,tc_Option_Ooption(U_17122)),U_17123),U_17124),hAPP(c_Option_Ooption_OSome(U_17122),U_17125)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_17121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_17121),U_17124),c_Orderings_Obot__class_Obot(tc_fun(U_17121,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_17121,U_17122,U_17123,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_17121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_17121),U_17124),c_Orderings_Obot__class_Obot(tc_fun(U_17121,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4162_2]) ).

fof(f_4163_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_4163_2,plain,
    ! [U_17129,U_17128,U_17127,U_17126] :
      ( hAPP(c_List_Orotate1(U_17127),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),U_17129)) = hAPP(hAPP(c_List_Oappend(U_17127),U_17129),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),c_List_Olist_ONil(U_17127)))
      & hAPP(c_List_Orotate1(U_17126),c_List_Olist_ONil(U_17126)) = c_List_Olist_ONil(U_17126) ),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

fof(f_4163_3,plain,
    ( ! [U_17129,U_17128,U_17127] : hAPP(c_List_Orotate1(U_17127),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),U_17129)) = hAPP(hAPP(c_List_Oappend(U_17127),U_17129),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),c_List_Olist_ONil(U_17127)))
    & ! [U_17126] : hAPP(c_List_Orotate1(U_17126),c_List_Olist_ONil(U_17126)) = c_List_Olist_ONil(U_17126) ),
    inference(miniscope,[status(thm)],[f_4163_2]) ).

cnf(f_4163_4,plain,
    hAPP(c_List_Orotate1(U_17126),c_List_Olist_ONil(U_17126)) = c_List_Olist_ONil(U_17126),
    inference(clausify,[status(thm)],[f_4163_3]) ).

cnf(f_4163_5,plain,
    hAPP(c_List_Orotate1(U_17127),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),U_17129)) = hAPP(hAPP(c_List_Oappend(U_17127),U_17129),hAPP(hAPP(c_List_Olist_OCons(U_17127),U_17128),c_List_Olist_ONil(U_17127))),
    inference(clausify,[status(thm)],[f_4163_3]) ).

fof(f_4164_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_4164_2,plain,
    ! [U_17131,U_17130] :
      ( hAPP(c_List_Orotate1(U_17130),U_17131) = U_17131
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17130)),U_17131)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

cnf(f_4164_3,plain,
    ( hAPP(c_List_Orotate1(U_17130),U_17131) = U_17131
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17130)),U_17131)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4164_2]) ).

fof(f_4165_1,plain,
    ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
      ( ( c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) )
      & ( c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__upd__upds__conv__if]) ).

fof(f_4165_2,plain,
    ! [U_17138,U_17137,U_17136,U_17135,U_17134,U_17133,U_17132] :
      ( ( c_Map_Omap__upds(U_17132,U_17134,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17132,tc_Option_Ooption(U_17134)),U_17137),U_17133),hAPP(c_Option_Ooption_OSome(U_17134),U_17138)),U_17136,U_17135) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17132,tc_Option_Ooption(U_17134)),c_Map_Omap__upds(U_17132,U_17134,U_17137,U_17136,U_17135)),U_17133),hAPP(c_Option_Ooption_OSome(U_17134),U_17138))
        | hBOOL(hAPP(hAPP(c_member(U_17132),U_17133),hAPP(c_List_Oset(U_17132),hAPP(hAPP(c_List_Otake(U_17132),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17134)),U_17135)),U_17136)))) )
      & ( c_Map_Omap__upds(U_17132,U_17134,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17132,tc_Option_Ooption(U_17134)),U_17137),U_17133),hAPP(c_Option_Ooption_OSome(U_17134),U_17138)),U_17136,U_17135) = c_Map_Omap__upds(U_17132,U_17134,U_17137,U_17136,U_17135)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17132),U_17133),hAPP(c_List_Oset(U_17132),hAPP(hAPP(c_List_Otake(U_17132),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17134)),U_17135)),U_17136)))) ) ),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

fof(f_4165_3,plain,
    ( ! [U_17152,U_17150,U_17148,U_17146,U_17144,U_17142,U_17140] :
        ( c_Map_Omap__upds(U_17140,U_17144,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17140,tc_Option_Ooption(U_17144)),U_17150),U_17142),hAPP(c_Option_Ooption_OSome(U_17144),U_17152)),U_17148,U_17146) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17140,tc_Option_Ooption(U_17144)),c_Map_Omap__upds(U_17140,U_17144,U_17150,U_17148,U_17146)),U_17142),hAPP(c_Option_Ooption_OSome(U_17144),U_17152))
        | hBOOL(hAPP(hAPP(c_member(U_17140),U_17142),hAPP(c_List_Oset(U_17140),hAPP(hAPP(c_List_Otake(U_17140),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17144)),U_17146)),U_17148)))) )
    & ! [U_17151,U_17149,U_17147,U_17145,U_17143,U_17141,U_17139] :
        ( c_Map_Omap__upds(U_17139,U_17143,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17139,tc_Option_Ooption(U_17143)),U_17149),U_17141),hAPP(c_Option_Ooption_OSome(U_17143),U_17151)),U_17147,U_17145) = c_Map_Omap__upds(U_17139,U_17143,U_17149,U_17147,U_17145)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17139),U_17141),hAPP(c_List_Oset(U_17139),hAPP(hAPP(c_List_Otake(U_17139),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17143)),U_17145)),U_17147)))) ) ),
    inference(miniscope,[status(thm)],[f_4165_2]) ).

cnf(f_4165_4,plain,
    ( c_Map_Omap__upds(U_17139,U_17143,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17139,tc_Option_Ooption(U_17143)),U_17149),U_17141),hAPP(c_Option_Ooption_OSome(U_17143),U_17151)),U_17147,U_17145) = c_Map_Omap__upds(U_17139,U_17143,U_17149,U_17147,U_17145)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17139),U_17141),hAPP(c_List_Oset(U_17139),hAPP(hAPP(c_List_Otake(U_17139),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17143)),U_17145)),U_17147)))) ),
    inference(clausify,[status(thm)],[f_4165_3]) ).

cnf(f_4165_5,plain,
    ( c_Map_Omap__upds(U_17140,U_17144,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17140,tc_Option_Ooption(U_17144)),U_17150),U_17142),hAPP(c_Option_Ooption_OSome(U_17144),U_17152)),U_17148,U_17146) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17140,tc_Option_Ooption(U_17144)),c_Map_Omap__upds(U_17140,U_17144,U_17150,U_17148,U_17146)),U_17142),hAPP(c_Option_Ooption_OSome(U_17144),U_17152))
    | hBOOL(hAPP(hAPP(c_member(U_17140),U_17142),hAPP(c_List_Oset(U_17140),hAPP(hAPP(c_List_Otake(U_17140),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17144)),U_17146)),U_17148)))) ),
    inference(clausify,[status(thm)],[f_4165_3]) ).

fof(f_4166_1,plain,
    ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),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_4166_2,plain,
    ! [U_17155,U_17154,U_17153] : c_Option_Ooption_Ooption__size(U_17153,U_17154,hAPP(c_Option_Ooption_OSome(U_17153),U_17155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_17154,U_17155)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

cnf(f_4166_3,plain,
    c_Option_Ooption_Ooption__size(U_17153,U_17154,hAPP(c_Option_Ooption_OSome(U_17153),U_17155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_17154,U_17155)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4166_2]) ).

fof(f_4167_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I5_J]) ).

fof(f_4167_2,plain,
    ! [U_17160,U_17159,U_17158,U_17157,U_17156] : hAPP(c_Option_Ooption_Ooption__case(U_17156,U_17157,U_17158,U_17159),hAPP(c_Option_Ooption_OSome(U_17157),U_17160)) = hAPP(U_17159,U_17160),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

cnf(f_4167_3,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_17156,U_17157,U_17158,U_17159),hAPP(c_Option_Ooption_OSome(U_17157),U_17160)) = hAPP(U_17159,U_17160),
    inference(clausify,[status(thm)],[f_4167_2]) ).

fof(f_4168_1,plain,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Some]) ).

fof(f_4168_2,plain,
    ! [U_17162,U_17161] : c_Fun_Oinj__on(U_17161,tc_Option_Ooption(U_17161),c_Option_Ooption_OSome(U_17161),U_17162),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

cnf(f_4168_3,plain,
    c_Fun_Oinj__on(U_17161,tc_Option_Ooption(U_17161),c_Option_Ooption_OSome(U_17161),U_17162),
    inference(clausify,[status(thm)],[f_4168_2]) ).

fof(f_4169_1,plain,
    ! [V_a_H_2,V_a_2,T_a] :
      ( ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
        | V_a_2 != V_a_H_2 )
      & ( V_a_2 = V_a_H_2
        | hAPP(c_Option_Ooption_OSome(T_a),V_a_2) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_option_Oinject]) ).

fof(f_4169_2,plain,
    ! [U_17165,U_17164,U_17163] :
      ( ( hAPP(c_Option_Ooption_OSome(U_17163),U_17164) = hAPP(c_Option_Ooption_OSome(U_17163),U_17165)
        | U_17164 != U_17165 )
      & ( U_17164 = U_17165
        | hAPP(c_Option_Ooption_OSome(U_17163),U_17164) != hAPP(c_Option_Ooption_OSome(U_17163),U_17165) ) ),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

fof(f_4169_3,plain,
    ( ! [U_17171,U_17169] :
        ( ! [U_17167] : hAPP(c_Option_Ooption_OSome(U_17167),U_17169) = hAPP(c_Option_Ooption_OSome(U_17167),U_17171)
        | U_17169 != U_17171 )
    & ! [U_17170,U_17168] :
        ( ! [U_17166] : hAPP(c_Option_Ooption_OSome(U_17166),U_17168) != hAPP(c_Option_Ooption_OSome(U_17166),U_17170)
        | U_17168 = U_17170 ) ),
    inference(miniscope,[status(thm)],[f_4169_2]) ).

cnf(f_4169_4,plain,
    ( hAPP(c_Option_Ooption_OSome(U_17166),U_17168) != hAPP(c_Option_Ooption_OSome(U_17166),U_17170)
    | U_17168 = U_17170 ),
    inference(clausify,[status(thm)],[f_4169_3]) ).

cnf(f_4169_5,plain,
    ( hAPP(c_Option_Ooption_OSome(U_17167),U_17169) = hAPP(c_Option_Ooption_OSome(U_17167),U_17171)
    | U_17169 != U_17171 ),
    inference(clausify,[status(thm)],[f_4169_3]) ).

fof(f_4170_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_4170_2,plain,
    ! [U_17173,U_17172] : hAPP(c_Option_Othe(U_17172),hAPP(c_Option_Ooption_OSome(U_17172),U_17173)) = U_17173,
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

cnf(f_4170_3,plain,
    hAPP(c_Option_Othe(U_17172),hAPP(c_Option_Ooption_OSome(U_17172),U_17173)) = U_17173,
    inference(clausify,[status(thm)],[f_4170_2]) ).

fof(f_4171_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_4171_2,plain,
    ! [U_17175] :
      ( ? [U_17174] : hAPP(c_Com_Obody,U_17175) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_17174)
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17175))) ),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

fof(f_4171_3,plain,
    ! [U_17175] :
      ( hAPP(c_Com_Obody,U_17175) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK449(U_17175))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17175))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_17174,sK449(U_17175))],[f_4171_2]) ).

cnf(f_4171_4,plain,
    ( hAPP(c_Com_Obody,U_17175) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK449(U_17175))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_17175))) ),
    inference(clausify,[status(thm)],[f_4171_3]) ).

fof(f_4172_1,plain,
    ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Option_Oset_Osimps_I2_J]) ).

fof(f_4172_2,plain,
    ! [U_17177,U_17176] : c_Option_Oset(U_17176,hAPP(c_Option_Ooption_OSome(U_17176),U_17177)) = hAPP(hAPP(c_Set_Oinsert(U_17176),U_17177),c_Orderings_Obot__class_Obot(tc_fun(U_17176,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

cnf(f_4172_3,plain,
    c_Option_Oset(U_17176,hAPP(c_Option_Ooption_OSome(U_17176),U_17177)) = hAPP(hAPP(c_Set_Oinsert(U_17176),U_17177),c_Orderings_Obot__class_Obot(tc_fun(U_17176,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4172_2]) ).

fof(f_4173_1,plain,
    ! [V_xo_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
        | V_xo_2 != hAPP(c_Option_Ooption_OSome(T_a),V_x_2) )
      & ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_elem__set]) ).

fof(f_4173_2,plain,
    ! [U_17180,U_17179,U_17178] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_17178),U_17179),c_Option_Oset(U_17178,U_17180)))
        | U_17180 != hAPP(c_Option_Ooption_OSome(U_17178),U_17179) )
      & ( U_17180 = hAPP(c_Option_Ooption_OSome(U_17178),U_17179)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17178),U_17179),c_Option_Oset(U_17178,U_17180))) ) ),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

fof(f_4173_3,plain,
    ( ! [U_17186,U_17184,U_17182] :
        ( hBOOL(hAPP(hAPP(c_member(U_17182),U_17184),c_Option_Oset(U_17182,U_17186)))
        | U_17186 != hAPP(c_Option_Ooption_OSome(U_17182),U_17184) )
    & ! [U_17185,U_17183,U_17181] :
        ( U_17185 = hAPP(c_Option_Ooption_OSome(U_17181),U_17183)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17181),U_17183),c_Option_Oset(U_17181,U_17185))) ) ),
    inference(miniscope,[status(thm)],[f_4173_2]) ).

cnf(f_4173_4,plain,
    ( U_17185 = hAPP(c_Option_Ooption_OSome(U_17181),U_17183)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17181),U_17183),c_Option_Oset(U_17181,U_17185))) ),
    inference(clausify,[status(thm)],[f_4173_3]) ).

cnf(f_4173_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17182),U_17184),c_Option_Oset(U_17182,U_17186)))
    | U_17186 != hAPP(c_Option_Ooption_OSome(U_17182),U_17184) ),
    inference(clausify,[status(thm)],[f_4173_3]) ).

fof(f_4174_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_4174_2,plain,
    ! [U_17190,U_17189,U_17188,U_17187] :
      ( hAPP(hAPP(c_List_Olist__update(U_17188,U_17189),U_17187),U_17190) = hAPP(hAPP(c_List_Oappend(U_17188),hAPP(hAPP(c_List_Otake(U_17188),U_17187),U_17189)),hAPP(hAPP(c_List_Olist_OCons(U_17188),U_17190),hAPP(hAPP(c_List_Odrop(U_17188),hAPP(c_Nat_OSuc,U_17187)),U_17189)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17188)),U_17189))) ),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

cnf(f_4174_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_17188,U_17189),U_17187),U_17190) = hAPP(hAPP(c_List_Oappend(U_17188),hAPP(hAPP(c_List_Otake(U_17188),U_17187),U_17189)),hAPP(hAPP(c_List_Olist_OCons(U_17188),U_17190),hAPP(hAPP(c_List_Odrop(U_17188),hAPP(c_Nat_OSuc,U_17187)),U_17189)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17188)),U_17189))) ),
    inference(clausify,[status(thm)],[f_4174_2]) ).

fof(f_4175_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_4175_2,plain,
    ! [U_17193,U_17192,U_17191] :
      ( U_17193 = hAPP(hAPP(c_List_Oappend(U_17192),hAPP(hAPP(c_List_Otake(U_17192),U_17191),U_17193)),hAPP(hAPP(c_List_Olist_OCons(U_17192),hAPP(hAPP(c_List_Onth(U_17192),U_17193),U_17191)),hAPP(hAPP(c_List_Odrop(U_17192),hAPP(c_Nat_OSuc,U_17191)),U_17193)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17191),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17192)),U_17193))) ),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

cnf(f_4175_3,plain,
    ( U_17193 = hAPP(hAPP(c_List_Oappend(U_17192),hAPP(hAPP(c_List_Otake(U_17192),U_17191),U_17193)),hAPP(hAPP(c_List_Olist_OCons(U_17192),hAPP(hAPP(c_List_Onth(U_17192),U_17193),U_17191)),hAPP(hAPP(c_List_Odrop(U_17192),hAPP(c_Nat_OSuc,U_17191)),U_17193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17191),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17192)),U_17193))) ),
    inference(clausify,[status(thm)],[f_4175_2]) ).

fof(f_4176_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_4176_2,plain,
    ! [U_17195,U_17194] : hAPP(hAPP(c_List_Odrop(U_17194),U_17195),c_List_Olist_ONil(U_17194)) = c_List_Olist_ONil(U_17194),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

cnf(f_4176_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17194),U_17195),c_List_Olist_ONil(U_17194)) = c_List_Olist_ONil(U_17194),
    inference(clausify,[status(thm)],[f_4176_2]) ).

fof(f_4177_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_4177_2,plain,
    ! [U_17198,U_17197,U_17196] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17196),hAPP(hAPP(c_List_Odrop(U_17196),U_17198),U_17197)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17196),U_17197)) ),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

cnf(f_4177_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17196),hAPP(hAPP(c_List_Odrop(U_17196),U_17198),U_17197)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17196),U_17197)) ),
    inference(clausify,[status(thm)],[f_4177_2]) ).

fof(f_4178_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_4178_2,plain,
    ! [U_17201,U_17200,U_17199] : hAPP(hAPP(c_List_Odrop(U_17199),U_17200),c_List_Obutlast(U_17199,U_17201)) = c_List_Obutlast(U_17199,hAPP(hAPP(c_List_Odrop(U_17199),U_17200),U_17201)),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

cnf(f_4178_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17199),U_17200),c_List_Obutlast(U_17199,U_17201)) = c_List_Obutlast(U_17199,hAPP(hAPP(c_List_Odrop(U_17199),U_17200),U_17201)),
    inference(clausify,[status(thm)],[f_4178_2]) ).

fof(f_4179_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_4179_2,plain,
    ! [U_17204,U_17203,U_17202] : c_List_Obutlast(U_17202,hAPP(hAPP(c_List_Odrop(U_17202),U_17203),U_17204)) = hAPP(hAPP(c_List_Odrop(U_17202),U_17203),c_List_Obutlast(U_17202,U_17204)),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

cnf(f_4179_3,plain,
    c_List_Obutlast(U_17202,hAPP(hAPP(c_List_Odrop(U_17202),U_17203),U_17204)) = hAPP(hAPP(c_List_Odrop(U_17202),U_17203),c_List_Obutlast(U_17202,U_17204)),
    inference(clausify,[status(thm)],[f_4179_2]) ).

fof(f_4180_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_4180_2,plain,
    ! [U_17208,U_17207,U_17206,U_17205] : hAPP(hAPP(c_List_Otake(U_17205),U_17206),hAPP(hAPP(c_List_Odrop(U_17205),U_17207),U_17208)) = hAPP(hAPP(c_List_Odrop(U_17205),U_17207),hAPP(hAPP(c_List_Otake(U_17205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17206),U_17207)),U_17208)),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

cnf(f_4180_3,plain,
    hAPP(hAPP(c_List_Otake(U_17205),U_17206),hAPP(hAPP(c_List_Odrop(U_17205),U_17207),U_17208)) = hAPP(hAPP(c_List_Odrop(U_17205),U_17207),hAPP(hAPP(c_List_Otake(U_17205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17206),U_17207)),U_17208)),
    inference(clausify,[status(thm)],[f_4180_2]) ).

fof(f_4181_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_4181_2,plain,
    ! [U_17212,U_17211,U_17210,U_17209] : hAPP(hAPP(c_List_Odrop(U_17209),U_17210),hAPP(hAPP(c_List_Otake(U_17209),U_17211),U_17212)) = hAPP(hAPP(c_List_Otake(U_17209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17211),U_17210)),hAPP(hAPP(c_List_Odrop(U_17209),U_17210),U_17212)),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

cnf(f_4181_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17209),U_17210),hAPP(hAPP(c_List_Otake(U_17209),U_17211),U_17212)) = hAPP(hAPP(c_List_Otake(U_17209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17211),U_17210)),hAPP(hAPP(c_List_Odrop(U_17209),U_17210),U_17212)),
    inference(clausify,[status(thm)],[f_4181_2]) ).

fof(f_4182_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_4182_2,plain,
    ! [U_17216,U_17215,U_17214,U_17213] : hAPP(hAPP(c_List_Odrop(U_17213),U_17214),hAPP(hAPP(c_List_Odrop(U_17213),U_17215),U_17216)) = hAPP(hAPP(c_List_Odrop(U_17213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17214),U_17215)),U_17216),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

cnf(f_4182_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17213),U_17214),hAPP(hAPP(c_List_Odrop(U_17213),U_17215),U_17216)) = hAPP(hAPP(c_List_Odrop(U_17213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17214),U_17215)),U_17216),
    inference(clausify,[status(thm)],[f_4182_2]) ).

fof(f_4183_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_4183_2,plain,
    ! [U_17218,U_17217] : hAPP(hAPP(c_List_Odrop(U_17217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_17218) = U_17218,
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

cnf(f_4183_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_17218) = U_17218,
    inference(clausify,[status(thm)],[f_4183_2]) ).

fof(f_4184_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_4184_2,plain,
    ! [U_17223,U_17222,U_17221,U_17220,U_17219] : hAPP(hAPP(c_List_Odrop(tc_prod(U_17219,U_17220)),U_17221),hAPP(hAPP(c_List_Ozip(U_17219,U_17220),U_17222),U_17223)) = hAPP(hAPP(c_List_Ozip(U_17219,U_17220),hAPP(hAPP(c_List_Odrop(U_17219),U_17221),U_17222)),hAPP(hAPP(c_List_Odrop(U_17220),U_17221),U_17223)),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

cnf(f_4184_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_17219,U_17220)),U_17221),hAPP(hAPP(c_List_Ozip(U_17219,U_17220),U_17222),U_17223)) = hAPP(hAPP(c_List_Ozip(U_17219,U_17220),hAPP(hAPP(c_List_Odrop(U_17219),U_17221),U_17222)),hAPP(hAPP(c_List_Odrop(U_17220),U_17221),U_17223)),
    inference(clausify,[status(thm)],[f_4184_2]) ).

fof(f_4185_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_4185_2,plain,
    ! [U_17226,U_17225,U_17224] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),hAPP(hAPP(c_List_Odrop(U_17224),U_17225),U_17226)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),U_17226)),U_17225),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

cnf(f_4185_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),hAPP(hAPP(c_List_Odrop(U_17224),U_17225),U_17226)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),U_17226)),U_17225),
    inference(clausify,[status(thm)],[f_4185_2]) ).

fof(f_4186_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__dropD]) ).

fof(f_4186_2,plain,
    ! [U_17230,U_17229,U_17228,U_17227] :
      ( hBOOL(hAPP(hAPP(c_member(U_17227),U_17228),hAPP(c_List_Oset(U_17227),U_17230)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17227),U_17228),hAPP(c_List_Oset(U_17227),hAPP(hAPP(c_List_Odrop(U_17227),U_17229),U_17230)))) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

cnf(f_4186_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17227),U_17228),hAPP(c_List_Oset(U_17227),U_17230)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17227),U_17228),hAPP(c_List_Oset(U_17227),hAPP(hAPP(c_List_Odrop(U_17227),U_17229),U_17230)))) ),
    inference(clausify,[status(thm)],[f_4186_2]) ).

fof(f_4187_1,plain,
    ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__drop__subset]) ).

fof(f_4187_2,plain,
    ! [U_17233,U_17232,U_17231] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17231,tc_HOL_Obool)),hAPP(c_List_Oset(U_17231),hAPP(hAPP(c_List_Odrop(U_17231),U_17232),U_17233))),hAPP(c_List_Oset(U_17231),U_17233))),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

cnf(f_4187_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17231,tc_HOL_Obool)),hAPP(c_List_Oset(U_17231),hAPP(hAPP(c_List_Odrop(U_17231),U_17232),U_17233))),hAPP(c_List_Oset(U_17231),U_17233))),
    inference(clausify,[status(thm)],[f_4187_2]) ).

fof(f_4188_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_4188_2,plain,
    ! [U_17237,U_17236,U_17235,U_17234] : hAPP(hAPP(c_List_Odrop(U_17234),hAPP(c_Nat_OSuc,U_17235)),hAPP(hAPP(c_List_Olist_OCons(U_17234),U_17236),U_17237)) = hAPP(hAPP(c_List_Odrop(U_17234),U_17235),U_17237),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

cnf(f_4188_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17234),hAPP(c_Nat_OSuc,U_17235)),hAPP(hAPP(c_List_Olist_OCons(U_17234),U_17236),U_17237)) = hAPP(hAPP(c_List_Odrop(U_17234),U_17235),U_17237),
    inference(clausify,[status(thm)],[f_4188_2]) ).

fof(f_4189_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_4189_2,plain,
    ! [U_17240,U_17239,U_17238] : hAPP(hAPP(c_List_Odrop(U_17238),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_17238),U_17239),U_17240)) = U_17240,
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

cnf(f_4189_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17238),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_17238),U_17239),U_17240)) = U_17240,
    inference(clausify,[status(thm)],[f_4189_2]) ).

fof(f_4190_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_4190_2,plain,
    ! [U_17245,U_17244,U_17243,U_17242,U_17241] :
      ( hAPP(hAPP(c_List_Onth(U_17241),U_17243),U_17242) = U_17244
      | hAPP(hAPP(c_List_Odrop(U_17241),U_17242),U_17243) != hAPP(hAPP(c_List_Olist_OCons(U_17241),U_17244),U_17245) ),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

cnf(f_4190_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_17241),U_17243),U_17242) = U_17244
    | hAPP(hAPP(c_List_Odrop(U_17241),U_17242),U_17243) != hAPP(hAPP(c_List_Olist_OCons(U_17241),U_17244),U_17245) ),
    inference(clausify,[status(thm)],[f_4190_2]) ).

fof(f_4191_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_4191_2,plain,
    ! [U_17248,U_17247,U_17246] : hAPP(hAPP(c_List_Oappend(U_17246),hAPP(hAPP(c_List_Otake(U_17246),U_17247),U_17248)),hAPP(hAPP(c_List_Odrop(U_17246),U_17247),U_17248)) = U_17248,
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

cnf(f_4191_3,plain,
    hAPP(hAPP(c_List_Oappend(U_17246),hAPP(hAPP(c_List_Otake(U_17246),U_17247),U_17248)),hAPP(hAPP(c_List_Odrop(U_17246),U_17247),U_17248)) = U_17248,
    inference(clausify,[status(thm)],[f_4191_2]) ).

fof(f_4192_1,plain,
    ! [V_xs_2,T_a,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),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_4192_2,plain,
    ! [U_17252,U_17251,U_17250,U_17249] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17251,tc_HOL_Obool)),hAPP(c_List_Oset(U_17251),hAPP(hAPP(c_List_Odrop(U_17251),U_17250),U_17252))),hAPP(c_List_Oset(U_17251),hAPP(hAPP(c_List_Odrop(U_17251),U_17249),U_17252))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17249),U_17250)) ),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

cnf(f_4192_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17251,tc_HOL_Obool)),hAPP(c_List_Oset(U_17251),hAPP(hAPP(c_List_Odrop(U_17251),U_17250),U_17252))),hAPP(c_List_Oset(U_17251),hAPP(hAPP(c_List_Odrop(U_17251),U_17249),U_17252))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17249),U_17250)) ),
    inference(clausify,[status(thm)],[f_4192_2]) ).

fof(f_4193_1,plain,
    ! [V_xs_2,V_n_2,T_a] :
      ( ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = 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_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_a)),V_xs_2)),V_n_2))
        | hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil]) ).

fof(f_4193_2,plain,
    ! [U_17255,U_17254,U_17253] :
      ( ( hAPP(hAPP(c_List_Odrop(U_17253),U_17254),U_17255) = c_List_Olist_ONil(U_17253)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17253)),U_17255)),U_17254)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17253)),U_17255)),U_17254))
        | hAPP(hAPP(c_List_Odrop(U_17253),U_17254),U_17255) != c_List_Olist_ONil(U_17253) ) ),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

fof(f_4193_3,plain,
    ( ! [U_17261,U_17259,U_17257] :
        ( hAPP(hAPP(c_List_Odrop(U_17257),U_17259),U_17261) = c_List_Olist_ONil(U_17257)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17257)),U_17261)),U_17259)) )
    & ! [U_17260,U_17258,U_17256] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17256)),U_17260)),U_17258))
        | hAPP(hAPP(c_List_Odrop(U_17256),U_17258),U_17260) != c_List_Olist_ONil(U_17256) ) ),
    inference(miniscope,[status(thm)],[f_4193_2]) ).

cnf(f_4193_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17256)),U_17260)),U_17258))
    | hAPP(hAPP(c_List_Odrop(U_17256),U_17258),U_17260) != c_List_Olist_ONil(U_17256) ),
    inference(clausify,[status(thm)],[f_4193_3]) ).

cnf(f_4193_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17257),U_17259),U_17261) = c_List_Olist_ONil(U_17257)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17257)),U_17261)),U_17259)) ),
    inference(clausify,[status(thm)],[f_4193_3]) ).

fof(f_4194_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_4194_2,plain,
    ! [U_17264,U_17263,U_17262] :
      ( hAPP(hAPP(c_List_Odrop(U_17262),U_17264),U_17263) = c_List_Olist_ONil(U_17262)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17262)),U_17263)),U_17264)) ),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

cnf(f_4194_3,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17262),U_17264),U_17263) = c_List_Olist_ONil(U_17262)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17262)),U_17263)),U_17264)) ),
    inference(clausify,[status(thm)],[f_4194_2]) ).

fof(f_4195_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_4195_2,plain,
    ! [U_17268,U_17267,U_17266,U_17265] : hAPP(hAPP(c_List_Odrop(U_17265),U_17266),hAPP(hAPP(c_List_Oappend(U_17265),U_17267),U_17268)) = hAPP(hAPP(c_List_Oappend(U_17265),hAPP(hAPP(c_List_Odrop(U_17265),U_17266),U_17267)),hAPP(hAPP(c_List_Odrop(U_17265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17266),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17265)),U_17267))),U_17268)),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

cnf(f_4195_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17265),U_17266),hAPP(hAPP(c_List_Oappend(U_17265),U_17267),U_17268)) = hAPP(hAPP(c_List_Oappend(U_17265),hAPP(hAPP(c_List_Odrop(U_17265),U_17266),U_17267)),hAPP(hAPP(c_List_Odrop(U_17265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17266),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17265)),U_17267))),U_17268)),
    inference(clausify,[status(thm)],[f_4195_2]) ).

fof(f_4196_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
        | V_ys_2 != hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) )
      & ( ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)
          & V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) != V_zs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj]) ).

fof(f_4196_2,plain,
    ! [U_17272,U_17271,U_17270,U_17269] :
      ( ( hAPP(hAPP(c_List_Oappend(U_17269),U_17270),U_17271) = U_17272
        | U_17271 != hAPP(hAPP(c_List_Odrop(U_17269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17269)),U_17270)),U_17272)
        | U_17270 != hAPP(hAPP(c_List_Otake(U_17269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17269)),U_17270)),U_17272) )
      & ( ( U_17271 = hAPP(hAPP(c_List_Odrop(U_17269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17269)),U_17270)),U_17272)
          & U_17270 = hAPP(hAPP(c_List_Otake(U_17269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17269)),U_17270)),U_17272) )
        | hAPP(hAPP(c_List_Oappend(U_17269),U_17270),U_17271) != U_17272 ) ),
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

fof(f_4196_3,plain,
    ( ! [U_17280,U_17278,U_17276,U_17274] :
        ( hAPP(hAPP(c_List_Oappend(U_17274),U_17276),U_17278) = U_17280
        | U_17278 != hAPP(hAPP(c_List_Odrop(U_17274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17274)),U_17276)),U_17280)
        | U_17276 != hAPP(hAPP(c_List_Otake(U_17274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17274)),U_17276)),U_17280) )
    & ! [U_17279,U_17277,U_17275,U_17273] :
        ( ( U_17277 = hAPP(hAPP(c_List_Odrop(U_17273),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17273)),U_17275)),U_17279)
          & U_17275 = hAPP(hAPP(c_List_Otake(U_17273),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17273)),U_17275)),U_17279) )
        | hAPP(hAPP(c_List_Oappend(U_17273),U_17275),U_17277) != U_17279 ) ),
    inference(miniscope,[status(thm)],[f_4196_2]) ).

cnf(f_4196_4,plain,
    ( U_17275 = hAPP(hAPP(c_List_Otake(U_17273),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17273)),U_17275)),U_17279)
    | hAPP(hAPP(c_List_Oappend(U_17273),U_17275),U_17277) != U_17279 ),
    inference(clausify,[status(thm)],[f_4196_3]) ).

cnf(f_4196_5,plain,
    ( U_17277 = hAPP(hAPP(c_List_Odrop(U_17273),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17273)),U_17275)),U_17279)
    | hAPP(hAPP(c_List_Oappend(U_17273),U_17275),U_17277) != U_17279 ),
    inference(clausify,[status(thm)],[f_4196_3]) ).

cnf(f_4196_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17274),U_17276),U_17278) = U_17280
    | U_17278 != hAPP(hAPP(c_List_Odrop(U_17274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17274)),U_17276)),U_17280)
    | U_17276 != hAPP(hAPP(c_List_Otake(U_17274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17274)),U_17276)),U_17280) ),
    inference(clausify,[status(thm)],[f_4196_3]) ).

fof(f_4197_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons]) ).

fof(f_4197_2,plain,
    ! [U_17284,U_17283,U_17282,U_17281] : hAPP(hAPP(c_List_Odrop(U_17281),U_17282),hAPP(hAPP(c_List_Olist_OCons(U_17281),U_17283),U_17284)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_17281),hAPP(hAPP(c_List_Olist_OCons(U_17281),U_17283),U_17284),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_17281),tc_List_Olist(U_17281)),c_List_Odrop(U_17281)),U_17284),U_17282),
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

cnf(f_4197_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17281),U_17282),hAPP(hAPP(c_List_Olist_OCons(U_17281),U_17283),U_17284)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_17281),hAPP(hAPP(c_List_Olist_OCons(U_17281),U_17283),U_17284),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_17281),tc_List_Olist(U_17281)),c_List_Odrop(U_17281)),U_17284),U_17282),
    inference(clausify,[status(thm)],[f_4197_2]) ).

fof(f_4198_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_4198_2,plain,
    ! [U_17288,U_17287,U_17286,U_17285] :
      ( ( hAPP(hAPP(c_List_Odrop(U_17286),U_17285),hAPP(hAPP(c_List_Olist_OCons(U_17286),U_17287),U_17288)) = hAPP(hAPP(c_List_Odrop(U_17286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17285),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17288)
        | U_17285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_17286),U_17285),hAPP(hAPP(c_List_Olist_OCons(U_17286),U_17287),U_17288)) = hAPP(hAPP(c_List_Olist_OCons(U_17286),U_17287),U_17288)
        | U_17285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

fof(f_4198_3,plain,
    ( ! [U_17296,U_17294,U_17292,U_17290] :
        ( hAPP(hAPP(c_List_Odrop(U_17292),U_17290),hAPP(hAPP(c_List_Olist_OCons(U_17292),U_17294),U_17296)) = hAPP(hAPP(c_List_Odrop(U_17292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17290),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17296)
        | U_17290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17295,U_17293,U_17291,U_17289] :
        ( hAPP(hAPP(c_List_Odrop(U_17291),U_17289),hAPP(hAPP(c_List_Olist_OCons(U_17291),U_17293),U_17295)) = hAPP(hAPP(c_List_Olist_OCons(U_17291),U_17293),U_17295)
        | U_17289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4198_2]) ).

cnf(f_4198_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17291),U_17289),hAPP(hAPP(c_List_Olist_OCons(U_17291),U_17293),U_17295)) = hAPP(hAPP(c_List_Olist_OCons(U_17291),U_17293),U_17295)
    | U_17289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4198_3]) ).

cnf(f_4198_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17292),U_17290),hAPP(hAPP(c_List_Olist_OCons(U_17292),U_17294),U_17296)) = hAPP(hAPP(c_List_Odrop(U_17292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17290),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17296)
    | U_17290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4198_3]) ).

fof(f_4199_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_4199_2,plain,
    ! [U_17300,U_17299,U_17298,U_17297] :
      ( hAPP(hAPP(c_List_Onth(U_17299),hAPP(hAPP(c_List_Odrop(U_17299),U_17297),U_17300)),U_17298) = hAPP(hAPP(c_List_Onth(U_17299),U_17300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17297),U_17298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17297),U_17298)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17299)),U_17300))) ),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

cnf(f_4199_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_17299),hAPP(hAPP(c_List_Odrop(U_17299),U_17297),U_17300)),U_17298) = hAPP(hAPP(c_List_Onth(U_17299),U_17300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17297),U_17298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17297),U_17298)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17299)),U_17300))) ),
    inference(clausify,[status(thm)],[f_4199_2]) ).

fof(f_4200_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_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
        | ( ( hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) )
        | ( ( V_xs_092_060_094isub_0622_2 != hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) )
          & ( ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) ) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) != hAPP(hAPP(c_List_Oappend(T_a),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_4200_2,plain,
    ! [U_17305,U_17304,U_17303,U_17302,U_17301] :
      ( ( hAPP(hAPP(c_List_Oappend(U_17301),U_17302),U_17303) = hAPP(hAPP(c_List_Oappend(U_17301),U_17304),U_17305)
        | ( ( hAPP(hAPP(c_List_Oappend(U_17301),hAPP(hAPP(c_List_Odrop(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304)),U_17302)),U_17303) != U_17305
            | hAPP(hAPP(c_List_Otake(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304)),U_17302) != U_17304 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304))) )
        | ( ( U_17303 != hAPP(hAPP(c_List_Oappend(U_17301),hAPP(hAPP(c_List_Odrop(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),U_17304)),U_17305)
            | U_17302 != hAPP(hAPP(c_List_Otake(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),U_17304) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_17301),hAPP(hAPP(c_List_Odrop(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304)),U_17302)),U_17303) = U_17305
              & hAPP(hAPP(c_List_Otake(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304)),U_17302) = U_17304 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304))) )
          & ( ( U_17303 = hAPP(hAPP(c_List_Oappend(U_17301),hAPP(hAPP(c_List_Odrop(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),U_17304)),U_17305)
              & U_17302 = hAPP(hAPP(c_List_Otake(U_17301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),U_17304) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17302)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17301)),U_17304))) ) )
        | hAPP(hAPP(c_List_Oappend(U_17301),U_17302),U_17303) != hAPP(hAPP(c_List_Oappend(U_17301),U_17304),U_17305) ) ),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

fof(f_4200_3,plain,
    ( ! [U_17315,U_17313,U_17311,U_17309,U_17307] :
        ( hAPP(hAPP(c_List_Oappend(U_17307),U_17309),U_17311) = hAPP(hAPP(c_List_Oappend(U_17307),U_17313),U_17315)
        | ( ( hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309)),U_17311) != U_17315
            | hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309) != U_17313 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313))) )
        | ( ( U_17311 != hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313)),U_17315)
            | U_17309 != hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313))) ) )
    & ! [U_17314,U_17312,U_17310,U_17308,U_17306] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_17306),hAPP(hAPP(c_List_Odrop(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)),U_17308)),U_17310) = U_17314
              & hAPP(hAPP(c_List_Otake(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)),U_17308) = U_17312 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312))) )
          & ( ( U_17310 = hAPP(hAPP(c_List_Oappend(U_17306),hAPP(hAPP(c_List_Odrop(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),U_17312)),U_17314)
              & U_17308 = hAPP(hAPP(c_List_Otake(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),U_17312) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312))) ) )
        | hAPP(hAPP(c_List_Oappend(U_17306),U_17308),U_17310) != hAPP(hAPP(c_List_Oappend(U_17306),U_17312),U_17314) ) ),
    inference(miniscope,[status(thm)],[f_4200_2]) ).

cnf(f_4200_4,plain,
    ( U_17308 = hAPP(hAPP(c_List_Otake(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),U_17312)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)))
    | hAPP(hAPP(c_List_Oappend(U_17306),U_17308),U_17310) != hAPP(hAPP(c_List_Oappend(U_17306),U_17312),U_17314) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_5,plain,
    ( U_17310 = hAPP(hAPP(c_List_Oappend(U_17306),hAPP(hAPP(c_List_Odrop(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),U_17312)),U_17314)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)))
    | hAPP(hAPP(c_List_Oappend(U_17306),U_17308),U_17310) != hAPP(hAPP(c_List_Oappend(U_17306),U_17312),U_17314) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)),U_17308) = U_17312
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)))
    | hAPP(hAPP(c_List_Oappend(U_17306),U_17308),U_17310) != hAPP(hAPP(c_List_Oappend(U_17306),U_17312),U_17314) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17306),hAPP(hAPP(c_List_Odrop(U_17306),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)),U_17308)),U_17310) = U_17314
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17308)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17306)),U_17312)))
    | hAPP(hAPP(c_List_Oappend(U_17306),U_17308),U_17310) != hAPP(hAPP(c_List_Oappend(U_17306),U_17312),U_17314) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)))
    | hAPP(hAPP(c_List_Oappend(U_17307),U_17309),U_17311) = hAPP(hAPP(c_List_Oappend(U_17307),U_17313),U_17315) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_9,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309)),U_17311) != U_17315
    | hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309) != U_17313
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)))
    | hAPP(hAPP(c_List_Oappend(U_17307),U_17309),U_17311) = hAPP(hAPP(c_List_Oappend(U_17307),U_17313),U_17315) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)))
    | U_17311 != hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313)),U_17315)
    | U_17309 != hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313)
    | hAPP(hAPP(c_List_Oappend(U_17307),U_17309),U_17311) = hAPP(hAPP(c_List_Oappend(U_17307),U_17313),U_17315) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309)),U_17311) != U_17315
    | hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17313)),U_17309) != U_17313
    | U_17311 != hAPP(hAPP(c_List_Oappend(U_17307),hAPP(hAPP(c_List_Odrop(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313)),U_17315)
    | U_17309 != hAPP(hAPP(c_List_Otake(U_17307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17307)),U_17309)),U_17313)
    | hAPP(hAPP(c_List_Oappend(U_17307),U_17309),U_17311) = hAPP(hAPP(c_List_Oappend(U_17307),U_17313),U_17315) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

fof(f_4201_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_4201_2,plain,
    ! [U_17318,U_17317,U_17316] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_17317),hAPP(hAPP(c_List_Onth(U_17317),U_17318),U_17316)),hAPP(hAPP(c_List_Odrop(U_17317),hAPP(c_Nat_OSuc,U_17316)),U_17318)) = hAPP(hAPP(c_List_Odrop(U_17317),U_17316),U_17318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17316),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17317)),U_17318))) ),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

cnf(f_4201_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_17317),hAPP(hAPP(c_List_Onth(U_17317),U_17318),U_17316)),hAPP(hAPP(c_List_Odrop(U_17317),hAPP(c_Nat_OSuc,U_17316)),U_17318)) = hAPP(hAPP(c_List_Odrop(U_17317),U_17316),U_17318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17316),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17317)),U_17318))) ),
    inference(clausify,[status(thm)],[f_4201_2]) ).

fof(f_4202_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_4202_2,plain,
    ! [U_17322,U_17321,U_17320,U_17319] :
      ( ( hAPP(hAPP(c_List_Odrop(U_17320),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17319)),hAPP(hAPP(c_List_Olist_OCons(U_17320),U_17321),U_17322)) = hAPP(hAPP(c_List_Odrop(U_17320),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17319)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17322)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_17320),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17319)),hAPP(hAPP(c_List_Olist_OCons(U_17320),U_17321),U_17322)) = hAPP(hAPP(c_List_Olist_OCons(U_17320),U_17321),U_17322)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17319) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

fof(f_4202_3,plain,
    ( ! [U_17330,U_17328,U_17326,U_17324] :
        ( hAPP(hAPP(c_List_Odrop(U_17326),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324)),hAPP(hAPP(c_List_Olist_OCons(U_17326),U_17328),U_17330)) = hAPP(hAPP(c_List_Odrop(U_17326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17330)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17329,U_17327,U_17325,U_17323] :
        ( hAPP(hAPP(c_List_Odrop(U_17325),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17323)),hAPP(hAPP(c_List_Olist_OCons(U_17325),U_17327),U_17329)) = hAPP(hAPP(c_List_Olist_OCons(U_17325),U_17327),U_17329)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17323) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4202_2]) ).

cnf(f_4202_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17325),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17323)),hAPP(hAPP(c_List_Olist_OCons(U_17325),U_17327),U_17329)) = hAPP(hAPP(c_List_Olist_OCons(U_17325),U_17327),U_17329)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17323) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4202_3]) ).

cnf(f_4202_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_17326),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324)),hAPP(hAPP(c_List_Olist_OCons(U_17326),U_17328),U_17330)) = hAPP(hAPP(c_List_Odrop(U_17326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_17330)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4202_3]) ).

fof(f_4203_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_4203_2,plain,
    ! [U_17334,U_17333,U_17332,U_17331] :
      ( hAPP(hAPP(c_List_Otake(U_17333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17331),U_17332)),U_17334) = hAPP(hAPP(c_List_Oappend(U_17333),hAPP(hAPP(c_List_Otake(U_17333),U_17331),U_17334)),hAPP(hAPP(c_List_Otake(U_17333),U_17332),hAPP(hAPP(c_List_Odrop(U_17333),U_17331),U_17334)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17331),U_17332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17333)),U_17334))) ),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

cnf(f_4203_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_17333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17331),U_17332)),U_17334) = hAPP(hAPP(c_List_Oappend(U_17333),hAPP(hAPP(c_List_Otake(U_17333),U_17331),U_17334)),hAPP(hAPP(c_List_Otake(U_17333),U_17332),hAPP(hAPP(c_List_Odrop(U_17333),U_17331),U_17334)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17331),U_17332)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17333)),U_17334))) ),
    inference(clausify,[status(thm)],[f_4203_2]) ).

fof(f_4204_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_4204_2,plain,
    ! [U_17339,U_17338,U_17337,U_17336,U_17335] : hAPP(hAPP(c_List_Ozip(U_17335,U_17336),U_17337),hAPP(hAPP(c_List_Oappend(U_17336),U_17338),U_17339)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17335,U_17336)),hAPP(hAPP(c_List_Ozip(U_17335,U_17336),hAPP(hAPP(c_List_Otake(U_17335),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17336)),U_17338)),U_17337)),U_17338)),hAPP(hAPP(c_List_Ozip(U_17335,U_17336),hAPP(hAPP(c_List_Odrop(U_17335),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17336)),U_17338)),U_17337)),U_17339)),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

cnf(f_4204_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17335,U_17336),U_17337),hAPP(hAPP(c_List_Oappend(U_17336),U_17338),U_17339)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17335,U_17336)),hAPP(hAPP(c_List_Ozip(U_17335,U_17336),hAPP(hAPP(c_List_Otake(U_17335),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17336)),U_17338)),U_17337)),U_17338)),hAPP(hAPP(c_List_Ozip(U_17335,U_17336),hAPP(hAPP(c_List_Odrop(U_17335),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17336)),U_17338)),U_17337)),U_17339)),
    inference(clausify,[status(thm)],[f_4204_2]) ).

fof(f_4205_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_4205_2,plain,
    ! [U_17344,U_17343,U_17342,U_17341,U_17340] : hAPP(hAPP(c_List_Ozip(U_17340,U_17341),hAPP(hAPP(c_List_Oappend(U_17340),U_17342),U_17343)),U_17344) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17340,U_17341)),hAPP(hAPP(c_List_Ozip(U_17340,U_17341),U_17342),hAPP(hAPP(c_List_Otake(U_17341),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17340)),U_17342)),U_17344))),hAPP(hAPP(c_List_Ozip(U_17340,U_17341),U_17343),hAPP(hAPP(c_List_Odrop(U_17341),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17340)),U_17342)),U_17344))),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

cnf(f_4205_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17340,U_17341),hAPP(hAPP(c_List_Oappend(U_17340),U_17342),U_17343)),U_17344) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17340,U_17341)),hAPP(hAPP(c_List_Ozip(U_17340,U_17341),U_17342),hAPP(hAPP(c_List_Otake(U_17341),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17340)),U_17342)),U_17344))),hAPP(hAPP(c_List_Ozip(U_17340,U_17341),U_17343),hAPP(hAPP(c_List_Odrop(U_17341),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17340)),U_17342)),U_17344))),
    inference(clausify,[status(thm)],[f_4205_2]) ).

fof(f_4206_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_4206_2,plain,
    ! [U_17347,U_17346,U_17345] :
      ( hAPP(hAPP(c_List_Oappend(U_17346),hAPP(hAPP(c_List_Otake(U_17346),U_17345),U_17347)),hAPP(hAPP(c_List_Olist_OCons(U_17346),hAPP(c_List_Ohd(U_17346),hAPP(hAPP(c_List_Odrop(U_17346),U_17345),U_17347))),c_List_Olist_ONil(U_17346))) = hAPP(hAPP(c_List_Otake(U_17346),hAPP(c_Nat_OSuc,U_17345)),U_17347)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17345),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17346)),U_17347))) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

cnf(f_4206_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17346),hAPP(hAPP(c_List_Otake(U_17346),U_17345),U_17347)),hAPP(hAPP(c_List_Olist_OCons(U_17346),hAPP(c_List_Ohd(U_17346),hAPP(hAPP(c_List_Odrop(U_17346),U_17345),U_17347))),c_List_Olist_ONil(U_17346))) = hAPP(hAPP(c_List_Otake(U_17346),hAPP(c_Nat_OSuc,U_17345)),U_17347)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17345),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17346)),U_17347))) ),
    inference(clausify,[status(thm)],[f_4206_2]) ).

fof(f_4207_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_4207_2,plain,
    ! [U_17350,U_17349,U_17348] :
      ( hAPP(c_List_Ohd(U_17349),hAPP(hAPP(c_List_Odrop(U_17349),U_17350),U_17348)) = hAPP(hAPP(c_List_Onth(U_17349),U_17348),U_17350)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17350),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17349)),U_17348)))
      | U_17348 = c_List_Olist_ONil(U_17349) ),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

cnf(f_4207_3,plain,
    ( hAPP(c_List_Ohd(U_17349),hAPP(hAPP(c_List_Odrop(U_17349),U_17350),U_17348)) = hAPP(hAPP(c_List_Onth(U_17349),U_17348),U_17350)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17350),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17349)),U_17348)))
    | U_17348 = c_List_Olist_ONil(U_17349) ),
    inference(clausify,[status(thm)],[f_4207_2]) ).

fof(f_4208_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_4208_2,plain,
    ! [U_17353,U_17352,U_17351] : hAPP(c_List_Ohd(U_17351),hAPP(hAPP(c_List_Olist_OCons(U_17351),U_17352),U_17353)) = U_17352,
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

cnf(f_4208_3,plain,
    hAPP(c_List_Ohd(U_17351),hAPP(hAPP(c_List_Olist_OCons(U_17351),U_17352),U_17353)) = U_17352,
    inference(clausify,[status(thm)],[f_4208_2]) ).

fof(f_4209_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_4209_2,plain,
    ! [U_17356,U_17355,U_17354] :
      ( ( hAPP(c_List_Ohd(U_17355),hAPP(hAPP(c_List_Oappend(U_17355),U_17354),U_17356)) = hAPP(c_List_Ohd(U_17355),U_17354)
        | U_17354 = c_List_Olist_ONil(U_17355) )
      & ( hAPP(c_List_Ohd(U_17355),hAPP(hAPP(c_List_Oappend(U_17355),U_17354),U_17356)) = hAPP(c_List_Ohd(U_17355),U_17356)
        | U_17354 != c_List_Olist_ONil(U_17355) ) ),
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

fof(f_4209_3,plain,
    ( ! [U_17362,U_17360,U_17358] :
        ( hAPP(c_List_Ohd(U_17360),hAPP(hAPP(c_List_Oappend(U_17360),U_17358),U_17362)) = hAPP(c_List_Ohd(U_17360),U_17358)
        | U_17358 = c_List_Olist_ONil(U_17360) )
    & ! [U_17361,U_17359,U_17357] :
        ( hAPP(c_List_Ohd(U_17359),hAPP(hAPP(c_List_Oappend(U_17359),U_17357),U_17361)) = hAPP(c_List_Ohd(U_17359),U_17361)
        | U_17357 != c_List_Olist_ONil(U_17359) ) ),
    inference(miniscope,[status(thm)],[f_4209_2]) ).

cnf(f_4209_4,plain,
    ( hAPP(c_List_Ohd(U_17359),hAPP(hAPP(c_List_Oappend(U_17359),U_17357),U_17361)) = hAPP(c_List_Ohd(U_17359),U_17361)
    | U_17357 != c_List_Olist_ONil(U_17359) ),
    inference(clausify,[status(thm)],[f_4209_3]) ).

cnf(f_4209_5,plain,
    ( hAPP(c_List_Ohd(U_17360),hAPP(hAPP(c_List_Oappend(U_17360),U_17358),U_17362)) = hAPP(c_List_Ohd(U_17360),U_17358)
    | U_17358 = c_List_Olist_ONil(U_17360) ),
    inference(clausify,[status(thm)],[f_4209_3]) ).

fof(f_4210_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_4210_2,plain,
    ! [U_17365,U_17364,U_17363] :
      ( hAPP(c_List_Ohd(U_17364),hAPP(hAPP(c_List_Oappend(U_17364),U_17363),U_17365)) = hAPP(c_List_Ohd(U_17364),U_17363)
      | U_17363 = c_List_Olist_ONil(U_17364) ),
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

cnf(f_4210_3,plain,
    ( hAPP(c_List_Ohd(U_17364),hAPP(hAPP(c_List_Oappend(U_17364),U_17363),U_17365)) = hAPP(c_List_Ohd(U_17364),U_17363)
    | U_17363 = c_List_Olist_ONil(U_17364) ),
    inference(clausify,[status(thm)],[f_4210_2]) ).

fof(f_4211_1,plain,
    ! [T_a,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__in__set]) ).

fof(f_4211_2,plain,
    ! [U_17367,U_17366] :
      ( hBOOL(hAPP(hAPP(c_member(U_17367),hAPP(c_List_Ohd(U_17367),U_17366)),hAPP(c_List_Oset(U_17367),U_17366)))
      | U_17366 = c_List_Olist_ONil(U_17367) ),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

cnf(f_4211_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17367),hAPP(c_List_Ohd(U_17367),U_17366)),hAPP(c_List_Oset(U_17367),U_17366)))
    | U_17366 = c_List_Olist_ONil(U_17367) ),
    inference(clausify,[status(thm)],[f_4211_2]) ).

fof(f_4212_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_4212_2,plain,
    ! [U_17369,U_17368] :
      ( hAPP(c_List_Ohd(U_17369),U_17368) = hAPP(hAPP(c_List_Onth(U_17369),U_17368),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_17368 = c_List_Olist_ONil(U_17369) ),
    inference(variable_rename,[status(thm)],[f_4212_1]) ).

cnf(f_4212_3,plain,
    ( hAPP(c_List_Ohd(U_17369),U_17368) = hAPP(hAPP(c_List_Onth(U_17369),U_17368),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_17368 = c_List_Olist_ONil(U_17369) ),
    inference(clausify,[status(thm)],[f_4212_2]) ).

fof(f_4213_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_4213_2,plain,
    ! [U_17371,U_17370] :
      ( hAPP(c_List_Orotate1(U_17371),U_17370) = hAPP(hAPP(c_List_Oappend(U_17371),hAPP(c_List_Otl(U_17371),U_17370)),hAPP(hAPP(c_List_Olist_OCons(U_17371),hAPP(c_List_Ohd(U_17371),U_17370)),c_List_Olist_ONil(U_17371)))
      | U_17370 = c_List_Olist_ONil(U_17371) ),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

cnf(f_4213_3,plain,
    ( hAPP(c_List_Orotate1(U_17371),U_17370) = hAPP(hAPP(c_List_Oappend(U_17371),hAPP(c_List_Otl(U_17371),U_17370)),hAPP(hAPP(c_List_Olist_OCons(U_17371),hAPP(c_List_Ohd(U_17371),U_17370)),c_List_Olist_ONil(U_17371)))
    | U_17370 = c_List_Olist_ONil(U_17371) ),
    inference(clausify,[status(thm)],[f_4213_2]) ).

fof(f_4214_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_4214_2,plain,
    ! [U_17373,U_17372] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_17372)),hAPP(c_Option_Ooption_OSome(U_17372),U_17373)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4214_1]) ).

cnf(f_4214_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_17372)),hAPP(c_Option_Ooption_OSome(U_17372),U_17373)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4214_2]) ).

fof(f_4215_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_4215_2,plain,
    ! [U_17376,U_17375,U_17374] : hAPP(c_List_Otl(U_17374),hAPP(hAPP(c_List_Odrop(U_17374),U_17375),U_17376)) = hAPP(hAPP(c_List_Odrop(U_17374),U_17375),hAPP(c_List_Otl(U_17374),U_17376)),
    inference(variable_rename,[status(thm)],[f_4215_1]) ).

cnf(f_4215_3,plain,
    hAPP(c_List_Otl(U_17374),hAPP(hAPP(c_List_Odrop(U_17374),U_17375),U_17376)) = hAPP(hAPP(c_List_Odrop(U_17374),U_17375),hAPP(c_List_Otl(U_17374),U_17376)),
    inference(clausify,[status(thm)],[f_4215_2]) ).

fof(f_4216_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_4216_2,plain,
    ! [U_17379,U_17378,U_17377] : hAPP(hAPP(c_List_Odrop(U_17377),U_17378),hAPP(c_List_Otl(U_17377),U_17379)) = hAPP(c_List_Otl(U_17377),hAPP(hAPP(c_List_Odrop(U_17377),U_17378),U_17379)),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

cnf(f_4216_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17377),U_17378),hAPP(c_List_Otl(U_17377),U_17379)) = hAPP(c_List_Otl(U_17377),hAPP(hAPP(c_List_Odrop(U_17377),U_17378),U_17379)),
    inference(clausify,[status(thm)],[f_4216_2]) ).

fof(f_4217_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_4217_2,plain,
    ! [U_17380] : hAPP(c_List_Otl(U_17380),c_List_Olist_ONil(U_17380)) = c_List_Olist_ONil(U_17380),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

cnf(f_4217_3,plain,
    hAPP(c_List_Otl(U_17380),c_List_Olist_ONil(U_17380)) = c_List_Olist_ONil(U_17380),
    inference(clausify,[status(thm)],[f_4217_2]) ).

fof(f_4218_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_4218_2,plain,
    ! [U_17382,U_17381] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17381),hAPP(c_List_Otl(U_17381),U_17382)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17381),U_17382)) ),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

cnf(f_4218_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17381),hAPP(c_List_Otl(U_17381),U_17382)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17381),U_17382)) ),
    inference(clausify,[status(thm)],[f_4218_2]) ).

fof(f_4219_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_4219_2,plain,
    ! [U_17385,U_17384,U_17383] : hAPP(c_List_Otl(U_17383),hAPP(hAPP(c_List_Olist_OCons(U_17383),U_17384),U_17385)) = U_17385,
    inference(variable_rename,[status(thm)],[f_4219_1]) ).

cnf(f_4219_3,plain,
    hAPP(c_List_Otl(U_17383),hAPP(hAPP(c_List_Olist_OCons(U_17383),U_17384),U_17385)) = U_17385,
    inference(clausify,[status(thm)],[f_4219_2]) ).

fof(f_4220_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_4220_2,plain,
    ! [U_17388,U_17387,U_17386] :
      ( hAPP(c_List_Otl(U_17387),hAPP(hAPP(c_List_Oappend(U_17387),U_17386),U_17388)) = hAPP(hAPP(c_List_Oappend(U_17387),hAPP(c_List_Otl(U_17387),U_17386)),U_17388)
      | U_17386 = c_List_Olist_ONil(U_17387) ),
    inference(variable_rename,[status(thm)],[f_4220_1]) ).

cnf(f_4220_3,plain,
    ( hAPP(c_List_Otl(U_17387),hAPP(hAPP(c_List_Oappend(U_17387),U_17386),U_17388)) = hAPP(hAPP(c_List_Oappend(U_17387),hAPP(c_List_Otl(U_17387),U_17386)),U_17388)
    | U_17386 = c_List_Olist_ONil(U_17387) ),
    inference(clausify,[status(thm)],[f_4220_2]) ).

fof(f_4221_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_4221_2,plain,
    ! [U_17391,U_17390,U_17389] : hAPP(hAPP(c_List_Otake(U_17389),U_17390),hAPP(c_List_Otl(U_17389),U_17391)) = hAPP(c_List_Otl(U_17389),hAPP(hAPP(c_List_Otake(U_17389),hAPP(c_Nat_OSuc,U_17390)),U_17391)),
    inference(variable_rename,[status(thm)],[f_4221_1]) ).

cnf(f_4221_3,plain,
    hAPP(hAPP(c_List_Otake(U_17389),U_17390),hAPP(c_List_Otl(U_17389),U_17391)) = hAPP(c_List_Otl(U_17389),hAPP(hAPP(c_List_Otake(U_17389),hAPP(c_Nat_OSuc,U_17390)),U_17391)),
    inference(clausify,[status(thm)],[f_4221_2]) ).

fof(f_4222_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_4222_2,plain,
    ! [U_17394,U_17393,U_17392] : hAPP(hAPP(c_List_Odrop(U_17392),hAPP(c_Nat_OSuc,U_17393)),U_17394) = hAPP(hAPP(c_List_Odrop(U_17392),U_17393),hAPP(c_List_Otl(U_17392),U_17394)),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

cnf(f_4222_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17392),hAPP(c_Nat_OSuc,U_17393)),U_17394) = hAPP(hAPP(c_List_Odrop(U_17392),U_17393),hAPP(c_List_Otl(U_17392),U_17394)),
    inference(clausify,[status(thm)],[f_4222_2]) ).

fof(f_4223_1,plain,
    ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_tl__append]) ).

fof(f_4223_2,plain,
    ! [U_17397,U_17396,U_17395] : hAPP(c_List_Otl(U_17395),hAPP(hAPP(c_List_Oappend(U_17395),U_17396),U_17397)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_17395),U_17395,hAPP(c_List_Otl(U_17395),U_17397),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17395),tc_List_Olist(U_17395)),U_17395),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17395),tc_List_Olist(U_17395),tc_List_Olist(U_17395)),c_List_Oappend(U_17395)),U_17397))),U_17396),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

cnf(f_4223_3,plain,
    hAPP(c_List_Otl(U_17395),hAPP(hAPP(c_List_Oappend(U_17395),U_17396),U_17397)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_17395),U_17395,hAPP(c_List_Otl(U_17395),U_17397),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17395),tc_List_Olist(U_17395)),U_17395),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17395),tc_List_Olist(U_17395),tc_List_Olist(U_17395)),c_List_Oappend(U_17395)),U_17397))),U_17396),
    inference(clausify,[status(thm)],[f_4223_2]) ).

fof(f_4224_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_4224_2,plain,
    ! [U_17399,U_17398] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),hAPP(c_List_Otl(U_17398),U_17399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17399)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4224_1]) ).

cnf(f_4224_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),hAPP(c_List_Otl(U_17398),U_17399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17399)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4224_2]) ).

fof(f_4225_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_4225_2,plain,
    ! [U_17402,U_17401,U_17400] : hAPP(c_List_Otl(U_17400),hAPP(hAPP(c_List_Otake(U_17400),U_17401),U_17402)) = hAPP(hAPP(c_List_Otake(U_17400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17401),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_17400),U_17402)),
    inference(variable_rename,[status(thm)],[f_4225_1]) ).

cnf(f_4225_3,plain,
    hAPP(c_List_Otl(U_17400),hAPP(hAPP(c_List_Otake(U_17400),U_17401),U_17402)) = hAPP(hAPP(c_List_Otake(U_17400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17401),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_17400),U_17402)),
    inference(clausify,[status(thm)],[f_4225_2]) ).

fof(f_4226_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_4226_2,plain,
    ! [U_17405,U_17404,U_17403] :
      ( hAPP(hAPP(c_List_Otake(U_17404),hAPP(c_Nat_OSuc,U_17405)),U_17403) = hAPP(hAPP(c_List_Olist_OCons(U_17404),hAPP(c_List_Ohd(U_17404),U_17403)),hAPP(hAPP(c_List_Otake(U_17404),U_17405),hAPP(c_List_Otl(U_17404),U_17403)))
      | U_17403 = c_List_Olist_ONil(U_17404) ),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

cnf(f_4226_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_17404),hAPP(c_Nat_OSuc,U_17405)),U_17403) = hAPP(hAPP(c_List_Olist_OCons(U_17404),hAPP(c_List_Ohd(U_17404),U_17403)),hAPP(hAPP(c_List_Otake(U_17404),U_17405),hAPP(c_List_Otl(U_17404),U_17403)))
    | U_17403 = c_List_Olist_ONil(U_17404) ),
    inference(clausify,[status(thm)],[f_4226_2]) ).

fof(f_4227_1,plain,
    ! [V_xs_2,T_a] :
      ( hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_a)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__set]) ).

fof(f_4227_2,plain,
    ! [U_17407,U_17406] :
      ( hAPP(c_Finite__Set_Ofold1(U_17406,c_Groups_Otimes__class_Otimes(U_17406)),hAPP(c_List_Oset(U_17406),U_17407)) = hAPP(c_List_Ofoldl(U_17406,U_17406,c_Groups_Otimes__class_Otimes(U_17406),hAPP(c_List_Ohd(U_17406),U_17407)),hAPP(c_List_Otl(U_17406),U_17407))
      | U_17407 = c_List_Olist_ONil(U_17406)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_17406) ),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

cnf(f_4227_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_17406,c_Groups_Otimes__class_Otimes(U_17406)),hAPP(c_List_Oset(U_17406),U_17407)) = hAPP(c_List_Ofoldl(U_17406,U_17406,c_Groups_Otimes__class_Otimes(U_17406),hAPP(c_List_Ohd(U_17406),U_17407)),hAPP(c_List_Otl(U_17406),U_17407))
    | U_17407 = c_List_Olist_ONil(U_17406)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_17406) ),
    inference(clausify,[status(thm)],[f_4227_2]) ).

fof(f_4228_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_4228_2,plain,
    ! [U_17410,U_17409,U_17408] :
      ( hAPP(c_List_Ohd(U_17409),hAPP(c_List_Orotate(U_17409,U_17410),U_17408)) = hAPP(hAPP(c_List_Onth(U_17409),U_17408),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17410,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17409)),U_17408)))
      | U_17408 = c_List_Olist_ONil(U_17409) ),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

cnf(f_4228_3,plain,
    ( hAPP(c_List_Ohd(U_17409),hAPP(c_List_Orotate(U_17409,U_17410),U_17408)) = hAPP(hAPP(c_List_Onth(U_17409),U_17408),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17410,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17409)),U_17408)))
    | U_17408 = c_List_Olist_ONil(U_17409) ),
    inference(clausify,[status(thm)],[f_4228_2]) ).

fof(f_4229_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_4229_2,plain,
    ! [U_17413,U_17412,U_17411] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17411)),hAPP(c_List_Orotate(U_17411,U_17412),U_17413)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17411)),U_17413),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

cnf(f_4229_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17411)),hAPP(c_List_Orotate(U_17411,U_17412),U_17413)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17411)),U_17413),
    inference(clausify,[status(thm)],[f_4229_2]) ).

fof(f_4230_1,plain,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__append]) ).

fof(f_4230_2,plain,
    ! [U_17419,U_17418,U_17417,U_17416,U_17415,U_17414] : hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,U_17417),hAPP(hAPP(c_List_Oappend(U_17415),U_17418),U_17419)) = hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,U_17417),U_17418)),U_17419),
    inference(variable_rename,[status(thm)],[f_4230_1]) ).

cnf(f_4230_3,plain,
    hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,U_17417),hAPP(hAPP(c_List_Oappend(U_17415),U_17418),U_17419)) = hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,hAPP(c_List_Ofoldl(U_17414,U_17415,U_17416,U_17417),U_17418)),U_17419),
    inference(clausify,[status(thm)],[f_4230_2]) ).

fof(f_4231_1,plain,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,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_4231_2,plain,
    ! [U_17425,U_17424,U_17423,U_17422,U_17421,U_17420] : hAPP(c_List_Ofoldl(U_17420,U_17421,U_17422,U_17423),hAPP(hAPP(c_List_Olist_OCons(U_17421),U_17424),U_17425)) = hAPP(c_List_Ofoldl(U_17420,U_17421,U_17422,hAPP(hAPP(U_17422,U_17423),U_17424)),U_17425),
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

cnf(f_4231_3,plain,
    hAPP(c_List_Ofoldl(U_17420,U_17421,U_17422,U_17423),hAPP(hAPP(c_List_Olist_OCons(U_17421),U_17424),U_17425)) = hAPP(c_List_Ofoldl(U_17420,U_17421,U_17422,hAPP(hAPP(U_17422,U_17423),U_17424)),U_17425),
    inference(clausify,[status(thm)],[f_4231_2]) ).

fof(f_4232_1,plain,
    ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate]) ).

fof(f_4232_2,plain,
    ! [U_17428,U_17427,U_17426] : hAPP(c_List_Oset(U_17426),hAPP(c_List_Orotate(U_17426,U_17427),U_17428)) = hAPP(c_List_Oset(U_17426),U_17428),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

cnf(f_4232_3,plain,
    hAPP(c_List_Oset(U_17426),hAPP(c_List_Orotate(U_17426,U_17427),U_17428)) = hAPP(c_List_Oset(U_17426),U_17428),
    inference(clausify,[status(thm)],[f_4232_2]) ).

fof(f_4233_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_4233_2,plain,
    ! [U_17431,U_17430,U_17429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17429),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17430),U_17431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17429),U_17430)) ),
    inference(variable_rename,[status(thm)],[f_4233_1]) ).

cnf(f_4233_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17429),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17430),U_17431)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17429),U_17430)) ),
    inference(clausify,[status(thm)],[f_4233_2]) ).

fof(f_4234_1,plain,
    ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)),
    inference(fof_nnf,[status(thm)],[fact_rotate0]) ).

fof(f_4234_2,plain,
    ! [U_17432] : c_List_Orotate(U_17432,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_17432)),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

cnf(f_4234_3,plain,
    c_List_Orotate(U_17432,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_17432)),
    inference(clausify,[status(thm)],[f_4234_2]) ).

fof(f_4235_1,plain,
    ! [V_zs_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2)
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__absorb0]) ).

fof(f_4235_2,plain,
    ! [U_17435,U_17434,U_17433] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17433),U_17434),hAPP(c_List_Ofoldl(U_17433,U_17433,c_Groups_Oplus__class_Oplus(U_17433),c_Groups_Ozero__class_Ozero(U_17433)),U_17435)) = hAPP(c_List_Ofoldl(U_17433,U_17433,c_Groups_Oplus__class_Oplus(U_17433),U_17434),U_17435)
      | ~ class_Groups_Omonoid__add(U_17433) ),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

cnf(f_4235_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17433),U_17434),hAPP(c_List_Ofoldl(U_17433,U_17433,c_Groups_Oplus__class_Oplus(U_17433),c_Groups_Ozero__class_Ozero(U_17433)),U_17435)) = hAPP(c_List_Ofoldl(U_17433,U_17433,c_Groups_Oplus__class_Oplus(U_17433),U_17434),U_17435)
    | ~ class_Groups_Omonoid__add(U_17433) ),
    inference(clausify,[status(thm)],[f_4235_2]) ).

fof(f_4236_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_a] :
      ( hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2))
      | ~ class_Groups_Osemigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__assoc]) ).

fof(f_4236_2,plain,
    ! [U_17439,U_17438,U_17437,U_17436] :
      ( hAPP(c_List_Ofoldl(U_17436,U_17436,c_Groups_Oplus__class_Oplus(U_17436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17436),U_17437),U_17438)),U_17439) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17436),U_17437),hAPP(c_List_Ofoldl(U_17436,U_17436,c_Groups_Oplus__class_Oplus(U_17436),U_17438),U_17439))
      | ~ class_Groups_Osemigroup__add(U_17436) ),
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

cnf(f_4236_3,plain,
    ( hAPP(c_List_Ofoldl(U_17436,U_17436,c_Groups_Oplus__class_Oplus(U_17436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17436),U_17437),U_17438)),U_17439) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17436),U_17437),hAPP(c_List_Ofoldl(U_17436,U_17436,c_Groups_Oplus__class_Oplus(U_17436),U_17438),U_17439))
    | ~ class_Groups_Osemigroup__add(U_17436) ),
    inference(clausify,[status(thm)],[f_4236_2]) ).

fof(f_4237_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_4237_2,plain,
    ! [U_17443,U_17442,U_17441,U_17440] : hAPP(c_List_Orotate(U_17440,U_17441),hAPP(c_List_Orotate(U_17440,U_17442),U_17443)) = hAPP(c_List_Orotate(U_17440,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17441),U_17442)),U_17443),
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

cnf(f_4237_3,plain,
    hAPP(c_List_Orotate(U_17440,U_17441),hAPP(c_List_Orotate(U_17440,U_17442),U_17443)) = hAPP(c_List_Orotate(U_17440,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17441),U_17442)),U_17443),
    inference(clausify,[status(thm)],[f_4237_2]) ).

fof(f_4238_1,plain,
    ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__add]) ).

fof(f_4238_2,plain,
    ! [U_17446,U_17445,U_17444] : c_List_Orotate(U_17444,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17445),U_17446)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_17444),tc_List_Olist(U_17444),tc_List_Olist(U_17444),c_List_Orotate(U_17444,U_17445)),c_List_Orotate(U_17444,U_17446)),
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

cnf(f_4238_3,plain,
    c_List_Orotate(U_17444,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17445),U_17446)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_17444),tc_List_Olist(U_17444),tc_List_Olist(U_17444),c_List_Orotate(U_17444,U_17445)),c_List_Orotate(U_17444,U_17446)),
    inference(clausify,[status(thm)],[f_4238_2]) ).

fof(f_4239_1,plain,
    ! [V_xs_2,V_n_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rotate]) ).

fof(f_4239_2,plain,
    ! [U_17449,U_17448,U_17447] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17447),hAPP(c_List_Orotate(U_17447,U_17448),U_17449)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17447),U_17449)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_17447),U_17449))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17447),hAPP(c_List_Orotate(U_17447,U_17448),U_17449))) ) ),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

fof(f_4239_3,plain,
    ( ! [U_17455,U_17453,U_17451] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17451),hAPP(c_List_Orotate(U_17451,U_17453),U_17455)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17451),U_17455)) )
    & ! [U_17454,U_17452,U_17450] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17450),U_17454))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17450),hAPP(c_List_Orotate(U_17450,U_17452),U_17454))) ) ),
    inference(miniscope,[status(thm)],[f_4239_2]) ).

cnf(f_4239_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17450),U_17454))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17450),hAPP(c_List_Orotate(U_17450,U_17452),U_17454))) ),
    inference(clausify,[status(thm)],[f_4239_3]) ).

cnf(f_4239_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17451),hAPP(c_List_Orotate(U_17451,U_17453),U_17455)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17451),U_17455)) ),
    inference(clausify,[status(thm)],[f_4239_3]) ).

fof(f_4240_1,plain,
    ! [V_xs_2,V_n_2,T_a] :
      ( ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv]) ).

fof(f_4240_2,plain,
    ! [U_17458,U_17457,U_17456] :
      ( ( hAPP(c_List_Orotate(U_17456,U_17457),U_17458) = c_List_Olist_ONil(U_17456)
        | U_17458 != c_List_Olist_ONil(U_17456) )
      & ( U_17458 = c_List_Olist_ONil(U_17456)
        | hAPP(c_List_Orotate(U_17456,U_17457),U_17458) != c_List_Olist_ONil(U_17456) ) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

fof(f_4240_3,plain,
    ( ! [U_17464,U_17462,U_17460] :
        ( hAPP(c_List_Orotate(U_17460,U_17462),U_17464) = c_List_Olist_ONil(U_17460)
        | U_17464 != c_List_Olist_ONil(U_17460) )
    & ! [U_17463,U_17461,U_17459] :
        ( U_17463 = c_List_Olist_ONil(U_17459)
        | hAPP(c_List_Orotate(U_17459,U_17461),U_17463) != c_List_Olist_ONil(U_17459) ) ),
    inference(miniscope,[status(thm)],[f_4240_2]) ).

cnf(f_4240_4,plain,
    ( U_17463 = c_List_Olist_ONil(U_17459)
    | hAPP(c_List_Orotate(U_17459,U_17461),U_17463) != c_List_Olist_ONil(U_17459) ),
    inference(clausify,[status(thm)],[f_4240_3]) ).

cnf(f_4240_5,plain,
    ( hAPP(c_List_Orotate(U_17460,U_17462),U_17464) = c_List_Olist_ONil(U_17460)
    | U_17464 != c_List_Olist_ONil(U_17460) ),
    inference(clausify,[status(thm)],[f_4240_3]) ).

fof(f_4241_1,plain,
    ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldl__Nil]) ).

fof(f_4241_2,plain,
    ! [U_17468,U_17467,U_17466,U_17465] : hAPP(c_List_Ofoldl(U_17465,U_17466,U_17467,U_17468),c_List_Olist_ONil(U_17466)) = U_17468,
    inference(variable_rename,[status(thm)],[f_4241_1]) ).

cnf(f_4241_3,plain,
    hAPP(c_List_Ofoldl(U_17465,U_17466,U_17467,U_17468),c_List_Olist_ONil(U_17466)) = U_17468,
    inference(clausify,[status(thm)],[f_4241_2]) ).

fof(f_4242_1,plain,
    ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)),
    inference(fof_nnf,[status(thm)],[fact_rotate__def]) ).

fof(f_4242_2,plain,
    ! [U_17470,U_17469] : c_List_Orotate(U_17469,U_17470) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_17469),tc_List_Olist(U_17469)),U_17470),c_List_Orotate1(U_17469)),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

cnf(f_4242_3,plain,
    c_List_Orotate(U_17469,U_17470) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_17469),tc_List_Olist(U_17469)),U_17470),c_List_Orotate1(U_17469)),
    inference(clausify,[status(thm)],[f_4242_2]) ).

fof(f_4243_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_4243_2,plain,
    ! [U_17473,U_17472,U_17471] : hAPP(c_List_Orotate1(U_17471),hAPP(c_List_Orotate(U_17471,U_17472),U_17473)) = hAPP(c_List_Orotate(U_17471,U_17472),hAPP(c_List_Orotate1(U_17471),U_17473)),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

cnf(f_4243_3,plain,
    hAPP(c_List_Orotate1(U_17471),hAPP(c_List_Orotate(U_17471,U_17472),U_17473)) = hAPP(c_List_Orotate(U_17471,U_17472),hAPP(c_List_Orotate1(U_17471),U_17473)),
    inference(clausify,[status(thm)],[f_4243_2]) ).

fof(f_4244_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_4244_2,plain,
    ! [U_17476,U_17475,U_17474] : hAPP(c_List_Orotate(U_17474,U_17475),U_17476) = hAPP(c_List_Orotate(U_17474,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17475,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17474)),U_17476))),U_17476),
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

cnf(f_4244_3,plain,
    hAPP(c_List_Orotate(U_17474,U_17475),U_17476) = hAPP(c_List_Orotate(U_17474,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17475,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17474)),U_17476))),U_17476),
    inference(clausify,[status(thm)],[f_4244_2]) ).

fof(f_4245_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_4245_2,plain,
    ! [U_17479,U_17478,U_17477] : hAPP(c_List_Orotate(U_17477,hAPP(c_Nat_OSuc,U_17478)),U_17479) = hAPP(c_List_Orotate1(U_17477),hAPP(c_List_Orotate(U_17477,U_17478),U_17479)),
    inference(variable_rename,[status(thm)],[f_4245_1]) ).

cnf(f_4245_3,plain,
    hAPP(c_List_Orotate(U_17477,hAPP(c_Nat_OSuc,U_17478)),U_17479) = hAPP(c_List_Orotate1(U_17477),hAPP(c_List_Orotate(U_17477,U_17478),U_17479)),
    inference(clausify,[status(thm)],[f_4245_2]) ).

fof(f_4246_1,plain,
    ! [T_a] :
      ( c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__foldl]) ).

fof(f_4246_2,plain,
    ! [U_17480] :
      ( c_List_Omonoid__add__class_Olistsum(U_17480) = c_List_Ofoldl(U_17480,U_17480,c_Groups_Oplus__class_Oplus(U_17480),c_Groups_Ozero__class_Ozero(U_17480))
      | ~ class_Groups_Omonoid__add(U_17480) ),
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

cnf(f_4246_3,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_17480) = c_List_Ofoldl(U_17480,U_17480,c_Groups_Oplus__class_Oplus(U_17480),c_Groups_Ozero__class_Ozero(U_17480))
    | ~ class_Groups_Omonoid__add(U_17480) ),
    inference(clausify,[status(thm)],[f_4246_2]) ).

fof(f_4247_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_4247_2,plain,
    ! [U_17484,U_17483] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17483),U_17484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_17482] :
            ( U_17482 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17482),hAPP(c_List_Oset(tc_Nat_Onat),U_17484))) )
        | U_17483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_17481] :
              ( U_17481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17481),hAPP(c_List_Oset(tc_Nat_Onat),U_17484))) )
          & U_17483 = 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_17483),U_17484) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

fof(f_4247_3,plain,
    ( ! [U_17488,U_17486] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17486),U_17488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_17482] :
            ( U_17482 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17482),hAPP(c_List_Oset(tc_Nat_Onat),U_17488))) )
        | U_17486 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17487,U_17485] :
        ( ( ! [U_17481] :
              ( U_17481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17481),hAPP(c_List_Oset(tc_Nat_Onat),U_17487))) )
          & U_17485 = 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_17485),U_17487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4247_2]) ).

fof(f_4247_4,plain,
    ( ! [U_17488,U_17486] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17486),U_17488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK450(U_17488,U_17486) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK450(U_17488,U_17486)),hAPP(c_List_Oset(tc_Nat_Onat),U_17488))) )
        | U_17486 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17487,U_17485] :
        ( ( ! [U_17481] :
              ( U_17481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17481),hAPP(c_List_Oset(tc_Nat_Onat),U_17487))) )
          & U_17485 = 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_17485),U_17487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_17482,sK450(U_17488,U_17486))],[f_4247_3]) ).

cnf(f_4247_5,plain,
    ( U_17485 = 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_17485),U_17487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

cnf(f_4247_6,plain,
    ( U_17481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17481),hAPP(c_List_Oset(tc_Nat_Onat),U_17487)))
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17485),U_17487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

cnf(f_4247_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK450(U_17488,U_17486)),hAPP(c_List_Oset(tc_Nat_Onat),U_17488)))
    | U_17486 != 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_17486),U_17488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

cnf(f_4247_8,plain,
    ( sK450(U_17488,U_17486) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_17486 != 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_17486),U_17488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

fof(f_4248_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_4248_2,plain,
    ! [U_17491,U_17490,U_17489] :
      ( hAPP(c_List_Orotate(U_17490,U_17489),U_17491) = U_17491
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17489,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17490)),U_17491)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

cnf(f_4248_3,plain,
    ( hAPP(c_List_Orotate(U_17490,U_17489),U_17491) = U_17491
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17489,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17490)),U_17491)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4248_2]) ).

fof(f_4249_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_4249_2,plain,
    ! [U_17494,U_17493,U_17492] :
      ( hAPP(c_List_Orotate(U_17492,U_17494),U_17493) = U_17493
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17492)),U_17493)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

cnf(f_4249_3,plain,
    ( hAPP(c_List_Orotate(U_17492,U_17494),U_17493) = U_17493
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17492)),U_17493)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4249_2]) ).

fof(f_4250_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set]) ).

fof(f_4250_2,plain,
    ! [U_17499,U_17498,U_17497,U_17496,U_17495] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_17495,U_17496,U_17497),U_17498),hAPP(c_List_Oset(U_17495),U_17499)) = hAPP(c_List_Ofoldl(U_17496,U_17495,hAPP(c_COMBC(U_17495,U_17496,U_17496),U_17497),U_17498),U_17499)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_17495,U_17496,U_17497) ),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

cnf(f_4250_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_17495,U_17496,U_17497),U_17498),hAPP(c_List_Oset(U_17495),U_17499)) = hAPP(c_List_Ofoldl(U_17496,U_17495,hAPP(c_COMBC(U_17495,U_17496,U_17496),U_17497),U_17498),U_17499)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_17495,U_17496,U_17497) ),
    inference(clausify,[status(thm)],[f_4250_2]) ).

fof(f_4251_1,plain,
    ! [V_xs_2,T_a] :
      ( c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__set__fold]) ).

fof(f_4251_2,plain,
    ! [U_17501,U_17500] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17500,hAPP(c_List_Oset(U_17500),U_17501)) = hAPP(c_List_Ofoldl(U_17500,U_17500,c_Lattices_Osemilattice__sup__class_Osup(U_17500),c_Orderings_Obot__class_Obot(U_17500)),U_17501)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17500) ),
    inference(variable_rename,[status(thm)],[f_4251_1]) ).

cnf(f_4251_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17500,hAPP(c_List_Oset(U_17500),U_17501)) = hAPP(c_List_Ofoldl(U_17500,U_17500,c_Lattices_Osemilattice__sup__class_Osup(U_17500),c_Orderings_Obot__class_Obot(U_17500)),U_17501)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17500) ),
    inference(clausify,[status(thm)],[f_4251_2]) ).

fof(f_4252_1,plain,
    ! [V_xs_2,T_a] :
      ( c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__set__fold]) ).

fof(f_4252_2,plain,
    ! [U_17503,U_17502] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17502,hAPP(c_List_Oset(U_17502),U_17503)) = hAPP(c_List_Ofoldl(U_17502,U_17502,c_Lattices_Osemilattice__inf__class_Oinf(U_17502),c_Orderings_Otop__class_Otop(U_17502)),U_17503)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17502) ),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

cnf(f_4252_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17502,hAPP(c_List_Oset(U_17502),U_17503)) = hAPP(c_List_Ofoldl(U_17502,U_17502,c_Lattices_Osemilattice__inf__class_Oinf(U_17502),c_Orderings_Otop__class_Otop(U_17502)),U_17503)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17502) ),
    inference(clausify,[status(thm)],[f_4252_2]) ).

fof(f_4253_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold]) ).

fof(f_4253_2,plain,
    ! [U_17506,U_17505,U_17504] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_17504,hAPP(c_List_Oset(U_17504),hAPP(hAPP(c_List_Olist_OCons(U_17504),U_17505),U_17506))) = hAPP(c_List_Ofoldl(U_17504,U_17504,c_Lattices_Osemilattice__sup__class_Osup(U_17504),U_17505),U_17506)
      | ~ class_Lattices_Olattice(U_17504) ),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

cnf(f_4253_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_17504,hAPP(c_List_Oset(U_17504),hAPP(hAPP(c_List_Olist_OCons(U_17504),U_17505),U_17506))) = hAPP(c_List_Ofoldl(U_17504,U_17504,c_Lattices_Osemilattice__sup__class_Osup(U_17504),U_17505),U_17506)
    | ~ class_Lattices_Olattice(U_17504) ),
    inference(clausify,[status(thm)],[f_4253_2]) ).

fof(f_4254_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold]) ).

fof(f_4254_2,plain,
    ! [U_17509,U_17508,U_17507] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_17507,hAPP(c_List_Oset(U_17507),hAPP(hAPP(c_List_Olist_OCons(U_17507),U_17508),U_17509))) = hAPP(c_List_Ofoldl(U_17507,U_17507,c_Lattices_Osemilattice__inf__class_Oinf(U_17507),U_17508),U_17509)
      | ~ class_Lattices_Olattice(U_17507) ),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

cnf(f_4254_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_17507,hAPP(c_List_Oset(U_17507),hAPP(hAPP(c_List_Olist_OCons(U_17507),U_17508),U_17509))) = hAPP(c_List_Ofoldl(U_17507,U_17507,c_Lattices_Osemilattice__inf__class_Oinf(U_17507),U_17508),U_17509)
    | ~ class_Lattices_Olattice(U_17507) ),
    inference(clausify,[status(thm)],[f_4254_2]) ).

fof(f_4255_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold]) ).

fof(f_4255_2,plain,
    ! [U_17512,U_17511,U_17510] :
      ( c_Big__Operators_Olinorder__class_OMin(U_17510,hAPP(c_List_Oset(U_17510),hAPP(hAPP(c_List_Olist_OCons(U_17510),U_17511),U_17512))) = hAPP(c_List_Ofoldl(U_17510,U_17510,c_Orderings_Oord__class_Omin(U_17510),U_17511),U_17512)
      | ~ class_Orderings_Olinorder(U_17510) ),
    inference(variable_rename,[status(thm)],[f_4255_1]) ).

cnf(f_4255_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_17510,hAPP(c_List_Oset(U_17510),hAPP(hAPP(c_List_Olist_OCons(U_17510),U_17511),U_17512))) = hAPP(c_List_Ofoldl(U_17510,U_17510,c_Orderings_Oord__class_Omin(U_17510),U_17511),U_17512)
    | ~ class_Orderings_Olinorder(U_17510) ),
    inference(clausify,[status(thm)],[f_4255_2]) ).

fof(f_4256_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold]) ).

fof(f_4256_2,plain,
    ! [U_17515,U_17514,U_17513] :
      ( c_Big__Operators_Olinorder__class_OMax(U_17513,hAPP(c_List_Oset(U_17513),hAPP(hAPP(c_List_Olist_OCons(U_17513),U_17514),U_17515))) = hAPP(c_List_Ofoldl(U_17513,U_17513,c_Orderings_Oord__class_Omax(U_17513),U_17514),U_17515)
      | ~ class_Orderings_Olinorder(U_17513) ),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

cnf(f_4256_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_17513,hAPP(c_List_Oset(U_17513),hAPP(hAPP(c_List_Olist_OCons(U_17513),U_17514),U_17515))) = hAPP(c_List_Ofoldl(U_17513,U_17513,c_Orderings_Oord__class_Omax(U_17513),U_17514),U_17515)
    | ~ class_Orderings_Olinorder(U_17513) ),
    inference(clausify,[status(thm)],[f_4256_2]) ).

fof(f_4257_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold]) ).

fof(f_4257_2,plain,
    ! [U_17518,U_17517,U_17516] :
      ( c_Big__Operators_Olattice_OInf__fin(U_17516,c_Orderings_Oord__class_Omin(U_17516),hAPP(c_List_Oset(U_17516),hAPP(hAPP(c_List_Olist_OCons(U_17516),U_17517),U_17518))) = hAPP(c_List_Ofoldl(U_17516,U_17516,c_Orderings_Oord__class_Omin(U_17516),U_17517),U_17518)
      | ~ class_Orderings_Olinorder(U_17516) ),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

cnf(f_4257_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_17516,c_Orderings_Oord__class_Omin(U_17516),hAPP(c_List_Oset(U_17516),hAPP(hAPP(c_List_Olist_OCons(U_17516),U_17517),U_17518))) = hAPP(c_List_Ofoldl(U_17516,U_17516,c_Orderings_Oord__class_Omin(U_17516),U_17517),U_17518)
    | ~ class_Orderings_Olinorder(U_17516) ),
    inference(clausify,[status(thm)],[f_4257_2]) ).

fof(f_4258_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold]) ).

fof(f_4258_2,plain,
    ! [U_17521,U_17520,U_17519] :
      ( c_Big__Operators_Olattice_OSup__fin(U_17519,c_Orderings_Oord__class_Omax(U_17519),hAPP(c_List_Oset(U_17519),hAPP(hAPP(c_List_Olist_OCons(U_17519),U_17520),U_17521))) = hAPP(c_List_Ofoldl(U_17519,U_17519,c_Orderings_Oord__class_Omax(U_17519),U_17520),U_17521)
      | ~ class_Orderings_Olinorder(U_17519) ),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

cnf(f_4258_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_17519,c_Orderings_Oord__class_Omax(U_17519),hAPP(c_List_Oset(U_17519),hAPP(hAPP(c_List_Olist_OCons(U_17519),U_17520),U_17521))) = hAPP(c_List_Ofoldl(U_17519,U_17519,c_Orderings_Oord__class_Omax(U_17519),U_17520),U_17521)
    | ~ class_Orderings_Olinorder(U_17519) ),
    inference(clausify,[status(thm)],[f_4258_2]) ).

fof(f_4259_1,plain,
    ! [V_f_2,V_xs_2,T_b,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold]) ).

fof(f_4259_2,plain,
    ! [U_17525,U_17524,U_17523,U_17522] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17523,U_17522),hAPP(c_List_Oset(U_17523),U_17524)),U_17525) = hAPP(c_List_Ofoldl(U_17522,U_17523,hAPP(c_COMBC(U_17523,U_17522,U_17522),hAPP(hAPP(c_COMBB(U_17522,tc_fun(U_17522,U_17522),U_17523),c_Lattices_Osemilattice__sup__class_Osup(U_17522)),U_17525)),c_Orderings_Obot__class_Obot(U_17522)),U_17524)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17522) ),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

cnf(f_4259_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17523,U_17522),hAPP(c_List_Oset(U_17523),U_17524)),U_17525) = hAPP(c_List_Ofoldl(U_17522,U_17523,hAPP(c_COMBC(U_17523,U_17522,U_17522),hAPP(hAPP(c_COMBB(U_17522,tc_fun(U_17522,U_17522),U_17523),c_Lattices_Osemilattice__sup__class_Osup(U_17522)),U_17525)),c_Orderings_Obot__class_Obot(U_17522)),U_17524)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17522) ),
    inference(clausify,[status(thm)],[f_4259_2]) ).

fof(f_4260_1,plain,
    ! [V_f_2,V_xs_2,T_b,T_a] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__set__fold]) ).

fof(f_4260_2,plain,
    ! [U_17529,U_17528,U_17527,U_17526] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17527,U_17526),hAPP(c_List_Oset(U_17527),U_17528)),U_17529) = hAPP(c_List_Ofoldl(U_17526,U_17527,hAPP(c_COMBC(U_17527,U_17526,U_17526),hAPP(hAPP(c_COMBB(U_17526,tc_fun(U_17526,U_17526),U_17527),c_Lattices_Osemilattice__inf__class_Oinf(U_17526)),U_17529)),c_Orderings_Otop__class_Otop(U_17526)),U_17528)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17526) ),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

cnf(f_4260_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17527,U_17526),hAPP(c_List_Oset(U_17527),U_17528)),U_17529) = hAPP(c_List_Ofoldl(U_17526,U_17527,hAPP(c_COMBC(U_17527,U_17526,U_17526),hAPP(hAPP(c_COMBB(U_17526,tc_fun(U_17526,U_17526),U_17527),c_Lattices_Osemilattice__inf__class_Oinf(U_17526)),U_17529)),c_Orderings_Otop__class_Otop(U_17526)),U_17528)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17526) ),
    inference(clausify,[status(thm)],[f_4260_2]) ).

fof(f_4261_1,plain,
    ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__upds__fold__map__upd]) ).

fof(f_4261_2,plain,
    ! [U_17534,U_17533,U_17532,U_17531,U_17530] : c_Map_Omap__upds(U_17530,U_17531,U_17532,U_17533,U_17534) = hAPP(c_List_Ofoldl(tc_fun(U_17530,tc_Option_Ooption(U_17531)),tc_prod(U_17530,U_17531),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),tc_fun(tc_prod(U_17530,U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),c_Product__Type_Oprod_Oprod__case(U_17530,U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),hAPP(hAPP(c_COMBC(tc_fun(U_17530,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),c_COMBC(U_17530,tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531)))),tc_fun(U_17530,tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531))),tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),U_17530),c_COMBB(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531)),U_17531))),c_Fun_Ofun__upd(U_17530,tc_Option_Ooption(U_17531))))),c_Option_Ooption_OSome(U_17531))),U_17532),hAPP(hAPP(c_List_Ozip(U_17530,U_17531),U_17533),U_17534)),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

cnf(f_4261_3,plain,
    c_Map_Omap__upds(U_17530,U_17531,U_17532,U_17533,U_17534) = hAPP(c_List_Ofoldl(tc_fun(U_17530,tc_Option_Ooption(U_17531)),tc_prod(U_17530,U_17531),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),tc_fun(tc_prod(U_17530,U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),c_Product__Type_Oprod_Oprod__case(U_17530,U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),hAPP(hAPP(c_COMBC(tc_fun(U_17530,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17530,tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),c_COMBC(U_17530,tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),hAPP(hAPP(c_COMBB(tc_fun(U_17530,tc_fun(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531)))),tc_fun(U_17530,tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531))))),tc_fun(U_17530,tc_Option_Ooption(U_17531))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531))),tc_fun(tc_fun(U_17531,tc_Option_Ooption(U_17531)),tc_fun(U_17531,tc_fun(U_17530,tc_Option_Ooption(U_17531)))),U_17530),c_COMBB(tc_Option_Ooption(U_17531),tc_fun(U_17530,tc_Option_Ooption(U_17531)),U_17531))),c_Fun_Ofun__upd(U_17530,tc_Option_Ooption(U_17531))))),c_Option_Ooption_OSome(U_17531))),U_17532),hAPP(hAPP(c_List_Ozip(U_17530,U_17531),U_17533),U_17534)),
    inference(clausify,[status(thm)],[f_4261_2]) ).

fof(f_4262_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_4262_2,plain,
    ! [U_17536,U_17535] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17535),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_17536)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17535),hAPP(c_List_Oset(tc_Nat_Onat),U_17536))) ),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

cnf(f_4262_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17535),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_17536)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17535),hAPP(c_List_Oset(tc_Nat_Onat),U_17536))) ),
    inference(clausify,[status(thm)],[f_4262_2]) ).

fof(f_4263_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_4263_2,plain,
    ! [U_17539,U_17538,U_17537] : hAPP(c_List_Orotate(U_17537,U_17538),U_17539) = hAPP(hAPP(c_List_Oappend(U_17537),hAPP(hAPP(c_List_Odrop(U_17537),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17538,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17537)),U_17539))),U_17539)),hAPP(hAPP(c_List_Otake(U_17537),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17538,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17537)),U_17539))),U_17539)),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

cnf(f_4263_3,plain,
    hAPP(c_List_Orotate(U_17537,U_17538),U_17539) = hAPP(hAPP(c_List_Oappend(U_17537),hAPP(hAPP(c_List_Odrop(U_17537),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17538,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17537)),U_17539))),U_17539)),hAPP(hAPP(c_List_Otake(U_17537),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_17538,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17537)),U_17539))),U_17539)),
    inference(clausify,[status(thm)],[f_4263_2]) ).

fof(f_4264_1,plain,
    ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))),
    inference(fof_nnf,[status(thm)],[fact_ran__def]) ).

fof(f_4264_2,plain,
    ! [U_17542,U_17541,U_17540] : c_Map_Oran(U_17540,U_17541,U_17542) = hAPP(c_Set_OCollect(U_17541),hAPP(hAPP(c_COMBB(tc_fun(U_17540,tc_HOL_Obool),tc_HOL_Obool,U_17541),c_HOL_OEx(U_17540)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17541),tc_fun(U_17540,tc_HOL_Obool),U_17541),hAPP(c_COMBC(U_17540,tc_Option_Ooption(U_17541),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17541),tc_fun(tc_Option_Ooption(U_17541),tc_HOL_Obool),U_17540),c_fequal),U_17542))),c_Option_Ooption_OSome(U_17541)))),
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

cnf(f_4264_3,plain,
    c_Map_Oran(U_17540,U_17541,U_17542) = hAPP(c_Set_OCollect(U_17541),hAPP(hAPP(c_COMBB(tc_fun(U_17540,tc_HOL_Obool),tc_HOL_Obool,U_17541),c_HOL_OEx(U_17540)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17541),tc_fun(U_17540,tc_HOL_Obool),U_17541),hAPP(c_COMBC(U_17540,tc_Option_Ooption(U_17541),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17541),tc_fun(tc_Option_Ooption(U_17541),tc_HOL_Obool),U_17540),c_fequal),U_17542))),c_Option_Ooption_OSome(U_17541)))),
    inference(clausify,[status(thm)],[f_4264_2]) ).

fof(f_4265_1,plain,
    ! [V_r_2,V_x_2,T_a,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2)))
      | ! [B_b,B_z] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI]) ).

fof(f_4265_2,plain,
    ! [U_17548,U_17547,U_17546,U_17545] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17546),tc_List_Olist(U_17546))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17546),tc_List_Olist(U_17546)),U_17547),hAPP(hAPP(c_List_Oappend(U_17546),U_17547),U_17545))),c_List_Olexord(U_17546,U_17548)))
      | ! [U_17544,U_17543] : U_17545 != hAPP(hAPP(c_List_Olist_OCons(U_17546),U_17544),U_17543) ),
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

cnf(f_4265_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17546),tc_List_Olist(U_17546))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17546),tc_List_Olist(U_17546)),U_17547),hAPP(hAPP(c_List_Oappend(U_17546),U_17547),U_17545))),c_List_Olexord(U_17546,U_17548)))
    | U_17545 != hAPP(hAPP(c_List_Olist_OCons(U_17546),U_17544),U_17543) ),
    inference(clausify,[status(thm)],[f_4265_2]) ).

fof(f_4266_1,plain,
    ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)))
      | hAPP(V_m_2,V_a_2) != hAPP(c_Option_Ooption_OSome(T_a),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_ranI]) ).

fof(f_4266_2,plain,
    ! [U_17553,U_17552,U_17551,U_17550,U_17549] :
      ( hBOOL(hAPP(hAPP(c_member(U_17551),U_17552),c_Map_Oran(U_17553,U_17551,U_17549)))
      | hAPP(U_17549,U_17550) != hAPP(c_Option_Ooption_OSome(U_17551),U_17552) ),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

cnf(f_4266_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17551),U_17552),c_Map_Oran(U_17553,U_17551,U_17549)))
    | hAPP(U_17549,U_17550) != hAPP(c_Option_Ooption_OSome(U_17551),U_17552) ),
    inference(clausify,[status(thm)],[f_4266_2]) ).

fof(f_4267_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert]) ).

fof(f_4267_2,plain,
    ! [U_17556,U_17555,U_17554] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17554,hAPP(hAPP(c_Set_Oinsert(U_17554),U_17556),U_17555)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17554,U_17554,c_COMBI(U_17554)),U_17556),c_List_Olinorder__class_Osorted__list__of__set(U_17554,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17554,tc_HOL_Obool)),U_17555),hAPP(hAPP(c_Set_Oinsert(U_17554),U_17556),c_Orderings_Obot__class_Obot(tc_fun(U_17554,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17554),U_17555))
      | ~ class_Orderings_Olinorder(U_17554) ),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

cnf(f_4267_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17554,hAPP(hAPP(c_Set_Oinsert(U_17554),U_17556),U_17555)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17554,U_17554,c_COMBI(U_17554)),U_17556),c_List_Olinorder__class_Osorted__list__of__set(U_17554,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17554,tc_HOL_Obool)),U_17555),hAPP(hAPP(c_Set_Oinsert(U_17554),U_17556),c_Orderings_Obot__class_Obot(tc_fun(U_17554,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17554),U_17555))
    | ~ class_Orderings_Olinorder(U_17554) ),
    inference(clausify,[status(thm)],[f_4267_2]) ).

fof(f_4268_1,plain,
    ! [V_r_2,V_y_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2)))
        | ! [B_a,B_x] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) )
      & ( ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left]) ).

fof(f_4268_2,plain,
    ! [U_17563,U_17562,U_17561] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17561),tc_List_Olist(U_17561))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17561),tc_List_Olist(U_17561)),c_List_Olist_ONil(U_17561)),U_17562)),c_List_Olexord(U_17561,U_17563)))
        | ! [U_17560,U_17559] : U_17562 != hAPP(hAPP(c_List_Olist_OCons(U_17561),U_17560),U_17559) )
      & ( ? [U_17558,U_17557] : U_17562 = hAPP(hAPP(c_List_Olist_OCons(U_17561),U_17558),U_17557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17561),tc_List_Olist(U_17561))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17561),tc_List_Olist(U_17561)),c_List_Olist_ONil(U_17561)),U_17562)),c_List_Olexord(U_17561,U_17563))) ) ),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

fof(f_4268_3,plain,
    ( ! [U_17569,U_17567,U_17565] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17565),tc_List_Olist(U_17565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17565),tc_List_Olist(U_17565)),c_List_Olist_ONil(U_17565)),U_17567)),c_List_Olexord(U_17565,U_17569)))
        | ! [U_17560,U_17559] : U_17567 != hAPP(hAPP(c_List_Olist_OCons(U_17565),U_17560),U_17559) )
    & ! [U_17568,U_17566,U_17564] :
        ( ? [U_17558,U_17557] : U_17566 = hAPP(hAPP(c_List_Olist_OCons(U_17564),U_17558),U_17557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17564),tc_List_Olist(U_17564))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17564),tc_List_Olist(U_17564)),c_List_Olist_ONil(U_17564)),U_17566)),c_List_Olexord(U_17564,U_17568))) ) ),
    inference(miniscope,[status(thm)],[f_4268_2]) ).

fof(f_4268_4,plain,
    ( ! [U_17569,U_17567,U_17565] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17565),tc_List_Olist(U_17565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17565),tc_List_Olist(U_17565)),c_List_Olist_ONil(U_17565)),U_17567)),c_List_Olexord(U_17565,U_17569)))
        | ! [U_17560,U_17559] : U_17567 != hAPP(hAPP(c_List_Olist_OCons(U_17565),U_17560),U_17559) )
    & ! [U_17568,U_17566,U_17564] :
        ( ? [U_17557] : U_17566 = hAPP(hAPP(c_List_Olist_OCons(U_17564),sK451(U_17568,U_17566,U_17564)),U_17557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17564),tc_List_Olist(U_17564))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17564),tc_List_Olist(U_17564)),c_List_Olist_ONil(U_17564)),U_17566)),c_List_Olexord(U_17564,U_17568))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_17558,sK451(U_17568,U_17566,U_17564))],[f_4268_3]) ).

fof(f_4268_5,plain,
    ( ! [U_17569,U_17567,U_17565] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17565),tc_List_Olist(U_17565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17565),tc_List_Olist(U_17565)),c_List_Olist_ONil(U_17565)),U_17567)),c_List_Olexord(U_17565,U_17569)))
        | ! [U_17560,U_17559] : U_17567 != hAPP(hAPP(c_List_Olist_OCons(U_17565),U_17560),U_17559) )
    & ! [U_17568,U_17566,U_17564] :
        ( U_17566 = hAPP(hAPP(c_List_Olist_OCons(U_17564),sK451(U_17568,U_17566,U_17564)),sK452(U_17568,U_17566,U_17564))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17564),tc_List_Olist(U_17564))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17564),tc_List_Olist(U_17564)),c_List_Olist_ONil(U_17564)),U_17566)),c_List_Olexord(U_17564,U_17568))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_17557,sK452(U_17568,U_17566,U_17564))],[f_4268_4]) ).

cnf(f_4268_6,plain,
    ( U_17566 = hAPP(hAPP(c_List_Olist_OCons(U_17564),sK451(U_17568,U_17566,U_17564)),sK452(U_17568,U_17566,U_17564))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17564),tc_List_Olist(U_17564))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17564),tc_List_Olist(U_17564)),c_List_Olist_ONil(U_17564)),U_17566)),c_List_Olexord(U_17564,U_17568))) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

cnf(f_4268_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17565),tc_List_Olist(U_17565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17565),tc_List_Olist(U_17565)),c_List_Olist_ONil(U_17565)),U_17567)),c_List_Olexord(U_17565,U_17569)))
    | U_17567 != hAPP(hAPP(c_List_Olist_OCons(U_17565),U_17560),U_17559) ),
    inference(clausify,[status(thm)],[f_4268_5]) ).

fof(f_4269_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_length__insort]) ).

fof(f_4269_2,plain,
    ! [U_17574,U_17573,U_17572,U_17571,U_17570] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17571)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17571,U_17570,U_17572),U_17573),U_17574)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17571)),U_17574))
      | ~ class_Orderings_Olinorder(U_17570) ),
    inference(variable_rename,[status(thm)],[f_4269_1]) ).

cnf(f_4269_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17571)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17571,U_17570,U_17572),U_17573),U_17574)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17571)),U_17574))
    | ~ class_Orderings_Olinorder(U_17570) ),
    inference(clausify,[status(thm)],[f_4269_2]) ).

fof(f_4270_1,plain,
    ! [V_x_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J]) ).

fof(f_4270_2,plain,
    ! [U_17578,U_17577,U_17576,U_17575] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17576,U_17575,U_17577),U_17578),c_List_Olist_ONil(U_17576)) = hAPP(hAPP(c_List_Olist_OCons(U_17576),U_17578),c_List_Olist_ONil(U_17576))
      | ~ class_Orderings_Olinorder(U_17575) ),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

cnf(f_4270_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17576,U_17575,U_17577),U_17578),c_List_Olist_ONil(U_17576)) = hAPP(hAPP(c_List_Olist_OCons(U_17576),U_17578),c_List_Olist_ONil(U_17576))
    | ~ class_Orderings_Olinorder(U_17575) ),
    inference(clausify,[status(thm)],[f_4270_2]) ).

fof(f_4271_1,plain,
    ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(f_4271_2,plain,
    ! [U_17584,U_17583,U_17582,U_17581,U_17580,U_17579] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584)) = hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),U_17584))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17579),hAPP(U_17580,U_17581)),hAPP(U_17580,U_17582))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584)) = hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17579),hAPP(U_17580,U_17581)),hAPP(U_17580,U_17582))) ) )
      | ~ class_Orderings_Olinorder(U_17579) ),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

cnf(f_4271_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584)) = hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17579),hAPP(U_17580,U_17581)),hAPP(U_17580,U_17582)))
    | ~ class_Orderings_Olinorder(U_17579) ),
    inference(clausify,[status(thm)],[f_4271_2]) ).

cnf(f_4271_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),U_17584)) = hAPP(hAPP(c_List_Olist_OCons(U_17583),U_17582),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17583,U_17579,U_17580),U_17581),U_17584))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17579),hAPP(U_17580,U_17581)),hAPP(U_17580,U_17582)))
    | ~ class_Orderings_Olinorder(U_17579) ),
    inference(clausify,[status(thm)],[f_4271_2]) ).

fof(f_4272_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort]) ).

fof(f_4272_2,plain,
    ! [U_17589,U_17588,U_17587,U_17586,U_17585] :
      ( hAPP(c_List_Oset(U_17586),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17586,U_17585,U_17587),U_17588),U_17589)) = hAPP(hAPP(c_Set_Oinsert(U_17586),U_17588),hAPP(c_List_Oset(U_17586),U_17589))
      | ~ class_Orderings_Olinorder(U_17585) ),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

cnf(f_4272_3,plain,
    ( hAPP(c_List_Oset(U_17586),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17586,U_17585,U_17587),U_17588),U_17589)) = hAPP(hAPP(c_Set_Oinsert(U_17586),U_17588),hAPP(c_List_Oset(U_17586),U_17589))
    | ~ class_Orderings_Olinorder(U_17585) ),
    inference(clausify,[status(thm)],[f_4272_2]) ).

fof(f_4273_1,plain,
    ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,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_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm]) ).

fof(f_4273_2,plain,
    ! [U_17595,U_17594,U_17593,U_17592,U_17591,U_17590] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17593),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17592),U_17595)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17592),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17593),U_17595))
      | hAPP(U_17591,U_17592) = hAPP(U_17591,U_17593)
      | ~ class_Orderings_Olinorder(U_17590) ),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

cnf(f_4273_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17593),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17592),U_17595)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17592),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17594,U_17590,U_17591),U_17593),U_17595))
    | hAPP(U_17591,U_17592) = hAPP(U_17591,U_17593)
    | ~ class_Orderings_Olinorder(U_17590) ),
    inference(clausify,[status(thm)],[f_4273_2]) ).

fof(f_4274_1,plain,
    ! [V_xs_2,V_y_2,V_x_2,T_a] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__left__comm]) ).

fof(f_4274_2,plain,
    ! [U_17599,U_17598,U_17597,U_17596] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17597),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),U_17599)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17597),U_17599))
      | ~ class_Orderings_Olinorder(U_17596) ),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

cnf(f_4274_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17597),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),U_17599)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17597),U_17599))
    | ~ class_Orderings_Olinorder(U_17596) ),
    inference(clausify,[status(thm)],[f_4274_2]) ).

fof(f_4275_1,plain,
    ! [T_a] :
      ( c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort]) ).

fof(f_4275_2,plain,
    ! [U_17600] :
      ( c_Finite__Set_Ofun__left__comm(U_17600,tc_List_Olist(U_17600),c_List_Olinorder__class_Oinsort__key(U_17600,U_17600,c_COMBI(U_17600)))
      | ~ class_Orderings_Olinorder(U_17600) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

cnf(f_4275_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_17600,tc_List_Olist(U_17600),c_List_Olinorder__class_Oinsort__key(U_17600,U_17600,c_COMBI(U_17600)))
    | ~ class_Orderings_Olinorder(U_17600) ),
    inference(clausify,[status(thm)],[f_4275_2]) ).

fof(f_4276_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__insort]) ).

fof(f_4276_2,plain,
    ! [U_17603,U_17602,U_17601] :
      ( c_List_Oremove1(U_17601,U_17602,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17601,U_17601,c_COMBI(U_17601)),U_17602),U_17603)) = U_17603
      | ~ class_Orderings_Olinorder(U_17601) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

cnf(f_4276_3,plain,
    ( c_List_Oremove1(U_17601,U_17602,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17601,U_17601,c_COMBI(U_17601)),U_17602),U_17603)) = U_17603
    | ~ class_Orderings_Olinorder(U_17601) ),
    inference(clausify,[status(thm)],[f_4276_2]) ).

fof(f_4277_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__not__Nil]) ).

fof(f_4277_2,plain,
    ! [U_17608,U_17607,U_17606,U_17605,U_17604] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17605,U_17604,U_17606),U_17607),U_17608) != c_List_Olist_ONil(U_17605)
      | ~ class_Orderings_Olinorder(U_17604) ),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

cnf(f_4277_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17605,U_17604,U_17606),U_17607),U_17608) != c_List_Olist_ONil(U_17605)
    | ~ class_Orderings_Olinorder(U_17604) ),
    inference(clausify,[status(thm)],[f_4277_2]) ).

fof(f_4278_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
          | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
            & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort]) ).

fof(f_4278_2,plain,
    ! [U_17613,U_17612,U_17611,U_17610,U_17609] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_17610),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17610,U_17609,U_17611),U_17612),U_17613)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17610),U_17613))
          | hBOOL(hAPP(hAPP(c_member(U_17610),U_17612),hAPP(c_List_Oset(U_17610),U_17613))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_17610),U_17613))
            & ~ hBOOL(hAPP(hAPP(c_member(U_17610),U_17612),hAPP(c_List_Oset(U_17610),U_17613))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17610),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17610,U_17609,U_17611),U_17612),U_17613))) ) )
      | ~ class_Orderings_Olinorder(U_17609) ),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

cnf(f_4278_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17610),U_17612),hAPP(c_List_Oset(U_17610),U_17613)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17610),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17610,U_17609,U_17611),U_17612),U_17613)))
    | ~ class_Orderings_Olinorder(U_17609) ),
    inference(clausify,[status(thm)],[f_4278_2]) ).

cnf(f_4278_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17610),U_17613))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17610),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17610,U_17609,U_17611),U_17612),U_17613)))
    | ~ class_Orderings_Olinorder(U_17609) ),
    inference(clausify,[status(thm)],[f_4278_2]) ).

cnf(f_4278_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17610),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17610,U_17609,U_17611),U_17612),U_17613)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17610),U_17613))
    | hBOOL(hAPP(hAPP(c_member(U_17610),U_17612),hAPP(c_List_Oset(U_17610),U_17613)))
    | ~ class_Orderings_Olinorder(U_17609) ),
    inference(clausify,[status(thm)],[f_4278_2]) ).

fof(f_4279_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(f_4279_2,plain,
    ! [U_17618,U_17617,U_17616,U_17615,U_17614] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_17617,U_17614,U_17615,U_17616,U_17618) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17617,U_17614,U_17615),U_17616),U_17618)
      | hBOOL(hAPP(hAPP(c_member(U_17614),hAPP(U_17615,U_17616)),hAPP(c_Set_Oimage(U_17617,U_17614,U_17615),hAPP(c_List_Oset(U_17617),U_17618))))
      | ~ class_Orderings_Olinorder(U_17614) ),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

cnf(f_4279_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_17617,U_17614,U_17615,U_17616,U_17618) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17617,U_17614,U_17615),U_17616),U_17618)
    | hBOOL(hAPP(hAPP(c_member(U_17614),hAPP(U_17615,U_17616)),hAPP(c_Set_Oimage(U_17617,U_17614,U_17615),hAPP(c_List_Oset(U_17617),U_17618))))
    | ~ class_Orderings_Olinorder(U_17614) ),
    inference(clausify,[status(thm)],[f_4279_2]) ).

fof(f_4280_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort]) ).

fof(f_4280_2,plain,
    ! [U_17621,U_17620,U_17619] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_17619,U_17619,c_COMBI(U_17619),U_17620,U_17621) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17619,U_17619,c_COMBI(U_17619)),U_17620),U_17621)
      | hBOOL(hAPP(hAPP(c_member(U_17619),U_17620),hAPP(c_List_Oset(U_17619),U_17621)))
      | ~ class_Orderings_Olinorder(U_17619) ),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

cnf(f_4280_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_17619,U_17619,c_COMBI(U_17619),U_17620,U_17621) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17619,U_17619,c_COMBI(U_17619)),U_17620),U_17621)
    | hBOOL(hAPP(hAPP(c_member(U_17619),U_17620),hAPP(c_List_Oset(U_17619),U_17621)))
    | ~ class_Orderings_Olinorder(U_17619) ),
    inference(clausify,[status(thm)],[f_4280_2]) ).

fof(f_4281_1,plain,
    ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert]) ).

fof(f_4281_2,plain,
    ! [U_17626,U_17625,U_17624,U_17623,U_17622] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17623),c_List_Olinorder__class_Oinsort__insert__key(U_17623,U_17622,U_17625,U_17626,U_17624)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17623),U_17624))
      | ~ class_Orderings_Olinorder(U_17622) ),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

cnf(f_4281_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17623),c_List_Olinorder__class_Oinsort__insert__key(U_17623,U_17622,U_17625,U_17626,U_17624)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17623),U_17624))
    | ~ class_Orderings_Olinorder(U_17622) ),
    inference(clausify,[status(thm)],[f_4281_2]) ).

fof(f_4282_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__triv]) ).

fof(f_4282_2,plain,
    ! [U_17629,U_17628,U_17627] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_17627,U_17627,c_COMBI(U_17627),U_17628,U_17629) = U_17629
      | ~ hBOOL(hAPP(hAPP(c_member(U_17627),U_17628),hAPP(c_List_Oset(U_17627),U_17629)))
      | ~ class_Orderings_Olinorder(U_17627) ),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

cnf(f_4282_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_17627,U_17627,c_COMBI(U_17627),U_17628,U_17629) = U_17629
    | ~ hBOOL(hAPP(hAPP(c_member(U_17627),U_17628),hAPP(c_List_Oset(U_17627),U_17629)))
    | ~ class_Orderings_Olinorder(U_17627) ),
    inference(clausify,[status(thm)],[f_4282_2]) ).

fof(f_4283_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort__insert]) ).

fof(f_4283_2,plain,
    ! [U_17632,U_17631,U_17630] :
      ( hAPP(c_List_Oset(U_17630),c_List_Olinorder__class_Oinsort__insert__key(U_17630,U_17630,c_COMBI(U_17630),U_17631,U_17632)) = hAPP(hAPP(c_Set_Oinsert(U_17630),U_17631),hAPP(c_List_Oset(U_17630),U_17632))
      | ~ class_Orderings_Olinorder(U_17630) ),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

cnf(f_4283_3,plain,
    ( hAPP(c_List_Oset(U_17630),c_List_Olinorder__class_Oinsort__insert__key(U_17630,U_17630,c_COMBI(U_17630),U_17631,U_17632)) = hAPP(hAPP(c_Set_Oinsert(U_17630),U_17631),hAPP(c_List_Oset(U_17630),U_17632))
    | ~ class_Orderings_Olinorder(U_17630) ),
    inference(clausify,[status(thm)],[f_4283_2]) ).

fof(f_4284_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv]) ).

fof(f_4284_2,plain,
    ! [U_17637,U_17636,U_17635,U_17634,U_17633] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_17636,U_17633,U_17634,U_17635,U_17637) = U_17637
      | ~ hBOOL(hAPP(hAPP(c_member(U_17633),hAPP(U_17634,U_17635)),hAPP(c_Set_Oimage(U_17636,U_17633,U_17634),hAPP(c_List_Oset(U_17636),U_17637))))
      | ~ class_Orderings_Olinorder(U_17633) ),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

cnf(f_4284_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_17636,U_17633,U_17634,U_17635,U_17637) = U_17637
    | ~ hBOOL(hAPP(hAPP(c_member(U_17633),hAPP(U_17634,U_17635)),hAPP(c_Set_Oimage(U_17636,U_17633,U_17634),hAPP(c_List_Oset(U_17636),U_17637))))
    | ~ class_Orderings_Olinorder(U_17633) ),
    inference(clausify,[status(thm)],[f_4284_2]) ).

fof(f_4285_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_4285_2,plain,
    ! [U_17641,U_17640,U_17639,U_17638] :
      ( ( ( c_List_Olast(U_17639,hAPP(hAPP(c_List_Olist__update(U_17639,U_17638),U_17640),U_17641)) = c_List_Olast(U_17639,U_17638)
          | U_17640 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17639)),U_17638)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_17639,hAPP(hAPP(c_List_Olist__update(U_17639,U_17638),U_17640),U_17641)) = U_17641
          | U_17640 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17639)),U_17638)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_17638 = c_List_Olist_ONil(U_17639) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

cnf(f_4285_3,plain,
    ( c_List_Olast(U_17639,hAPP(hAPP(c_List_Olist__update(U_17639,U_17638),U_17640),U_17641)) = U_17641
    | U_17640 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17639)),U_17638)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_17638 = c_List_Olist_ONil(U_17639) ),
    inference(clausify,[status(thm)],[f_4285_2]) ).

cnf(f_4285_4,plain,
    ( c_List_Olast(U_17639,hAPP(hAPP(c_List_Olist__update(U_17639,U_17638),U_17640),U_17641)) = c_List_Olast(U_17639,U_17638)
    | U_17640 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17639)),U_17638)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_17638 = c_List_Olist_ONil(U_17639) ),
    inference(clausify,[status(thm)],[f_4285_2]) ).

fof(f_4286_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_4286_2,plain,
    ! [U_17643,U_17642] :
      ( c_List_Olast(U_17643,U_17642) = hAPP(hAPP(c_List_Onth(U_17643),U_17642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17643)),U_17642)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_17642 = c_List_Olist_ONil(U_17643) ),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

cnf(f_4286_3,plain,
    ( c_List_Olast(U_17643,U_17642) = hAPP(hAPP(c_List_Onth(U_17643),U_17642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17643)),U_17642)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_17642 = c_List_Olist_ONil(U_17643) ),
    inference(clausify,[status(thm)],[f_4286_2]) ).

fof(f_4287_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_4287_2,plain,
    ! [U_17646,U_17645,U_17644] :
      ( c_List_Olast(U_17645,hAPP(hAPP(c_List_Oappend(U_17645),U_17646),U_17644)) = c_List_Olast(U_17645,U_17646)
      | U_17644 != c_List_Olist_ONil(U_17645) ),
    inference(variable_rename,[status(thm)],[f_4287_1]) ).

cnf(f_4287_3,plain,
    ( c_List_Olast(U_17645,hAPP(hAPP(c_List_Oappend(U_17645),U_17646),U_17644)) = c_List_Olast(U_17645,U_17646)
    | U_17644 != c_List_Olist_ONil(U_17645) ),
    inference(clausify,[status(thm)],[f_4287_2]) ).

fof(f_4288_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_4288_2,plain,
    ! [U_17649,U_17648,U_17647] :
      ( c_List_Olast(U_17648,hAPP(hAPP(c_List_Oappend(U_17648),U_17649),U_17647)) = c_List_Olast(U_17648,U_17647)
      | U_17647 = c_List_Olist_ONil(U_17648) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

cnf(f_4288_3,plain,
    ( c_List_Olast(U_17648,hAPP(hAPP(c_List_Oappend(U_17648),U_17649),U_17647)) = c_List_Olast(U_17648,U_17647)
    | U_17647 = c_List_Olist_ONil(U_17648) ),
    inference(clausify,[status(thm)],[f_4288_2]) ).

fof(f_4289_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_4289_2,plain,
    ! [U_17652,U_17651,U_17650] :
      ( ( c_List_Olast(U_17651,hAPP(hAPP(c_List_Oappend(U_17651),U_17652),U_17650)) = c_List_Olast(U_17651,U_17650)
        | U_17650 = c_List_Olist_ONil(U_17651) )
      & ( c_List_Olast(U_17651,hAPP(hAPP(c_List_Oappend(U_17651),U_17652),U_17650)) = c_List_Olast(U_17651,U_17652)
        | U_17650 != c_List_Olist_ONil(U_17651) ) ),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

fof(f_4289_3,plain,
    ( ! [U_17658,U_17656,U_17654] :
        ( c_List_Olast(U_17656,hAPP(hAPP(c_List_Oappend(U_17656),U_17658),U_17654)) = c_List_Olast(U_17656,U_17654)
        | U_17654 = c_List_Olist_ONil(U_17656) )
    & ! [U_17657,U_17655,U_17653] :
        ( c_List_Olast(U_17655,hAPP(hAPP(c_List_Oappend(U_17655),U_17657),U_17653)) = c_List_Olast(U_17655,U_17657)
        | U_17653 != c_List_Olist_ONil(U_17655) ) ),
    inference(miniscope,[status(thm)],[f_4289_2]) ).

cnf(f_4289_4,plain,
    ( c_List_Olast(U_17655,hAPP(hAPP(c_List_Oappend(U_17655),U_17657),U_17653)) = c_List_Olast(U_17655,U_17657)
    | U_17653 != c_List_Olist_ONil(U_17655) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

cnf(f_4289_5,plain,
    ( c_List_Olast(U_17656,hAPP(hAPP(c_List_Oappend(U_17656),U_17658),U_17654)) = c_List_Olast(U_17656,U_17654)
    | U_17654 = c_List_Olist_ONil(U_17656) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

fof(f_4290_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_4290_2,plain,
    ! [U_17661,U_17660,U_17659] :
      ( c_List_Olast(U_17660,hAPP(hAPP(c_List_Olist_OCons(U_17660),U_17661),U_17659)) = U_17661
      | U_17659 != c_List_Olist_ONil(U_17660) ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

cnf(f_4290_3,plain,
    ( c_List_Olast(U_17660,hAPP(hAPP(c_List_Olist_OCons(U_17660),U_17661),U_17659)) = U_17661
    | U_17659 != c_List_Olist_ONil(U_17660) ),
    inference(clausify,[status(thm)],[f_4290_2]) ).

fof(f_4291_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_4291_2,plain,
    ! [U_17664,U_17663,U_17662] :
      ( c_List_Olast(U_17663,hAPP(hAPP(c_List_Olist_OCons(U_17663),U_17664),U_17662)) = c_List_Olast(U_17663,U_17662)
      | U_17662 = c_List_Olist_ONil(U_17663) ),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

cnf(f_4291_3,plain,
    ( c_List_Olast(U_17663,hAPP(hAPP(c_List_Olist_OCons(U_17663),U_17664),U_17662)) = c_List_Olast(U_17663,U_17662)
    | U_17662 = c_List_Olist_ONil(U_17663) ),
    inference(clausify,[status(thm)],[f_4291_2]) ).

fof(f_4292_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_4292_2,plain,
    ! [U_17667,U_17666,U_17665] :
      ( ( c_List_Olast(U_17666,hAPP(hAPP(c_List_Olist_OCons(U_17666),U_17667),U_17665)) = c_List_Olast(U_17666,U_17665)
        | U_17665 = c_List_Olist_ONil(U_17666) )
      & ( c_List_Olast(U_17666,hAPP(hAPP(c_List_Olist_OCons(U_17666),U_17667),U_17665)) = U_17667
        | U_17665 != c_List_Olist_ONil(U_17666) ) ),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

fof(f_4292_3,plain,
    ( ! [U_17673,U_17671,U_17669] :
        ( c_List_Olast(U_17671,hAPP(hAPP(c_List_Olist_OCons(U_17671),U_17673),U_17669)) = c_List_Olast(U_17671,U_17669)
        | U_17669 = c_List_Olist_ONil(U_17671) )
    & ! [U_17672,U_17670,U_17668] :
        ( c_List_Olast(U_17670,hAPP(hAPP(c_List_Olist_OCons(U_17670),U_17672),U_17668)) = U_17672
        | U_17668 != c_List_Olist_ONil(U_17670) ) ),
    inference(miniscope,[status(thm)],[f_4292_2]) ).

cnf(f_4292_4,plain,
    ( c_List_Olast(U_17670,hAPP(hAPP(c_List_Olist_OCons(U_17670),U_17672),U_17668)) = U_17672
    | U_17668 != c_List_Olist_ONil(U_17670) ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

cnf(f_4292_5,plain,
    ( c_List_Olast(U_17671,hAPP(hAPP(c_List_Olist_OCons(U_17671),U_17673),U_17669)) = c_List_Olast(U_17671,U_17669)
    | U_17669 = c_List_Olist_ONil(U_17671) ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

fof(f_4293_1,plain,
    ! [T_a,V_as_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2)))
      | V_as_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__in__set]) ).

fof(f_4293_2,plain,
    ! [U_17675,U_17674] :
      ( hBOOL(hAPP(hAPP(c_member(U_17675),c_List_Olast(U_17675,U_17674)),hAPP(c_List_Oset(U_17675),U_17674)))
      | U_17674 = c_List_Olist_ONil(U_17675) ),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

cnf(f_4293_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17675),c_List_Olast(U_17675,U_17674)),hAPP(c_List_Oset(U_17675),U_17674)))
    | U_17674 = c_List_Olist_ONil(U_17675) ),
    inference(clausify,[status(thm)],[f_4293_2]) ).

fof(f_4294_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_4294_2,plain,
    ! [U_17678,U_17677,U_17676] : c_List_Olast(U_17676,hAPP(hAPP(c_List_Oappend(U_17676),U_17677),hAPP(hAPP(c_List_Olist_OCons(U_17676),U_17678),c_List_Olist_ONil(U_17676)))) = U_17678,
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

cnf(f_4294_3,plain,
    c_List_Olast(U_17676,hAPP(hAPP(c_List_Oappend(U_17676),U_17677),hAPP(hAPP(c_List_Olist_OCons(U_17676),U_17678),c_List_Olist_ONil(U_17676)))) = U_17678,
    inference(clausify,[status(thm)],[f_4294_2]) ).

fof(f_4295_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_4295_2,plain,
    ! [U_17681,U_17680,U_17679] :
      ( c_List_Olast(U_17680,hAPP(hAPP(c_List_Odrop(U_17680),U_17679),U_17681)) = c_List_Olast(U_17680,U_17681)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17679),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17680)),U_17681))) ),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

cnf(f_4295_3,plain,
    ( c_List_Olast(U_17680,hAPP(hAPP(c_List_Odrop(U_17680),U_17679),U_17681)) = c_List_Olast(U_17680,U_17681)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17679),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17680)),U_17681))) ),
    inference(clausify,[status(thm)],[f_4295_2]) ).

fof(f_4296_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_4296_2,plain,
    ! [U_17683,U_17682] :
      ( hAPP(hAPP(c_List_Oappend(U_17683),c_List_Obutlast(U_17683,U_17682)),hAPP(hAPP(c_List_Olist_OCons(U_17683),c_List_Olast(U_17683,U_17682)),c_List_Olist_ONil(U_17683))) = U_17682
      | U_17682 = c_List_Olist_ONil(U_17683) ),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

cnf(f_4296_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17683),c_List_Obutlast(U_17683,U_17682)),hAPP(hAPP(c_List_Olist_OCons(U_17683),c_List_Olast(U_17683,U_17682)),c_List_Olist_ONil(U_17683))) = U_17682
    | U_17682 = c_List_Olist_ONil(U_17683) ),
    inference(clausify,[status(thm)],[f_4296_2]) ).

fof(f_4297_1,plain,
    ! [V_ys_2,V_x_2,V_xs_2,T_a] :
      ( ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2
        | c_List_Olast(T_a,V_ys_2) != V_x_2
        | c_List_Obutlast(T_a,V_ys_2) != V_xs_2
        | V_ys_2 = c_List_Olist_ONil(T_a) )
      & ( ( c_List_Olast(T_a,V_ys_2) = V_x_2
          & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
          & V_ys_2 != c_List_Olist_ONil(T_a) )
        | hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast]) ).

fof(f_4297_2,plain,
    ! [U_17687,U_17686,U_17685,U_17684] :
      ( ( hAPP(hAPP(c_List_Oappend(U_17684),U_17685),hAPP(hAPP(c_List_Olist_OCons(U_17684),U_17686),c_List_Olist_ONil(U_17684))) = U_17687
        | c_List_Olast(U_17684,U_17687) != U_17686
        | c_List_Obutlast(U_17684,U_17687) != U_17685
        | U_17687 = c_List_Olist_ONil(U_17684) )
      & ( ( c_List_Olast(U_17684,U_17687) = U_17686
          & c_List_Obutlast(U_17684,U_17687) = U_17685
          & U_17687 != c_List_Olist_ONil(U_17684) )
        | hAPP(hAPP(c_List_Oappend(U_17684),U_17685),hAPP(hAPP(c_List_Olist_OCons(U_17684),U_17686),c_List_Olist_ONil(U_17684))) != U_17687 ) ),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

fof(f_4297_3,plain,
    ( ! [U_17695,U_17693,U_17691,U_17689] :
        ( hAPP(hAPP(c_List_Oappend(U_17689),U_17691),hAPP(hAPP(c_List_Olist_OCons(U_17689),U_17693),c_List_Olist_ONil(U_17689))) = U_17695
        | c_List_Olast(U_17689,U_17695) != U_17693
        | c_List_Obutlast(U_17689,U_17695) != U_17691
        | U_17695 = c_List_Olist_ONil(U_17689) )
    & ! [U_17694,U_17692,U_17690,U_17688] :
        ( ( c_List_Olast(U_17688,U_17694) = U_17692
          & c_List_Obutlast(U_17688,U_17694) = U_17690
          & U_17694 != c_List_Olist_ONil(U_17688) )
        | hAPP(hAPP(c_List_Oappend(U_17688),U_17690),hAPP(hAPP(c_List_Olist_OCons(U_17688),U_17692),c_List_Olist_ONil(U_17688))) != U_17694 ) ),
    inference(miniscope,[status(thm)],[f_4297_2]) ).

cnf(f_4297_4,plain,
    ( U_17694 != c_List_Olist_ONil(U_17688)
    | hAPP(hAPP(c_List_Oappend(U_17688),U_17690),hAPP(hAPP(c_List_Olist_OCons(U_17688),U_17692),c_List_Olist_ONil(U_17688))) != U_17694 ),
    inference(clausify,[status(thm)],[f_4297_3]) ).

cnf(f_4297_5,plain,
    ( c_List_Obutlast(U_17688,U_17694) = U_17690
    | hAPP(hAPP(c_List_Oappend(U_17688),U_17690),hAPP(hAPP(c_List_Olist_OCons(U_17688),U_17692),c_List_Olist_ONil(U_17688))) != U_17694 ),
    inference(clausify,[status(thm)],[f_4297_3]) ).

cnf(f_4297_6,plain,
    ( c_List_Olast(U_17688,U_17694) = U_17692
    | hAPP(hAPP(c_List_Oappend(U_17688),U_17690),hAPP(hAPP(c_List_Olist_OCons(U_17688),U_17692),c_List_Olist_ONil(U_17688))) != U_17694 ),
    inference(clausify,[status(thm)],[f_4297_3]) ).

cnf(f_4297_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_17689),U_17691),hAPP(hAPP(c_List_Olist_OCons(U_17689),U_17693),c_List_Olist_ONil(U_17689))) = U_17695
    | c_List_Olast(U_17689,U_17695) != U_17693
    | c_List_Obutlast(U_17689,U_17695) != U_17691
    | U_17695 = c_List_Olist_ONil(U_17689) ),
    inference(clausify,[status(thm)],[f_4297_3]) ).

fof(f_4298_1,plain,
    ! [V_A_2,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
        | ( ! [B_a,B_l] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
              | V_a_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) )
          & V_a_2 != c_List_Olist_ONil(T_a) ) )
      & ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_a)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lists_Osimps]) ).

fof(f_4298_2,plain,
    ! [U_17702,U_17701,U_17700] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17700)),U_17701),c_List_Olists(U_17700,U_17702)))
        | ( ! [U_17699,U_17698] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17700)),U_17698),c_List_Olists(U_17700,U_17702)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17700),U_17699),U_17702))
              | U_17701 != hAPP(hAPP(c_List_Olist_OCons(U_17700),U_17699),U_17698) )
          & U_17701 != c_List_Olist_ONil(U_17700) ) )
      & ( ? [U_17697,U_17696] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17700)),U_17696),c_List_Olists(U_17700,U_17702)))
            & hBOOL(hAPP(hAPP(c_member(U_17700),U_17697),U_17702))
            & U_17701 = hAPP(hAPP(c_List_Olist_OCons(U_17700),U_17697),U_17696) )
        | U_17701 = c_List_Olist_ONil(U_17700)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17700)),U_17701),c_List_Olists(U_17700,U_17702))) ) ),
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

fof(f_4298_3,plain,
    ( ! [U_17708,U_17706,U_17704] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17706),c_List_Olists(U_17704,U_17708)))
        | ( ! [U_17699] :
              ( ! [U_17698] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17698),c_List_Olists(U_17704,U_17708)))
                  | U_17706 != hAPP(hAPP(c_List_Olist_OCons(U_17704),U_17699),U_17698) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17699),U_17708)) )
          & U_17706 != c_List_Olist_ONil(U_17704) ) )
    & ! [U_17707,U_17705,U_17703] :
        ( ? [U_17697] :
            ( ? [U_17696] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17696),c_List_Olists(U_17703,U_17707)))
                & U_17705 = hAPP(hAPP(c_List_Olist_OCons(U_17703),U_17697),U_17696) )
            & hBOOL(hAPP(hAPP(c_member(U_17703),U_17697),U_17707)) )
        | U_17705 = c_List_Olist_ONil(U_17703)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ) ),
    inference(miniscope,[status(thm)],[f_4298_2]) ).

fof(f_4298_4,plain,
    ( ! [U_17708,U_17706,U_17704] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17706),c_List_Olists(U_17704,U_17708)))
        | ( ! [U_17699] :
              ( ! [U_17698] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17698),c_List_Olists(U_17704,U_17708)))
                  | U_17706 != hAPP(hAPP(c_List_Olist_OCons(U_17704),U_17699),U_17698) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17699),U_17708)) )
          & U_17706 != c_List_Olist_ONil(U_17704) ) )
    & ! [U_17707,U_17705,U_17703] :
        ( ( ? [U_17696] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17696),c_List_Olists(U_17703,U_17707)))
              & U_17705 = hAPP(hAPP(c_List_Olist_OCons(U_17703),sK453(U_17707,U_17705,U_17703)),U_17696) )
          & hBOOL(hAPP(hAPP(c_member(U_17703),sK453(U_17707,U_17705,U_17703)),U_17707)) )
        | U_17705 = c_List_Olist_ONil(U_17703)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_17697,sK453(U_17707,U_17705,U_17703))],[f_4298_3]) ).

fof(f_4298_5,plain,
    ( ! [U_17708,U_17706,U_17704] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17706),c_List_Olists(U_17704,U_17708)))
        | ( ! [U_17699] :
              ( ! [U_17698] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17698),c_List_Olists(U_17704,U_17708)))
                  | U_17706 != hAPP(hAPP(c_List_Olist_OCons(U_17704),U_17699),U_17698) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17699),U_17708)) )
          & U_17706 != c_List_Olist_ONil(U_17704) ) )
    & ! [U_17707,U_17705,U_17703] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),sK454(U_17707,U_17705,U_17703)),c_List_Olists(U_17703,U_17707)))
          & U_17705 = hAPP(hAPP(c_List_Olist_OCons(U_17703),sK453(U_17707,U_17705,U_17703)),sK454(U_17707,U_17705,U_17703))
          & hBOOL(hAPP(hAPP(c_member(U_17703),sK453(U_17707,U_17705,U_17703)),U_17707)) )
        | U_17705 = c_List_Olist_ONil(U_17703)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_17696,sK454(U_17707,U_17705,U_17703))],[f_4298_4]) ).

cnf(f_4298_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17703),sK453(U_17707,U_17705,U_17703)),U_17707))
    | U_17705 = c_List_Olist_ONil(U_17703)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ),
    inference(clausify,[status(thm)],[f_4298_5]) ).

cnf(f_4298_7,plain,
    ( U_17705 = hAPP(hAPP(c_List_Olist_OCons(U_17703),sK453(U_17707,U_17705,U_17703)),sK454(U_17707,U_17705,U_17703))
    | U_17705 = c_List_Olist_ONil(U_17703)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ),
    inference(clausify,[status(thm)],[f_4298_5]) ).

cnf(f_4298_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),sK454(U_17707,U_17705,U_17703)),c_List_Olists(U_17703,U_17707)))
    | U_17705 = c_List_Olist_ONil(U_17703)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17703)),U_17705),c_List_Olists(U_17703,U_17707))) ),
    inference(clausify,[status(thm)],[f_4298_5]) ).

cnf(f_4298_9,plain,
    ( U_17706 != c_List_Olist_ONil(U_17704)
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17706),c_List_Olists(U_17704,U_17708))) ),
    inference(clausify,[status(thm)],[f_4298_5]) ).

cnf(f_4298_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17698),c_List_Olists(U_17704,U_17708)))
    | U_17706 != hAPP(hAPP(c_List_Olist_OCons(U_17704),U_17699),U_17698)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17699),U_17708))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17704)),U_17706),c_List_Olists(U_17704,U_17708))) ),
    inference(clausify,[status(thm)],[f_4298_5]) ).

fof(f_4299_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
      ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_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_a)),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_a)),V_ys_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__upd]) ).

fof(f_4299_2,plain,
    ! [U_17716,U_17715,U_17714,U_17713,U_17712,U_17711,U_17710,U_17709] :
      ( hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17710)) = hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17713))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17711,tc_Option_Ooption(U_17709)),hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17710))),U_17714),hAPP(c_Option_Ooption_OSome(U_17709),U_17715)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17711,tc_Option_Ooption(U_17709)),hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17713))),U_17714),hAPP(c_Option_Ooption_OSome(U_17709),U_17716))
      | hBOOL(hAPP(hAPP(c_member(U_17711),U_17714),hAPP(c_List_Oset(U_17711),U_17712)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17709)),U_17713) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17709)),U_17710) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) ),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

cnf(f_4299_3,plain,
    ( hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17710)) = hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17713))
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17711,tc_Option_Ooption(U_17709)),hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17710))),U_17714),hAPP(c_Option_Ooption_OSome(U_17709),U_17715)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17711,tc_Option_Ooption(U_17709)),hAPP(c_Map_Omap__of(U_17711,U_17709),hAPP(hAPP(c_List_Ozip(U_17711,U_17709),U_17712),U_17713))),U_17714),hAPP(c_Option_Ooption_OSome(U_17709),U_17716))
    | hBOOL(hAPP(hAPP(c_member(U_17711),U_17714),hAPP(c_List_Oset(U_17711),U_17712)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17709)),U_17713) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17709)),U_17710) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) ),
    inference(clausify,[status(thm)],[f_4299_2]) ).

fof(f_4300_1,plain,
    ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__dom__map__of]) ).

fof(f_4300_2,plain,
    ! [U_17719,U_17718,U_17717] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17717),c_Map_Odom(U_17717,U_17718,hAPP(c_Map_Omap__of(U_17717,U_17718),U_17719)))),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

cnf(f_4300_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17717),c_Map_Odom(U_17717,U_17718,hAPP(c_Map_Omap__of(U_17717,U_17718),U_17719)))),
    inference(clausify,[status(thm)],[f_4300_2]) ).

fof(f_4301_1,plain,
    ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
      ( V_ys_2 = V_zs_2
      | hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) != hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a)),V_ys_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__inject]) ).

fof(f_4301_2,plain,
    ! [U_17724,U_17723,U_17722,U_17721,U_17720] :
      ( U_17721 = U_17724
      | hAPP(c_Map_Omap__of(U_17722,U_17720),hAPP(hAPP(c_List_Ozip(U_17722,U_17720),U_17723),U_17721)) != hAPP(c_Map_Omap__of(U_17722,U_17720),hAPP(hAPP(c_List_Ozip(U_17722,U_17720),U_17723),U_17724))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17722),U_17723))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17724) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),U_17723)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17721) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),U_17723) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

cnf(f_4301_3,plain,
    ( U_17721 = U_17724
    | hAPP(c_Map_Omap__of(U_17722,U_17720),hAPP(hAPP(c_List_Ozip(U_17722,U_17720),U_17723),U_17721)) != hAPP(c_Map_Omap__of(U_17722,U_17720),hAPP(hAPP(c_List_Ozip(U_17722,U_17720),U_17723),U_17724))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17722),U_17723))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17724) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),U_17723)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17721) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),U_17723) ),
    inference(clausify,[status(thm)],[f_4301_2]) ).

fof(f_4302_1,plain,
    c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),
    inference(fof_nnf,[status(thm)],[fact_body__def]) ).

cnf(f_4302_2,plain,
    c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),
    inference(clausify,[status(thm)],[f_4302_1]) ).

fof(f_4303_1,plain,
    ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
      ( ( hAPP(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(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k)
        | V_l = V_k )
      & ( hAPP(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_4303_2,plain,
    ! [U_17730,U_17729,U_17728,U_17727,U_17726,U_17725] :
      ( ( hAPP(hAPP(c_Map_Omap__of(U_17727,U_17728),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17727,U_17728)),hAPP(hAPP(c_Product__Type_OPair(U_17727,U_17728),U_17725),U_17729)),U_17730)),U_17726) = hAPP(hAPP(c_Map_Omap__of(U_17727,U_17728),U_17730),U_17726)
        | U_17725 = U_17726 )
      & ( hAPP(hAPP(c_Map_Omap__of(U_17727,U_17728),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17727,U_17728)),hAPP(hAPP(c_Product__Type_OPair(U_17727,U_17728),U_17725),U_17729)),U_17730)),U_17726) = hAPP(c_Option_Ooption_OSome(U_17728),U_17729)
        | U_17725 != U_17726 ) ),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

fof(f_4303_3,plain,
    ( ! [U_17742,U_17740,U_17738,U_17736,U_17734,U_17732] :
        ( hAPP(hAPP(c_Map_Omap__of(U_17736,U_17738),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17736,U_17738)),hAPP(hAPP(c_Product__Type_OPair(U_17736,U_17738),U_17732),U_17740)),U_17742)),U_17734) = hAPP(hAPP(c_Map_Omap__of(U_17736,U_17738),U_17742),U_17734)
        | U_17732 = U_17734 )
    & ! [U_17741,U_17739,U_17737,U_17735,U_17733,U_17731] :
        ( hAPP(hAPP(c_Map_Omap__of(U_17735,U_17737),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17735,U_17737)),hAPP(hAPP(c_Product__Type_OPair(U_17735,U_17737),U_17731),U_17739)),U_17741)),U_17733) = hAPP(c_Option_Ooption_OSome(U_17737),U_17739)
        | U_17731 != U_17733 ) ),
    inference(miniscope,[status(thm)],[f_4303_2]) ).

cnf(f_4303_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_17735,U_17737),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17735,U_17737)),hAPP(hAPP(c_Product__Type_OPair(U_17735,U_17737),U_17731),U_17739)),U_17741)),U_17733) = hAPP(c_Option_Ooption_OSome(U_17737),U_17739)
    | U_17731 != U_17733 ),
    inference(clausify,[status(thm)],[f_4303_3]) ).

cnf(f_4303_5,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_17736,U_17738),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17736,U_17738)),hAPP(hAPP(c_Product__Type_OPair(U_17736,U_17738),U_17732),U_17740)),U_17742)),U_17734) = hAPP(hAPP(c_Map_Omap__of(U_17736,U_17738),U_17742),U_17734)
    | U_17732 = U_17734 ),
    inference(clausify,[status(thm)],[f_4303_3]) ).

fof(f_4304_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2))
      | hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) != hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom]) ).

fof(f_4304_2,plain,
    ! [U_17746,U_17745,U_17744,U_17743] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17743,U_17744),U_17743,c_Product__Type_Ofst(U_17743,U_17744)),hAPP(c_List_Oset(tc_prod(U_17743,U_17744)),U_17745)) = hAPP(c_Set_Oimage(tc_prod(U_17743,U_17744),U_17743,c_Product__Type_Ofst(U_17743,U_17744)),hAPP(c_List_Oset(tc_prod(U_17743,U_17744)),U_17746))
      | hAPP(c_Map_Omap__of(U_17743,U_17744),U_17745) != hAPP(c_Map_Omap__of(U_17743,U_17744),U_17746) ),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

cnf(f_4304_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_17743,U_17744),U_17743,c_Product__Type_Ofst(U_17743,U_17744)),hAPP(c_List_Oset(tc_prod(U_17743,U_17744)),U_17745)) = hAPP(c_Set_Oimage(tc_prod(U_17743,U_17744),U_17743,c_Product__Type_Ofst(U_17743,U_17744)),hAPP(c_List_Oset(tc_prod(U_17743,U_17744)),U_17746))
    | hAPP(c_Map_Omap__of(U_17743,U_17744),U_17745) != hAPP(c_Map_Omap__of(U_17743,U_17744),U_17746) ),
    inference(clausify,[status(thm)],[f_4304_2]) ).

fof(f_4305_1,plain,
    ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_finite__range__map__of]) ).

fof(f_4305_2,plain,
    ! [U_17749,U_17748,U_17747] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17747)),hAPP(c_Set_Oimage(U_17748,tc_Option_Ooption(U_17747),hAPP(c_Map_Omap__of(U_17748,U_17747),U_17749)),c_Orderings_Otop__class_Otop(tc_fun(U_17748,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

cnf(f_4305_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17747)),hAPP(c_Set_Oimage(U_17748,tc_Option_Ooption(U_17747),hAPP(c_Map_Omap__of(U_17748,U_17747),U_17749)),c_Orderings_Otop__class_Otop(tc_fun(U_17748,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4305_2]) ).

fof(f_4306_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))
      | hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD]) ).

fof(f_4306_2,plain,
    ! [U_17754,U_17753,U_17752,U_17751,U_17750] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17750,U_17751)),hAPP(hAPP(c_Product__Type_OPair(U_17750,U_17751),U_17753),U_17754)),hAPP(c_List_Oset(tc_prod(U_17750,U_17751)),U_17752)))
      | hAPP(hAPP(c_Map_Omap__of(U_17750,U_17751),U_17752),U_17753) != hAPP(c_Option_Ooption_OSome(U_17751),U_17754) ),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

cnf(f_4306_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17750,U_17751)),hAPP(hAPP(c_Product__Type_OPair(U_17750,U_17751),U_17753),U_17754)),hAPP(c_List_Oset(tc_prod(U_17750,U_17751)),U_17752)))
    | hAPP(hAPP(c_Map_Omap__of(U_17750,U_17751),U_17752),U_17753) != hAPP(c_Option_Ooption_OSome(U_17751),U_17754) ),
    inference(clausify,[status(thm)],[f_4306_2]) ).

fof(f_4307_1,plain,
    ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2)))
      | hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__SomeD]) ).

fof(f_4307_2,plain,
    ! [U_17759,U_17758,U_17757,U_17756,U_17755] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17755,U_17756)),hAPP(hAPP(c_Product__Type_OPair(U_17755,U_17756),U_17758),U_17759)),hAPP(c_List_Oset(tc_prod(U_17755,U_17756)),U_17757)))
      | hAPP(hAPP(c_Map_Omap__of(U_17755,U_17756),U_17757),U_17758) != hAPP(c_Option_Ooption_OSome(U_17756),U_17759) ),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

cnf(f_4307_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17755,U_17756)),hAPP(hAPP(c_Product__Type_OPair(U_17755,U_17756),U_17758),U_17759)),hAPP(c_List_Oset(tc_prod(U_17755,U_17756)),U_17757)))
    | hAPP(hAPP(c_Map_Omap__of(U_17755,U_17756),U_17757),U_17758) != hAPP(c_Option_Ooption_OSome(U_17756),U_17759) ),
    inference(clausify,[status(thm)],[f_4307_2]) ).

fof(f_4308_1,plain,
    ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__of__conv__image__fst]) ).

fof(f_4308_2,plain,
    ! [U_17762,U_17761,U_17760] : c_Map_Odom(U_17760,U_17761,hAPP(c_Map_Omap__of(U_17760,U_17761),U_17762)) = hAPP(c_Set_Oimage(tc_prod(U_17760,U_17761),U_17760,c_Product__Type_Ofst(U_17760,U_17761)),hAPP(c_List_Oset(tc_prod(U_17760,U_17761)),U_17762)),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

cnf(f_4308_3,plain,
    c_Map_Odom(U_17760,U_17761,hAPP(c_Map_Omap__of(U_17760,U_17761),U_17762)) = hAPP(c_Set_Oimage(tc_prod(U_17760,U_17761),U_17760,c_Product__Type_Ofst(U_17760,U_17761)),hAPP(c_List_Oset(tc_prod(U_17760,U_17761)),U_17762)),
    inference(clausify,[status(thm)],[f_4308_2]) ).

fof(f_4309_1,plain,
    ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
          | ! [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),B_y) )
        & ( ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y)
          | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__Some]) ).

fof(f_4309_2,plain,
    ! [U_17769,U_17768,U_17767,U_17766,U_17765] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766)))
          | ! [U_17764] : hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) != hAPP(c_Option_Ooption_OSome(U_17767),U_17764) )
        & ( ? [U_17763] : hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) = hAPP(c_Option_Ooption_OSome(U_17767),U_17763)
          | ~ hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17767)),U_17768) ),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

fof(f_4309_3,plain,
    ! [U_17769,U_17768,U_17767,U_17766,U_17765] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766)))
          | ! [U_17764] : hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) != hAPP(c_Option_Ooption_OSome(U_17767),U_17764) )
        & ( hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) = hAPP(c_Option_Ooption_OSome(U_17767),sK455(U_17769,U_17768,U_17767,U_17766,U_17765))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17767)),U_17768) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_17763,sK455(U_17769,U_17768,U_17767,U_17766,U_17765))],[f_4309_2]) ).

cnf(f_4309_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) = hAPP(c_Option_Ooption_OSome(U_17767),sK455(U_17769,U_17768,U_17767,U_17766,U_17765))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17767)),U_17768) ),
    inference(clausify,[status(thm)],[f_4309_3]) ).

cnf(f_4309_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17765),U_17769),hAPP(c_List_Oset(U_17765),U_17766)))
    | hAPP(hAPP(c_Map_Omap__of(U_17765,U_17767),hAPP(hAPP(c_List_Ozip(U_17765,U_17767),U_17766),U_17768)),U_17769) != hAPP(c_Option_Ooption_OSome(U_17767),U_17764)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17765)),U_17766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17767)),U_17768) ),
    inference(clausify,[status(thm)],[f_4309_3]) ).

fof(f_4310_1,plain,
    ! [V_ys_2,T_b,V_xs_2,T_a] :
      ( c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip]) ).

fof(f_4310_2,plain,
    ! [U_17773,U_17772,U_17771,U_17770] :
      ( c_Map_Odom(U_17770,U_17772,hAPP(c_Map_Omap__of(U_17770,U_17772),hAPP(hAPP(c_List_Ozip(U_17770,U_17772),U_17771),U_17773))) = hAPP(c_List_Oset(U_17770),U_17771)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17770),U_17771))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17770)),U_17771) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17772)),U_17773) ),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

cnf(f_4310_3,plain,
    ( c_Map_Odom(U_17770,U_17772,hAPP(c_Map_Omap__of(U_17770,U_17772),hAPP(hAPP(c_List_Ozip(U_17770,U_17772),U_17771),U_17773))) = hAPP(c_List_Oset(U_17770),U_17771)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17770),U_17771))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17770)),U_17771) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17772)),U_17773) ),
    inference(clausify,[status(thm)],[f_4310_2]) ).

fof(f_4311_1,plain,
    ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))),
    inference(fof_nnf,[status(thm)],[fact_map__of_Osimps_I2_J]) ).

fof(f_4311_2,plain,
    ! [U_17777,U_17776,U_17775,U_17774] : hAPP(c_Map_Omap__of(U_17774,U_17775),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17774,U_17775)),U_17776),U_17777)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17774,tc_Option_Ooption(U_17775)),hAPP(c_Map_Omap__of(U_17774,U_17775),U_17777)),hAPP(c_Product__Type_Ofst(U_17774,U_17775),U_17776)),hAPP(c_Option_Ooption_OSome(U_17775),hAPP(c_Product__Type_Osnd(U_17774,U_17775),U_17776))),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

cnf(f_4311_3,plain,
    hAPP(c_Map_Omap__of(U_17774,U_17775),hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17774,U_17775)),U_17776),U_17777)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17774,tc_Option_Ooption(U_17775)),hAPP(c_Map_Omap__of(U_17774,U_17775),U_17777)),hAPP(c_Product__Type_Ofst(U_17774,U_17775),U_17776)),hAPP(c_Option_Ooption_OSome(U_17775),hAPP(c_Product__Type_Osnd(U_17774,U_17775),U_17776))),
    inference(clausify,[status(thm)],[f_4311_2]) ).

fof(f_4312_1,plain,
    ! [V_al_2,T_b,T_a] :
      ( c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ran__distinct]) ).

fof(f_4312_2,plain,
    ! [U_17780,U_17779,U_17778] :
      ( c_Map_Oran(U_17778,U_17779,hAPP(c_Map_Omap__of(U_17778,U_17779),U_17780)) = hAPP(c_Set_Oimage(tc_prod(U_17778,U_17779),U_17779,c_Product__Type_Osnd(U_17778,U_17779)),hAPP(c_List_Oset(tc_prod(U_17778,U_17779)),U_17780))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17778),hAPP(hAPP(c_List_Omap(tc_prod(U_17778,U_17779),U_17778),c_Product__Type_Ofst(U_17778,U_17779)),U_17780))) ),
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

cnf(f_4312_3,plain,
    ( c_Map_Oran(U_17778,U_17779,hAPP(c_Map_Omap__of(U_17778,U_17779),U_17780)) = hAPP(c_Set_Oimage(tc_prod(U_17778,U_17779),U_17779,c_Product__Type_Osnd(U_17778,U_17779)),hAPP(c_List_Oset(tc_prod(U_17778,U_17779)),U_17780))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17778),hAPP(hAPP(c_List_Omap(tc_prod(U_17778,U_17779),U_17778),c_Product__Type_Ofst(U_17778,U_17779)),U_17780))) ),
    inference(clausify,[status(thm)],[f_4312_2]) ).

fof(f_4313_1,plain,
    ! [V_xs_2,T_b,T_a] :
      ( hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_set__map__of__compr]) ).

fof(f_4313_2,plain,
    ! [U_17783,U_17782,U_17781] :
      ( hAPP(c_List_Oset(tc_prod(U_17781,U_17782)),U_17783) = hAPP(c_Set_OCollect(tc_prod(U_17781,U_17782)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17781,U_17782,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17781,tc_fun(U_17782,tc_Option_Ooption(U_17782)),tc_fun(U_17782,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17782),tc_HOL_Obool),tc_fun(tc_fun(U_17782,tc_Option_Ooption(U_17782)),tc_fun(U_17782,tc_HOL_Obool)),U_17781),c_COMBB(tc_Option_Ooption(U_17782),tc_HOL_Obool,U_17782)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17782),tc_fun(tc_Option_Ooption(U_17782),tc_HOL_Obool),U_17781),c_fequal),hAPP(c_Map_Omap__of(U_17781,U_17782),U_17783)))),c_Option_Ooption_OSome(U_17782))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17781),hAPP(hAPP(c_List_Omap(tc_prod(U_17781,U_17782),U_17781),c_Product__Type_Ofst(U_17781,U_17782)),U_17783))) ),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

cnf(f_4313_3,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17781,U_17782)),U_17783) = hAPP(c_Set_OCollect(tc_prod(U_17781,U_17782)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17781,U_17782,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17781,tc_fun(U_17782,tc_Option_Ooption(U_17782)),tc_fun(U_17782,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17782),tc_HOL_Obool),tc_fun(tc_fun(U_17782,tc_Option_Ooption(U_17782)),tc_fun(U_17782,tc_HOL_Obool)),U_17781),c_COMBB(tc_Option_Ooption(U_17782),tc_HOL_Obool,U_17782)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17782),tc_fun(tc_Option_Ooption(U_17782),tc_HOL_Obool),U_17781),c_fequal),hAPP(c_Map_Omap__of(U_17781,U_17782),U_17783)))),c_Option_Ooption_OSome(U_17782))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17781),hAPP(hAPP(c_List_Omap(tc_prod(U_17781,U_17782),U_17781),c_Product__Type_Ofst(U_17781,U_17782)),U_17783))) ),
    inference(clausify,[status(thm)],[f_4313_2]) ).

fof(f_4314_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapI]) ).

fof(f_4314_2,plain,
    ! [U_17786,U_17785,U_17784] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17784),tc_List_Olist(U_17785),hAPP(c_List_Omap(U_17784,U_17785),U_17786),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17784,U_17785,U_17786,c_Orderings_Otop__class_Otop(tc_fun(U_17784,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

cnf(f_4314_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17784),tc_List_Olist(U_17785),hAPP(c_List_Omap(U_17784,U_17785),U_17786),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17784,U_17785,U_17786,c_Orderings_Otop__class_Otop(tc_fun(U_17784,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4314_2]) ).

fof(f_4315_1,plain,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__abs]) ).

fof(f_4315_2,plain,
    ! [U_17788,U_17787] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17787),hAPP(c_Groups_Oabs__class_Oabs(U_17787),hAPP(c_List_Omonoid__add__class_Olistsum(U_17787),U_17788))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17787),hAPP(hAPP(c_List_Omap(U_17787,U_17787),c_Groups_Oabs__class_Oabs(U_17787)),U_17788))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_17787) ),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

cnf(f_4315_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17787),hAPP(c_Groups_Oabs__class_Oabs(U_17787),hAPP(c_List_Omonoid__add__class_Olistsum(U_17787),U_17788))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17787),hAPP(hAPP(c_List_Omap(U_17787,U_17787),c_Groups_Oabs__class_Oabs(U_17787)),U_17788))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_17787) ),
    inference(clausify,[status(thm)],[f_4315_2]) ).

fof(f_4316_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__map]) ).

fof(f_4316_2,plain,
    ! [U_17795,U_17794,U_17793,U_17792,U_17791,U_17790,U_17789] : hAPP(c_List_Ofoldl(U_17789,U_17790,U_17791,U_17792),hAPP(hAPP(c_List_Omap(U_17793,U_17790),U_17794),U_17795)) = hAPP(c_List_Ofoldl(U_17789,U_17793,hAPP(hAPP(c_COMBC(U_17789,tc_fun(U_17793,U_17790),tc_fun(U_17793,U_17789)),hAPP(hAPP(c_COMBB(tc_fun(U_17790,U_17789),tc_fun(tc_fun(U_17793,U_17790),tc_fun(U_17793,U_17789)),U_17789),c_COMBB(U_17790,U_17789,U_17793)),U_17791)),U_17794),U_17792),U_17795),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

cnf(f_4316_3,plain,
    hAPP(c_List_Ofoldl(U_17789,U_17790,U_17791,U_17792),hAPP(hAPP(c_List_Omap(U_17793,U_17790),U_17794),U_17795)) = hAPP(c_List_Ofoldl(U_17789,U_17793,hAPP(hAPP(c_COMBC(U_17789,tc_fun(U_17793,U_17790),tc_fun(U_17793,U_17789)),hAPP(hAPP(c_COMBB(tc_fun(U_17790,U_17789),tc_fun(tc_fun(U_17793,U_17790),tc_fun(U_17793,U_17789)),U_17789),c_COMBB(U_17790,U_17789,U_17793)),U_17791)),U_17794),U_17792),U_17795),
    inference(clausify,[status(thm)],[f_4316_2]) ).

fof(f_4317_1,plain,
    ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map2]) ).

fof(f_4317_2,plain,
    ! [U_17801,U_17800,U_17799,U_17798,U_17797,U_17796] : hAPP(hAPP(c_List_Ozip(U_17796,U_17797),U_17798),hAPP(hAPP(c_List_Omap(U_17799,U_17797),U_17800),U_17801)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17796,U_17799),tc_prod(U_17796,U_17797)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17796,U_17799,tc_prod(U_17796,U_17797)),hAPP(hAPP(c_COMBC(U_17796,tc_fun(U_17799,U_17797),tc_fun(U_17799,tc_prod(U_17796,U_17797))),hAPP(hAPP(c_COMBB(tc_fun(U_17797,tc_prod(U_17796,U_17797)),tc_fun(tc_fun(U_17799,U_17797),tc_fun(U_17799,tc_prod(U_17796,U_17797))),U_17796),c_COMBB(U_17797,tc_prod(U_17796,U_17797),U_17799)),c_Product__Type_OPair(U_17796,U_17797))),U_17800))),hAPP(hAPP(c_List_Ozip(U_17796,U_17799),U_17798),U_17801)),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

cnf(f_4317_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17796,U_17797),U_17798),hAPP(hAPP(c_List_Omap(U_17799,U_17797),U_17800),U_17801)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17796,U_17799),tc_prod(U_17796,U_17797)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17796,U_17799,tc_prod(U_17796,U_17797)),hAPP(hAPP(c_COMBC(U_17796,tc_fun(U_17799,U_17797),tc_fun(U_17799,tc_prod(U_17796,U_17797))),hAPP(hAPP(c_COMBB(tc_fun(U_17797,tc_prod(U_17796,U_17797)),tc_fun(tc_fun(U_17799,U_17797),tc_fun(U_17799,tc_prod(U_17796,U_17797))),U_17796),c_COMBB(U_17797,tc_prod(U_17796,U_17797),U_17799)),c_Product__Type_OPair(U_17796,U_17797))),U_17800))),hAPP(hAPP(c_List_Ozip(U_17796,U_17799),U_17798),U_17801)),
    inference(clausify,[status(thm)],[f_4317_2]) ).

fof(f_4318_1,plain,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map2]) ).

fof(f_4318_2,plain,
    ! [U_17809,U_17808,U_17807,U_17806,U_17805,U_17804,U_17803,U_17802] : hAPP(hAPP(c_List_Omap(tc_prod(U_17802,U_17803),U_17804),U_17805),hAPP(hAPP(c_List_Ozip(U_17802,U_17803),U_17806),hAPP(hAPP(c_List_Omap(U_17807,U_17803),U_17808),U_17809))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17802,U_17807),U_17804),hAPP(c_Product__Type_Oprod_Oprod__case(U_17802,U_17807,U_17804),hAPP(hAPP(c_COMBB(tc_fun(U_17807,tc_prod(U_17802,U_17803)),tc_fun(U_17807,U_17804),U_17802),hAPP(c_COMBB(tc_prod(U_17802,U_17803),U_17804,U_17807),U_17805)),hAPP(hAPP(c_COMBC(U_17802,tc_fun(U_17807,U_17803),tc_fun(U_17807,tc_prod(U_17802,U_17803))),hAPP(hAPP(c_COMBB(tc_fun(U_17803,tc_prod(U_17802,U_17803)),tc_fun(tc_fun(U_17807,U_17803),tc_fun(U_17807,tc_prod(U_17802,U_17803))),U_17802),c_COMBB(U_17803,tc_prod(U_17802,U_17803),U_17807)),c_Product__Type_OPair(U_17802,U_17803))),U_17808)))),hAPP(hAPP(c_List_Ozip(U_17802,U_17807),U_17806),U_17809)),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

cnf(f_4318_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17802,U_17803),U_17804),U_17805),hAPP(hAPP(c_List_Ozip(U_17802,U_17803),U_17806),hAPP(hAPP(c_List_Omap(U_17807,U_17803),U_17808),U_17809))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17802,U_17807),U_17804),hAPP(c_Product__Type_Oprod_Oprod__case(U_17802,U_17807,U_17804),hAPP(hAPP(c_COMBB(tc_fun(U_17807,tc_prod(U_17802,U_17803)),tc_fun(U_17807,U_17804),U_17802),hAPP(c_COMBB(tc_prod(U_17802,U_17803),U_17804,U_17807),U_17805)),hAPP(hAPP(c_COMBC(U_17802,tc_fun(U_17807,U_17803),tc_fun(U_17807,tc_prod(U_17802,U_17803))),hAPP(hAPP(c_COMBB(tc_fun(U_17803,tc_prod(U_17802,U_17803)),tc_fun(tc_fun(U_17807,U_17803),tc_fun(U_17807,tc_prod(U_17802,U_17803))),U_17802),c_COMBB(U_17803,tc_prod(U_17802,U_17803),U_17807)),c_Product__Type_OPair(U_17802,U_17803))),U_17808)))),hAPP(hAPP(c_List_Ozip(U_17802,U_17807),U_17806),U_17809)),
    inference(clausify,[status(thm)],[f_4318_2]) ).

fof(f_4319_1,plain,
    ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map]) ).

fof(f_4319_2,plain,
    ! [U_17817,U_17816,U_17815,U_17814,U_17813,U_17812,U_17811,U_17810] : hAPP(hAPP(c_List_Omap(tc_prod(U_17810,U_17811),U_17812),U_17813),hAPP(hAPP(c_List_Ozip(U_17810,U_17811),hAPP(hAPP(c_List_Omap(U_17814,U_17810),U_17815),U_17816)),U_17817)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17814,U_17811),U_17812),hAPP(c_Product__Type_Oprod_Oprod__case(U_17814,U_17811,U_17812),hAPP(hAPP(c_COMBB(tc_fun(U_17811,tc_prod(U_17810,U_17811)),tc_fun(U_17811,U_17812),U_17814),hAPP(c_COMBB(tc_prod(U_17810,U_17811),U_17812,U_17811),U_17813)),hAPP(hAPP(c_COMBB(U_17810,tc_fun(U_17811,tc_prod(U_17810,U_17811)),U_17814),c_Product__Type_OPair(U_17810,U_17811)),U_17815)))),hAPP(hAPP(c_List_Ozip(U_17814,U_17811),U_17816),U_17817)),
    inference(variable_rename,[status(thm)],[f_4319_1]) ).

cnf(f_4319_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17810,U_17811),U_17812),U_17813),hAPP(hAPP(c_List_Ozip(U_17810,U_17811),hAPP(hAPP(c_List_Omap(U_17814,U_17810),U_17815),U_17816)),U_17817)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17814,U_17811),U_17812),hAPP(c_Product__Type_Oprod_Oprod__case(U_17814,U_17811,U_17812),hAPP(hAPP(c_COMBB(tc_fun(U_17811,tc_prod(U_17810,U_17811)),tc_fun(U_17811,U_17812),U_17814),hAPP(c_COMBB(tc_prod(U_17810,U_17811),U_17812,U_17811),U_17813)),hAPP(hAPP(c_COMBB(U_17810,tc_fun(U_17811,tc_prod(U_17810,U_17811)),U_17814),c_Product__Type_OPair(U_17810,U_17811)),U_17815)))),hAPP(hAPP(c_List_Ozip(U_17814,U_17811),U_17816),U_17817)),
    inference(clausify,[status(thm)],[f_4319_2]) ).

fof(f_4320_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map1]) ).

fof(f_4320_2,plain,
    ! [U_17823,U_17822,U_17821,U_17820,U_17819,U_17818] : hAPP(hAPP(c_List_Ozip(U_17818,U_17819),hAPP(hAPP(c_List_Omap(U_17820,U_17818),U_17821),U_17822)),U_17823) = hAPP(hAPP(c_List_Omap(tc_prod(U_17820,U_17819),tc_prod(U_17818,U_17819)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17820,U_17819,tc_prod(U_17818,U_17819)),hAPP(hAPP(c_COMBB(U_17818,tc_fun(U_17819,tc_prod(U_17818,U_17819)),U_17820),c_Product__Type_OPair(U_17818,U_17819)),U_17821))),hAPP(hAPP(c_List_Ozip(U_17820,U_17819),U_17822),U_17823)),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

cnf(f_4320_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17818,U_17819),hAPP(hAPP(c_List_Omap(U_17820,U_17818),U_17821),U_17822)),U_17823) = hAPP(hAPP(c_List_Omap(tc_prod(U_17820,U_17819),tc_prod(U_17818,U_17819)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17820,U_17819,tc_prod(U_17818,U_17819)),hAPP(hAPP(c_COMBB(U_17818,tc_fun(U_17819,tc_prod(U_17818,U_17819)),U_17820),c_Product__Type_OPair(U_17818,U_17819)),U_17821))),hAPP(hAPP(c_List_Ozip(U_17820,U_17819),U_17822),U_17823)),
    inference(clausify,[status(thm)],[f_4320_2]) ).

fof(f_4321_1,plain,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map__map]) ).

fof(f_4321_2,plain,
    ! [U_17831,U_17830,U_17829,U_17828,U_17827,U_17826,U_17825,U_17824] : hAPP(hAPP(c_List_Ozip(U_17824,U_17825),hAPP(hAPP(c_List_Omap(U_17826,U_17824),U_17827),U_17828)),hAPP(hAPP(c_List_Omap(U_17829,U_17825),U_17830),U_17831)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17826,U_17829),tc_prod(U_17824,U_17825)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17829,tc_prod(U_17824,U_17825)),hAPP(hAPP(c_COMBC(U_17826,tc_fun(U_17829,U_17825),tc_fun(U_17829,tc_prod(U_17824,U_17825))),hAPP(hAPP(c_COMBB(tc_fun(U_17825,tc_prod(U_17824,U_17825)),tc_fun(tc_fun(U_17829,U_17825),tc_fun(U_17829,tc_prod(U_17824,U_17825))),U_17826),c_COMBB(U_17825,tc_prod(U_17824,U_17825),U_17829)),hAPP(hAPP(c_COMBB(U_17824,tc_fun(U_17825,tc_prod(U_17824,U_17825)),U_17826),c_Product__Type_OPair(U_17824,U_17825)),U_17827))),U_17830))),hAPP(hAPP(c_List_Ozip(U_17826,U_17829),U_17828),U_17831)),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

cnf(f_4321_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17824,U_17825),hAPP(hAPP(c_List_Omap(U_17826,U_17824),U_17827),U_17828)),hAPP(hAPP(c_List_Omap(U_17829,U_17825),U_17830),U_17831)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17826,U_17829),tc_prod(U_17824,U_17825)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17826,U_17829,tc_prod(U_17824,U_17825)),hAPP(hAPP(c_COMBC(U_17826,tc_fun(U_17829,U_17825),tc_fun(U_17829,tc_prod(U_17824,U_17825))),hAPP(hAPP(c_COMBB(tc_fun(U_17825,tc_prod(U_17824,U_17825)),tc_fun(tc_fun(U_17829,U_17825),tc_fun(U_17829,tc_prod(U_17824,U_17825))),U_17826),c_COMBB(U_17825,tc_prod(U_17824,U_17825),U_17829)),hAPP(hAPP(c_COMBB(U_17824,tc_fun(U_17825,tc_prod(U_17824,U_17825)),U_17826),c_Product__Type_OPair(U_17824,U_17825)),U_17827))),U_17830))),hAPP(hAPP(c_List_Ozip(U_17826,U_17829),U_17828),U_17831)),
    inference(clausify,[status(thm)],[f_4321_2]) ).

fof(f_4322_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(f_4322_2,plain,
    ! [U_17836,U_17835,U_17834,U_17833,U_17832] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17832),tc_List_Olist(U_17833),tc_List_Olist(U_17834),hAPP(c_List_Omap(U_17832,U_17833),U_17835)),hAPP(c_List_Omap(U_17834,U_17832),U_17836)) = hAPP(c_List_Omap(U_17834,U_17833),hAPP(c_Fun_Ocomp(U_17832,U_17833,U_17834,U_17835),U_17836)),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

cnf(f_4322_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17832),tc_List_Olist(U_17833),tc_List_Olist(U_17834),hAPP(c_List_Omap(U_17832,U_17833),U_17835)),hAPP(c_List_Omap(U_17834,U_17832),U_17836)) = hAPP(c_List_Omap(U_17834,U_17833),hAPP(c_Fun_Ocomp(U_17832,U_17833,U_17834,U_17835),U_17836)),
    inference(clausify,[status(thm)],[f_4322_2]) ).

fof(f_4323_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__comp__map]) ).

fof(f_4323_2,plain,
    ! [U_17841,U_17840,U_17839,U_17838,U_17837] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17837),tc_List_Olist(U_17838),tc_List_Olist(U_17839),hAPP(c_List_Omap(U_17837,U_17838),U_17840)),hAPP(c_List_Omap(U_17839,U_17837),U_17841)) = hAPP(c_List_Omap(U_17839,U_17838),hAPP(c_Fun_Ocomp(U_17837,U_17838,U_17839,U_17840),U_17841)),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

cnf(f_4323_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17837),tc_List_Olist(U_17838),tc_List_Olist(U_17839),hAPP(c_List_Omap(U_17837,U_17838),U_17840)),hAPP(c_List_Omap(U_17839,U_17837),U_17841)) = hAPP(c_List_Omap(U_17839,U_17838),hAPP(c_Fun_Ocomp(U_17837,U_17838,U_17839,U_17840),U_17841)),
    inference(clausify,[status(thm)],[f_4323_2]) ).

fof(f_4324_1,plain,
    ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(f_4324_2,plain,
    ! [U_17847,U_17846,U_17845,U_17844,U_17843,U_17842] : hAPP(hAPP(c_List_Omap(U_17842,U_17843),U_17844),hAPP(hAPP(c_List_Omap(U_17845,U_17842),U_17846),U_17847)) = hAPP(hAPP(c_List_Omap(U_17845,U_17843),hAPP(c_Fun_Ocomp(U_17842,U_17843,U_17845,U_17844),U_17846)),U_17847),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

cnf(f_4324_3,plain,
    hAPP(hAPP(c_List_Omap(U_17842,U_17843),U_17844),hAPP(hAPP(c_List_Omap(U_17845,U_17842),U_17846),U_17847)) = hAPP(hAPP(c_List_Omap(U_17845,U_17843),hAPP(c_Fun_Ocomp(U_17842,U_17843,U_17845,U_17844),U_17846)),U_17847),
    inference(clausify,[status(thm)],[f_4324_2]) ).

fof(f_4325_1,plain,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_map__map]) ).

fof(f_4325_2,plain,
    ! [U_17853,U_17852,U_17851,U_17850,U_17849,U_17848] : hAPP(hAPP(c_List_Omap(U_17848,U_17849),U_17850),hAPP(hAPP(c_List_Omap(U_17851,U_17848),U_17852),U_17853)) = hAPP(hAPP(c_List_Omap(U_17851,U_17849),hAPP(c_Fun_Ocomp(U_17848,U_17849,U_17851,U_17850),U_17852)),U_17853),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

cnf(f_4325_3,plain,
    hAPP(hAPP(c_List_Omap(U_17848,U_17849),U_17850),hAPP(hAPP(c_List_Omap(U_17851,U_17848),U_17852),U_17853)) = hAPP(hAPP(c_List_Omap(U_17851,U_17849),hAPP(c_Fun_Ocomp(U_17848,U_17849,U_17851,U_17850),U_17852)),U_17853),
    inference(clausify,[status(thm)],[f_4325_2]) ).

fof(f_4326_1,plain,
    ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(f_4326_2,plain,
    ! [U_17854] : hAPP(c_List_Omap(U_17854,U_17854),c_COMBI(U_17854)) = c_Fun_Oid(tc_List_Olist(U_17854)),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

cnf(f_4326_3,plain,
    hAPP(c_List_Omap(U_17854,U_17854),c_COMBI(U_17854)) = c_Fun_Oid(tc_List_Olist(U_17854)),
    inference(clausify,[status(thm)],[f_4326_2]) ).

fof(f_4327_1,plain,
    ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oid]) ).

fof(f_4327_2,plain,
    ! [U_17855] : hAPP(c_List_Omap(U_17855,U_17855),c_Fun_Oid(U_17855)) = c_Fun_Oid(tc_List_Olist(U_17855)),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

cnf(f_4327_3,plain,
    hAPP(c_List_Omap(U_17855,U_17855),c_Fun_Oid(U_17855)) = c_Fun_Oid(tc_List_Olist(U_17855)),
    inference(clausify,[status(thm)],[f_4327_2]) ).

fof(f_4328_1,plain,
    ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_list__size__map]) ).

fof(f_4328_2,plain,
    ! [U_17860,U_17859,U_17858,U_17857,U_17856] : c_List_Olist_Olist__size(U_17856,U_17857,hAPP(hAPP(c_List_Omap(U_17858,U_17856),U_17859),U_17860)) = c_List_Olist_Olist__size(U_17858,hAPP(c_Fun_Ocomp(U_17856,tc_Nat_Onat,U_17858,U_17857),U_17859),U_17860),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

cnf(f_4328_3,plain,
    c_List_Olist_Olist__size(U_17856,U_17857,hAPP(hAPP(c_List_Omap(U_17858,U_17856),U_17859),U_17860)) = c_List_Olist_Olist__size(U_17858,hAPP(c_Fun_Ocomp(U_17856,tc_Nat_Onat,U_17858,U_17857),U_17859),U_17860),
    inference(clausify,[status(thm)],[f_4328_2]) ).

fof(f_4329_1,plain,
    ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__map]) ).

fof(f_4329_2,plain,
    ! [U_17865,U_17864,U_17863,U_17862,U_17861] :
      ( hAPP(hAPP(c_List_Onth(U_17864),hAPP(hAPP(c_List_Omap(U_17862,U_17864),U_17865),U_17863)),U_17861) = hAPP(U_17865,hAPP(hAPP(c_List_Onth(U_17862),U_17863),U_17861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17861),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17862)),U_17863))) ),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

cnf(f_4329_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_17864),hAPP(hAPP(c_List_Omap(U_17862,U_17864),U_17865),U_17863)),U_17861) = hAPP(U_17865,hAPP(hAPP(c_List_Onth(U_17862),U_17863),U_17861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17861),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17862)),U_17863))) ),
    inference(clausify,[status(thm)],[f_4329_2]) ).

fof(f_4330_1,plain,
    ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
      ( hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__fun__upd]) ).

fof(f_4330_2,plain,
    ! [U_17871,U_17870,U_17869,U_17868,U_17867,U_17866] :
      ( hAPP(hAPP(c_List_Omap(U_17866,U_17869),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17866,U_17869),U_17870),U_17867),U_17871)),U_17868) = hAPP(hAPP(c_List_Omap(U_17866,U_17869),U_17870),U_17868)
      | hBOOL(hAPP(hAPP(c_member(U_17866),U_17867),hAPP(c_List_Oset(U_17866),U_17868))) ),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

cnf(f_4330_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17866,U_17869),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17866,U_17869),U_17870),U_17867),U_17871)),U_17868) = hAPP(hAPP(c_List_Omap(U_17866,U_17869),U_17870),U_17868)
    | hBOOL(hAPP(hAPP(c_member(U_17866),U_17867),hAPP(c_List_Oset(U_17866),U_17868))) ),
    inference(clausify,[status(thm)],[f_4330_2]) ).

fof(f_4331_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__tl]) ).

fof(f_4331_2,plain,
    ! [U_17875,U_17874,U_17873,U_17872] : hAPP(hAPP(c_List_Omap(U_17872,U_17873),U_17874),hAPP(c_List_Otl(U_17872),U_17875)) = hAPP(c_List_Otl(U_17873),hAPP(hAPP(c_List_Omap(U_17872,U_17873),U_17874),U_17875)),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

cnf(f_4331_3,plain,
    hAPP(hAPP(c_List_Omap(U_17872,U_17873),U_17874),hAPP(c_List_Otl(U_17872),U_17875)) = hAPP(c_List_Otl(U_17873),hAPP(hAPP(c_List_Omap(U_17872,U_17873),U_17874),U_17875)),
    inference(clausify,[status(thm)],[f_4331_2]) ).

fof(f_4332_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),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_length__map]) ).

fof(f_4332_2,plain,
    ! [U_17879,U_17878,U_17877,U_17876] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17876)),hAPP(hAPP(c_List_Omap(U_17877,U_17876),U_17878),U_17879)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17877)),U_17879),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

cnf(f_4332_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17876)),hAPP(hAPP(c_List_Omap(U_17877,U_17876),U_17878),U_17879)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17877)),U_17879),
    inference(clausify,[status(thm)],[f_4332_2]) ).

fof(f_4333_1,plain,
    ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,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(T_b,T_a),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq]) ).

fof(f_4333_2,plain,
    ! [U_17886,U_17885,U_17884,U_17883,U_17882,U_17881,U_17880] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17880)),U_17883) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17884)),U_17886)
      | hAPP(hAPP(c_List_Omap(U_17880,U_17881),U_17882),U_17883) != hAPP(hAPP(c_List_Omap(U_17884,U_17881),U_17885),U_17886) ),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

cnf(f_4333_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17880)),U_17883) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17884)),U_17886)
    | hAPP(hAPP(c_List_Omap(U_17880,U_17881),U_17882),U_17883) != hAPP(hAPP(c_List_Omap(U_17884,U_17881),U_17885),U_17886) ),
    inference(clausify,[status(thm)],[f_4333_2]) ).

fof(f_4334_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__map]) ).

fof(f_4334_2,plain,
    ! [U_17890,U_17889,U_17888,U_17887] : hAPP(c_List_Oset(U_17887),hAPP(hAPP(c_List_Omap(U_17888,U_17887),U_17889),U_17890)) = hAPP(c_Set_Oimage(U_17888,U_17887,U_17889),hAPP(c_List_Oset(U_17888),U_17890)),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

cnf(f_4334_3,plain,
    hAPP(c_List_Oset(U_17887),hAPP(hAPP(c_List_Omap(U_17888,U_17887),U_17889),U_17890)) = hAPP(c_Set_Oimage(U_17888,U_17887,U_17889),hAPP(c_List_Oset(U_17888),U_17890)),
    inference(clausify,[status(thm)],[f_4334_2]) ).

fof(f_4335_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__append]) ).

fof(f_4335_2,plain,
    ! [U_17895,U_17894,U_17893,U_17892,U_17891] : hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),hAPP(hAPP(c_List_Oappend(U_17891),U_17894),U_17895)) = hAPP(hAPP(c_List_Oappend(U_17892),hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),U_17894)),hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),U_17895)),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

cnf(f_4335_3,plain,
    hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),hAPP(hAPP(c_List_Oappend(U_17891),U_17894),U_17895)) = hAPP(hAPP(c_List_Oappend(U_17892),hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),U_17894)),hAPP(hAPP(c_List_Omap(U_17891,U_17892),U_17893),U_17895)),
    inference(clausify,[status(thm)],[f_4335_2]) ).

fof(f_4336_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(f_4336_2,plain,
    ! [U_17900,U_17899,U_17898,U_17897,U_17896] : hAPP(hAPP(c_List_Omap(U_17896,U_17897),U_17898),hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17899),U_17900)) = hAPP(hAPP(c_List_Olist_OCons(U_17897),hAPP(U_17898,U_17899)),hAPP(hAPP(c_List_Omap(U_17896,U_17897),U_17898),U_17900)),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

cnf(f_4336_3,plain,
    hAPP(hAPP(c_List_Omap(U_17896,U_17897),U_17898),hAPP(hAPP(c_List_Olist_OCons(U_17896),U_17899),U_17900)) = hAPP(hAPP(c_List_Olist_OCons(U_17897),hAPP(U_17898,U_17899)),hAPP(hAPP(c_List_Omap(U_17896,U_17897),U_17898),U_17900)),
    inference(clausify,[status(thm)],[f_4336_2]) ).

fof(f_4337_1,plain,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),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_4337_2,plain,
    ! [U_17906,U_17905,U_17904,U_17903,U_17902,U_17901] : hAPP(hAPP(c_List_Omap(U_17901,U_17902),U_17903),hAPP(hAPP(c_List_Olist__update(U_17901,U_17904),U_17905),U_17906)) = hAPP(hAPP(c_List_Olist__update(U_17902,hAPP(hAPP(c_List_Omap(U_17901,U_17902),U_17903),U_17904)),U_17905),hAPP(U_17903,U_17906)),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

cnf(f_4337_3,plain,
    hAPP(hAPP(c_List_Omap(U_17901,U_17902),U_17903),hAPP(hAPP(c_List_Olist__update(U_17901,U_17904),U_17905),U_17906)) = hAPP(hAPP(c_List_Olist__update(U_17902,hAPP(hAPP(c_List_Omap(U_17901,U_17902),U_17903),U_17904)),U_17905),hAPP(U_17903,U_17906)),
    inference(clausify,[status(thm)],[f_4337_2]) ).

fof(f_4338_1,plain,
    ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),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_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( 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))) )
        | hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__conv]) ).

fof(f_4338_2,plain,
    ! [U_17913,U_17912,U_17911,U_17910,U_17909] :
      ( ( hAPP(hAPP(c_List_Omap(U_17909,U_17910),U_17911),U_17912) = hAPP(hAPP(c_List_Omap(U_17909,U_17910),U_17913),U_17912)
        | ? [U_17908] :
            ( hAPP(U_17911,U_17908) != hAPP(U_17913,U_17908)
            & hBOOL(hAPP(hAPP(c_member(U_17909),U_17908),hAPP(c_List_Oset(U_17909),U_17912))) ) )
      & ( ! [U_17907] :
            ( hAPP(U_17911,U_17907) = hAPP(U_17913,U_17907)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17909),U_17907),hAPP(c_List_Oset(U_17909),U_17912))) )
        | hAPP(hAPP(c_List_Omap(U_17909,U_17910),U_17911),U_17912) != hAPP(hAPP(c_List_Omap(U_17909,U_17910),U_17913),U_17912) ) ),
    inference(variable_rename,[status(thm)],[f_4338_1]) ).

fof(f_4338_3,plain,
    ( ! [U_17923,U_17921,U_17919,U_17917,U_17915] :
        ( hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17919),U_17921) = hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17923),U_17921)
        | ? [U_17908] :
            ( hAPP(U_17919,U_17908) != hAPP(U_17923,U_17908)
            & hBOOL(hAPP(hAPP(c_member(U_17915),U_17908),hAPP(c_List_Oset(U_17915),U_17921))) ) )
    & ! [U_17922,U_17920,U_17918,U_17916,U_17914] :
        ( ! [U_17907] :
            ( hAPP(U_17918,U_17907) = hAPP(U_17922,U_17907)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17914),U_17907),hAPP(c_List_Oset(U_17914),U_17920))) )
        | hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17918),U_17920) != hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17922),U_17920) ) ),
    inference(miniscope,[status(thm)],[f_4338_2]) ).

fof(f_4338_4,plain,
    ( ! [U_17923,U_17921,U_17919,U_17917,U_17915] :
        ( hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17919),U_17921) = hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17923),U_17921)
        | ( hAPP(U_17919,sK456(U_17923,U_17921,U_17919,U_17917,U_17915)) != hAPP(U_17923,sK456(U_17923,U_17921,U_17919,U_17917,U_17915))
          & hBOOL(hAPP(hAPP(c_member(U_17915),sK456(U_17923,U_17921,U_17919,U_17917,U_17915)),hAPP(c_List_Oset(U_17915),U_17921))) ) )
    & ! [U_17922,U_17920,U_17918,U_17916,U_17914] :
        ( ! [U_17907] :
            ( hAPP(U_17918,U_17907) = hAPP(U_17922,U_17907)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17914),U_17907),hAPP(c_List_Oset(U_17914),U_17920))) )
        | hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17918),U_17920) != hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17922),U_17920) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_17908,sK456(U_17923,U_17921,U_17919,U_17917,U_17915))],[f_4338_3]) ).

cnf(f_4338_5,plain,
    ( hAPP(U_17918,U_17907) = hAPP(U_17922,U_17907)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17914),U_17907),hAPP(c_List_Oset(U_17914),U_17920)))
    | hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17918),U_17920) != hAPP(hAPP(c_List_Omap(U_17914,U_17916),U_17922),U_17920) ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

cnf(f_4338_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17915),sK456(U_17923,U_17921,U_17919,U_17917,U_17915)),hAPP(c_List_Oset(U_17915),U_17921)))
    | hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17919),U_17921) = hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17923),U_17921) ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

cnf(f_4338_7,plain,
    ( hAPP(U_17919,sK456(U_17923,U_17921,U_17919,U_17917,U_17915)) != hAPP(U_17923,sK456(U_17923,U_17921,U_17919,U_17917,U_17915))
    | hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17919),U_17921) = hAPP(hAPP(c_List_Omap(U_17915,U_17917),U_17923),U_17921) ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

fof(f_4339_1,plain,
    ! [V_xs_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__0]) ).

fof(f_4339_2,plain,
    ! [U_17926,U_17925,U_17924] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17924),hAPP(hAPP(c_List_Omap(U_17925,U_17924),hAPP(c_COMBK(U_17924,U_17925),c_Groups_Ozero__class_Ozero(U_17924))),U_17926)) = c_Groups_Ozero__class_Ozero(U_17924)
      | ~ class_Groups_Omonoid__add(U_17924) ),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

cnf(f_4339_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17924),hAPP(hAPP(c_List_Omap(U_17925,U_17924),hAPP(c_COMBK(U_17924,U_17925),c_Groups_Ozero__class_Ozero(U_17924))),U_17926)) = c_Groups_Ozero__class_Ozero(U_17924)
    | ~ class_Groups_Omonoid__add(U_17924) ),
    inference(clausify,[status(thm)],[f_4339_2]) ).

fof(f_4340_1,plain,
    ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2)
      | ~ class_Rings_Osemiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mult__const]) ).

fof(f_4340_2,plain,
    ! [U_17931,U_17930,U_17929,U_17928,U_17927] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17927),hAPP(hAPP(c_COMBC(U_17928,U_17927,U_17927),hAPP(hAPP(c_COMBB(U_17927,tc_fun(U_17927,U_17927),U_17928),c_Groups_Otimes__class_Otimes(U_17927)),U_17929)),U_17930)),U_17931)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17927),hAPP(c_List_Omonoid__add__class_Olistsum(U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17927),U_17929),U_17931))),U_17930)
      | ~ class_Rings_Osemiring__0(U_17927) ),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

cnf(f_4340_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17927),hAPP(hAPP(c_COMBC(U_17928,U_17927,U_17927),hAPP(hAPP(c_COMBB(U_17927,tc_fun(U_17927,U_17927),U_17928),c_Groups_Otimes__class_Otimes(U_17927)),U_17929)),U_17930)),U_17931)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17927),hAPP(c_List_Omonoid__add__class_Olistsum(U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17927),U_17929),U_17931))),U_17930)
    | ~ class_Rings_Osemiring__0(U_17927) ),
    inference(clausify,[status(thm)],[f_4340_2]) ).

fof(f_4341_1,plain,
    ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
      | ~ class_Rings_Osemiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__const__mult]) ).

fof(f_4341_2,plain,
    ! [U_17936,U_17935,U_17934,U_17933,U_17932] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17932),hAPP(hAPP(c_List_Omap(U_17933,U_17932),hAPP(hAPP(c_COMBB(U_17932,U_17932,U_17933),hAPP(c_Groups_Otimes__class_Otimes(U_17932),U_17934)),U_17935)),U_17936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17932),U_17934),hAPP(c_List_Omonoid__add__class_Olistsum(U_17932),hAPP(hAPP(c_List_Omap(U_17933,U_17932),U_17935),U_17936)))
      | ~ class_Rings_Osemiring__0(U_17932) ),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

cnf(f_4341_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17932),hAPP(hAPP(c_List_Omap(U_17933,U_17932),hAPP(hAPP(c_COMBB(U_17932,U_17932,U_17933),hAPP(c_Groups_Otimes__class_Otimes(U_17932),U_17934)),U_17935)),U_17936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17932),U_17934),hAPP(c_List_Omonoid__add__class_Olistsum(U_17932),hAPP(hAPP(c_List_Omap(U_17933,U_17932),U_17935),U_17936)))
    | ~ class_Rings_Osemiring__0(U_17932) ),
    inference(clausify,[status(thm)],[f_4341_2]) ).

fof(f_4342_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__subtractf]) ).

fof(f_4342_2,plain,
    ! [U_17941,U_17940,U_17939,U_17938,U_17937] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),hAPP(hAPP(c_COMBS(U_17938,U_17937,U_17937),hAPP(hAPP(c_COMBB(U_17937,tc_fun(U_17937,U_17937),U_17938),c_Groups_Ominus__class_Ominus(U_17937)),U_17939)),U_17940)),U_17941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_17937),hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),U_17939),U_17941))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),U_17940),U_17941)))
      | ~ class_Groups_Oab__group__add(U_17937) ),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

cnf(f_4342_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),hAPP(hAPP(c_COMBS(U_17938,U_17937,U_17937),hAPP(hAPP(c_COMBB(U_17937,tc_fun(U_17937,U_17937),U_17938),c_Groups_Ominus__class_Ominus(U_17937)),U_17939)),U_17940)),U_17941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_17937),hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),U_17939),U_17941))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17937),hAPP(hAPP(c_List_Omap(U_17938,U_17937),U_17940),U_17941)))
    | ~ class_Groups_Oab__group__add(U_17937) ),
    inference(clausify,[status(thm)],[f_4342_2]) ).

fof(f_4343_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__addf]) ).

fof(f_4343_2,plain,
    ! [U_17946,U_17945,U_17944,U_17943,U_17942] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),hAPP(hAPP(c_COMBS(U_17943,U_17942,U_17942),hAPP(hAPP(c_COMBB(U_17942,tc_fun(U_17942,U_17942),U_17943),c_Groups_Oplus__class_Oplus(U_17942)),U_17944)),U_17945)),U_17946)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17942),hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),U_17944),U_17946))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),U_17945),U_17946)))
      | ~ class_Groups_Ocomm__monoid__add(U_17942) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

cnf(f_4343_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),hAPP(hAPP(c_COMBS(U_17943,U_17942,U_17942),hAPP(hAPP(c_COMBB(U_17942,tc_fun(U_17942,U_17942),U_17943),c_Groups_Oplus__class_Oplus(U_17942)),U_17944)),U_17945)),U_17946)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17942),hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),U_17944),U_17946))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17942),hAPP(hAPP(c_List_Omap(U_17943,U_17942),U_17945),U_17946)))
    | ~ class_Groups_Ocomm__monoid__add(U_17942) ),
    inference(clausify,[status(thm)],[f_4343_2]) ).

fof(f_4344_1,plain,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__ident]) ).

fof(f_4344_2,plain,
    ! [U_17948,U_17947] : hAPP(hAPP(c_List_Omap(U_17947,U_17947),c_COMBI(U_17947)),U_17948) = U_17948,
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

cnf(f_4344_3,plain,
    hAPP(hAPP(c_List_Omap(U_17947,U_17947),c_COMBI(U_17947)),U_17948) = U_17948,
    inference(clausify,[status(thm)],[f_4344_2]) ).

fof(f_4345_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_take__map]) ).

fof(f_4345_2,plain,
    ! [U_17953,U_17952,U_17951,U_17950,U_17949] : hAPP(hAPP(c_List_Otake(U_17949),U_17950),hAPP(hAPP(c_List_Omap(U_17951,U_17949),U_17952),U_17953)) = hAPP(hAPP(c_List_Omap(U_17951,U_17949),U_17952),hAPP(hAPP(c_List_Otake(U_17951),U_17950),U_17953)),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

cnf(f_4345_3,plain,
    hAPP(hAPP(c_List_Otake(U_17949),U_17950),hAPP(hAPP(c_List_Omap(U_17951,U_17949),U_17952),U_17953)) = hAPP(hAPP(c_List_Omap(U_17951,U_17949),U_17952),hAPP(hAPP(c_List_Otake(U_17951),U_17950),U_17953)),
    inference(clausify,[status(thm)],[f_4345_2]) ).

fof(f_4346_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__butlast]) ).

fof(f_4346_2,plain,
    ! [U_17957,U_17956,U_17955,U_17954] : hAPP(hAPP(c_List_Omap(U_17954,U_17955),U_17956),c_List_Obutlast(U_17954,U_17957)) = c_List_Obutlast(U_17955,hAPP(hAPP(c_List_Omap(U_17954,U_17955),U_17956),U_17957)),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

cnf(f_4346_3,plain,
    hAPP(hAPP(c_List_Omap(U_17954,U_17955),U_17956),c_List_Obutlast(U_17954,U_17957)) = c_List_Obutlast(U_17955,hAPP(hAPP(c_List_Omap(U_17954,U_17955),U_17956),U_17957)),
    inference(clausify,[status(thm)],[f_4346_2]) ).

fof(f_4347_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),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_a) != hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv]) ).

fof(f_4347_2,plain,
    ! [U_17961,U_17960,U_17959,U_17958] :
      ( ( c_List_Olist_ONil(U_17958) = hAPP(hAPP(c_List_Omap(U_17959,U_17958),U_17960),U_17961)
        | U_17961 != c_List_Olist_ONil(U_17959) )
      & ( U_17961 = c_List_Olist_ONil(U_17959)
        | c_List_Olist_ONil(U_17958) != hAPP(hAPP(c_List_Omap(U_17959,U_17958),U_17960),U_17961) ) ),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

fof(f_4347_3,plain,
    ( ! [U_17969,U_17967,U_17965] :
        ( ! [U_17963] : c_List_Olist_ONil(U_17963) = hAPP(hAPP(c_List_Omap(U_17965,U_17963),U_17967),U_17969)
        | U_17969 != c_List_Olist_ONil(U_17965) )
    & ! [U_17968,U_17966,U_17964] :
        ( ! [U_17962] : c_List_Olist_ONil(U_17962) != hAPP(hAPP(c_List_Omap(U_17964,U_17962),U_17966),U_17968)
        | U_17968 = c_List_Olist_ONil(U_17964) ) ),
    inference(miniscope,[status(thm)],[f_4347_2]) ).

cnf(f_4347_4,plain,
    ( c_List_Olist_ONil(U_17962) != hAPP(hAPP(c_List_Omap(U_17964,U_17962),U_17966),U_17968)
    | U_17968 = c_List_Olist_ONil(U_17964) ),
    inference(clausify,[status(thm)],[f_4347_3]) ).

cnf(f_4347_5,plain,
    ( c_List_Olist_ONil(U_17963) = hAPP(hAPP(c_List_Omap(U_17965,U_17963),U_17967),U_17969)
    | U_17969 != c_List_Olist_ONil(U_17965) ),
    inference(clausify,[status(thm)],[f_4347_3]) ).

fof(f_4348_1,plain,
    ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(f_4348_2,plain,
    ! [U_17972,U_17971,U_17970] : hAPP(hAPP(c_List_Omap(U_17970,U_17971),U_17972),c_List_Olist_ONil(U_17970)) = c_List_Olist_ONil(U_17971),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

cnf(f_4348_3,plain,
    hAPP(hAPP(c_List_Omap(U_17970,U_17971),U_17972),c_List_Olist_ONil(U_17970)) = c_List_Olist_ONil(U_17971),
    inference(clausify,[status(thm)],[f_4348_2]) ).

fof(f_4349_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv]) ).

fof(f_4349_2,plain,
    ! [U_17976,U_17975,U_17974,U_17973] :
      ( ( hAPP(hAPP(c_List_Omap(U_17973,U_17974),U_17975),U_17976) = c_List_Olist_ONil(U_17974)
        | U_17976 != c_List_Olist_ONil(U_17973) )
      & ( U_17976 = c_List_Olist_ONil(U_17973)
        | hAPP(hAPP(c_List_Omap(U_17973,U_17974),U_17975),U_17976) != c_List_Olist_ONil(U_17974) ) ),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

fof(f_4349_3,plain,
    ( ! [U_17984,U_17982,U_17980,U_17978] :
        ( hAPP(hAPP(c_List_Omap(U_17978,U_17980),U_17982),U_17984) = c_List_Olist_ONil(U_17980)
        | U_17984 != c_List_Olist_ONil(U_17978) )
    & ! [U_17983,U_17981,U_17979,U_17977] :
        ( U_17983 = c_List_Olist_ONil(U_17977)
        | hAPP(hAPP(c_List_Omap(U_17977,U_17979),U_17981),U_17983) != c_List_Olist_ONil(U_17979) ) ),
    inference(miniscope,[status(thm)],[f_4349_2]) ).

cnf(f_4349_4,plain,
    ( U_17983 = c_List_Olist_ONil(U_17977)
    | hAPP(hAPP(c_List_Omap(U_17977,U_17979),U_17981),U_17983) != c_List_Olist_ONil(U_17979) ),
    inference(clausify,[status(thm)],[f_4349_3]) ).

cnf(f_4349_5,plain,
    ( hAPP(hAPP(c_List_Omap(U_17978,U_17980),U_17982),U_17984) = c_List_Olist_ONil(U_17980)
    | U_17984 != c_List_Olist_ONil(U_17978) ),
    inference(clausify,[status(thm)],[f_4349_3]) ).

fof(f_4350_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map]) ).

fof(f_4350_2,plain,
    ! [U_17989,U_17988,U_17987,U_17986,U_17985] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17988) = hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17989)
          | U_17988 != U_17989 )
        & ( U_17988 = U_17989
          | hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17988) != hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17989) ) )
      | ~ c_Fun_Oinj__on(U_17985,U_17986,U_17987,c_Orderings_Otop__class_Otop(tc_fun(U_17985,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

cnf(f_4350_3,plain,
    ( U_17988 = U_17989
    | hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17988) != hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17989)
    | ~ c_Fun_Oinj__on(U_17985,U_17986,U_17987,c_Orderings_Otop__class_Otop(tc_fun(U_17985,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4350_2]) ).

cnf(f_4350_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17988) = hAPP(hAPP(c_List_Omap(U_17985,U_17986),U_17987),U_17989)
    | U_17988 != U_17989
    | ~ c_Fun_Oinj__on(U_17985,U_17986,U_17987,c_Orderings_Otop__class_Otop(tc_fun(U_17985,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4350_2]) ).

fof(f_4351_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__injective]) ).

fof(f_4351_2,plain,
    ! [U_17994,U_17993,U_17992,U_17991,U_17990] :
      ( U_17993 = U_17994
      | ~ c_Fun_Oinj__on(U_17990,U_17991,U_17992,c_Orderings_Otop__class_Otop(tc_fun(U_17990,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17990,U_17991),U_17992),U_17993) != hAPP(hAPP(c_List_Omap(U_17990,U_17991),U_17992),U_17994) ),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

cnf(f_4351_3,plain,
    ( U_17993 = U_17994
    | ~ c_Fun_Oinj__on(U_17990,U_17991,U_17992,c_Orderings_Otop__class_Otop(tc_fun(U_17990,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_17990,U_17991),U_17992),U_17993) != hAPP(hAPP(c_List_Omap(U_17990,U_17991),U_17992),U_17994) ),
    inference(clausify,[status(thm)],[f_4351_2]) ).

fof(f_4352_1,plain,
    ! [V_f_2,T_b,T_a,V_xs_2] :
      ( hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__map]) ).

fof(f_4352_2,plain,
    ! [U_17998,U_17997,U_17996,U_17995] :
      ( hAPP(c_List_Ohd(U_17997),hAPP(hAPP(c_List_Omap(U_17996,U_17997),U_17998),U_17995)) = hAPP(U_17998,hAPP(c_List_Ohd(U_17996),U_17995))
      | U_17995 = c_List_Olist_ONil(U_17996) ),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

cnf(f_4352_3,plain,
    ( hAPP(c_List_Ohd(U_17997),hAPP(hAPP(c_List_Omap(U_17996,U_17997),U_17998),U_17995)) = hAPP(U_17998,hAPP(c_List_Ohd(U_17996),U_17995))
    | U_17995 = c_List_Olist_ONil(U_17996) ),
    inference(clausify,[status(thm)],[f_4352_2]) ).

fof(f_4353_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_drop__map]) ).

fof(f_4353_2,plain,
    ! [U_18003,U_18002,U_18001,U_18000,U_17999] : hAPP(hAPP(c_List_Odrop(U_17999),U_18000),hAPP(hAPP(c_List_Omap(U_18001,U_17999),U_18002),U_18003)) = hAPP(hAPP(c_List_Omap(U_18001,U_17999),U_18002),hAPP(hAPP(c_List_Odrop(U_18001),U_18000),U_18003)),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

cnf(f_4353_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17999),U_18000),hAPP(hAPP(c_List_Omap(U_18001,U_17999),U_18002),U_18003)) = hAPP(hAPP(c_List_Omap(U_18001,U_17999),U_18002),hAPP(hAPP(c_List_Odrop(U_18001),U_18000),U_18003)),
    inference(clausify,[status(thm)],[f_4353_2]) ).

fof(f_4354_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_b,T_a,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_a),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__inj__on]) ).

fof(f_4354_2,plain,
    ! [U_18008,U_18007,U_18006,U_18005,U_18004] :
      ( U_18007 = U_18008
      | ~ c_Fun_Oinj__on(U_18004,U_18005,U_18006,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18004,tc_HOL_Obool)),hAPP(c_List_Oset(U_18004),U_18007)),hAPP(c_List_Oset(U_18004),U_18008)))
      | hAPP(hAPP(c_List_Omap(U_18004,U_18005),U_18006),U_18007) != hAPP(hAPP(c_List_Omap(U_18004,U_18005),U_18006),U_18008) ),
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

cnf(f_4354_3,plain,
    ( U_18007 = U_18008
    | ~ c_Fun_Oinj__on(U_18004,U_18005,U_18006,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18004,tc_HOL_Obool)),hAPP(c_List_Oset(U_18004),U_18007)),hAPP(c_List_Oset(U_18004),U_18008)))
    | hAPP(hAPP(c_List_Omap(U_18004,U_18005),U_18006),U_18007) != hAPP(hAPP(c_List_Omap(U_18004,U_18005),U_18006),U_18008) ),
    inference(clausify,[status(thm)],[f_4354_2]) ).

fof(f_4355_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map]) ).

fof(f_4355_2,plain,
    ! [U_18013,U_18012,U_18011,U_18010,U_18009] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18012) = hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18013)
          | U_18012 != U_18013 )
        & ( U_18012 = U_18013
          | hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18012) != hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18013) ) )
      | ~ c_Fun_Oinj__on(U_18009,U_18010,U_18011,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18009,tc_HOL_Obool)),hAPP(c_List_Oset(U_18009),U_18012)),hAPP(c_List_Oset(U_18009),U_18013))) ),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

cnf(f_4355_3,plain,
    ( U_18012 = U_18013
    | hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18012) != hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18013)
    | ~ c_Fun_Oinj__on(U_18009,U_18010,U_18011,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18009,tc_HOL_Obool)),hAPP(c_List_Oset(U_18009),U_18012)),hAPP(c_List_Oset(U_18009),U_18013))) ),
    inference(clausify,[status(thm)],[f_4355_2]) ).

cnf(f_4355_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18012) = hAPP(hAPP(c_List_Omap(U_18009,U_18010),U_18011),U_18013)
    | U_18012 != U_18013
    | ~ c_Fun_Oinj__on(U_18009,U_18010,U_18011,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18009,tc_HOL_Obool)),hAPP(c_List_Oset(U_18009),U_18012)),hAPP(c_List_Oset(U_18009),U_18013))) ),
    inference(clausify,[status(thm)],[f_4355_2]) ).

fof(f_4356_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__map]) ).

fof(f_4356_2,plain,
    ! [U_18018,U_18017,U_18016,U_18015,U_18014] : hAPP(c_List_Orotate(U_18014,U_18015),hAPP(hAPP(c_List_Omap(U_18016,U_18014),U_18017),U_18018)) = hAPP(hAPP(c_List_Omap(U_18016,U_18014),U_18017),hAPP(c_List_Orotate(U_18016,U_18015),U_18018)),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

cnf(f_4356_3,plain,
    hAPP(c_List_Orotate(U_18014,U_18015),hAPP(hAPP(c_List_Omap(U_18016,U_18014),U_18017),U_18018)) = hAPP(hAPP(c_List_Omap(U_18016,U_18014),U_18017),hAPP(c_List_Orotate(U_18016,U_18015),U_18018)),
    inference(clausify,[status(thm)],[f_4356_2]) ).

fof(f_4357_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
        | ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2))
          & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__map]) ).

fof(f_4357_2,plain,
    ! [U_18022,U_18021,U_18020,U_18019] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18019),hAPP(hAPP(c_List_Omap(U_18020,U_18019),U_18021),U_18022)))
        | ~ c_Fun_Oinj__on(U_18020,U_18019,U_18021,hAPP(c_List_Oset(U_18020),U_18022))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18020),U_18022)) )
      & ( ( c_Fun_Oinj__on(U_18020,U_18019,U_18021,hAPP(c_List_Oset(U_18020),U_18022))
          & hBOOL(hAPP(c_List_Odistinct(U_18020),U_18022)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18019),hAPP(hAPP(c_List_Omap(U_18020,U_18019),U_18021),U_18022))) ) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

fof(f_4357_3,plain,
    ( ! [U_18030,U_18028,U_18026,U_18024] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18024),hAPP(hAPP(c_List_Omap(U_18026,U_18024),U_18028),U_18030)))
        | ~ c_Fun_Oinj__on(U_18026,U_18024,U_18028,hAPP(c_List_Oset(U_18026),U_18030))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18026),U_18030)) )
    & ! [U_18029,U_18027,U_18025,U_18023] :
        ( ( c_Fun_Oinj__on(U_18025,U_18023,U_18027,hAPP(c_List_Oset(U_18025),U_18029))
          & hBOOL(hAPP(c_List_Odistinct(U_18025),U_18029)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18023),hAPP(hAPP(c_List_Omap(U_18025,U_18023),U_18027),U_18029))) ) ),
    inference(miniscope,[status(thm)],[f_4357_2]) ).

cnf(f_4357_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18025),U_18029))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18023),hAPP(hAPP(c_List_Omap(U_18025,U_18023),U_18027),U_18029))) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

cnf(f_4357_5,plain,
    ( c_Fun_Oinj__on(U_18025,U_18023,U_18027,hAPP(c_List_Oset(U_18025),U_18029))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18023),hAPP(hAPP(c_List_Omap(U_18025,U_18023),U_18027),U_18029))) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

cnf(f_4357_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18024),hAPP(hAPP(c_List_Omap(U_18026,U_18024),U_18028),U_18030)))
    | ~ c_Fun_Oinj__on(U_18026,U_18024,U_18028,hAPP(c_List_Oset(U_18026),U_18030))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18026),U_18030)) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

fof(f_4358_1,plain,
    ! [V_f_2,T_b,T_a,V_xs_2] :
      ( c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__map]) ).

fof(f_4358_2,plain,
    ! [U_18034,U_18033,U_18032,U_18031] :
      ( c_List_Olast(U_18033,hAPP(hAPP(c_List_Omap(U_18032,U_18033),U_18034),U_18031)) = hAPP(U_18034,c_List_Olast(U_18032,U_18031))
      | U_18031 = c_List_Olist_ONil(U_18032) ),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

cnf(f_4358_3,plain,
    ( c_List_Olast(U_18033,hAPP(hAPP(c_List_Omap(U_18032,U_18033),U_18034),U_18031)) = hAPP(U_18034,c_List_Olast(U_18032,U_18031))
    | U_18031 = c_List_Olist_ONil(U_18032) ),
    inference(clausify,[status(thm)],[f_4358_2]) ).

fof(f_4359_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map]) ).

fof(f_4359_2,plain,
    ! [U_18038,U_18037,U_18036,U_18035] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18035),hAPP(c_List_Omonoid__add__class_Olistsum(U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18035),U_18037),U_18038))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18035),hAPP(c_Fun_Ocomp(U_18035,U_18035,U_18036,c_Groups_Ouminus__class_Ouminus(U_18035)),U_18037)),U_18038))
      | ~ class_Groups_Oab__group__add(U_18035) ),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

cnf(f_4359_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18035),hAPP(c_List_Omonoid__add__class_Olistsum(U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18035),U_18037),U_18038))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18035),hAPP(c_Fun_Ocomp(U_18035,U_18035,U_18036,c_Groups_Ouminus__class_Ouminus(U_18035)),U_18037)),U_18038))
    | ~ class_Groups_Oab__group__add(U_18035) ),
    inference(clausify,[status(thm)],[f_4359_2]) ).

fof(f_4360_1,plain,
    ! [V_A_2,V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__mapI]) ).

fof(f_4360_2,plain,
    ! [U_18042,U_18041,U_18040,U_18039] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_18039),tc_List_Olist(U_18040),hAPP(c_List_Omap(U_18039,U_18040),U_18041),U_18042)
      | ~ c_Fun_Oinj__on(U_18039,U_18040,U_18041,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_18039,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_18039),tc_fun(U_18039,tc_HOL_Obool),c_List_Oset(U_18039)),U_18042))) ),
    inference(variable_rename,[status(thm)],[f_4360_1]) ).

cnf(f_4360_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_18039),tc_List_Olist(U_18040),hAPP(c_List_Omap(U_18039,U_18040),U_18041),U_18042)
    | ~ c_Fun_Oinj__on(U_18039,U_18040,U_18041,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_18039,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_18039),tc_fun(U_18039,tc_HOL_Obool),c_List_Oset(U_18039)),U_18042))) ),
    inference(clausify,[status(thm)],[f_4360_2]) ).

fof(f_4361_1,plain,
    ! [V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__fst__zip]) ).

fof(f_4361_2,plain,
    ! [U_18046,U_18045,U_18044,U_18043] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18043,U_18045),U_18043),c_Product__Type_Ofst(U_18043,U_18045)),hAPP(hAPP(c_List_Ozip(U_18043,U_18045),U_18044),U_18046)) = U_18044
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18043)),U_18044) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18045)),U_18046) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

cnf(f_4361_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18043,U_18045),U_18043),c_Product__Type_Ofst(U_18043,U_18045)),hAPP(hAPP(c_List_Ozip(U_18043,U_18045),U_18044),U_18046)) = U_18044
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18043)),U_18044) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18045)),U_18046) ),
    inference(clausify,[status(thm)],[f_4361_2]) ).

fof(f_4362_1,plain,
    ! [V_ys_2,T_b,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__snd__zip]) ).

fof(f_4362_2,plain,
    ! [U_18050,U_18049,U_18048,U_18047] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18047,U_18049),U_18049),c_Product__Type_Osnd(U_18047,U_18049)),hAPP(hAPP(c_List_Ozip(U_18047,U_18049),U_18048),U_18050)) = U_18050
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18047)),U_18048) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18049)),U_18050) ),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

cnf(f_4362_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18047,U_18049),U_18049),c_Product__Type_Osnd(U_18047,U_18049)),hAPP(hAPP(c_List_Ozip(U_18047,U_18049),U_18048),U_18050)) = U_18050
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18047)),U_18048) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18049)),U_18050) ),
    inference(clausify,[status(thm)],[f_4362_2]) ).

fof(f_4363_1,plain,
    ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2,
    inference(fof_nnf,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(f_4363_2,plain,
    ! [U_18053,U_18052,U_18051] : hAPP(hAPP(c_List_Ozip(U_18051,U_18052),hAPP(hAPP(c_List_Omap(tc_prod(U_18051,U_18052),U_18051),c_Product__Type_Ofst(U_18051,U_18052)),U_18053)),hAPP(hAPP(c_List_Omap(tc_prod(U_18051,U_18052),U_18052),c_Product__Type_Osnd(U_18051,U_18052)),U_18053)) = U_18053,
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

cnf(f_4363_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18051,U_18052),hAPP(hAPP(c_List_Omap(tc_prod(U_18051,U_18052),U_18051),c_Product__Type_Ofst(U_18051,U_18052)),U_18053)),hAPP(hAPP(c_List_Omap(tc_prod(U_18051,U_18052),U_18052),c_Product__Type_Osnd(U_18051,U_18052)),U_18053)) = U_18053,
    inference(clausify,[status(thm)],[f_4363_2]) ).

fof(f_4364_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map]) ).

fof(f_4364_2,plain,
    ! [U_18056,U_18055,U_18054] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_18054),tc_List_Olist(U_18055),hAPP(c_List_Omap(U_18054,U_18055),U_18056),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18054),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_18054,U_18055,U_18056,c_Orderings_Otop__class_Otop(tc_fun(U_18054,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_18054,U_18055,U_18056,c_Orderings_Otop__class_Otop(tc_fun(U_18054,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_18054),tc_List_Olist(U_18055),hAPP(c_List_Omap(U_18054,U_18055),U_18056),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18054),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

fof(f_4364_3,plain,
    ( ! [U_18062,U_18060,U_18058] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_18058),tc_List_Olist(U_18060),hAPP(c_List_Omap(U_18058,U_18060),U_18062),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18058),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_18058,U_18060,U_18062,c_Orderings_Otop__class_Otop(tc_fun(U_18058,tc_HOL_Obool))) )
    & ! [U_18061,U_18059,U_18057] :
        ( c_Fun_Oinj__on(U_18057,U_18059,U_18061,c_Orderings_Otop__class_Otop(tc_fun(U_18057,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_18057),tc_List_Olist(U_18059),hAPP(c_List_Omap(U_18057,U_18059),U_18061),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18057),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4364_2]) ).

cnf(f_4364_4,plain,
    ( c_Fun_Oinj__on(U_18057,U_18059,U_18061,c_Orderings_Otop__class_Otop(tc_fun(U_18057,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_18057),tc_List_Olist(U_18059),hAPP(c_List_Omap(U_18057,U_18059),U_18061),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18057),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4364_3]) ).

cnf(f_4364_5,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_18058),tc_List_Olist(U_18060),hAPP(c_List_Omap(U_18058,U_18060),U_18062),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18058),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_18058,U_18060,U_18062,c_Orderings_Otop__class_Otop(tc_fun(U_18058,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4364_3]) ).

fof(f_4365_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapD]) ).

fof(f_4365_2,plain,
    ! [U_18065,U_18064,U_18063] :
      ( c_Fun_Oinj__on(U_18063,U_18064,U_18065,c_Orderings_Otop__class_Otop(tc_fun(U_18063,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_18063),tc_List_Olist(U_18064),hAPP(c_List_Omap(U_18063,U_18064),U_18065),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18063),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

cnf(f_4365_3,plain,
    ( c_Fun_Oinj__on(U_18063,U_18064,U_18065,c_Orderings_Otop__class_Otop(tc_fun(U_18063,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_18063),tc_List_Olist(U_18064),hAPP(c_List_Omap(U_18063,U_18064),U_18065),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_18063),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4365_2]) ).

fof(f_4366_1,plain,
    ! [V_xs_2,T_a,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__member]) ).

fof(f_4366_2,plain,
    ! [U_18068,U_18067,U_18066] :
      ( hBOOL(hAPP(hAPP(c_member(U_18067),hAPP(c_Random_Opick(U_18067,U_18068),U_18066)),hAPP(c_List_Oset(U_18067),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18067),U_18067),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18067)),U_18068))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18066),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_18067),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18067)),U_18068)))) ),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

cnf(f_4366_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18067),hAPP(c_Random_Opick(U_18067,U_18068),U_18066)),hAPP(c_List_Oset(U_18067),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18067),U_18067),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18067)),U_18068))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18066),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_18067),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18067)),U_18068)))) ),
    inference(clausify,[status(thm)],[f_4366_2]) ).

fof(f_4367_1,plain,
    ! [V_f_2,V_xs_2,T_a,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set]) ).

fof(f_4367_2,plain,
    ! [U_18072,U_18071,U_18070,U_18069] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18069),hAPP(hAPP(c_List_Omap(U_18070,U_18069),U_18072),U_18071)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18070,U_18069),U_18072),hAPP(c_List_Oset(U_18070),U_18071))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18070),U_18071))
      | ~ class_Groups_Ocomm__monoid__add(U_18069) ),
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

cnf(f_4367_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18069),hAPP(hAPP(c_List_Omap(U_18070,U_18069),U_18072),U_18071)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18070,U_18069),U_18072),hAPP(c_List_Oset(U_18070),U_18071))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18070),U_18071))
    | ~ class_Groups_Ocomm__monoid__add(U_18069) ),
    inference(clausify,[status(thm)],[f_4367_2]) ).

fof(f_4368_1,plain,
    ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( ( ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) != V_ys_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) != V_xs_2 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2
            & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 )
          | hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) != V_zs_2 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_zip__eq__conv]) ).

fof(f_4368_2,plain,
    ! [U_18077,U_18076,U_18075,U_18074,U_18073] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_18073,U_18075),U_18074),U_18076) = U_18077
          | hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18075),c_Product__Type_Osnd(U_18073,U_18075)),U_18077) != U_18076
          | hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18073),c_Product__Type_Ofst(U_18073,U_18075)),U_18077) != U_18074 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18075),c_Product__Type_Osnd(U_18073,U_18075)),U_18077) = U_18076
            & hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18073),c_Product__Type_Ofst(U_18073,U_18075)),U_18077) = U_18074 )
          | hAPP(hAPP(c_List_Ozip(U_18073,U_18075),U_18074),U_18076) != U_18077 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18073)),U_18074) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18075)),U_18076) ),
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

cnf(f_4368_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18073),c_Product__Type_Ofst(U_18073,U_18075)),U_18077) = U_18074
    | hAPP(hAPP(c_List_Ozip(U_18073,U_18075),U_18074),U_18076) != U_18077
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18073)),U_18074) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18075)),U_18076) ),
    inference(clausify,[status(thm)],[f_4368_2]) ).

cnf(f_4368_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18075),c_Product__Type_Osnd(U_18073,U_18075)),U_18077) = U_18076
    | hAPP(hAPP(c_List_Ozip(U_18073,U_18075),U_18074),U_18076) != U_18077
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18073)),U_18074) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18075)),U_18076) ),
    inference(clausify,[status(thm)],[f_4368_2]) ).

cnf(f_4368_5,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18073,U_18075),U_18074),U_18076) = U_18077
    | hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18075),c_Product__Type_Osnd(U_18073,U_18075)),U_18077) != U_18076
    | hAPP(hAPP(c_List_Omap(tc_prod(U_18073,U_18075),U_18073),c_Product__Type_Ofst(U_18073,U_18075)),U_18077) != U_18074
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18073)),U_18074) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18075)),U_18076) ),
    inference(clausify,[status(thm)],[f_4368_2]) ).

fof(f_4369_1,plain,
    ! [V_xs_2,V_r_2,T_b,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__triv]) ).

fof(f_4369_2,plain,
    ! [U_18081,U_18080,U_18079,U_18078] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18078),hAPP(hAPP(c_List_Omap(U_18079,U_18078),hAPP(c_COMBK(U_18078,U_18079),U_18080)),U_18081)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18078),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18078),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18079)),U_18081))),U_18080)
      | ~ class_Rings_Osemiring__1(U_18078) ),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

cnf(f_4369_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18078),hAPP(hAPP(c_List_Omap(U_18079,U_18078),hAPP(c_COMBK(U_18078,U_18079),U_18080)),U_18081)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18078),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18078),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18079)),U_18081))),U_18080)
    | ~ class_Rings_Osemiring__1(U_18078) ),
    inference(clausify,[status(thm)],[f_4369_2]) ).

fof(f_4370_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( ( ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
          | hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) != hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) )
        & ( hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)
          | hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) != hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__inject__set]) ).

fof(f_4370_2,plain,
    ! [U_18085,U_18084,U_18083,U_18082] :
      ( ( ( hAPP(c_Map_Omap__of(U_18082,U_18083),U_18084) = hAPP(c_Map_Omap__of(U_18082,U_18083),U_18085)
          | hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18084) != hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18085) )
        & ( hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18084) = hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18085)
          | hAPP(c_Map_Omap__of(U_18082,U_18083),U_18084) != hAPP(c_Map_Omap__of(U_18082,U_18083),U_18085) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18085)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18084))) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

cnf(f_4370_3,plain,
    ( hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18084) = hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18085)
    | hAPP(c_Map_Omap__of(U_18082,U_18083),U_18084) != hAPP(c_Map_Omap__of(U_18082,U_18083),U_18085)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18085)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18084))) ),
    inference(clausify,[status(thm)],[f_4370_2]) ).

cnf(f_4370_4,plain,
    ( hAPP(c_Map_Omap__of(U_18082,U_18083),U_18084) = hAPP(c_Map_Omap__of(U_18082,U_18083),U_18085)
    | hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18084) != hAPP(c_List_Oset(tc_prod(U_18082,U_18083)),U_18085)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18085)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18082),hAPP(hAPP(c_List_Omap(tc_prod(U_18082,U_18083),U_18082),c_Product__Type_Ofst(U_18082,U_18083)),U_18084))) ),
    inference(clausify,[status(thm)],[f_4370_2]) ).

fof(f_4371_1,plain,
    ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1]) ).

fof(f_4371_2,plain,
    ! [U_18090,U_18089,U_18088,U_18087,U_18086] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18086),hAPP(hAPP(c_List_Omap(U_18087,U_18086),U_18090),U_18089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18086),hAPP(U_18090,U_18088)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18086),hAPP(hAPP(c_List_Omap(U_18087,U_18086),U_18090),c_List_Oremove1(U_18087,U_18088,U_18089))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18087),U_18088),hAPP(c_List_Oset(U_18087),U_18089)))
      | ~ class_Groups_Ocomm__monoid__add(U_18086) ),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

cnf(f_4371_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18086),hAPP(hAPP(c_List_Omap(U_18087,U_18086),U_18090),U_18089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18086),hAPP(U_18090,U_18088)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18086),hAPP(hAPP(c_List_Omap(U_18087,U_18086),U_18090),c_List_Oremove1(U_18087,U_18088,U_18089))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18087),U_18088),hAPP(c_List_Oset(U_18087),U_18089)))
    | ~ class_Groups_Ocomm__monoid__add(U_18086) ),
    inference(clausify,[status(thm)],[f_4371_2]) ).

fof(f_4372_1,plain,
    ! [V_s_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_select__weight__member]) ).

fof(f_4372_2,plain,
    ! [U_18093,U_18092,U_18091] :
      ( hBOOL(hAPP(hAPP(c_member(U_18091),hAPP(c_Product__Type_Ofst(U_18091,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18091,U_18092),U_18093))),hAPP(c_List_Oset(U_18091),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18091),U_18091),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18091)),U_18092))))
      | ~ 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_18091),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18091)),U_18092)))) ),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

cnf(f_4372_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18091),hAPP(c_Product__Type_Ofst(U_18091,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18091,U_18092),U_18093))),hAPP(c_List_Oset(U_18091),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18091),U_18091),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18091)),U_18092))))
    | ~ 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_18091),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18091)),U_18092)))) ),
    inference(clausify,[status(thm)],[f_4372_2]) ).

fof(f_4373_1,plain,
    ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,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_a,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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_select__weight__def]) ).

fof(f_4373_2,plain,
    ! [U_18095,U_18094] : c_Random_Oselect__weight(U_18094,U_18095) = 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_18094,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_18094),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18094)),U_18095)))),hAPP(hAPP(c_COMBB(U_18094,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18094,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18094,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18094,U_18095))),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

cnf(f_4373_3,plain,
    c_Random_Oselect__weight(U_18094,U_18095) = 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_18094,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_18094),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18094)),U_18095)))),hAPP(hAPP(c_COMBB(U_18094,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18094,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18094,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18094,U_18095))),
    inference(clausify,[status(thm)],[f_4373_2]) ).

fof(f_4374_1,plain,
    ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,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_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2)
      | hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_c),V_x_2)
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__mapk__SomeI]) ).

fof(f_4374_2,plain,
    ! [U_18102,U_18101,U_18100,U_18099,U_18098,U_18097,U_18096] :
      ( hAPP(hAPP(c_Map_Omap__of(U_18097,U_18099),hAPP(hAPP(c_List_Omap(tc_prod(U_18096,U_18099),tc_prod(U_18097,U_18099)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18096,U_18099,tc_prod(U_18097,U_18099)),hAPP(hAPP(c_COMBB(U_18097,tc_fun(U_18099,tc_prod(U_18097,U_18099)),U_18096),c_Product__Type_OPair(U_18097,U_18099)),U_18098))),U_18100)),hAPP(U_18098,U_18101)) = hAPP(c_Option_Ooption_OSome(U_18099),U_18102)
      | hAPP(hAPP(c_Map_Omap__of(U_18096,U_18099),U_18100),U_18101) != hAPP(c_Option_Ooption_OSome(U_18099),U_18102)
      | ~ c_Fun_Oinj__on(U_18096,U_18097,U_18098,c_Orderings_Otop__class_Otop(tc_fun(U_18096,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

cnf(f_4374_3,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18097,U_18099),hAPP(hAPP(c_List_Omap(tc_prod(U_18096,U_18099),tc_prod(U_18097,U_18099)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18096,U_18099,tc_prod(U_18097,U_18099)),hAPP(hAPP(c_COMBB(U_18097,tc_fun(U_18099,tc_prod(U_18097,U_18099)),U_18096),c_Product__Type_OPair(U_18097,U_18099)),U_18098))),U_18100)),hAPP(U_18098,U_18101)) = hAPP(c_Option_Ooption_OSome(U_18099),U_18102)
    | hAPP(hAPP(c_Map_Omap__of(U_18096,U_18099),U_18100),U_18101) != hAPP(c_Option_Ooption_OSome(U_18099),U_18102)
    | ~ c_Fun_Oinj__on(U_18096,U_18097,U_18098,c_Orderings_Otop__class_Otop(tc_fun(U_18096,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4374_2]) ).

fof(f_4375_1,plain,
    ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
      ( ( ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
          | hAPP(c_Option_Ooption_OSome(T_b),V_y_2) != hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Some__eq__map__of__iff]) ).

fof(f_4375_2,plain,
    ! [U_18107,U_18106,U_18105,U_18104,U_18103] :
      ( ( ( hAPP(c_Option_Ooption_OSome(U_18104),U_18106) = hAPP(hAPP(c_Map_Omap__of(U_18103,U_18104),U_18105),U_18107)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18103,U_18104)),hAPP(hAPP(c_Product__Type_OPair(U_18103,U_18104),U_18107),U_18106)),hAPP(c_List_Oset(tc_prod(U_18103,U_18104)),U_18105))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18103,U_18104)),hAPP(hAPP(c_Product__Type_OPair(U_18103,U_18104),U_18107),U_18106)),hAPP(c_List_Oset(tc_prod(U_18103,U_18104)),U_18105)))
          | hAPP(c_Option_Ooption_OSome(U_18104),U_18106) != hAPP(hAPP(c_Map_Omap__of(U_18103,U_18104),U_18105),U_18107) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18103),hAPP(hAPP(c_List_Omap(tc_prod(U_18103,U_18104),U_18103),c_Product__Type_Ofst(U_18103,U_18104)),U_18105))) ),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

cnf(f_4375_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18103,U_18104)),hAPP(hAPP(c_Product__Type_OPair(U_18103,U_18104),U_18107),U_18106)),hAPP(c_List_Oset(tc_prod(U_18103,U_18104)),U_18105)))
    | hAPP(c_Option_Ooption_OSome(U_18104),U_18106) != hAPP(hAPP(c_Map_Omap__of(U_18103,U_18104),U_18105),U_18107)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18103),hAPP(hAPP(c_List_Omap(tc_prod(U_18103,U_18104),U_18103),c_Product__Type_Ofst(U_18103,U_18104)),U_18105))) ),
    inference(clausify,[status(thm)],[f_4375_2]) ).

cnf(f_4375_4,plain,
    ( hAPP(c_Option_Ooption_OSome(U_18104),U_18106) = hAPP(hAPP(c_Map_Omap__of(U_18103,U_18104),U_18105),U_18107)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18103,U_18104)),hAPP(hAPP(c_Product__Type_OPair(U_18103,U_18104),U_18107),U_18106)),hAPP(c_List_Oset(tc_prod(U_18103,U_18104)),U_18105)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18103),hAPP(hAPP(c_List_Omap(tc_prod(U_18103,U_18104),U_18103),c_Product__Type_Ofst(U_18103,U_18104)),U_18105))) ),
    inference(clausify,[status(thm)],[f_4375_2]) ).

fof(f_4376_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
      ( ( ( hAPP(hAPP(c_Map_Omap__of(T_a,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_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
          | hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) != hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__Some__iff]) ).

fof(f_4376_2,plain,
    ! [U_18112,U_18111,U_18110,U_18109,U_18108] :
      ( ( ( hAPP(hAPP(c_Map_Omap__of(U_18108,U_18109),U_18110),U_18111) = hAPP(c_Option_Ooption_OSome(U_18109),U_18112)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18108,U_18109)),hAPP(hAPP(c_Product__Type_OPair(U_18108,U_18109),U_18111),U_18112)),hAPP(c_List_Oset(tc_prod(U_18108,U_18109)),U_18110))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18108,U_18109)),hAPP(hAPP(c_Product__Type_OPair(U_18108,U_18109),U_18111),U_18112)),hAPP(c_List_Oset(tc_prod(U_18108,U_18109)),U_18110)))
          | hAPP(hAPP(c_Map_Omap__of(U_18108,U_18109),U_18110),U_18111) != hAPP(c_Option_Ooption_OSome(U_18109),U_18112) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18108),hAPP(hAPP(c_List_Omap(tc_prod(U_18108,U_18109),U_18108),c_Product__Type_Ofst(U_18108,U_18109)),U_18110))) ),
    inference(variable_rename,[status(thm)],[f_4376_1]) ).

cnf(f_4376_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18108,U_18109)),hAPP(hAPP(c_Product__Type_OPair(U_18108,U_18109),U_18111),U_18112)),hAPP(c_List_Oset(tc_prod(U_18108,U_18109)),U_18110)))
    | hAPP(hAPP(c_Map_Omap__of(U_18108,U_18109),U_18110),U_18111) != hAPP(c_Option_Ooption_OSome(U_18109),U_18112)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18108),hAPP(hAPP(c_List_Omap(tc_prod(U_18108,U_18109),U_18108),c_Product__Type_Ofst(U_18108,U_18109)),U_18110))) ),
    inference(clausify,[status(thm)],[f_4376_2]) ).

cnf(f_4376_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18108,U_18109),U_18110),U_18111) = hAPP(c_Option_Ooption_OSome(U_18109),U_18112)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18108,U_18109)),hAPP(hAPP(c_Product__Type_OPair(U_18108,U_18109),U_18111),U_18112)),hAPP(c_List_Oset(tc_prod(U_18108,U_18109)),U_18110)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18108),hAPP(hAPP(c_List_Omap(tc_prod(U_18108,U_18109),U_18108),c_Product__Type_Ofst(U_18108,U_18109)),U_18110))) ),
    inference(clausify,[status(thm)],[f_4376_2]) ).

fof(f_4377_1,plain,
    ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
      ( hAPP(hAPP(c_Map_Omap__of(T_a,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_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeI]) ).

fof(f_4377_2,plain,
    ! [U_18117,U_18116,U_18115,U_18114,U_18113] :
      ( hAPP(hAPP(c_Map_Omap__of(U_18113,U_18114),U_18115),U_18116) = hAPP(c_Option_Ooption_OSome(U_18114),U_18117)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18113,U_18114)),hAPP(hAPP(c_Product__Type_OPair(U_18113,U_18114),U_18116),U_18117)),hAPP(c_List_Oset(tc_prod(U_18113,U_18114)),U_18115)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18113),hAPP(hAPP(c_List_Omap(tc_prod(U_18113,U_18114),U_18113),c_Product__Type_Ofst(U_18113,U_18114)),U_18115))) ),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

cnf(f_4377_3,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18113,U_18114),U_18115),U_18116) = hAPP(c_Option_Ooption_OSome(U_18114),U_18117)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18113,U_18114)),hAPP(hAPP(c_Product__Type_OPair(U_18113,U_18114),U_18116),U_18117)),hAPP(c_List_Oset(tc_prod(U_18113,U_18114)),U_18115)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18113),hAPP(hAPP(c_List_Omap(tc_prod(U_18113,U_18114),U_18113),c_Product__Type_Ofst(U_18113,U_18114)),U_18115))) ),
    inference(clausify,[status(thm)],[f_4377_2]) ).

fof(f_4378_1,plain,
    ! [V_f_2,V_A_2,T_a,T_b] :
      ( ( ( c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) )
        & ( c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(f_4378_2,plain,
    ! [U_18121,U_18120,U_18119,U_18118] :
      ( ( ( c_Nitpick_Osetsum_H(U_18119,U_18118,U_18121,U_18120) = c_Groups_Ozero__class_Ozero(U_18118)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18119),U_18120)) )
        & ( c_Nitpick_Osetsum_H(U_18119,U_18118,U_18121,U_18120) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18118),hAPP(hAPP(c_List_Omap(U_18119,U_18118),U_18121),c_Hilbert__Choice_OEps(tc_List_Olist(U_18119),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18119),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_18119)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18119),tc_fun(U_18119,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18119,tc_HOL_Obool),tc_fun(tc_fun(U_18119,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18119)),c_fequal),c_List_Oset(U_18119))),U_18120))),c_List_Odistinct(U_18119)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18119),U_18120)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_18118) ),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

cnf(f_4378_3,plain,
    ( c_Nitpick_Osetsum_H(U_18119,U_18118,U_18121,U_18120) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18118),hAPP(hAPP(c_List_Omap(U_18119,U_18118),U_18121),c_Hilbert__Choice_OEps(tc_List_Olist(U_18119),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18119),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_18119)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18119),tc_fun(U_18119,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18119,tc_HOL_Obool),tc_fun(tc_fun(U_18119,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18119)),c_fequal),c_List_Oset(U_18119))),U_18120))),c_List_Odistinct(U_18119)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18119),U_18120))
    | ~ class_Groups_Ocomm__monoid__add(U_18118) ),
    inference(clausify,[status(thm)],[f_4378_2]) ).

cnf(f_4378_4,plain,
    ( c_Nitpick_Osetsum_H(U_18119,U_18118,U_18121,U_18120) = c_Groups_Ozero__class_Ozero(U_18118)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18119),U_18120))
    | ~ class_Groups_Ocomm__monoid__add(U_18118) ),
    inference(clausify,[status(thm)],[f_4378_2]) ).

fof(f_4379_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(T_b)
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mono]) ).

fof(f_4379_2,plain,
    ! [U_18127,U_18126,U_18125,U_18124,U_18123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18126),U_18125))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18127),U_18125))))
      | ? [U_18122] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(U_18126,U_18122)),hAPP(U_18127,U_18122)))
          & hBOOL(hAPP(hAPP(c_member(U_18124),U_18122),hAPP(c_List_Oset(U_18124),U_18125))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_18123)
      | ~ class_Groups_Omonoid__add(U_18123) ),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

fof(f_4379_3,plain,
    ! [U_18127,U_18126,U_18125,U_18124,U_18123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18126),U_18125))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18127),U_18125))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(U_18126,sK457(U_18127,U_18126,U_18125,U_18124,U_18123))),hAPP(U_18127,sK457(U_18127,U_18126,U_18125,U_18124,U_18123))))
        & hBOOL(hAPP(hAPP(c_member(U_18124),sK457(U_18127,U_18126,U_18125,U_18124,U_18123)),hAPP(c_List_Oset(U_18124),U_18125))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_18123)
      | ~ class_Groups_Omonoid__add(U_18123) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_18122,sK457(U_18127,U_18126,U_18125,U_18124,U_18123))],[f_4379_2]) ).

cnf(f_4379_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18124),sK457(U_18127,U_18126,U_18125,U_18124,U_18123)),hAPP(c_List_Oset(U_18124),U_18125)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18126),U_18125))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18127),U_18125))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_18123)
    | ~ class_Groups_Omonoid__add(U_18123) ),
    inference(clausify,[status(thm)],[f_4379_3]) ).

cnf(f_4379_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(U_18126,sK457(U_18127,U_18126,U_18125,U_18124,U_18123))),hAPP(U_18127,sK457(U_18127,U_18126,U_18125,U_18124,U_18123))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18123),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18126),U_18125))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18123),hAPP(hAPP(c_List_Omap(U_18124,U_18123),U_18127),U_18125))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_18123)
    | ~ class_Groups_Omonoid__add(U_18123) ),
    inference(clausify,[status(thm)],[f_4379_3]) ).

fof(f_4380_1,plain,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__same__conv__map]) ).

fof(f_4380_2,plain,
    ! [U_18129,U_18128] : hAPP(hAPP(c_List_Ozip(U_18128,U_18128),U_18129),U_18129) = hAPP(hAPP(c_List_Omap(U_18128,tc_prod(U_18128,U_18128)),hAPP(hAPP(c_COMBS(U_18128,U_18128,tc_prod(U_18128,U_18128)),c_Product__Type_OPair(U_18128,U_18128)),c_COMBI(U_18128))),U_18129),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

cnf(f_4380_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18128,U_18128),U_18129),U_18129) = hAPP(hAPP(c_List_Omap(U_18128,tc_prod(U_18128,U_18128)),hAPP(hAPP(c_COMBS(U_18128,U_18128,tc_prod(U_18128,U_18128)),c_Product__Type_OPair(U_18128,U_18128)),c_COMBI(U_18128))),U_18129),
    inference(clausify,[status(thm)],[f_4380_2]) ).

fof(f_4381_1,plain,
    ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,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_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(f_4381_2,plain,
    ! [U_18132,U_18131,U_18130] : c_List_Olist_Olist__size(U_18130,U_18131,U_18132) = 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_18130,tc_Nat_Onat),U_18131),U_18132))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18130)),U_18132)),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

cnf(f_4381_3,plain,
    c_List_Olist_Olist__size(U_18130,U_18131,U_18132) = 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_18130,tc_Nat_Onat),U_18131),U_18132))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18130)),U_18132)),
    inference(clausify,[status(thm)],[f_4381_2]) ).

fof(f_4382_1,plain,
    ! [V_l_2,V_k_2,V_f_2,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int]) ).

fof(f_4382_2,plain,
    ! [U_18136,U_18135,U_18134,U_18133] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18133),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18133),U_18134),c_List_Oupto(U_18135,U_18136))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18133),U_18134),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18135,U_18136)))
      | ~ class_Groups_Ocomm__monoid__add(U_18133) ),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

cnf(f_4382_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18133),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18133),U_18134),c_List_Oupto(U_18135,U_18136))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18133),U_18134),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18135,U_18136)))
    | ~ class_Groups_Ocomm__monoid__add(U_18133) ),
    inference(clausify,[status(thm)],[f_4382_2]) ).

fof(f_4383_1,plain,
    ! [V_j_2,V_i_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int]) ).

fof(f_4383_2,plain,
    ! [U_18140,U_18139,U_18138,U_18137] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18137),U_18138),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18139,U_18140))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18137),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18137),U_18138),c_List_Oupto(U_18139,U_18140)))
      | ~ class_Groups_Ocomm__monoid__add(U_18137) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

cnf(f_4383_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18137),U_18138),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18139,U_18140))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18137),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18137),U_18138),c_List_Oupto(U_18139,U_18140)))
    | ~ class_Groups_Ocomm__monoid__add(U_18137) ),
    inference(clausify,[status(thm)],[f_4383_2]) ).

fof(f_4384_1,plain,
    ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__map__restrict]) ).

fof(f_4384_2,plain,
    ! [U_18144,U_18143,U_18142,U_18141] : hAPP(c_Map_Omap__of(U_18141,U_18142),hAPP(hAPP(c_List_Omap(U_18141,tc_prod(U_18141,U_18142)),hAPP(hAPP(c_COMBS(U_18141,U_18142,tc_prod(U_18141,U_18142)),c_Product__Type_OPair(U_18141,U_18142)),U_18143)),U_18144)) = c_Map_Orestrict__map(U_18141,U_18142,hAPP(c_Fun_Ocomp(U_18142,tc_Option_Ooption(U_18142),U_18141,c_Option_Ooption_OSome(U_18142)),U_18143),hAPP(c_List_Oset(U_18141),U_18144)),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

cnf(f_4384_3,plain,
    hAPP(c_Map_Omap__of(U_18141,U_18142),hAPP(hAPP(c_List_Omap(U_18141,tc_prod(U_18141,U_18142)),hAPP(hAPP(c_COMBS(U_18141,U_18142,tc_prod(U_18141,U_18142)),c_Product__Type_OPair(U_18141,U_18142)),U_18143)),U_18144)) = c_Map_Orestrict__map(U_18141,U_18142,hAPP(c_Fun_Ocomp(U_18142,tc_Option_Ooption(U_18142),U_18141,c_Option_Ooption_OSome(U_18142)),U_18143),hAPP(c_List_Oset(U_18141),U_18144)),
    inference(clausify,[status(thm)],[f_4384_2]) ).

fof(f_4385_1,plain,
    ! [V_m_2,T_b,V_xs_2,T_a] :
      ( hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2
      | hAPP(c_List_Oset(T_a),V_xs_2) != c_Map_Odom(T_a,T_b,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__map__keys]) ).

fof(f_4385_2,plain,
    ! [U_18148,U_18147,U_18146,U_18145] :
      ( hAPP(c_Map_Omap__of(U_18145,U_18147),hAPP(hAPP(c_List_Omap(U_18145,tc_prod(U_18145,U_18147)),hAPP(hAPP(c_COMBS(U_18145,U_18147,tc_prod(U_18145,U_18147)),c_Product__Type_OPair(U_18145,U_18147)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18147),U_18147,U_18145),c_Option_Othe(U_18147)),U_18148))),U_18146)) = U_18148
      | hAPP(c_List_Oset(U_18145),U_18146) != c_Map_Odom(U_18145,U_18147,U_18148) ),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

cnf(f_4385_3,plain,
    ( hAPP(c_Map_Omap__of(U_18145,U_18147),hAPP(hAPP(c_List_Omap(U_18145,tc_prod(U_18145,U_18147)),hAPP(hAPP(c_COMBS(U_18145,U_18147,tc_prod(U_18145,U_18147)),c_Product__Type_OPair(U_18145,U_18147)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18147),U_18147,U_18145),c_Option_Othe(U_18147)),U_18148))),U_18146)) = U_18148
    | hAPP(c_List_Oset(U_18145),U_18146) != c_Map_Odom(U_18145,U_18147,U_18148) ),
    inference(clausify,[status(thm)],[f_4385_2]) ).

fof(f_4386_1,plain,
    ! [T_a,V_xs_2] :
      ( c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2)
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__select]) ).

fof(f_4386_2,plain,
    ! [U_18150,U_18149] :
      ( c_Random_Oselect__weight(U_18150,hAPP(hAPP(c_List_Omap(U_18150,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18150)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18150),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18149)) = c_Random_Oselect(U_18150,U_18149)
      | U_18149 = c_List_Olist_ONil(U_18150) ),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

cnf(f_4386_3,plain,
    ( c_Random_Oselect__weight(U_18150,hAPP(hAPP(c_List_Omap(U_18150,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18150)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18150),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18149)) = c_Random_Oselect(U_18150,U_18149)
    | U_18149 = c_List_Olist_ONil(U_18150) ),
    inference(clausify,[status(thm)],[f_4386_2]) ).

fof(f_4387_1,plain,
    ! [V_xs_2,T_a,V_l_2] :
      ( hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),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_a),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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__same]) ).

fof(f_4387_2,plain,
    ! [U_18153,U_18152,U_18151] :
      ( hAPP(c_Random_Opick(U_18152,hAPP(hAPP(c_List_Omap(U_18152,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18152)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18152),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18153)),hAPP(c_Code__Numeral_Oof__nat,U_18151)) = hAPP(hAPP(c_List_Onth(U_18152),U_18153),U_18151)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18151),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18152)),U_18153))) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

cnf(f_4387_3,plain,
    ( hAPP(c_Random_Opick(U_18152,hAPP(hAPP(c_List_Omap(U_18152,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18152)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18152),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18153)),hAPP(c_Code__Numeral_Oof__nat,U_18151)) = hAPP(hAPP(c_List_Onth(U_18152),U_18153),U_18151)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18151),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18152)),U_18153))) ),
    inference(clausify,[status(thm)],[f_4387_2]) ).

fof(f_4388_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__map]) ).

fof(f_4388_2,plain,
    ! [U_18158,U_18157,U_18156,U_18155,U_18154] : hAPP(c_Map_Omap__of(U_18154,U_18155),hAPP(hAPP(c_List_Omap(tc_prod(U_18154,U_18156),tc_prod(U_18154,U_18155)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18156,tc_prod(U_18154,U_18155)),hAPP(hAPP(c_COMBC(U_18154,tc_fun(U_18156,U_18155),tc_fun(U_18156,tc_prod(U_18154,U_18155))),hAPP(hAPP(c_COMBB(tc_fun(U_18155,tc_prod(U_18154,U_18155)),tc_fun(tc_fun(U_18156,U_18155),tc_fun(U_18156,tc_prod(U_18154,U_18155))),U_18154),c_COMBB(U_18155,tc_prod(U_18154,U_18155),U_18156)),c_Product__Type_OPair(U_18154,U_18155))),U_18157))),U_18158)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18156),tc_Option_Ooption(U_18155),U_18154,hAPP(c_Option_Omap(U_18156,U_18155),U_18157)),hAPP(c_Map_Omap__of(U_18154,U_18156),U_18158)),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

cnf(f_4388_3,plain,
    hAPP(c_Map_Omap__of(U_18154,U_18155),hAPP(hAPP(c_List_Omap(tc_prod(U_18154,U_18156),tc_prod(U_18154,U_18155)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18156,tc_prod(U_18154,U_18155)),hAPP(hAPP(c_COMBC(U_18154,tc_fun(U_18156,U_18155),tc_fun(U_18156,tc_prod(U_18154,U_18155))),hAPP(hAPP(c_COMBB(tc_fun(U_18155,tc_prod(U_18154,U_18155)),tc_fun(tc_fun(U_18156,U_18155),tc_fun(U_18156,tc_prod(U_18154,U_18155))),U_18154),c_COMBB(U_18155,tc_prod(U_18154,U_18155),U_18156)),c_Product__Type_OPair(U_18154,U_18155))),U_18157))),U_18158)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18156),tc_Option_Ooption(U_18155),U_18154,hAPP(c_Option_Omap(U_18156,U_18155),U_18157)),hAPP(c_Map_Omap__of(U_18154,U_18156),U_18158)),
    inference(clausify,[status(thm)],[f_4388_2]) ).

fof(f_4389_1,plain,
    ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2),
    inference(fof_nnf,[status(thm)],[fact_option__map__comp]) ).

fof(f_4389_2,plain,
    ! [U_18164,U_18163,U_18162,U_18161,U_18160,U_18159] : hAPP(hAPP(c_Option_Omap(U_18159,U_18160),U_18161),hAPP(hAPP(c_Option_Omap(U_18162,U_18159),U_18163),U_18164)) = hAPP(hAPP(c_Option_Omap(U_18162,U_18160),hAPP(c_Fun_Ocomp(U_18159,U_18160,U_18162,U_18161),U_18163)),U_18164),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

cnf(f_4389_3,plain,
    hAPP(hAPP(c_Option_Omap(U_18159,U_18160),U_18161),hAPP(hAPP(c_Option_Omap(U_18162,U_18159),U_18163),U_18164)) = hAPP(hAPP(c_Option_Omap(U_18162,U_18160),hAPP(c_Fun_Ocomp(U_18159,U_18160,U_18162,U_18161),U_18163)),U_18164),
    inference(clausify,[status(thm)],[f_4389_2]) ).

fof(f_4390_1,plain,
    ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Ocompositionality]) ).

fof(f_4390_2,plain,
    ! [U_18170,U_18169,U_18168,U_18167,U_18166,U_18165] : hAPP(hAPP(c_Option_Omap(U_18165,U_18166),U_18167),hAPP(hAPP(c_Option_Omap(U_18168,U_18165),U_18169),U_18170)) = hAPP(hAPP(c_Option_Omap(U_18168,U_18166),hAPP(c_Fun_Ocomp(U_18165,U_18166,U_18168,U_18167),U_18169)),U_18170),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

cnf(f_4390_3,plain,
    hAPP(hAPP(c_Option_Omap(U_18165,U_18166),U_18167),hAPP(hAPP(c_Option_Omap(U_18168,U_18165),U_18169),U_18170)) = hAPP(hAPP(c_Option_Omap(U_18168,U_18166),hAPP(c_Fun_Ocomp(U_18165,U_18166,U_18168,U_18167),U_18169)),U_18170),
    inference(clausify,[status(thm)],[f_4390_2]) ).

fof(f_4391_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Ocomp]) ).

fof(f_4391_2,plain,
    ! [U_18175,U_18174,U_18173,U_18172,U_18171] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18171),tc_Option_Ooption(U_18172),tc_Option_Ooption(U_18173),hAPP(c_Option_Omap(U_18171,U_18172),U_18174)),hAPP(c_Option_Omap(U_18173,U_18171),U_18175)) = hAPP(c_Option_Omap(U_18173,U_18172),hAPP(c_Fun_Ocomp(U_18171,U_18172,U_18173,U_18174),U_18175)),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

cnf(f_4391_3,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18171),tc_Option_Ooption(U_18172),tc_Option_Ooption(U_18173),hAPP(c_Option_Omap(U_18171,U_18172),U_18174)),hAPP(c_Option_Omap(U_18173,U_18171),U_18175)) = hAPP(c_Option_Omap(U_18173,U_18172),hAPP(c_Fun_Ocomp(U_18171,U_18172,U_18173,U_18174),U_18175)),
    inference(clausify,[status(thm)],[f_4391_2]) ).

fof(f_4392_1,plain,
    ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))),
    inference(fof_nnf,[status(thm)],[fact_option__map__o__map__upd]) ).

fof(f_4392_2,plain,
    ! [U_18182,U_18181,U_18180,U_18179,U_18178,U_18177,U_18176] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18176),tc_Option_Ooption(U_18177),U_18178,hAPP(c_Option_Omap(U_18176,U_18177),U_18179)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18178,tc_Option_Ooption(U_18176)),U_18180),U_18181),hAPP(c_Option_Ooption_OSome(U_18176),U_18182))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18178,tc_Option_Ooption(U_18177)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18176),tc_Option_Ooption(U_18177),U_18178,hAPP(c_Option_Omap(U_18176,U_18177),U_18179)),U_18180)),U_18181),hAPP(c_Option_Ooption_OSome(U_18177),hAPP(U_18179,U_18182))),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

cnf(f_4392_3,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18176),tc_Option_Ooption(U_18177),U_18178,hAPP(c_Option_Omap(U_18176,U_18177),U_18179)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18178,tc_Option_Ooption(U_18176)),U_18180),U_18181),hAPP(c_Option_Ooption_OSome(U_18176),U_18182))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18178,tc_Option_Ooption(U_18177)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18176),tc_Option_Ooption(U_18177),U_18178,hAPP(c_Option_Omap(U_18176,U_18177),U_18179)),U_18180)),U_18181),hAPP(c_Option_Ooption_OSome(U_18177),hAPP(U_18179,U_18182))),
    inference(clausify,[status(thm)],[f_4392_2]) ).

fof(f_4393_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]) ).

cnf(f_4393_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(clausify,[status(thm)],[f_4393_1]) ).

fof(f_4394_1,plain,
    ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Oidentity]) ).

fof(f_4394_2,plain,
    ! [U_18183] : hAPP(c_Option_Omap(U_18183,U_18183),c_COMBI(U_18183)) = c_Fun_Oid(tc_Option_Ooption(U_18183)),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

cnf(f_4394_3,plain,
    hAPP(c_Option_Omap(U_18183,U_18183),c_COMBI(U_18183)) = c_Fun_Oid(tc_Option_Ooption(U_18183)),
    inference(clausify,[status(thm)],[f_4394_2]) ).

fof(f_4395_1,plain,
    ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap_Oid]) ).

fof(f_4395_2,plain,
    ! [U_18184] : hAPP(c_Option_Omap(U_18184,U_18184),c_Fun_Oid(U_18184)) = c_Fun_Oid(tc_Option_Ooption(U_18184)),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

cnf(f_4395_3,plain,
    hAPP(c_Option_Omap(U_18184,U_18184),c_Fun_Oid(U_18184)) = c_Fun_Oid(tc_Option_Ooption(U_18184)),
    inference(clausify,[status(thm)],[f_4395_2]) ).

fof(f_4396_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_4396_2,plain,
    ! [U_18186,U_18185] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_18185) = hAPP(c_Code__Numeral_Oof__nat,U_18186)
          | U_18185 != U_18186 )
        & ( U_18185 = U_18186
          | hAPP(c_Code__Numeral_Oof__nat,U_18185) != hAPP(c_Code__Numeral_Oof__nat,U_18186) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

cnf(f_4396_3,plain,
    ( U_18185 = U_18186
    | hAPP(c_Code__Numeral_Oof__nat,U_18185) != hAPP(c_Code__Numeral_Oof__nat,U_18186)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4396_2]) ).

cnf(f_4396_4,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_18185) = hAPP(c_Code__Numeral_Oof__nat,U_18186)
    | U_18185 != U_18186
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4396_2]) ).

fof(f_4397_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_4397_2,plain,
    ! [U_18188,U_18187] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18187)),hAPP(c_Code__Numeral_Oof__nat,U_18188)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),U_18188)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18187),U_18188))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18187)),hAPP(c_Code__Numeral_Oof__nat,U_18188))) ) ),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

fof(f_4397_3,plain,
    ( ! [U_18192,U_18190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18190)),hAPP(c_Code__Numeral_Oof__nat,U_18192)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18190),U_18192)) )
    & ! [U_18191,U_18189] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18189),U_18191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18189)),hAPP(c_Code__Numeral_Oof__nat,U_18191))) ) ),
    inference(miniscope,[status(thm)],[f_4397_2]) ).

cnf(f_4397_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18189),U_18191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18189)),hAPP(c_Code__Numeral_Oof__nat,U_18191))) ),
    inference(clausify,[status(thm)],[f_4397_3]) ).

cnf(f_4397_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18190)),hAPP(c_Code__Numeral_Oof__nat,U_18192)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18190),U_18192)) ),
    inference(clausify,[status(thm)],[f_4397_3]) ).

fof(f_4398_1,plain,
    ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_option__map__Some]) ).

fof(f_4398_2,plain,
    ! [U_18196,U_18195,U_18194,U_18193] : hAPP(hAPP(c_Option_Omap(U_18193,U_18194),U_18195),hAPP(c_Option_Ooption_OSome(U_18193),U_18196)) = hAPP(c_Option_Ooption_OSome(U_18194),hAPP(U_18195,U_18196)),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

cnf(f_4398_3,plain,
    hAPP(hAPP(c_Option_Omap(U_18193,U_18194),U_18195),hAPP(c_Option_Ooption_OSome(U_18193),U_18196)) = hAPP(c_Option_Ooption_OSome(U_18194),hAPP(U_18195,U_18196)),
    inference(clausify,[status(thm)],[f_4398_2]) ).

fof(f_4399_1,plain,
    ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
        | ! [B_z] :
            ( hAPP(V_f_2,B_z) != V_y_2
            | V_xo_2 != hAPP(c_Option_Ooption_OSome(T_b),B_z) ) )
      & ( ? [B_z] :
            ( hAPP(V_f_2,B_z) = V_y_2
            & V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) )
        | hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_option__map__eq__Some]) ).

fof(f_4399_2,plain,
    ! [U_18203,U_18202,U_18201,U_18200,U_18199] :
      ( ( hAPP(hAPP(c_Option_Omap(U_18199,U_18200),U_18201),U_18202) = hAPP(c_Option_Ooption_OSome(U_18200),U_18203)
        | ! [U_18198] :
            ( hAPP(U_18201,U_18198) != U_18203
            | U_18202 != hAPP(c_Option_Ooption_OSome(U_18199),U_18198) ) )
      & ( ? [U_18197] :
            ( hAPP(U_18201,U_18197) = U_18203
            & U_18202 = hAPP(c_Option_Ooption_OSome(U_18199),U_18197) )
        | hAPP(hAPP(c_Option_Omap(U_18199,U_18200),U_18201),U_18202) != hAPP(c_Option_Ooption_OSome(U_18200),U_18203) ) ),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

fof(f_4399_3,plain,
    ( ! [U_18213,U_18211,U_18209,U_18207,U_18205] :
        ( hAPP(hAPP(c_Option_Omap(U_18205,U_18207),U_18209),U_18211) = hAPP(c_Option_Ooption_OSome(U_18207),U_18213)
        | ! [U_18198] :
            ( hAPP(U_18209,U_18198) != U_18213
            | U_18211 != hAPP(c_Option_Ooption_OSome(U_18205),U_18198) ) )
    & ! [U_18212,U_18210,U_18208,U_18206,U_18204] :
        ( ? [U_18197] :
            ( hAPP(U_18208,U_18197) = U_18212
            & U_18210 = hAPP(c_Option_Ooption_OSome(U_18204),U_18197) )
        | hAPP(hAPP(c_Option_Omap(U_18204,U_18206),U_18208),U_18210) != hAPP(c_Option_Ooption_OSome(U_18206),U_18212) ) ),
    inference(miniscope,[status(thm)],[f_4399_2]) ).

fof(f_4399_4,plain,
    ( ! [U_18213,U_18211,U_18209,U_18207,U_18205] :
        ( hAPP(hAPP(c_Option_Omap(U_18205,U_18207),U_18209),U_18211) = hAPP(c_Option_Ooption_OSome(U_18207),U_18213)
        | ! [U_18198] :
            ( hAPP(U_18209,U_18198) != U_18213
            | U_18211 != hAPP(c_Option_Ooption_OSome(U_18205),U_18198) ) )
    & ! [U_18212,U_18210,U_18208,U_18206,U_18204] :
        ( ( hAPP(U_18208,sK458(U_18212,U_18210,U_18208,U_18206,U_18204)) = U_18212
          & U_18210 = hAPP(c_Option_Ooption_OSome(U_18204),sK458(U_18212,U_18210,U_18208,U_18206,U_18204)) )
        | hAPP(hAPP(c_Option_Omap(U_18204,U_18206),U_18208),U_18210) != hAPP(c_Option_Ooption_OSome(U_18206),U_18212) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18197,sK458(U_18212,U_18210,U_18208,U_18206,U_18204))],[f_4399_3]) ).

cnf(f_4399_5,plain,
    ( U_18210 = hAPP(c_Option_Ooption_OSome(U_18204),sK458(U_18212,U_18210,U_18208,U_18206,U_18204))
    | hAPP(hAPP(c_Option_Omap(U_18204,U_18206),U_18208),U_18210) != hAPP(c_Option_Ooption_OSome(U_18206),U_18212) ),
    inference(clausify,[status(thm)],[f_4399_4]) ).

cnf(f_4399_6,plain,
    ( hAPP(U_18208,sK458(U_18212,U_18210,U_18208,U_18206,U_18204)) = U_18212
    | hAPP(hAPP(c_Option_Omap(U_18204,U_18206),U_18208),U_18210) != hAPP(c_Option_Ooption_OSome(U_18206),U_18212) ),
    inference(clausify,[status(thm)],[f_4399_4]) ).

cnf(f_4399_7,plain,
    ( hAPP(hAPP(c_Option_Omap(U_18205,U_18207),U_18209),U_18211) = hAPP(c_Option_Ooption_OSome(U_18207),U_18213)
    | hAPP(U_18209,U_18198) != U_18213
    | U_18211 != hAPP(c_Option_Ooption_OSome(U_18205),U_18198) ),
    inference(clausify,[status(thm)],[f_4399_4]) ).

fof(f_4400_1,plain,
    ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2),
    inference(fof_nnf,[status(thm)],[fact_dom__option__map]) ).

fof(f_4400_2,plain,
    ! [U_18218,U_18217,U_18216,U_18215,U_18214] : c_Map_Odom(U_18214,U_18215,hAPP(hAPP(c_COMBS(U_18214,tc_Option_Ooption(U_18216),tc_Option_Ooption(U_18215)),hAPP(hAPP(c_COMBB(tc_fun(U_18216,U_18215),tc_fun(tc_Option_Ooption(U_18216),tc_Option_Ooption(U_18215)),U_18214),c_Option_Omap(U_18216,U_18215)),U_18217)),U_18218)) = c_Map_Odom(U_18214,U_18216,U_18218),
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

cnf(f_4400_3,plain,
    c_Map_Odom(U_18214,U_18215,hAPP(hAPP(c_COMBS(U_18214,tc_Option_Ooption(U_18216),tc_Option_Ooption(U_18215)),hAPP(hAPP(c_COMBB(tc_fun(U_18216,U_18215),tc_fun(tc_Option_Ooption(U_18216),tc_Option_Ooption(U_18215)),U_18214),c_Option_Omap(U_18216,U_18215)),U_18217)),U_18218)) = c_Map_Odom(U_18214,U_18216,U_18218),
    inference(clausify,[status(thm)],[f_4400_2]) ).

fof(f_4401_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]) ).

cnf(f_4401_2,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_4401_1]) ).

fof(f_4402_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_4402_2,plain,
    ! [U_18220,U_18219] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18219)),hAPP(c_Code__Numeral_Oof__nat,U_18220)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_18219),U_18220)),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

cnf(f_4402_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18219)),hAPP(c_Code__Numeral_Oof__nat,U_18220)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_18219),U_18220)),
    inference(clausify,[status(thm)],[f_4402_2]) ).

fof(f_4403_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_4403_2,plain,
    ! [U_18222,U_18221] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_18221) = hAPP(c_Code__Numeral_Oof__nat,U_18222)
        | U_18221 != U_18222 )
      & ( U_18221 = U_18222
        | hAPP(c_Code__Numeral_Oof__nat,U_18221) != hAPP(c_Code__Numeral_Oof__nat,U_18222) ) ),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

fof(f_4403_3,plain,
    ( ! [U_18226,U_18224] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_18224) = hAPP(c_Code__Numeral_Oof__nat,U_18226)
        | U_18224 != U_18226 )
    & ! [U_18225,U_18223] :
        ( U_18223 = U_18225
        | hAPP(c_Code__Numeral_Oof__nat,U_18223) != hAPP(c_Code__Numeral_Oof__nat,U_18225) ) ),
    inference(miniscope,[status(thm)],[f_4403_2]) ).

cnf(f_4403_4,plain,
    ( U_18223 = U_18225
    | hAPP(c_Code__Numeral_Oof__nat,U_18223) != hAPP(c_Code__Numeral_Oof__nat,U_18225) ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

cnf(f_4403_5,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_18224) = hAPP(c_Code__Numeral_Oof__nat,U_18226)
    | U_18224 != U_18226 ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

fof(f_4404_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]) ).

cnf(f_4404_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(clausify,[status(thm)],[f_4404_1]) ).

fof(f_4405_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]) ).

cnf(f_4405_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(clausify,[status(thm)],[f_4405_1]) ).

fof(f_4406_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_4406_2,plain,
    ! [U_18228,U_18227] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18227)),hAPP(c_Code__Numeral_Oof__nat,U_18228)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18227),U_18228)),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

cnf(f_4406_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18227)),hAPP(c_Code__Numeral_Oof__nat,U_18228)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18227),U_18228)),
    inference(clausify,[status(thm)],[f_4406_2]) ).

fof(f_4407_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_4407_2,plain,
    ! [U_18230,U_18229] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18229)),hAPP(c_Code__Numeral_Oof__nat,U_18230)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18229),U_18230)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18229),U_18230))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18229)),hAPP(c_Code__Numeral_Oof__nat,U_18230))) ) ),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

fof(f_4407_3,plain,
    ( ! [U_18234,U_18232] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18232)),hAPP(c_Code__Numeral_Oof__nat,U_18234)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18232),U_18234)) )
    & ! [U_18233,U_18231] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18231),U_18233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18231)),hAPP(c_Code__Numeral_Oof__nat,U_18233))) ) ),
    inference(miniscope,[status(thm)],[f_4407_2]) ).

cnf(f_4407_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18231),U_18233))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18231)),hAPP(c_Code__Numeral_Oof__nat,U_18233))) ),
    inference(clausify,[status(thm)],[f_4407_3]) ).

cnf(f_4407_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_18232)),hAPP(c_Code__Numeral_Oof__nat,U_18234)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18232),U_18234)) ),
    inference(clausify,[status(thm)],[f_4407_3]) ).

fof(f_4408_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_4408_2,plain,
    ! [U_18235] :
      ( ( U_18235 != 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_18235)) )
      & ( 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_18235))
        | U_18235 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

fof(f_4408_3,plain,
    ( ! [U_18237] :
        ( U_18237 != 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_18237)) )
    & ! [U_18236] :
        ( 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_18236))
        | U_18236 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4408_2]) ).

cnf(f_4408_4,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_18236))
    | U_18236 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4408_3]) ).

cnf(f_4408_5,plain,
    ( U_18237 != 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_18237)) ),
    inference(clausify,[status(thm)],[f_4408_3]) ).

fof(f_4409_1,plain,
    ! [V_xs_2,T_a] : c_Random_Oselect(T_a,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_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))),
    inference(fof_nnf,[status(thm)],[fact_select__def]) ).

fof(f_4409_2,plain,
    ! [U_18239,U_18238] : c_Random_Oselect(U_18238,U_18239) = 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_18238,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_18238)),U_18239)))),hAPP(hAPP(c_COMBB(U_18238,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18238,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18238),U_18239)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

cnf(f_4409_3,plain,
    c_Random_Oselect(U_18238,U_18239) = 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_18238,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_18238)),U_18239)))),hAPP(hAPP(c_COMBB(U_18238,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18238,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18238),U_18239)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4409_2]) ).

fof(f_4410_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_4410_2,plain,
    ! [U_18241,U_18240] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_18240)),hAPP(c_Code__Numeral_Oof__nat,U_18241)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18240),U_18241)),
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

cnf(f_4410_3,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_18240)),hAPP(c_Code__Numeral_Oof__nat,U_18241)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18240),U_18241)),
    inference(clausify,[status(thm)],[f_4410_2]) ).

fof(f_4411_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]) ).

cnf(f_4411_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(clausify,[status(thm)],[f_4411_1]) ).

fof(f_4412_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_4412_2,plain,
    ! [U_18243,U_18242] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_18242),U_18243) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18242)),hAPP(c_Code__Numeral_Onat__of,U_18243))),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

cnf(f_4412_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_18242),U_18243) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18242)),hAPP(c_Code__Numeral_Onat__of,U_18243))),
    inference(clausify,[status(thm)],[f_4412_2]) ).

fof(f_4413_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_4413_2,plain,
    ! [U_18244] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_18244)) = U_18244,
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

cnf(f_4413_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_18244)) = U_18244,
    inference(clausify,[status(thm)],[f_4413_2]) ).

fof(f_4414_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_4414_2,plain,
    ! [U_18245] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_18245)) = U_18245,
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

cnf(f_4414_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_18245)) = U_18245,
    inference(clausify,[status(thm)],[f_4414_2]) ).

fof(f_4415_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_4415_2,plain,
    ! [U_18246] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_18246)) = U_18246,
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

cnf(f_4415_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_18246)) = U_18246,
    inference(clausify,[status(thm)],[f_4415_2]) ).

fof(f_4416_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_4416_2,plain,
    ! [U_18248,U_18247] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_18247) = hAPP(c_Code__Numeral_Onat__of,U_18248)
        | U_18247 != U_18248 )
      & ( U_18247 = U_18248
        | hAPP(c_Code__Numeral_Onat__of,U_18247) != hAPP(c_Code__Numeral_Onat__of,U_18248) ) ),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

fof(f_4416_3,plain,
    ( ! [U_18252,U_18250] :
        ( hAPP(c_Code__Numeral_Onat__of,U_18250) = hAPP(c_Code__Numeral_Onat__of,U_18252)
        | U_18250 != U_18252 )
    & ! [U_18251,U_18249] :
        ( U_18249 = U_18251
        | hAPP(c_Code__Numeral_Onat__of,U_18249) != hAPP(c_Code__Numeral_Onat__of,U_18251) ) ),
    inference(miniscope,[status(thm)],[f_4416_2]) ).

cnf(f_4416_4,plain,
    ( U_18249 = U_18251
    | hAPP(c_Code__Numeral_Onat__of,U_18249) != hAPP(c_Code__Numeral_Onat__of,U_18251) ),
    inference(clausify,[status(thm)],[f_4416_3]) ).

cnf(f_4416_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_18250) = hAPP(c_Code__Numeral_Onat__of,U_18252)
    | U_18250 != U_18252 ),
    inference(clausify,[status(thm)],[f_4416_3]) ).

fof(f_4417_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_4417_2,plain,
    ! [U_18254,U_18253] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_18253) = hAPP(c_Code__Numeral_Onat__of,U_18254)
        | U_18253 != U_18254 )
      & ( U_18253 = U_18254
        | hAPP(c_Code__Numeral_Onat__of,U_18253) != hAPP(c_Code__Numeral_Onat__of,U_18254) ) ),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

fof(f_4417_3,plain,
    ( ! [U_18258,U_18256] :
        ( hAPP(c_Code__Numeral_Onat__of,U_18256) = hAPP(c_Code__Numeral_Onat__of,U_18258)
        | U_18256 != U_18258 )
    & ! [U_18257,U_18255] :
        ( U_18255 = U_18257
        | hAPP(c_Code__Numeral_Onat__of,U_18255) != hAPP(c_Code__Numeral_Onat__of,U_18257) ) ),
    inference(miniscope,[status(thm)],[f_4417_2]) ).

cnf(f_4417_4,plain,
    ( U_18255 = U_18257
    | hAPP(c_Code__Numeral_Onat__of,U_18255) != hAPP(c_Code__Numeral_Onat__of,U_18257) ),
    inference(clausify,[status(thm)],[f_4417_3]) ).

cnf(f_4417_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_18256) = hAPP(c_Code__Numeral_Onat__of,U_18258)
    | U_18256 != U_18258 ),
    inference(clausify,[status(thm)],[f_4417_3]) ).

fof(f_4418_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_4418_2,plain,
    ! [U_18260,U_18259] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18259),U_18260))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18259)),hAPP(c_Code__Numeral_Onat__of,U_18260))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18259)),hAPP(c_Code__Numeral_Onat__of,U_18260)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18259),U_18260)) ) ),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

fof(f_4418_3,plain,
    ( ! [U_18264,U_18262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18262),U_18264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18262)),hAPP(c_Code__Numeral_Onat__of,U_18264))) )
    & ! [U_18263,U_18261] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18261)),hAPP(c_Code__Numeral_Onat__of,U_18263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18261),U_18263)) ) ),
    inference(miniscope,[status(thm)],[f_4418_2]) ).

cnf(f_4418_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18261)),hAPP(c_Code__Numeral_Onat__of,U_18263)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18261),U_18263)) ),
    inference(clausify,[status(thm)],[f_4418_3]) ).

cnf(f_4418_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18262),U_18264))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18262)),hAPP(c_Code__Numeral_Onat__of,U_18264))) ),
    inference(clausify,[status(thm)],[f_4418_3]) ).

fof(f_4419_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_4419_2,plain,
    ! [U_18265] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18265)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

cnf(f_4419_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18265)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4419_2]) ).

fof(f_4420_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_4420_2,plain,
    ! [U_18266] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_18266)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18266),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

cnf(f_4420_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_18266)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18266),
    inference(clausify,[status(thm)],[f_4420_2]) ).

fof(f_4421_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]) ).

cnf(f_4421_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(clausify,[status(thm)],[f_4421_1]) ).

fof(f_4422_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_4422_2,plain,
    ! [U_18268,U_18267] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18267),U_18268))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18267)),hAPP(c_Code__Numeral_Onat__of,U_18268))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18267)),hAPP(c_Code__Numeral_Onat__of,U_18268)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18267),U_18268)) ) ),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

fof(f_4422_3,plain,
    ( ! [U_18272,U_18270] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18270),U_18272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18270)),hAPP(c_Code__Numeral_Onat__of,U_18272))) )
    & ! [U_18271,U_18269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18269)),hAPP(c_Code__Numeral_Onat__of,U_18271)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18269),U_18271)) ) ),
    inference(miniscope,[status(thm)],[f_4422_2]) ).

cnf(f_4422_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18269)),hAPP(c_Code__Numeral_Onat__of,U_18271)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18269),U_18271)) ),
    inference(clausify,[status(thm)],[f_4422_3]) ).

cnf(f_4422_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_18270),U_18272))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18270)),hAPP(c_Code__Numeral_Onat__of,U_18272))) ),
    inference(clausify,[status(thm)],[f_4422_3]) ).

fof(f_4423_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_4423_2,plain,
    ! [U_18273] : hAPP(c_Code__Numeral_Onat__of,U_18273) = c_Code__Numeral_Onat__of__aux(U_18273,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

cnf(f_4423_3,plain,
    hAPP(c_Code__Numeral_Onat__of,U_18273) = c_Code__Numeral_Onat__of__aux(U_18273,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4423_2]) ).

fof(f_4424_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_4424_2,plain,
    ! [U_18275,U_18274] : c_Code__Numeral_Onat__of__aux(U_18274,U_18275) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18274)),U_18275),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

cnf(f_4424_3,plain,
    c_Code__Numeral_Onat__of__aux(U_18274,U_18275) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18274)),U_18275),
    inference(clausify,[status(thm)],[f_4424_2]) ).

fof(f_4425_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_4425_2,plain,
    ! [U_18276] : c_Code__Numeral_OSuc__code__numeral(U_18276) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_18276))),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

cnf(f_4425_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_18276) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_18276))),
    inference(clausify,[status(thm)],[f_4425_2]) ).

fof(f_4426_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_4426_2,plain,
    ! [U_18278,U_18277] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18277),U_18278) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18277)),hAPP(c_Code__Numeral_Onat__of,U_18278))),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

cnf(f_4426_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18277),U_18278) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18277)),hAPP(c_Code__Numeral_Onat__of,U_18278))),
    inference(clausify,[status(thm)],[f_4426_2]) ).

fof(f_4427_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_4427_2,plain,
    ! [U_18279] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_18279)) = U_18279
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18279),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

cnf(f_4427_3,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_18279)) = U_18279
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18279),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4427_2]) ).

fof(f_4428_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_4428_2,plain,
    ! [U_18281,U_18280] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_18280),U_18281) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18280)),hAPP(c_Code__Numeral_Onat__of,U_18281))),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

cnf(f_4428_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_18280),U_18281) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18280)),hAPP(c_Code__Numeral_Onat__of,U_18281))),
    inference(clausify,[status(thm)],[f_4428_2]) ).

fof(f_4429_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_4429_2,plain,
    ! [U_18283,U_18282] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_18282),U_18283) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18282)),hAPP(c_Code__Numeral_Onat__of,U_18283))),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

cnf(f_4429_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_18282),U_18283) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_18282)),hAPP(c_Code__Numeral_Onat__of,U_18283))),
    inference(clausify,[status(thm)],[f_4429_2]) ).

fof(f_4430_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]) ).

cnf(f_4430_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_4430_1]) ).

fof(f_4431_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_4431_2,plain,
    ! [U_18285,U_18284] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18284),U_18285) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_18284),U_18285),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

cnf(f_4431_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18284),U_18285) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_18284),U_18285),
    inference(clausify,[status(thm)],[f_4431_2]) ).

fof(f_4432_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_4432_2,plain,
    ! [U_18287,U_18286] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_18286,U_18287) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_18286),hAPP(c_Code__Numeral_Onat__of,U_18287))),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

cnf(f_4432_3,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_18286,U_18287) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_18286),hAPP(c_Code__Numeral_Onat__of,U_18287))),
    inference(clausify,[status(thm)],[f_4432_2]) ).

fof(f_4433_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_4433_2,plain,
    ! [U_18288] :
      ( 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_18288)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_18288)))
      | U_18288 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

cnf(f_4433_3,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_18288)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_18288)))
    | U_18288 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4433_2]) ).

fof(f_4434_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_4434_2,plain,
    ! [U_18290,U_18289] : hAPP(c_New__DSequence_Opos__not__seq(U_18289),U_18290) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_18289,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_18290))),
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

cnf(f_4434_3,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_18289),U_18290) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_18289,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_18290))),
    inference(clausify,[status(thm)],[f_4434_2]) ).

fof(f_4435_1,plain,
    ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
      ( ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) ),
    inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI]) ).

fof(f_4435_2,plain,
    ! [U_18296,U_18295,U_18294,U_18293,U_18292] :
      ( ? [U_18291] : hAPP(hAPP(c_Map_Omap__of(U_18292,U_18293),U_18296),U_18294) = hAPP(c_Option_Ooption_OSome(U_18293),U_18291)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18292,U_18293)),hAPP(hAPP(c_Product__Type_OPair(U_18292,U_18293),U_18294),U_18295)),hAPP(c_List_Oset(tc_prod(U_18292,U_18293)),U_18296))) ),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

fof(f_4435_3,plain,
    ! [U_18296,U_18295,U_18294,U_18293,U_18292] :
      ( hAPP(hAPP(c_Map_Omap__of(U_18292,U_18293),U_18296),U_18294) = hAPP(c_Option_Ooption_OSome(U_18293),sK459(U_18296,U_18295,U_18294,U_18293,U_18292))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18292,U_18293)),hAPP(hAPP(c_Product__Type_OPair(U_18292,U_18293),U_18294),U_18295)),hAPP(c_List_Oset(tc_prod(U_18292,U_18293)),U_18296))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18291,sK459(U_18296,U_18295,U_18294,U_18293,U_18292))],[f_4435_2]) ).

cnf(f_4435_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18292,U_18293),U_18296),U_18294) = hAPP(c_Option_Ooption_OSome(U_18293),sK459(U_18296,U_18295,U_18294,U_18293,U_18292))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18292,U_18293)),hAPP(hAPP(c_Product__Type_OPair(U_18292,U_18293),U_18294),U_18295)),hAPP(c_List_Oset(tc_prod(U_18292,U_18293)),U_18296))) ),
    inference(clausify,[status(thm)],[f_4435_3]) ).

fof(f_4436_1,plain,
    ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__map]) ).

fof(f_4436_2,plain,
    ! [U_18301,U_18300,U_18299,U_18298,U_18297] :
      ( ( hAPP(hAPP(c_Map_Omap__of(U_18297,U_18300),hAPP(hAPP(c_List_Ozip(U_18297,U_18300),U_18299),hAPP(hAPP(c_List_Omap(U_18297,U_18300),U_18301),U_18299))),U_18298) = c_Option_Ooption_ONone(U_18300)
        | hBOOL(hAPP(hAPP(c_member(U_18297),U_18298),hAPP(c_List_Oset(U_18297),U_18299))) )
      & ( hAPP(hAPP(c_Map_Omap__of(U_18297,U_18300),hAPP(hAPP(c_List_Ozip(U_18297,U_18300),U_18299),hAPP(hAPP(c_List_Omap(U_18297,U_18300),U_18301),U_18299))),U_18298) = hAPP(c_Option_Ooption_OSome(U_18300),hAPP(U_18301,U_18298))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18297),U_18298),hAPP(c_List_Oset(U_18297),U_18299))) ) ),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

fof(f_4436_3,plain,
    ( ! [U_18311,U_18309,U_18307,U_18305,U_18303] :
        ( hAPP(hAPP(c_Map_Omap__of(U_18303,U_18309),hAPP(hAPP(c_List_Ozip(U_18303,U_18309),U_18307),hAPP(hAPP(c_List_Omap(U_18303,U_18309),U_18311),U_18307))),U_18305) = c_Option_Ooption_ONone(U_18309)
        | hBOOL(hAPP(hAPP(c_member(U_18303),U_18305),hAPP(c_List_Oset(U_18303),U_18307))) )
    & ! [U_18310,U_18308,U_18306,U_18304,U_18302] :
        ( hAPP(hAPP(c_Map_Omap__of(U_18302,U_18308),hAPP(hAPP(c_List_Ozip(U_18302,U_18308),U_18306),hAPP(hAPP(c_List_Omap(U_18302,U_18308),U_18310),U_18306))),U_18304) = hAPP(c_Option_Ooption_OSome(U_18308),hAPP(U_18310,U_18304))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18302),U_18304),hAPP(c_List_Oset(U_18302),U_18306))) ) ),
    inference(miniscope,[status(thm)],[f_4436_2]) ).

cnf(f_4436_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18302,U_18308),hAPP(hAPP(c_List_Ozip(U_18302,U_18308),U_18306),hAPP(hAPP(c_List_Omap(U_18302,U_18308),U_18310),U_18306))),U_18304) = hAPP(c_Option_Ooption_OSome(U_18308),hAPP(U_18310,U_18304))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18302),U_18304),hAPP(c_List_Oset(U_18302),U_18306))) ),
    inference(clausify,[status(thm)],[f_4436_3]) ).

cnf(f_4436_5,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18303,U_18309),hAPP(hAPP(c_List_Ozip(U_18303,U_18309),U_18307),hAPP(hAPP(c_List_Omap(U_18303,U_18309),U_18311),U_18307))),U_18305) = c_Option_Ooption_ONone(U_18309)
    | hBOOL(hAPP(hAPP(c_member(U_18303),U_18305),hAPP(c_List_Oset(U_18303),U_18307))) ),
    inference(clausify,[status(thm)],[f_4436_3]) ).

fof(f_4437_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2)
      | c_List_Opartition(T_a,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__set]) ).

fof(f_4437_2,plain,
    ! [U_18316,U_18315,U_18314,U_18313,U_18312] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18312,tc_HOL_Obool)),hAPP(c_List_Oset(U_18312),U_18315)),hAPP(c_List_Oset(U_18312),U_18316)) = hAPP(c_List_Oset(U_18312),U_18314)
      | c_List_Opartition(U_18312,U_18313,U_18314) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18315),U_18316) ),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

cnf(f_4437_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18312,tc_HOL_Obool)),hAPP(c_List_Oset(U_18312),U_18315)),hAPP(c_List_Oset(U_18312),U_18316)) = hAPP(c_List_Oset(U_18312),U_18314)
    | c_List_Opartition(U_18312,U_18313,U_18314) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18312),tc_List_Olist(U_18312)),U_18315),U_18316) ),
    inference(clausify,[status(thm)],[f_4437_2]) ).

fof(f_4438_1,plain,
    ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_option__map__o__empty]) ).

fof(f_4438_2,plain,
    ! [U_18321,U_18320,U_18319,U_18318,U_18317] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18317),tc_Option_Ooption(U_18318),U_18319,hAPP(c_Option_Omap(U_18317,U_18318),U_18320)),hAPP(c_COMBK(tc_Option_Ooption(U_18317),U_18319),c_Option_Ooption_ONone(U_18317))),U_18321) = c_Option_Ooption_ONone(U_18318),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

cnf(f_4438_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18317),tc_Option_Ooption(U_18318),U_18319,hAPP(c_Option_Omap(U_18317,U_18318),U_18320)),hAPP(c_COMBK(tc_Option_Ooption(U_18317),U_18319),c_Option_Ooption_ONone(U_18317))),U_18321) = c_Option_Ooption_ONone(U_18318),
    inference(clausify,[status(thm)],[f_4438_2]) ).

fof(f_4439_1,plain,
    ! [V_opt_2,V_f_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
        | V_opt_2 != c_Option_Ooption_ONone(T_b) )
      & ( V_opt_2 = c_Option_Ooption_ONone(T_b)
        | hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) != c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_option__map__is__None]) ).

fof(f_4439_2,plain,
    ! [U_18325,U_18324,U_18323,U_18322] :
      ( ( hAPP(hAPP(c_Option_Omap(U_18322,U_18323),U_18324),U_18325) = c_Option_Ooption_ONone(U_18323)
        | U_18325 != c_Option_Ooption_ONone(U_18322) )
      & ( U_18325 = c_Option_Ooption_ONone(U_18322)
        | hAPP(hAPP(c_Option_Omap(U_18322,U_18323),U_18324),U_18325) != c_Option_Ooption_ONone(U_18323) ) ),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

fof(f_4439_3,plain,
    ( ! [U_18333,U_18331,U_18329,U_18327] :
        ( hAPP(hAPP(c_Option_Omap(U_18327,U_18329),U_18331),U_18333) = c_Option_Ooption_ONone(U_18329)
        | U_18333 != c_Option_Ooption_ONone(U_18327) )
    & ! [U_18332,U_18330,U_18328,U_18326] :
        ( U_18332 = c_Option_Ooption_ONone(U_18326)
        | hAPP(hAPP(c_Option_Omap(U_18326,U_18328),U_18330),U_18332) != c_Option_Ooption_ONone(U_18328) ) ),
    inference(miniscope,[status(thm)],[f_4439_2]) ).

cnf(f_4439_4,plain,
    ( U_18332 = c_Option_Ooption_ONone(U_18326)
    | hAPP(hAPP(c_Option_Omap(U_18326,U_18328),U_18330),U_18332) != c_Option_Ooption_ONone(U_18328) ),
    inference(clausify,[status(thm)],[f_4439_3]) ).

cnf(f_4439_5,plain,
    ( hAPP(hAPP(c_Option_Omap(U_18327,U_18329),U_18331),U_18333) = c_Option_Ooption_ONone(U_18329)
    | U_18333 != c_Option_Ooption_ONone(U_18327) ),
    inference(clausify,[status(thm)],[f_4439_3]) ).

fof(f_4440_1,plain,
    ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_option__map__None]) ).

fof(f_4440_2,plain,
    ! [U_18336,U_18335,U_18334] : hAPP(hAPP(c_Option_Omap(U_18334,U_18335),U_18336),c_Option_Ooption_ONone(U_18334)) = c_Option_Ooption_ONone(U_18335),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

cnf(f_4440_3,plain,
    hAPP(hAPP(c_Option_Omap(U_18334,U_18335),U_18336),c_Option_Ooption_ONone(U_18334)) = c_Option_Ooption_ONone(U_18335),
    inference(clausify,[status(thm)],[f_4440_2]) ).

fof(f_4441_1,plain,
    ! [V_k,T_a,T_b] : hAPP(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_4441_2,plain,
    ! [U_18339,U_18338,U_18337] : hAPP(hAPP(c_Map_Omap__of(U_18337,U_18338),c_List_Olist_ONil(tc_prod(U_18337,U_18338))),U_18339) = c_Option_Ooption_ONone(U_18338),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

cnf(f_4441_3,plain,
    hAPP(hAPP(c_Map_Omap__of(U_18337,U_18338),c_List_Olist_ONil(tc_prod(U_18337,U_18338))),U_18339) = c_Option_Ooption_ONone(U_18338),
    inference(clausify,[status(thm)],[f_4441_2]) ).

fof(f_4442_1,plain,
    ! [V_xo_2,T_a] :
      ( ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_xo_2 != c_Option_Ooption_ONone(T_a) )
      & ( V_xo_2 = c_Option_Ooption_ONone(T_a)
        | c_Option_Oset(T_a,V_xo_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty__eq]) ).

fof(f_4442_2,plain,
    ! [U_18341,U_18340] :
      ( ( c_Option_Oset(U_18340,U_18341) = c_Orderings_Obot__class_Obot(tc_fun(U_18340,tc_HOL_Obool))
        | U_18341 != c_Option_Ooption_ONone(U_18340) )
      & ( U_18341 = c_Option_Ooption_ONone(U_18340)
        | c_Option_Oset(U_18340,U_18341) != c_Orderings_Obot__class_Obot(tc_fun(U_18340,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

fof(f_4442_3,plain,
    ( ! [U_18345,U_18343] :
        ( c_Option_Oset(U_18343,U_18345) = c_Orderings_Obot__class_Obot(tc_fun(U_18343,tc_HOL_Obool))
        | U_18345 != c_Option_Ooption_ONone(U_18343) )
    & ! [U_18344,U_18342] :
        ( U_18344 = c_Option_Ooption_ONone(U_18342)
        | c_Option_Oset(U_18342,U_18344) != c_Orderings_Obot__class_Obot(tc_fun(U_18342,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4442_2]) ).

cnf(f_4442_4,plain,
    ( U_18344 = c_Option_Ooption_ONone(U_18342)
    | c_Option_Oset(U_18342,U_18344) != c_Orderings_Obot__class_Obot(tc_fun(U_18342,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4442_3]) ).

cnf(f_4442_5,plain,
    ( c_Option_Oset(U_18343,U_18345) = c_Orderings_Obot__class_Obot(tc_fun(U_18343,tc_HOL_Obool))
    | U_18345 != c_Option_Ooption_ONone(U_18343) ),
    inference(clausify,[status(thm)],[f_4442_3]) ).

fof(f_4443_1,plain,
    ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Option_Oset_Osimps_I1_J]) ).

fof(f_4443_2,plain,
    ! [U_18346] : c_Option_Oset(U_18346,c_Option_Ooption_ONone(U_18346)) = c_Orderings_Obot__class_Obot(tc_fun(U_18346,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

cnf(f_4443_3,plain,
    c_Option_Oset(U_18346,c_Option_Ooption_ONone(U_18346)) = c_Orderings_Obot__class_Obot(tc_fun(U_18346,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4443_2]) ).

fof(f_4444_1,plain,
    ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_empty__upd__none]) ).

fof(f_4444_2,plain,
    ! [U_18350,U_18349,U_18348,U_18347] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18347,tc_Option_Ooption(U_18348)),hAPP(c_COMBK(tc_Option_Ooption(U_18348),U_18347),c_Option_Ooption_ONone(U_18348))),U_18349),c_Option_Ooption_ONone(U_18348)),U_18350) = c_Option_Ooption_ONone(U_18348),
    inference(variable_rename,[status(thm)],[f_4444_1]) ).

cnf(f_4444_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18347,tc_Option_Ooption(U_18348)),hAPP(c_COMBK(tc_Option_Ooption(U_18348),U_18347),c_Option_Ooption_ONone(U_18348))),U_18349),c_Option_Ooption_ONone(U_18348)),U_18350) = c_Option_Ooption_ONone(U_18348),
    inference(clausify,[status(thm)],[f_4444_2]) ).

fof(f_4445_1,plain,
    ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,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_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_dom__def]) ).

fof(f_4445_2,plain,
    ! [U_18353,U_18352,U_18351] : c_Map_Odom(U_18351,U_18352,U_18353) = hAPP(c_Set_OCollect(U_18351),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18351),c_fNot),hAPP(hAPP(c_COMBC(U_18351,tc_Option_Ooption(U_18352),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18352),tc_fun(tc_Option_Ooption(U_18352),tc_HOL_Obool),U_18351),c_fequal),U_18353)),c_Option_Ooption_ONone(U_18352)))),
    inference(variable_rename,[status(thm)],[f_4445_1]) ).

cnf(f_4445_3,plain,
    c_Map_Odom(U_18351,U_18352,U_18353) = hAPP(c_Set_OCollect(U_18351),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18351),c_fNot),hAPP(hAPP(c_COMBC(U_18351,tc_Option_Ooption(U_18352),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18352),tc_fun(tc_Option_Ooption(U_18352),tc_HOL_Obool),U_18351),c_fequal),U_18353)),c_Option_Ooption_ONone(U_18352)))),
    inference(clausify,[status(thm)],[f_4445_2]) ).

fof(f_4446_1,plain,
    ! [V_m_2,T_b,V_a_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
        | hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b) )
      & ( hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_domIff]) ).

fof(f_4446_2,plain,
    ! [U_18357,U_18356,U_18355,U_18354] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18354),U_18355),c_Map_Odom(U_18354,U_18356,U_18357)))
        | hAPP(U_18357,U_18355) = c_Option_Ooption_ONone(U_18356) )
      & ( hAPP(U_18357,U_18355) != c_Option_Ooption_ONone(U_18356)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18354),U_18355),c_Map_Odom(U_18354,U_18356,U_18357))) ) ),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

fof(f_4446_3,plain,
    ( ! [U_18365,U_18363,U_18361] :
        ( ! [U_18359] : hBOOL(hAPP(hAPP(c_member(U_18359),U_18361),c_Map_Odom(U_18359,U_18363,U_18365)))
        | hAPP(U_18365,U_18361) = c_Option_Ooption_ONone(U_18363) )
    & ! [U_18364,U_18362,U_18360] :
        ( ! [U_18358] : ~ hBOOL(hAPP(hAPP(c_member(U_18358),U_18360),c_Map_Odom(U_18358,U_18362,U_18364)))
        | hAPP(U_18364,U_18360) != c_Option_Ooption_ONone(U_18362) ) ),
    inference(miniscope,[status(thm)],[f_4446_2]) ).

cnf(f_4446_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18358),U_18360),c_Map_Odom(U_18358,U_18362,U_18364)))
    | hAPP(U_18364,U_18360) != c_Option_Ooption_ONone(U_18362) ),
    inference(clausify,[status(thm)],[f_4446_3]) ).

cnf(f_4446_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18359),U_18361),c_Map_Odom(U_18359,U_18363,U_18365)))
    | hAPP(U_18365,U_18361) = c_Option_Ooption_ONone(U_18363) ),
    inference(clausify,[status(thm)],[f_4446_3]) ).

fof(f_4447_1,plain,
    ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_dom__empty]) ).

fof(f_4447_2,plain,
    ! [U_18367,U_18366] : c_Map_Odom(U_18366,U_18367,hAPP(c_COMBK(tc_Option_Ooption(U_18367),U_18366),c_Option_Ooption_ONone(U_18367))) = c_Orderings_Obot__class_Obot(tc_fun(U_18366,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

cnf(f_4447_3,plain,
    c_Map_Odom(U_18366,U_18367,hAPP(c_COMBK(tc_Option_Ooption(U_18367),U_18366),c_Option_Ooption_ONone(U_18367))) = c_Orderings_Obot__class_Obot(tc_fun(U_18366,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4447_2]) ).

fof(f_4448_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
        | V_f_2 != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) )
      & ( V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))
        | c_Map_Odom(T_a,T_b,V_f_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv]) ).

fof(f_4448_2,plain,
    ! [U_18370,U_18369,U_18368] :
      ( ( c_Map_Odom(U_18368,U_18369,U_18370) = c_Orderings_Obot__class_Obot(tc_fun(U_18368,tc_HOL_Obool))
        | U_18370 != hAPP(c_COMBK(tc_Option_Ooption(U_18369),U_18368),c_Option_Ooption_ONone(U_18369)) )
      & ( U_18370 = hAPP(c_COMBK(tc_Option_Ooption(U_18369),U_18368),c_Option_Ooption_ONone(U_18369))
        | c_Map_Odom(U_18368,U_18369,U_18370) != c_Orderings_Obot__class_Obot(tc_fun(U_18368,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

fof(f_4448_3,plain,
    ( ! [U_18376,U_18374,U_18372] :
        ( c_Map_Odom(U_18372,U_18374,U_18376) = c_Orderings_Obot__class_Obot(tc_fun(U_18372,tc_HOL_Obool))
        | U_18376 != hAPP(c_COMBK(tc_Option_Ooption(U_18374),U_18372),c_Option_Ooption_ONone(U_18374)) )
    & ! [U_18375,U_18373,U_18371] :
        ( U_18375 = hAPP(c_COMBK(tc_Option_Ooption(U_18373),U_18371),c_Option_Ooption_ONone(U_18373))
        | c_Map_Odom(U_18371,U_18373,U_18375) != c_Orderings_Obot__class_Obot(tc_fun(U_18371,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4448_2]) ).

cnf(f_4448_4,plain,
    ( U_18375 = hAPP(c_COMBK(tc_Option_Ooption(U_18373),U_18371),c_Option_Ooption_ONone(U_18373))
    | c_Map_Odom(U_18371,U_18373,U_18375) != c_Orderings_Obot__class_Obot(tc_fun(U_18371,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

cnf(f_4448_5,plain,
    ( c_Map_Odom(U_18372,U_18374,U_18376) = c_Orderings_Obot__class_Obot(tc_fun(U_18372,tc_HOL_Obool))
    | U_18376 != hAPP(c_COMBK(tc_Option_Ooption(U_18374),U_18372),c_Option_Ooption_ONone(U_18374)) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

fof(f_4449_1,plain,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( ( hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
      & ( hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__def]) ).

fof(f_4449_2,plain,
    ! [U_18381,U_18380,U_18379,U_18378,U_18377] :
      ( ( hAPP(c_Map_Orestrict__map(U_18377,U_18380,U_18381,U_18379),U_18378) = c_Option_Ooption_ONone(U_18380)
        | hBOOL(hAPP(hAPP(c_member(U_18377),U_18378),U_18379)) )
      & ( hAPP(c_Map_Orestrict__map(U_18377,U_18380,U_18381,U_18379),U_18378) = hAPP(U_18381,U_18378)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18377),U_18378),U_18379)) ) ),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

fof(f_4449_3,plain,
    ( ! [U_18391,U_18389,U_18387,U_18385,U_18383] :
        ( hAPP(c_Map_Orestrict__map(U_18383,U_18389,U_18391,U_18387),U_18385) = c_Option_Ooption_ONone(U_18389)
        | hBOOL(hAPP(hAPP(c_member(U_18383),U_18385),U_18387)) )
    & ! [U_18390,U_18388,U_18386,U_18384,U_18382] :
        ( hAPP(c_Map_Orestrict__map(U_18382,U_18388,U_18390,U_18386),U_18384) = hAPP(U_18390,U_18384)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18382),U_18384),U_18386)) ) ),
    inference(miniscope,[status(thm)],[f_4449_2]) ).

cnf(f_4449_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_18382,U_18388,U_18390,U_18386),U_18384) = hAPP(U_18390,U_18384)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18382),U_18384),U_18386)) ),
    inference(clausify,[status(thm)],[f_4449_3]) ).

cnf(f_4449_5,plain,
    ( hAPP(c_Map_Orestrict__map(U_18383,U_18389,U_18391,U_18387),U_18385) = c_Option_Ooption_ONone(U_18389)
    | hBOOL(hAPP(hAPP(c_member(U_18383),U_18385),U_18387)) ),
    inference(clausify,[status(thm)],[f_4449_3]) ).

fof(f_4450_1,plain,
    ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
      ( hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_restrict__out]) ).

fof(f_4450_2,plain,
    ! [U_18396,U_18395,U_18394,U_18393,U_18392] :
      ( hAPP(c_Map_Orestrict__map(U_18392,U_18395,U_18396,U_18394),U_18393) = c_Option_Ooption_ONone(U_18395)
      | hBOOL(hAPP(hAPP(c_member(U_18392),U_18393),U_18394)) ),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

cnf(f_4450_3,plain,
    ( hAPP(c_Map_Orestrict__map(U_18392,U_18395,U_18396,U_18394),U_18393) = c_Option_Ooption_ONone(U_18395)
    | hBOOL(hAPP(hAPP(c_member(U_18392),U_18393),U_18394)) ),
    inference(clausify,[status(thm)],[f_4450_2]) ).

fof(f_4451_1,plain,
    ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__empty]) ).

fof(f_4451_2,plain,
    ! [U_18400,U_18399,U_18398,U_18397] : hAPP(c_Map_Orestrict__map(U_18397,U_18398,hAPP(c_COMBK(tc_Option_Ooption(U_18398),U_18397),c_Option_Ooption_ONone(U_18398)),U_18399),U_18400) = c_Option_Ooption_ONone(U_18398),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

cnf(f_4451_3,plain,
    hAPP(c_Map_Orestrict__map(U_18397,U_18398,hAPP(c_COMBK(tc_Option_Ooption(U_18398),U_18397),c_Option_Ooption_ONone(U_18398)),U_18399),U_18400) = c_Option_Ooption_ONone(U_18398),
    inference(clausify,[status(thm)],[f_4451_2]) ).

fof(f_4452_1,plain,
    ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_restrict__map__to__empty]) ).

fof(f_4452_2,plain,
    ! [U_18404,U_18403,U_18402,U_18401] : hAPP(c_Map_Orestrict__map(U_18401,U_18402,U_18403,c_Orderings_Obot__class_Obot(tc_fun(U_18401,tc_HOL_Obool))),U_18404) = c_Option_Ooption_ONone(U_18402),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

cnf(f_4452_3,plain,
    hAPP(c_Map_Orestrict__map(U_18401,U_18402,U_18403,c_Orderings_Obot__class_Obot(tc_fun(U_18401,tc_HOL_Obool))),U_18404) = c_Option_Ooption_ONone(U_18402),
    inference(clausify,[status(thm)],[f_4452_2]) ).

fof(f_4453_1,plain,
    ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_option_Osimps_I4_J]) ).

fof(f_4453_2,plain,
    ! [U_18408,U_18407,U_18406,U_18405] : hAPP(c_Option_Ooption_Ooption__case(U_18405,U_18406,U_18407,U_18408),c_Option_Ooption_ONone(U_18406)) = U_18407,
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

cnf(f_4453_3,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_18405,U_18406,U_18407,U_18408),c_Option_Ooption_ONone(U_18406)) = U_18407,
    inference(clausify,[status(thm)],[f_4453_2]) ).

fof(f_4454_1,plain,
    ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),
    inference(fof_nnf,[status(thm)],[fact_map__upd__nonempty]) ).

fof(f_4454_2,plain,
    ! [U_18413,U_18412,U_18411,U_18410,U_18409] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18409,tc_Option_Ooption(U_18410)),U_18411),U_18412),hAPP(c_Option_Ooption_OSome(U_18410),U_18413)) != hAPP(c_COMBK(tc_Option_Ooption(U_18410),U_18409),c_Option_Ooption_ONone(U_18410)),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

cnf(f_4454_3,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18409,tc_Option_Ooption(U_18410)),U_18411),U_18412),hAPP(c_Option_Ooption_OSome(U_18410),U_18413)) != hAPP(c_COMBK(tc_Option_Ooption(U_18410),U_18409),c_Option_Ooption_ONone(U_18410)),
    inference(clausify,[status(thm)],[f_4454_2]) ).

fof(f_4455_1,plain,
    ! [T_a,V_x_2] :
      ( ( V_x_2 != c_Option_Ooption_ONone(T_a)
        | ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) )
      & ( ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y)
        | V_x_2 = c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__None__eq]) ).

fof(f_4455_2,plain,
    ! [U_18417,U_18416] :
      ( ( U_18416 != c_Option_Ooption_ONone(U_18417)
        | ! [U_18415] : U_18416 != hAPP(c_Option_Ooption_OSome(U_18417),U_18415) )
      & ( ? [U_18414] : U_18416 = hAPP(c_Option_Ooption_OSome(U_18417),U_18414)
        | U_18416 = c_Option_Ooption_ONone(U_18417) ) ),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

fof(f_4455_3,plain,
    ( ! [U_18421,U_18419] :
        ( U_18419 != c_Option_Ooption_ONone(U_18421)
        | ! [U_18415] : U_18419 != hAPP(c_Option_Ooption_OSome(U_18421),U_18415) )
    & ! [U_18420,U_18418] :
        ( ? [U_18414] : U_18418 = hAPP(c_Option_Ooption_OSome(U_18420),U_18414)
        | U_18418 = c_Option_Ooption_ONone(U_18420) ) ),
    inference(miniscope,[status(thm)],[f_4455_2]) ).

fof(f_4455_4,plain,
    ( ! [U_18421,U_18419] :
        ( U_18419 != c_Option_Ooption_ONone(U_18421)
        | ! [U_18415] : U_18419 != hAPP(c_Option_Ooption_OSome(U_18421),U_18415) )
    & ! [U_18420,U_18418] :
        ( U_18418 = hAPP(c_Option_Ooption_OSome(U_18420),sK460(U_18420,U_18418))
        | U_18418 = c_Option_Ooption_ONone(U_18420) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18414,sK460(U_18420,U_18418))],[f_4455_3]) ).

cnf(f_4455_5,plain,
    ( U_18418 = hAPP(c_Option_Ooption_OSome(U_18420),sK460(U_18420,U_18418))
    | U_18418 = c_Option_Ooption_ONone(U_18420) ),
    inference(clausify,[status(thm)],[f_4455_4]) ).

cnf(f_4455_6,plain,
    ( U_18419 != c_Option_Ooption_ONone(U_18421)
    | U_18419 != hAPP(c_Option_Ooption_OSome(U_18421),U_18415) ),
    inference(clausify,[status(thm)],[f_4455_4]) ).

fof(f_4456_1,plain,
    ! [T_a,V_x_2] :
      ( ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
        | V_x_2 != c_Option_Ooption_ONone(T_a) )
      & ( V_x_2 = c_Option_Ooption_ONone(T_a)
        | ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__Some__eq]) ).

fof(f_4456_2,plain,
    ! [U_18425,U_18424] :
      ( ( ! [U_18423] : U_18424 != hAPP(c_Option_Ooption_OSome(U_18425),U_18423)
        | U_18424 != c_Option_Ooption_ONone(U_18425) )
      & ( U_18424 = c_Option_Ooption_ONone(U_18425)
        | ? [U_18422] : U_18424 = hAPP(c_Option_Ooption_OSome(U_18425),U_18422) ) ),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

fof(f_4456_3,plain,
    ( ! [U_18429,U_18427] :
        ( ! [U_18423] : U_18427 != hAPP(c_Option_Ooption_OSome(U_18429),U_18423)
        | U_18427 != c_Option_Ooption_ONone(U_18429) )
    & ! [U_18428,U_18426] :
        ( U_18426 = c_Option_Ooption_ONone(U_18428)
        | ? [U_18422] : U_18426 = hAPP(c_Option_Ooption_OSome(U_18428),U_18422) ) ),
    inference(miniscope,[status(thm)],[f_4456_2]) ).

fof(f_4456_4,plain,
    ( ! [U_18429,U_18427] :
        ( ! [U_18423] : U_18427 != hAPP(c_Option_Ooption_OSome(U_18429),U_18423)
        | U_18427 != c_Option_Ooption_ONone(U_18429) )
    & ! [U_18428,U_18426] :
        ( U_18426 = c_Option_Ooption_ONone(U_18428)
        | U_18426 = hAPP(c_Option_Ooption_OSome(U_18428),sK461(U_18428,U_18426)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18422,sK461(U_18428,U_18426))],[f_4456_3]) ).

cnf(f_4456_5,plain,
    ( U_18426 = c_Option_Ooption_ONone(U_18428)
    | U_18426 = hAPP(c_Option_Ooption_OSome(U_18428),sK461(U_18428,U_18426)) ),
    inference(clausify,[status(thm)],[f_4456_4]) ).

cnf(f_4456_6,plain,
    ( U_18427 != hAPP(c_Option_Ooption_OSome(U_18429),U_18423)
    | U_18427 != c_Option_Ooption_ONone(U_18429) ),
    inference(clausify,[status(thm)],[f_4456_4]) ).

fof(f_4457_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_4457_2,plain,
    ! [U_18431,U_18430] : hAPP(c_Option_Ooption_OSome(U_18430),U_18431) != c_Option_Ooption_ONone(U_18430),
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

cnf(f_4457_3,plain,
    hAPP(c_Option_Ooption_OSome(U_18430),U_18431) != c_Option_Ooption_ONone(U_18430),
    inference(clausify,[status(thm)],[f_4457_2]) ).

fof(f_4458_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_4458_2,plain,
    ! [U_18433,U_18432] : c_Option_Ooption_ONone(U_18432) != hAPP(c_Option_Ooption_OSome(U_18432),U_18433),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

cnf(f_4458_3,plain,
    c_Option_Ooption_ONone(U_18432) != hAPP(c_Option_Ooption_OSome(U_18432),U_18433),
    inference(clausify,[status(thm)],[f_4458_2]) ).

fof(f_4459_1,plain,
    ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_ran__empty]) ).

fof(f_4459_2,plain,
    ! [U_18435,U_18434] : c_Map_Oran(U_18434,U_18435,hAPP(c_COMBK(tc_Option_Ooption(U_18435),U_18434),c_Option_Ooption_ONone(U_18435))) = c_Orderings_Obot__class_Obot(tc_fun(U_18435,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

cnf(f_4459_3,plain,
    c_Map_Oran(U_18434,U_18435,hAPP(c_COMBK(tc_Option_Ooption(U_18435),U_18434),c_Option_Ooption_ONone(U_18435))) = c_Orderings_Obot__class_Obot(tc_fun(U_18435,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4459_2]) ).

fof(f_4460_1,plain,
    ! [V_x_1,T_b,T_a] : hAPP(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_4460_2,plain,
    ! [U_18438,U_18437,U_18436] : hAPP(hAPP(c_Map_Omap__of(U_18436,U_18437),c_List_Olist_ONil(tc_prod(U_18436,U_18437))),U_18438) = c_Option_Ooption_ONone(U_18437),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

cnf(f_4460_3,plain,
    hAPP(hAPP(c_Map_Omap__of(U_18436,U_18437),c_List_Olist_ONil(tc_prod(U_18436,U_18437))),U_18438) = c_Option_Ooption_ONone(U_18437),
    inference(clausify,[status(thm)],[f_4460_2]) ).

fof(f_4461_1,plain,
    ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_Option_Omap__def]) ).

fof(f_4461_2,plain,
    ! [U_18441,U_18440,U_18439] : hAPP(c_Option_Omap(U_18439,U_18440),U_18441) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_18440),U_18439,c_Option_Ooption_ONone(U_18440),hAPP(hAPP(c_COMBB(U_18440,tc_Option_Ooption(U_18440),U_18439),c_Option_Ooption_OSome(U_18440)),U_18441)),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

cnf(f_4461_3,plain,
    hAPP(c_Option_Omap(U_18439,U_18440),U_18441) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_18440),U_18439,c_Option_Ooption_ONone(U_18440),hAPP(hAPP(c_COMBB(U_18440,tc_Option_Ooption(U_18440),U_18439),c_Option_Ooption_OSome(U_18440)),U_18441)),
    inference(clausify,[status(thm)],[f_4461_2]) ).

fof(f_4462_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_4462_2,plain,
    ! [U_18442] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_18442)),c_Option_Ooption_ONone(U_18442)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

cnf(f_4462_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_18442)),c_Option_Ooption_ONone(U_18442)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4462_2]) ).

fof(f_4463_1,plain,
    ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_option_Osize_I1_J]) ).

fof(f_4463_2,plain,
    ! [U_18444,U_18443] : c_Option_Ooption_Ooption__size(U_18443,U_18444,c_Option_Ooption_ONone(U_18443)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

cnf(f_4463_3,plain,
    c_Option_Ooption_Ooption__size(U_18443,U_18444,c_Option_Ooption_ONone(U_18443)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4463_2]) ).

fof(f_4464_1,plain,
    ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2)
      | hAPP(V_f_2,V_x_2) != c_Option_Ooption_ONone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dom__minus]) ).

fof(f_4464_2,plain,
    ! [U_18449,U_18448,U_18447,U_18446,U_18445] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18448,tc_HOL_Obool)),c_Map_Odom(U_18448,U_18447,U_18445)),hAPP(hAPP(c_Set_Oinsert(U_18448),U_18446),U_18449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18448,tc_HOL_Obool)),c_Map_Odom(U_18448,U_18447,U_18445)),U_18449)
      | hAPP(U_18445,U_18446) != c_Option_Ooption_ONone(U_18447) ),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

cnf(f_4464_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18448,tc_HOL_Obool)),c_Map_Odom(U_18448,U_18447,U_18445)),hAPP(hAPP(c_Set_Oinsert(U_18448),U_18446),U_18449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18448,tc_HOL_Obool)),c_Map_Odom(U_18448,U_18447,U_18445)),U_18449)
    | hAPP(U_18445,U_18446) != c_Option_Ooption_ONone(U_18447) ),
    inference(clausify,[status(thm)],[f_4464_2]) ).

fof(f_4465_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_4465_2,plain,
    ! [U_18450] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_18450)))
      | hAPP(c_Com_Obody,U_18450) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

cnf(f_4465_3,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_18450)))
    | hAPP(c_Com_Obody,U_18450) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(clausify,[status(thm)],[f_4465_2]) ).

fof(f_4466_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
      ( ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) )
        & ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) ) )
      | c_List_Opartition(T_a,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__P]) ).

fof(f_4466_2,plain,
    ! [U_18457,U_18456,U_18455,U_18454,U_18453] :
      ( ( ! [U_18452] :
            ( ~ hBOOL(hAPP(U_18454,U_18452))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18453),U_18452),hAPP(c_List_Oset(U_18453),U_18457))) )
        & ! [U_18451] :
            ( hBOOL(hAPP(U_18454,U_18451))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18453),U_18451),hAPP(c_List_Oset(U_18453),U_18456))) ) )
      | c_List_Opartition(U_18453,U_18454,U_18455) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18453),tc_List_Olist(U_18453)),U_18456),U_18457) ),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

cnf(f_4466_3,plain,
    ( hBOOL(hAPP(U_18454,U_18451))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18453),U_18451),hAPP(c_List_Oset(U_18453),U_18456)))
    | c_List_Opartition(U_18453,U_18454,U_18455) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18453),tc_List_Olist(U_18453)),U_18456),U_18457) ),
    inference(clausify,[status(thm)],[f_4466_2]) ).

cnf(f_4466_4,plain,
    ( ~ hBOOL(hAPP(U_18454,U_18452))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18453),U_18452),hAPP(c_List_Oset(U_18453),U_18457)))
    | c_List_Opartition(U_18453,U_18454,U_18455) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18453),tc_List_Olist(U_18453)),U_18456),U_18457) ),
    inference(clausify,[status(thm)],[f_4466_2]) ).

fof(f_4467_1,plain,
    ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I1_J]) ).

fof(f_4467_2,plain,
    ! [U_18459,U_18458] : c_List_Opartition(U_18458,U_18459,c_List_Olist_ONil(U_18458)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18458),tc_List_Olist(U_18458)),c_List_Olist_ONil(U_18458)),c_List_Olist_ONil(U_18458)),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

cnf(f_4467_3,plain,
    c_List_Opartition(U_18458,U_18459,c_List_Olist_ONil(U_18458)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18458),tc_List_Olist(U_18458)),c_List_Olist_ONil(U_18458)),c_List_Olist_ONil(U_18458)),
    inference(clausify,[status(thm)],[f_4467_2]) ).

fof(f_4468_1,plain,
    ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
      ( c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))
      | hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ran__map__upd]) ).

fof(f_4468_2,plain,
    ! [U_18464,U_18463,U_18462,U_18461,U_18460] :
      ( c_Map_Oran(U_18463,U_18462,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18463,tc_Option_Ooption(U_18462)),U_18460),U_18461),hAPP(c_Option_Ooption_OSome(U_18462),U_18464))) = hAPP(hAPP(c_Set_Oinsert(U_18462),U_18464),c_Map_Oran(U_18463,U_18462,U_18460))
      | hAPP(U_18460,U_18461) != c_Option_Ooption_ONone(U_18462) ),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

cnf(f_4468_3,plain,
    ( c_Map_Oran(U_18463,U_18462,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18463,tc_Option_Ooption(U_18462)),U_18460),U_18461),hAPP(c_Option_Ooption_OSome(U_18462),U_18464))) = hAPP(hAPP(c_Set_Oinsert(U_18462),U_18464),c_Map_Oran(U_18463,U_18462,U_18460))
    | hAPP(U_18460,U_18461) != c_Option_Ooption_ONone(U_18462) ),
    inference(clausify,[status(thm)],[f_4468_2]) ).

fof(f_4469_1,plain,
    ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( ( ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b)
          | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
          | hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) != c_Option_Ooption_ONone(T_b) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__None]) ).

fof(f_4469_2,plain,
    ! [U_18469,U_18468,U_18467,U_18466,U_18465] :
      ( ( ( hAPP(hAPP(c_Map_Omap__of(U_18465,U_18467),hAPP(hAPP(c_List_Ozip(U_18465,U_18467),U_18466),U_18468)),U_18469) = c_Option_Ooption_ONone(U_18467)
          | hBOOL(hAPP(hAPP(c_member(U_18465),U_18469),hAPP(c_List_Oset(U_18465),U_18466))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(U_18465),U_18469),hAPP(c_List_Oset(U_18465),U_18466)))
          | hAPP(hAPP(c_Map_Omap__of(U_18465,U_18467),hAPP(hAPP(c_List_Ozip(U_18465,U_18467),U_18466),U_18468)),U_18469) != c_Option_Ooption_ONone(U_18467) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18465)),U_18466) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18467)),U_18468) ),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

cnf(f_4469_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18465),U_18469),hAPP(c_List_Oset(U_18465),U_18466)))
    | hAPP(hAPP(c_Map_Omap__of(U_18465,U_18467),hAPP(hAPP(c_List_Ozip(U_18465,U_18467),U_18466),U_18468)),U_18469) != c_Option_Ooption_ONone(U_18467)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18465)),U_18466) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18467)),U_18468) ),
    inference(clausify,[status(thm)],[f_4469_2]) ).

cnf(f_4469_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18465,U_18467),hAPP(hAPP(c_List_Ozip(U_18465,U_18467),U_18466),U_18468)),U_18469) = c_Option_Ooption_ONone(U_18467)
    | hBOOL(hAPP(hAPP(c_member(U_18465),U_18469),hAPP(c_List_Oset(U_18465),U_18466)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18465)),U_18466) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18467)),U_18468) ),
    inference(clausify,[status(thm)],[f_4469_2]) ).

fof(f_4470_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(f_4470_2,plain,
    ! [U_18473,U_18472,U_18471,U_18470] : c_List_Opartition(U_18470,U_18471,hAPP(hAPP(c_List_Olist_OCons(U_18470),U_18472),U_18473)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18470),tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_fun(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),c_COMBS(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_List_Olist(U_18470)),hAPP(c_If(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(U_18471,U_18472)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_List_Olist(U_18470)),c_Product__Type_OPair(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(c_List_Olist_OCons(U_18470),U_18472))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_fun(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),c_COMBB(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_List_Olist(U_18470))),c_Product__Type_OPair(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(c_List_Olist_OCons(U_18470),U_18472)))),c_List_Opartition(U_18470,U_18471,U_18473)),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

cnf(f_4470_3,plain,
    c_List_Opartition(U_18470,U_18471,hAPP(hAPP(c_List_Olist_OCons(U_18470),U_18472),U_18473)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18470),tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_fun(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),c_COMBS(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_List_Olist(U_18470),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_List_Olist(U_18470)),hAPP(c_If(tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(U_18471,U_18472)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_List_Olist(U_18470)),c_Product__Type_OPair(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),hAPP(c_List_Olist_OCons(U_18470),U_18472))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18470),tc_fun(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470))),tc_fun(tc_fun(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_fun(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),tc_List_Olist(U_18470)),c_COMBB(tc_List_Olist(U_18470),tc_prod(tc_List_Olist(U_18470),tc_List_Olist(U_18470)),tc_List_Olist(U_18470))),c_Product__Type_OPair(tc_List_Olist(U_18470),tc_List_Olist(U_18470)))),hAPP(c_List_Olist_OCons(U_18470),U_18472)))),c_List_Opartition(U_18470,U_18471,U_18473)),
    inference(clausify,[status(thm)],[f_4470_2]) ).

fof(f_4471_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
      ( ( c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2))
        | V_y_2 = c_Option_Ooption_ONone(T_a) )
      & ( c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,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_y_2 != c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__fun__upd]) ).

fof(f_4471_2,plain,
    ! [U_18478,U_18477,U_18476,U_18475,U_18474] :
      ( ( c_Map_Odom(U_18476,U_18475,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18476,tc_Option_Ooption(U_18475)),U_18477),U_18478),U_18474)) = hAPP(hAPP(c_Set_Oinsert(U_18476),U_18478),c_Map_Odom(U_18476,U_18475,U_18477))
        | U_18474 = c_Option_Ooption_ONone(U_18475) )
      & ( c_Map_Odom(U_18476,U_18475,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18476,tc_Option_Ooption(U_18475)),U_18477),U_18478),U_18474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18476,tc_HOL_Obool)),c_Map_Odom(U_18476,U_18475,U_18477)),hAPP(hAPP(c_Set_Oinsert(U_18476),U_18478),c_Orderings_Obot__class_Obot(tc_fun(U_18476,tc_HOL_Obool))))
        | U_18474 != c_Option_Ooption_ONone(U_18475) ) ),
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

fof(f_4471_3,plain,
    ( ! [U_18488,U_18486,U_18484,U_18482,U_18480] :
        ( c_Map_Odom(U_18484,U_18482,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18484,tc_Option_Ooption(U_18482)),U_18486),U_18488),U_18480)) = hAPP(hAPP(c_Set_Oinsert(U_18484),U_18488),c_Map_Odom(U_18484,U_18482,U_18486))
        | U_18480 = c_Option_Ooption_ONone(U_18482) )
    & ! [U_18487,U_18485,U_18483,U_18481,U_18479] :
        ( c_Map_Odom(U_18483,U_18481,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18483,tc_Option_Ooption(U_18481)),U_18485),U_18487),U_18479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18483,tc_HOL_Obool)),c_Map_Odom(U_18483,U_18481,U_18485)),hAPP(hAPP(c_Set_Oinsert(U_18483),U_18487),c_Orderings_Obot__class_Obot(tc_fun(U_18483,tc_HOL_Obool))))
        | U_18479 != c_Option_Ooption_ONone(U_18481) ) ),
    inference(miniscope,[status(thm)],[f_4471_2]) ).

cnf(f_4471_4,plain,
    ( c_Map_Odom(U_18483,U_18481,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18483,tc_Option_Ooption(U_18481)),U_18485),U_18487),U_18479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18483,tc_HOL_Obool)),c_Map_Odom(U_18483,U_18481,U_18485)),hAPP(hAPP(c_Set_Oinsert(U_18483),U_18487),c_Orderings_Obot__class_Obot(tc_fun(U_18483,tc_HOL_Obool))))
    | U_18479 != c_Option_Ooption_ONone(U_18481) ),
    inference(clausify,[status(thm)],[f_4471_3]) ).

cnf(f_4471_5,plain,
    ( c_Map_Odom(U_18484,U_18482,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18484,tc_Option_Ooption(U_18482)),U_18486),U_18488),U_18480)) = hAPP(hAPP(c_Set_Oinsert(U_18484),U_18488),c_Map_Odom(U_18484,U_18482,U_18486))
    | U_18480 = c_Option_Ooption_ONone(U_18482) ),
    inference(clausify,[status(thm)],[f_4471_3]) ).

fof(f_4472_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)),
    inference(fof_nnf,[status(thm)],[fact_restrict__complement__singleton__eq]) ).

fof(f_4472_2,plain,
    ! [U_18492,U_18491,U_18490,U_18489] : c_Map_Orestrict__map(U_18489,U_18490,U_18491,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_18489,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_18489),U_18492),c_Orderings_Obot__class_Obot(tc_fun(U_18489,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18489,tc_Option_Ooption(U_18490)),U_18491),U_18492),c_Option_Ooption_ONone(U_18490)),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

cnf(f_4472_3,plain,
    c_Map_Orestrict__map(U_18489,U_18490,U_18491,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_18489,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_18489),U_18492),c_Orderings_Obot__class_Obot(tc_fun(U_18489,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18489,tc_Option_Ooption(U_18490)),U_18491),U_18492),c_Option_Ooption_ONone(U_18490)),
    inference(clausify,[status(thm)],[f_4472_2]) ).

fof(f_4473_1,plain,
    ! [V_x_2,V_xys_2,T_a,T_b] :
      ( ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))))
        | hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) != c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eq__None__iff]) ).

fof(f_4473_2,plain,
    ! [U_18496,U_18495,U_18494,U_18493] :
      ( ( hAPP(hAPP(c_Map_Omap__of(U_18493,U_18494),U_18495),U_18496) = c_Option_Ooption_ONone(U_18494)
        | hBOOL(hAPP(hAPP(c_member(U_18493),U_18496),hAPP(c_Set_Oimage(tc_prod(U_18493,U_18494),U_18493,c_Product__Type_Ofst(U_18493,U_18494)),hAPP(c_List_Oset(tc_prod(U_18493,U_18494)),U_18495)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_18493),U_18496),hAPP(c_Set_Oimage(tc_prod(U_18493,U_18494),U_18493,c_Product__Type_Ofst(U_18493,U_18494)),hAPP(c_List_Oset(tc_prod(U_18493,U_18494)),U_18495))))
        | hAPP(hAPP(c_Map_Omap__of(U_18493,U_18494),U_18495),U_18496) != c_Option_Ooption_ONone(U_18494) ) ),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

fof(f_4473_3,plain,
    ( ! [U_18504,U_18502,U_18500,U_18498] :
        ( hAPP(hAPP(c_Map_Omap__of(U_18498,U_18500),U_18502),U_18504) = c_Option_Ooption_ONone(U_18500)
        | hBOOL(hAPP(hAPP(c_member(U_18498),U_18504),hAPP(c_Set_Oimage(tc_prod(U_18498,U_18500),U_18498,c_Product__Type_Ofst(U_18498,U_18500)),hAPP(c_List_Oset(tc_prod(U_18498,U_18500)),U_18502)))) )
    & ! [U_18503,U_18501,U_18499,U_18497] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_18497),U_18503),hAPP(c_Set_Oimage(tc_prod(U_18497,U_18499),U_18497,c_Product__Type_Ofst(U_18497,U_18499)),hAPP(c_List_Oset(tc_prod(U_18497,U_18499)),U_18501))))
        | hAPP(hAPP(c_Map_Omap__of(U_18497,U_18499),U_18501),U_18503) != c_Option_Ooption_ONone(U_18499) ) ),
    inference(miniscope,[status(thm)],[f_4473_2]) ).

cnf(f_4473_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18497),U_18503),hAPP(c_Set_Oimage(tc_prod(U_18497,U_18499),U_18497,c_Product__Type_Ofst(U_18497,U_18499)),hAPP(c_List_Oset(tc_prod(U_18497,U_18499)),U_18501))))
    | hAPP(hAPP(c_Map_Omap__of(U_18497,U_18499),U_18501),U_18503) != c_Option_Ooption_ONone(U_18499) ),
    inference(clausify,[status(thm)],[f_4473_3]) ).

cnf(f_4473_5,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18498,U_18500),U_18502),U_18504) = c_Option_Ooption_ONone(U_18500)
    | hBOOL(hAPP(hAPP(c_member(U_18498),U_18504),hAPP(c_Set_Oimage(tc_prod(U_18498,U_18500),U_18498,c_Product__Type_Ofst(U_18498,U_18500)),hAPP(c_List_Oset(tc_prod(U_18498,U_18500)),U_18502)))) ),
    inference(clausify,[status(thm)],[f_4473_3]) ).

fof(f_4474_1,plain,
    ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_UNIV__option__conv]) ).

fof(f_4474_2,plain,
    ! [U_18505] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_18505),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_18505)),c_Option_Ooption_ONone(U_18505)),hAPP(c_Set_Oimage(U_18505,tc_Option_Ooption(U_18505),c_Option_Ooption_OSome(U_18505)),c_Orderings_Otop__class_Otop(tc_fun(U_18505,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

cnf(f_4474_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_18505),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_18505)),c_Option_Ooption_ONone(U_18505)),hAPP(c_Set_Oimage(U_18505,tc_Option_Ooption(U_18505),c_Option_Ooption_OSome(U_18505)),c_Orderings_Otop__class_Otop(tc_fun(U_18505,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4474_2]) ).

fof(f_4475_1,plain,
    ! [V_x_2,V_f_2,T_b,T_a] :
      ( ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
        | ! [B_v] : V_f_2 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) )
      & ( ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v))
        | c_Map_Odom(T_a,T_b,V_f_2) != hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dom__eq__singleton__conv]) ).

fof(f_4475_2,plain,
    ! [U_18511,U_18510,U_18509,U_18508] :
      ( ( c_Map_Odom(U_18508,U_18509,U_18510) = hAPP(hAPP(c_Set_Oinsert(U_18508),U_18511),c_Orderings_Obot__class_Obot(tc_fun(U_18508,tc_HOL_Obool)))
        | ! [U_18507] : U_18510 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18508,tc_Option_Ooption(U_18509)),hAPP(c_COMBK(tc_Option_Ooption(U_18509),U_18508),c_Option_Ooption_ONone(U_18509))),U_18511),hAPP(c_Option_Ooption_OSome(U_18509),U_18507)) )
      & ( ? [U_18506] : U_18510 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18508,tc_Option_Ooption(U_18509)),hAPP(c_COMBK(tc_Option_Ooption(U_18509),U_18508),c_Option_Ooption_ONone(U_18509))),U_18511),hAPP(c_Option_Ooption_OSome(U_18509),U_18506))
        | c_Map_Odom(U_18508,U_18509,U_18510) != hAPP(hAPP(c_Set_Oinsert(U_18508),U_18511),c_Orderings_Obot__class_Obot(tc_fun(U_18508,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

fof(f_4475_3,plain,
    ( ! [U_18519,U_18517,U_18515,U_18513] :
        ( c_Map_Odom(U_18513,U_18515,U_18517) = hAPP(hAPP(c_Set_Oinsert(U_18513),U_18519),c_Orderings_Obot__class_Obot(tc_fun(U_18513,tc_HOL_Obool)))
        | ! [U_18507] : U_18517 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18513,tc_Option_Ooption(U_18515)),hAPP(c_COMBK(tc_Option_Ooption(U_18515),U_18513),c_Option_Ooption_ONone(U_18515))),U_18519),hAPP(c_Option_Ooption_OSome(U_18515),U_18507)) )
    & ! [U_18518,U_18516,U_18514,U_18512] :
        ( ? [U_18506] : U_18516 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18512,tc_Option_Ooption(U_18514)),hAPP(c_COMBK(tc_Option_Ooption(U_18514),U_18512),c_Option_Ooption_ONone(U_18514))),U_18518),hAPP(c_Option_Ooption_OSome(U_18514),U_18506))
        | c_Map_Odom(U_18512,U_18514,U_18516) != hAPP(hAPP(c_Set_Oinsert(U_18512),U_18518),c_Orderings_Obot__class_Obot(tc_fun(U_18512,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4475_2]) ).

fof(f_4475_4,plain,
    ( ! [U_18519,U_18517,U_18515,U_18513] :
        ( c_Map_Odom(U_18513,U_18515,U_18517) = hAPP(hAPP(c_Set_Oinsert(U_18513),U_18519),c_Orderings_Obot__class_Obot(tc_fun(U_18513,tc_HOL_Obool)))
        | ! [U_18507] : U_18517 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18513,tc_Option_Ooption(U_18515)),hAPP(c_COMBK(tc_Option_Ooption(U_18515),U_18513),c_Option_Ooption_ONone(U_18515))),U_18519),hAPP(c_Option_Ooption_OSome(U_18515),U_18507)) )
    & ! [U_18518,U_18516,U_18514,U_18512] :
        ( U_18516 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18512,tc_Option_Ooption(U_18514)),hAPP(c_COMBK(tc_Option_Ooption(U_18514),U_18512),c_Option_Ooption_ONone(U_18514))),U_18518),hAPP(c_Option_Ooption_OSome(U_18514),sK462(U_18518,U_18516,U_18514,U_18512)))
        | c_Map_Odom(U_18512,U_18514,U_18516) != hAPP(hAPP(c_Set_Oinsert(U_18512),U_18518),c_Orderings_Obot__class_Obot(tc_fun(U_18512,tc_HOL_Obool))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18506,sK462(U_18518,U_18516,U_18514,U_18512))],[f_4475_3]) ).

cnf(f_4475_5,plain,
    ( U_18516 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18512,tc_Option_Ooption(U_18514)),hAPP(c_COMBK(tc_Option_Ooption(U_18514),U_18512),c_Option_Ooption_ONone(U_18514))),U_18518),hAPP(c_Option_Ooption_OSome(U_18514),sK462(U_18518,U_18516,U_18514,U_18512)))
    | c_Map_Odom(U_18512,U_18514,U_18516) != hAPP(hAPP(c_Set_Oinsert(U_18512),U_18518),c_Orderings_Obot__class_Obot(tc_fun(U_18512,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_6,plain,
    ( c_Map_Odom(U_18513,U_18515,U_18517) = hAPP(hAPP(c_Set_Oinsert(U_18513),U_18519),c_Orderings_Obot__class_Obot(tc_fun(U_18513,tc_HOL_Obool)))
    | U_18517 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18513,tc_Option_Ooption(U_18515)),hAPP(c_COMBK(tc_Option_Ooption(U_18515),U_18513),c_Option_Ooption_ONone(U_18515))),U_18519),hAPP(c_Option_Ooption_OSome(U_18515),U_18507)) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

fof(f_4476_1,plain,
    ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__None__restrict]) ).

fof(f_4476_2,plain,
    ! [U_18524,U_18523,U_18522,U_18521,U_18520] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18520,tc_Option_Ooption(U_18523)),c_Map_Orestrict__map(U_18520,U_18523,U_18524,U_18522)),U_18521),c_Option_Ooption_ONone(U_18523)) = c_Map_Orestrict__map(U_18520,U_18523,U_18524,U_18522)
        | hBOOL(hAPP(hAPP(c_member(U_18520),U_18521),U_18522)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18520,tc_Option_Ooption(U_18523)),c_Map_Orestrict__map(U_18520,U_18523,U_18524,U_18522)),U_18521),c_Option_Ooption_ONone(U_18523)) = c_Map_Orestrict__map(U_18520,U_18523,U_18524,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18520,tc_HOL_Obool)),U_18522),hAPP(hAPP(c_Set_Oinsert(U_18520),U_18521),c_Orderings_Obot__class_Obot(tc_fun(U_18520,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18520),U_18521),U_18522)) ) ),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

fof(f_4476_3,plain,
    ( ! [U_18534,U_18532,U_18530,U_18528,U_18526] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18526,tc_Option_Ooption(U_18532)),c_Map_Orestrict__map(U_18526,U_18532,U_18534,U_18530)),U_18528),c_Option_Ooption_ONone(U_18532)) = c_Map_Orestrict__map(U_18526,U_18532,U_18534,U_18530)
        | hBOOL(hAPP(hAPP(c_member(U_18526),U_18528),U_18530)) )
    & ! [U_18533,U_18531,U_18529,U_18527,U_18525] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18525,tc_Option_Ooption(U_18531)),c_Map_Orestrict__map(U_18525,U_18531,U_18533,U_18529)),U_18527),c_Option_Ooption_ONone(U_18531)) = c_Map_Orestrict__map(U_18525,U_18531,U_18533,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18525,tc_HOL_Obool)),U_18529),hAPP(hAPP(c_Set_Oinsert(U_18525),U_18527),c_Orderings_Obot__class_Obot(tc_fun(U_18525,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18525),U_18527),U_18529)) ) ),
    inference(miniscope,[status(thm)],[f_4476_2]) ).

cnf(f_4476_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18525,tc_Option_Ooption(U_18531)),c_Map_Orestrict__map(U_18525,U_18531,U_18533,U_18529)),U_18527),c_Option_Ooption_ONone(U_18531)) = c_Map_Orestrict__map(U_18525,U_18531,U_18533,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18525,tc_HOL_Obool)),U_18529),hAPP(hAPP(c_Set_Oinsert(U_18525),U_18527),c_Orderings_Obot__class_Obot(tc_fun(U_18525,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18525),U_18527),U_18529)) ),
    inference(clausify,[status(thm)],[f_4476_3]) ).

cnf(f_4476_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18526,tc_Option_Ooption(U_18532)),c_Map_Orestrict__map(U_18526,U_18532,U_18534,U_18530)),U_18528),c_Option_Ooption_ONone(U_18532)) = c_Map_Orestrict__map(U_18526,U_18532,U_18534,U_18530)
    | hBOOL(hAPP(hAPP(c_member(U_18526),U_18528),U_18530)) ),
    inference(clausify,[status(thm)],[f_4476_3]) ).

fof(f_4477_1,plain,
    ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_lists__Int__eq]) ).

fof(f_4477_2,plain,
    ! [U_18537,U_18536,U_18535] : c_List_Olistsp(U_18535,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18535,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_18535,tc_fun(U_18535,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18535)),U_18536)),hAPP(hAPP(c_COMBC(U_18535,tc_fun(U_18535,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18535)),U_18537))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18535),tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18535))),c_List_Olists(U_18535,U_18536))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18535),tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18535))),c_List_Olists(U_18535,U_18537))),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

cnf(f_4477_3,plain,
    c_List_Olistsp(U_18535,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18535,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_18535,tc_fun(U_18535,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18535)),U_18536)),hAPP(hAPP(c_COMBC(U_18535,tc_fun(U_18535,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18535)),U_18537))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18535),tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18535))),c_List_Olists(U_18535,U_18536))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18535),tc_fun(tc_List_Olist(U_18535),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18535))),c_List_Olists(U_18535,U_18537))),
    inference(clausify,[status(thm)],[f_4477_2]) ).

fof(f_4478_1,plain,
    ! [V_B_2,V_A_2,V_l_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__IntI]) ).

fof(f_4478_2,plain,
    ! [U_18541,U_18540,U_18539,U_18538] :
      ( hBOOL(hAPP(c_List_Olistsp(U_18538,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18538,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_18538,tc_fun(U_18538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18538)),U_18540)),hAPP(hAPP(c_COMBC(U_18538,tc_fun(U_18538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18538)),U_18541))),U_18539))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18538)),U_18539),c_List_Olists(U_18538,U_18541)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18538)),U_18539),c_List_Olists(U_18538,U_18540))) ),
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

cnf(f_4478_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18538,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18538,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_18538,tc_fun(U_18538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18538)),U_18540)),hAPP(hAPP(c_COMBC(U_18538,tc_fun(U_18538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18538)),U_18541))),U_18539))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18538)),U_18539),c_List_Olists(U_18538,U_18541)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18538)),U_18539),c_List_Olists(U_18538,U_18540))) ),
    inference(clausify,[status(thm)],[f_4478_2]) ).

fof(f_4479_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_listsp_ONil]) ).

fof(f_4479_2,plain,
    ! [U_18543,U_18542] : hBOOL(hAPP(c_List_Olistsp(U_18542,U_18543),c_List_Olist_ONil(U_18542))),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

cnf(f_4479_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_18542,U_18543),c_List_Olist_ONil(U_18542))),
    inference(clausify,[status(thm)],[f_4479_2]) ).

fof(f_4480_1,plain,
    ! [V_ys_2,V_xs_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2))
          & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv]) ).

fof(f_4480_2,plain,
    ! [U_18547,U_18546,U_18545,U_18544] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),hAPP(hAPP(c_List_Oappend(U_18544),U_18546),U_18547)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),U_18547))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),U_18546)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),U_18547))
          & hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),U_18546)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18544,U_18545),hAPP(hAPP(c_List_Oappend(U_18544),U_18546),U_18547))) ) ),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ( ! [U_18555,U_18553,U_18551,U_18549] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),hAPP(hAPP(c_List_Oappend(U_18549),U_18553),U_18555)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),U_18555))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),U_18553)) )
    & ! [U_18554,U_18552,U_18550,U_18548] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),U_18554))
          & hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),U_18552)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),hAPP(hAPP(c_List_Oappend(U_18548),U_18552),U_18554))) ) ),
    inference(miniscope,[status(thm)],[f_4480_2]) ).

cnf(f_4480_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),U_18552))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),hAPP(hAPP(c_List_Oappend(U_18548),U_18552),U_18554))) ),
    inference(clausify,[status(thm)],[f_4480_3]) ).

cnf(f_4480_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),U_18554))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18548,U_18550),hAPP(hAPP(c_List_Oappend(U_18548),U_18552),U_18554))) ),
    inference(clausify,[status(thm)],[f_4480_3]) ).

cnf(f_4480_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),hAPP(hAPP(c_List_Oappend(U_18549),U_18553),U_18555)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),U_18555))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18549,U_18551),U_18553)) ),
    inference(clausify,[status(thm)],[f_4480_3]) ).

fof(f_4481_1,plain,
    ! [V_a2_2,V_a1_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2))
        | ~ hBOOL(hAPP(V_A_2,V_a1_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2))
          & hBOOL(hAPP(V_A_2,V_a1_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J]) ).

fof(f_4481_2,plain,
    ! [U_18559,U_18558,U_18557,U_18556] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_18556,U_18557),hAPP(hAPP(c_List_Olist_OCons(U_18556),U_18558),U_18559)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18556,U_18557),U_18559))
        | ~ hBOOL(hAPP(U_18557,U_18558)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_18556,U_18557),U_18559))
          & hBOOL(hAPP(U_18557,U_18558)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18556,U_18557),hAPP(hAPP(c_List_Olist_OCons(U_18556),U_18558),U_18559))) ) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

fof(f_4481_3,plain,
    ( ! [U_18567,U_18565,U_18563,U_18561] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18561,U_18563),hAPP(hAPP(c_List_Olist_OCons(U_18561),U_18565),U_18567)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18561,U_18563),U_18567))
        | ~ hBOOL(hAPP(U_18563,U_18565)) )
    & ! [U_18566,U_18564,U_18562,U_18560] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_18560,U_18562),U_18566))
          & hBOOL(hAPP(U_18562,U_18564)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18560,U_18562),hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18564),U_18566))) ) ),
    inference(miniscope,[status(thm)],[f_4481_2]) ).

cnf(f_4481_4,plain,
    ( hBOOL(hAPP(U_18562,U_18564))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18560,U_18562),hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18564),U_18566))) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

cnf(f_4481_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18560,U_18562),U_18566))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18560,U_18562),hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18564),U_18566))) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

cnf(f_4481_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18561,U_18563),hAPP(hAPP(c_List_Olist_OCons(U_18561),U_18565),U_18567)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18561,U_18563),U_18567))
    | ~ hBOOL(hAPP(U_18563,U_18565)) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

fof(f_4482_1,plain,
    ! [V_xs_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_A_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_A_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__listsp__conv__set]) ).

fof(f_4482_2,plain,
    ! [U_18572,U_18571,U_18570] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_18570,U_18571),U_18572))
        | ? [U_18569] :
            ( ~ hBOOL(hAPP(U_18571,U_18569))
            & hBOOL(hAPP(hAPP(c_member(U_18570),U_18569),hAPP(c_List_Oset(U_18570),U_18572))) ) )
      & ( ! [U_18568] :
            ( hBOOL(hAPP(U_18571,U_18568))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18570),U_18568),hAPP(c_List_Oset(U_18570),U_18572))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18570,U_18571),U_18572)) ) ),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

fof(f_4482_3,plain,
    ( ! [U_18578,U_18576,U_18574] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18574,U_18576),U_18578))
        | ? [U_18569] :
            ( ~ hBOOL(hAPP(U_18576,U_18569))
            & hBOOL(hAPP(hAPP(c_member(U_18574),U_18569),hAPP(c_List_Oset(U_18574),U_18578))) ) )
    & ! [U_18577,U_18575,U_18573] :
        ( ! [U_18568] :
            ( hBOOL(hAPP(U_18575,U_18568))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18573),U_18568),hAPP(c_List_Oset(U_18573),U_18577))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18573,U_18575),U_18577)) ) ),
    inference(miniscope,[status(thm)],[f_4482_2]) ).

fof(f_4482_4,plain,
    ( ! [U_18578,U_18576,U_18574] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18574,U_18576),U_18578))
        | ( ~ hBOOL(hAPP(U_18576,sK463(U_18578,U_18576,U_18574)))
          & hBOOL(hAPP(hAPP(c_member(U_18574),sK463(U_18578,U_18576,U_18574)),hAPP(c_List_Oset(U_18574),U_18578))) ) )
    & ! [U_18577,U_18575,U_18573] :
        ( ! [U_18568] :
            ( hBOOL(hAPP(U_18575,U_18568))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18573),U_18568),hAPP(c_List_Oset(U_18573),U_18577))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18573,U_18575),U_18577)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18569,sK463(U_18578,U_18576,U_18574))],[f_4482_3]) ).

cnf(f_4482_5,plain,
    ( hBOOL(hAPP(U_18575,U_18568))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18573),U_18568),hAPP(c_List_Oset(U_18573),U_18577)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18573,U_18575),U_18577)) ),
    inference(clausify,[status(thm)],[f_4482_4]) ).

cnf(f_4482_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18574),sK463(U_18578,U_18576,U_18574)),hAPP(c_List_Oset(U_18574),U_18578)))
    | hBOOL(hAPP(c_List_Olistsp(U_18574,U_18576),U_18578)) ),
    inference(clausify,[status(thm)],[f_4482_4]) ).

cnf(f_4482_7,plain,
    ( ~ hBOOL(hAPP(U_18576,sK463(U_18578,U_18576,U_18574)))
    | hBOOL(hAPP(c_List_Olistsp(U_18574,U_18576),U_18578)) ),
    inference(clausify,[status(thm)],[f_4482_4]) ).

fof(f_4483_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2))
          & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq]) ).

fof(f_4483_2,plain,
    ! [U_18582,U_18581,U_18580,U_18579] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_18579,hAPP(hAPP(c_COMBS(U_18579,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18579),c_fconj),U_18580)),U_18581)),U_18582))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18579,U_18581),U_18582))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18579,U_18580),U_18582)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_18579,U_18581),U_18582))
          & hBOOL(hAPP(c_List_Olistsp(U_18579,U_18580),U_18582)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18579,hAPP(hAPP(c_COMBS(U_18579,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18579),c_fconj),U_18580)),U_18581)),U_18582)) ) ),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

fof(f_4483_3,plain,
    ( ! [U_18590,U_18588,U_18586,U_18584] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18584,hAPP(hAPP(c_COMBS(U_18584,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18584),c_fconj),U_18586)),U_18588)),U_18590))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18584,U_18588),U_18590))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18584,U_18586),U_18590)) )
    & ! [U_18589,U_18587,U_18585,U_18583] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_18583,U_18587),U_18589))
          & hBOOL(hAPP(c_List_Olistsp(U_18583,U_18585),U_18589)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18583,hAPP(hAPP(c_COMBS(U_18583,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18583),c_fconj),U_18585)),U_18587)),U_18589)) ) ),
    inference(miniscope,[status(thm)],[f_4483_2]) ).

cnf(f_4483_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18583,U_18585),U_18589))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18583,hAPP(hAPP(c_COMBS(U_18583,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18583),c_fconj),U_18585)),U_18587)),U_18589)) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

cnf(f_4483_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18583,U_18587),U_18589))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18583,hAPP(hAPP(c_COMBS(U_18583,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18583),c_fconj),U_18585)),U_18587)),U_18589)) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

cnf(f_4483_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18584,hAPP(hAPP(c_COMBS(U_18584,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18584),c_fconj),U_18586)),U_18588)),U_18590))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18584,U_18588),U_18590))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18584,U_18586),U_18590)) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

fof(f_4484_1,plain,
    ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_listsp__inf__eq]) ).

fof(f_4484_2,plain,
    ! [U_18593,U_18592,U_18591] : c_List_Olistsp(U_18591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18591,tc_HOL_Obool)),U_18592),U_18593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_18591),tc_HOL_Obool)),c_List_Olistsp(U_18591,U_18592)),c_List_Olistsp(U_18591,U_18593)),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

cnf(f_4484_3,plain,
    c_List_Olistsp(U_18591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18591,tc_HOL_Obool)),U_18592),U_18593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_18591),tc_HOL_Obool)),c_List_Olistsp(U_18591,U_18592)),c_List_Olistsp(U_18591,U_18593)),
    inference(clausify,[status(thm)],[f_4484_2]) ).

fof(f_4485_1,plain,
    ! [V_B_2,V_l_2,V_A_2,T_a] :
      ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2))
      | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
      | ~ hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__infI]) ).

fof(f_4485_2,plain,
    ! [U_18597,U_18596,U_18595,U_18594] :
      ( hBOOL(hAPP(c_List_Olistsp(U_18594,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18594,tc_HOL_Obool)),U_18595),U_18597)),U_18596))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_18594,U_18597),U_18596))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_18594,U_18595),U_18596)) ),
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

cnf(f_4485_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18594,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18594,tc_HOL_Obool)),U_18595),U_18597)),U_18596))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18594,U_18597),U_18596))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18594,U_18595),U_18596)) ),
    inference(clausify,[status(thm)],[f_4485_2]) ).

fof(f_4486_1,plain,
    ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(f_4486_2,plain,
    ! [U_18599,U_18598] : hBOOL(hAPP(c_List_Olistsp(U_18598,U_18599),c_List_Olist_ONil(U_18598))),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

cnf(f_4486_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_18598,U_18599),c_List_Olist_ONil(U_18598))),
    inference(clausify,[status(thm)],[f_4486_2]) ).

fof(f_4487_1,plain,
    ! [V_B_2,V_A_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__mono]) ).

fof(f_4487_2,plain,
    ! [U_18602,U_18601,U_18600] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_18600),tc_HOL_Obool)),c_List_Olistsp(U_18600,U_18601)),c_List_Olistsp(U_18600,U_18602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18600,tc_HOL_Obool)),U_18601),U_18602)) ),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

cnf(f_4487_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_18600),tc_HOL_Obool)),c_List_Olistsp(U_18600,U_18601)),c_List_Olistsp(U_18600,U_18602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18600,tc_HOL_Obool)),U_18601),U_18602)) ),
    inference(clausify,[status(thm)],[f_4487_2]) ).

fof(f_4488_1,plain,
    ! [V_x_2,V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq]) ).

fof(f_4488_2,plain,
    ! [U_18605,U_18604,U_18603] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_18603,hAPP(hAPP(c_COMBC(U_18603,tc_fun(U_18603,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18603)),U_18604)),U_18605))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18603)),U_18605),c_List_Olists(U_18603,U_18604))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18603)),U_18605),c_List_Olists(U_18603,U_18604)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18603,hAPP(hAPP(c_COMBC(U_18603,tc_fun(U_18603,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18603)),U_18604)),U_18605)) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18611,U_18609,U_18607] :
        ( hBOOL(hAPP(c_List_Olistsp(U_18607,hAPP(hAPP(c_COMBC(U_18607,tc_fun(U_18607,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18607)),U_18609)),U_18611))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18607)),U_18611),c_List_Olists(U_18607,U_18609))) )
    & ! [U_18610,U_18608,U_18606] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18606)),U_18610),c_List_Olists(U_18606,U_18608)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_18606,hAPP(hAPP(c_COMBC(U_18606,tc_fun(U_18606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18606)),U_18608)),U_18610)) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

cnf(f_4488_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18606)),U_18610),c_List_Olists(U_18606,U_18608)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_18606,hAPP(hAPP(c_COMBC(U_18606,tc_fun(U_18606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18606)),U_18608)),U_18610)) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_18607,hAPP(hAPP(c_COMBC(U_18607,tc_fun(U_18607,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18607)),U_18609)),U_18611))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18607)),U_18611),c_List_Olists(U_18607,U_18609))) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

fof(f_4489_1,plain,
    ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_]) ).

fof(f_4489_2,plain,
    ! [U_18614,U_18613,U_18612] : c_Smallcheck_Oorelse(U_18612,U_18613,U_18614) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_18612),U_18612,U_18614,c_Option_Ooption_OSome(U_18612)),U_18613),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

cnf(f_4489_3,plain,
    c_Smallcheck_Oorelse(U_18612,U_18613,U_18614) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_18612),U_18612,U_18614,c_Option_Ooption_OSome(U_18612)),U_18613),
    inference(clausify,[status(thm)],[f_4489_2]) ).

fof(f_4490_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_product_Osimps_I2_J]) ).

fof(f_4490_2,plain,
    ! [U_18619,U_18618,U_18617,U_18616,U_18615] : c_Enum_Oproduct(U_18615,U_18616,hAPP(hAPP(c_List_Olist_OCons(U_18615),U_18617),U_18618),U_18619) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18615,U_18616)),hAPP(hAPP(c_List_Omap(U_18616,tc_prod(U_18615,U_18616)),hAPP(c_Product__Type_OPair(U_18615,U_18616),U_18617)),U_18619)),c_Enum_Oproduct(U_18615,U_18616,U_18618,U_18619)),
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

cnf(f_4490_3,plain,
    c_Enum_Oproduct(U_18615,U_18616,hAPP(hAPP(c_List_Olist_OCons(U_18615),U_18617),U_18618),U_18619) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18615,U_18616)),hAPP(hAPP(c_List_Omap(U_18616,tc_prod(U_18615,U_18616)),hAPP(c_Product__Type_OPair(U_18615,U_18616),U_18617)),U_18619)),c_Enum_Oproduct(U_18615,U_18616,U_18618,U_18619)),
    inference(clausify,[status(thm)],[f_4490_2]) ).

fof(f_4491_1,plain,
    ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(f_4491_2,plain,
    ! [U_18622,U_18621,U_18620] : c_Enum_Oproduct(U_18620,U_18621,c_List_Olist_ONil(U_18620),U_18622) = c_List_Olist_ONil(tc_prod(U_18620,U_18621)),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

cnf(f_4491_3,plain,
    c_Enum_Oproduct(U_18620,U_18621,c_List_Olist_ONil(U_18620),U_18622) = c_List_Olist_ONil(tc_prod(U_18620,U_18621)),
    inference(clausify,[status(thm)],[f_4491_2]) ).

fof(f_4492_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__product]) ).

fof(f_4492_2,plain,
    ! [U_18626,U_18625,U_18624,U_18623] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_18623,U_18625)),c_Enum_Oproduct(U_18623,U_18625,U_18624,U_18626)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18625),U_18626))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18623),U_18624)) ),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

cnf(f_4492_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_18623,U_18625)),c_Enum_Oproduct(U_18623,U_18625,U_18624,U_18626)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18625),U_18626))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18623),U_18624)) ),
    inference(clausify,[status(thm)],[f_4492_2]) ).

fof(f_4493_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))),
    inference(fof_nnf,[status(thm)],[fact_product__list__set]) ).

fof(f_4493_2,plain,
    ! [U_18630,U_18629,U_18628,U_18627] : hAPP(c_List_Oset(tc_prod(U_18627,U_18628)),c_Enum_Oproduct(U_18627,U_18628,U_18629,U_18630)) = hAPP(hAPP(c_Product__Type_OSigma(U_18627,U_18628),hAPP(c_List_Oset(U_18627),U_18629)),hAPP(c_COMBK(tc_fun(U_18628,tc_HOL_Obool),U_18627),hAPP(c_List_Oset(U_18628),U_18630))),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

cnf(f_4493_3,plain,
    hAPP(c_List_Oset(tc_prod(U_18627,U_18628)),c_Enum_Oproduct(U_18627,U_18628,U_18629,U_18630)) = hAPP(hAPP(c_Product__Type_OSigma(U_18627,U_18628),hAPP(c_List_Oset(U_18627),U_18629)),hAPP(c_COMBK(tc_fun(U_18628,tc_HOL_Obool),U_18627),hAPP(c_List_Oset(U_18628),U_18630))),
    inference(clausify,[status(thm)],[f_4493_2]) ).

fof(f_4494_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_sublists__powset]) ).

fof(f_4494_2,plain,
    ! [U_18632,U_18631] : hAPP(c_Set_Oimage(tc_List_Olist(U_18631),tc_fun(U_18631,tc_HOL_Obool),c_List_Oset(U_18631)),hAPP(c_List_Oset(tc_List_Olist(U_18631)),c_Enum_Osublists(U_18631,U_18632))) = hAPP(c_Set_OPow(U_18631),hAPP(c_List_Oset(U_18631),U_18632)),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

cnf(f_4494_3,plain,
    hAPP(c_Set_Oimage(tc_List_Olist(U_18631),tc_fun(U_18631,tc_HOL_Obool),c_List_Oset(U_18631)),hAPP(c_List_Oset(tc_List_Olist(U_18631)),c_Enum_Osublists(U_18631,U_18632))) = hAPP(c_Set_OPow(U_18631),hAPP(c_List_Oset(U_18631),U_18632)),
    inference(clausify,[status(thm)],[f_4494_2]) ).

fof(f_4495_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = 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_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_length__sublists]) ).

fof(f_4495_2,plain,
    ! [U_18634,U_18633] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18633))),c_Enum_Osublists(U_18633,U_18634)) = 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_Nat_Osize__class_Osize(tc_List_Olist(U_18633)),U_18634)),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

cnf(f_4495_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18633))),c_Enum_Osublists(U_18633,U_18634)) = 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_Nat_Osize__class_Osize(tc_List_Olist(U_18633)),U_18634)),
    inference(clausify,[status(thm)],[f_4495_2]) ).

fof(f_4496_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_4496_2,plain,
    ! [U_18635] : c_Enum_Osublists(U_18635,c_List_Olist_ONil(U_18635)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18635)),c_List_Olist_ONil(U_18635)),c_List_Olist_ONil(tc_List_Olist(U_18635))),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

cnf(f_4496_3,plain,
    c_Enum_Osublists(U_18635,c_List_Olist_ONil(U_18635)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18635)),c_List_Olist_ONil(U_18635)),c_List_Olist_ONil(tc_List_Olist(U_18635))),
    inference(clausify,[status(thm)],[f_4496_2]) ).

fof(f_4497_1,plain,
    ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))),
    inference(fof_nnf,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(f_4497_2,plain,
    ! [U_18638,U_18637,U_18636] : c_Enum_Osublists(U_18636,hAPP(hAPP(c_List_Olist_OCons(U_18636),U_18637),U_18638)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),c_Enum_Osublists(U_18636,U_18638)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_18636)),tc_fun(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),tc_List_Olist(tc_List_Olist(U_18636))),c_List_Oappend(tc_List_Olist(U_18636))),hAPP(c_List_Omap(tc_List_Olist(U_18636),tc_List_Olist(U_18636)),hAPP(c_List_Olist_OCons(U_18636),U_18637)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_18636))))),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

cnf(f_4497_3,plain,
    c_Enum_Osublists(U_18636,hAPP(hAPP(c_List_Olist_OCons(U_18636),U_18637),U_18638)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),c_Enum_Osublists(U_18636,U_18638)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_18636)),tc_fun(tc_List_Olist(tc_List_Olist(U_18636)),tc_List_Olist(tc_List_Olist(U_18636))),tc_List_Olist(tc_List_Olist(U_18636))),c_List_Oappend(tc_List_Olist(U_18636))),hAPP(c_List_Omap(tc_List_Olist(U_18636),tc_List_Olist(U_18636)),hAPP(c_List_Olist_OCons(U_18636),U_18637)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_18636))))),
    inference(clausify,[status(thm)],[f_4497_2]) ).

fof(f_4498_1,plain,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists]) ).

fof(f_4498_2,plain,
    ! [U_18640,U_18639] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_18639,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18639),tc_fun(U_18639,tc_HOL_Obool)),c_List_Oset(U_18639)),c_Enum_Osublists(U_18639,U_18640))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18639),U_18640)) ),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

cnf(f_4498_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_18639,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18639),tc_fun(U_18639,tc_HOL_Obool)),c_List_Oset(U_18639)),c_Enum_Osublists(U_18639,U_18640))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18639),U_18640)) ),
    inference(clausify,[status(thm)],[f_4498_2]) ).

fof(f_4499_1,plain,
    ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__n__lists]) ).

fof(f_4499_2,plain,
    ! [U_18643,U_18642,U_18641] : hAPP(c_List_Oset(tc_List_Olist(U_18641)),c_Enum_On__lists(U_18641,U_18642,U_18643)) = hAPP(c_Set_OCollect(tc_List_Olist(U_18641)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18641),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_18641)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18641),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_18641)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18641)))),U_18642))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18641),tc_fun(U_18641,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18641,tc_HOL_Obool),tc_fun(tc_fun(U_18641,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18641)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18641,tc_HOL_Obool))),c_List_Oset(U_18641))),hAPP(c_List_Oset(U_18641),U_18643)))),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

cnf(f_4499_3,plain,
    hAPP(c_List_Oset(tc_List_Olist(U_18641)),c_Enum_On__lists(U_18641,U_18642,U_18643)) = hAPP(c_Set_OCollect(tc_List_Olist(U_18641)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18641),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_18641)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18641),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_18641)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18641)))),U_18642))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18641),tc_fun(U_18641,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18641,tc_HOL_Obool),tc_fun(tc_fun(U_18641,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18641)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18641,tc_HOL_Obool))),c_List_Oset(U_18641))),hAPP(c_List_Oset(U_18641),U_18643)))),
    inference(clausify,[status(thm)],[f_4499_2]) ).

fof(f_4500_1,plain,
    ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2),
    inference(fof_nnf,[status(thm)],[fact_enum__the__def]) ).

fof(f_4500_2,plain,
    ! [U_18645,U_18644] : c_Enum_Oenum__the(U_18644,U_18645) = c_HOL_OThe(U_18644,U_18645),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

cnf(f_4500_3,plain,
    c_Enum_Oenum__the(U_18644,U_18645) = c_HOL_OThe(U_18644,U_18645),
    inference(clausify,[status(thm)],[f_4500_2]) ).

fof(f_4501_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_4501_2,plain,
    ! [U_18648,U_18647,U_18646] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18646)),c_Enum_On__lists(U_18646,U_18648,U_18647)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18646),U_18647)) ),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

cnf(f_4501_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18646)),c_Enum_On__lists(U_18646,U_18648,U_18647)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18646),U_18647)) ),
    inference(clausify,[status(thm)],[f_4501_2]) ).

fof(f_4502_1,plain,
    ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = 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_n__lists_Osimps_I1_J]) ).

fof(f_4502_2,plain,
    ! [U_18650,U_18649] : c_Enum_On__lists(U_18649,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18650) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18649)),c_List_Olist_ONil(U_18649)),c_List_Olist_ONil(tc_List_Olist(U_18649))),
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

cnf(f_4502_3,plain,
    c_Enum_On__lists(U_18649,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18650) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18649)),c_List_Olist_ONil(U_18649)),c_List_Olist_ONil(tc_List_Olist(U_18649))),
    inference(clausify,[status(thm)],[f_4502_2]) ).

fof(f_4503_1,plain,
    ! [T_a,V_n] :
      ( ( c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Enum_On__lists(T_a,V_n,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)))
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_n__lists__Nil]) ).

fof(f_4503_2,plain,
    ! [U_18652,U_18651] :
      ( ( c_Enum_On__lists(U_18652,U_18651,c_List_Olist_ONil(U_18652)) = c_List_Olist_ONil(tc_List_Olist(U_18652))
        | U_18651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Enum_On__lists(U_18652,U_18651,c_List_Olist_ONil(U_18652)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18652)),c_List_Olist_ONil(U_18652)),c_List_Olist_ONil(tc_List_Olist(U_18652)))
        | U_18651 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

fof(f_4503_3,plain,
    ( ! [U_18656,U_18654] :
        ( c_Enum_On__lists(U_18656,U_18654,c_List_Olist_ONil(U_18656)) = c_List_Olist_ONil(tc_List_Olist(U_18656))
        | U_18654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18655,U_18653] :
        ( c_Enum_On__lists(U_18655,U_18653,c_List_Olist_ONil(U_18655)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18655)),c_List_Olist_ONil(U_18655)),c_List_Olist_ONil(tc_List_Olist(U_18655)))
        | U_18653 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4503_2]) ).

cnf(f_4503_4,plain,
    ( c_Enum_On__lists(U_18655,U_18653,c_List_Olist_ONil(U_18655)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_18655)),c_List_Olist_ONil(U_18655)),c_List_Olist_ONil(tc_List_Olist(U_18655)))
    | U_18653 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4503_3]) ).

cnf(f_4503_5,plain,
    ( c_Enum_On__lists(U_18656,U_18654,c_List_Olist_ONil(U_18656)) = c_List_Olist_ONil(tc_List_Olist(U_18656))
    | U_18654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4503_3]) ).

fof(f_4504_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(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_4504_2,plain,
    ! [U_18659,U_18658,U_18657] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18657))),c_Enum_On__lists(U_18657,U_18658,U_18659)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18657)),U_18659)),U_18658),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

cnf(f_4504_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18657))),c_Enum_On__lists(U_18657,U_18658,U_18659)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18657)),U_18659)),U_18658),
    inference(clausify,[status(thm)],[f_4504_2]) ).

fof(f_4505_1,plain,
    ! [V_xs_2,V_n_2,V_ys_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem]) ).

fof(f_4505_2,plain,
    ! [U_18663,U_18662,U_18661,U_18660] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18660)),U_18661) = U_18662
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18660)),U_18661),hAPP(c_List_Oset(tc_List_Olist(U_18660)),c_Enum_On__lists(U_18660,U_18662,U_18663)))) ),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

cnf(f_4505_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18660)),U_18661) = U_18662
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18660)),U_18661),hAPP(c_List_Oset(tc_List_Olist(U_18660)),c_Enum_On__lists(U_18660,U_18662,U_18663)))) ),
    inference(clausify,[status(thm)],[f_4505_2]) ).

fof(f_4506_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_4506_2,plain,
    ! [U_18665,U_18664] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_18664,U_18665) = c_Smallcheck_Ofull__small_H(U_18664,hAPP(c_Code__Numeral_Oint__of,U_18665),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_18665))),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

cnf(f_4506_3,plain,
    c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_18664,U_18665) = c_Smallcheck_Ofull__small_H(U_18664,hAPP(c_Code__Numeral_Oint__of,U_18665),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_18665))),
    inference(clausify,[status(thm)],[f_4506_2]) ).

fof(f_4507_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_4507_2,plain,
    ! [U_18668,U_18667,U_18666] :
      ( ( c_Smallcheck_Osmall_H(U_18668,U_18666,U_18667) = 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_18668,U_18666,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18667),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_18668,U_18667))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18666),U_18667)) )
      & ( c_Smallcheck_Osmall_H(U_18668,U_18666,U_18667) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18666),U_18667)) ) ),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

fof(f_4507_3,plain,
    ( ! [U_18674,U_18672,U_18670] :
        ( c_Smallcheck_Osmall_H(U_18674,U_18670,U_18672) = 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_18674,U_18670,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18672),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_18674,U_18672))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18670),U_18672)) )
    & ! [U_18673,U_18671,U_18669] :
        ( c_Smallcheck_Osmall_H(U_18673,U_18669,U_18671) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18669),U_18671)) ) ),
    inference(miniscope,[status(thm)],[f_4507_2]) ).

cnf(f_4507_4,plain,
    ( c_Smallcheck_Osmall_H(U_18673,U_18669,U_18671) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18669),U_18671)) ),
    inference(clausify,[status(thm)],[f_4507_3]) ).

cnf(f_4507_5,plain,
    ( c_Smallcheck_Osmall_H(U_18674,U_18670,U_18672) = 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_18674,U_18670,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18672),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_18674,U_18672))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18670),U_18672)) ),
    inference(clausify,[status(thm)],[f_4507_3]) ).

fof(f_4508_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_4508_2,plain,
    ! [U_18677,U_18676,U_18675] :
      ( ( ( c_Smallcheck_Osmall_H(U_18675,U_18676,U_18677) = 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_18675,U_18676,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18677),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_18675,U_18677))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18676),U_18677)) )
        & ( c_Smallcheck_Osmall_H(U_18675,U_18676,U_18677) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18676),U_18677)) ) )
      | ~ 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_18675),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18676),U_18677)))) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

cnf(f_4508_3,plain,
    ( c_Smallcheck_Osmall_H(U_18675,U_18676,U_18677) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18676),U_18677))
    | ~ 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_18675),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18676),U_18677)))) ),
    inference(clausify,[status(thm)],[f_4508_2]) ).

cnf(f_4508_4,plain,
    ( c_Smallcheck_Osmall_H(U_18675,U_18676,U_18677) = 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_18675,U_18676,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18677),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_18675,U_18677))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18676),U_18677))
    | ~ 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_18675),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18676),U_18677)))) ),
    inference(clausify,[status(thm)],[f_4508_2]) ).

fof(f_4509_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_4509_2,plain,
    ! [U_18679,U_18678] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_18678),U_18679) = c_Smallcheck_Osmall_H(U_18678,hAPP(c_Code__Numeral_Oint__of,U_18679),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_18679))),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

cnf(f_4509_3,plain,
    hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_18678),U_18679) = c_Smallcheck_Osmall_H(U_18678,hAPP(c_Code__Numeral_Oint__of,U_18679),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_18679))),
    inference(clausify,[status(thm)],[f_4509_2]) ).

fof(f_4510_1,plain,
    ! [V_d_2,V_f_2,T_a,T_b] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,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_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2)
      | ~ class_Smallcheck_Osmall(T_a)
      | ~ class_Smallcheck_Osmall(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_small__prod__def]) ).

fof(f_4510_2,plain,
    ! [U_18683,U_18682,U_18681,U_18680] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_18681,U_18680)),U_18682),U_18683) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_18681),hAPP(hAPP(c_COMBC(U_18681,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_18680,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_18681),c_Smallcheck_Osmall__class_Osmall(U_18680)),hAPP(hAPP(c_COMBB(tc_fun(U_18680,tc_prod(U_18681,U_18680)),tc_fun(U_18680,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_18681),hAPP(c_COMBB(tc_prod(U_18681,U_18680),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_18680),U_18682)),c_Product__Type_OPair(U_18681,U_18680)))),U_18683)),U_18683)
      | ~ class_Smallcheck_Osmall(U_18681)
      | ~ class_Smallcheck_Osmall(U_18680) ),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

cnf(f_4510_3,plain,
    ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_18681,U_18680)),U_18682),U_18683) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_18681),hAPP(hAPP(c_COMBC(U_18681,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_18680,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_18681),c_Smallcheck_Osmall__class_Osmall(U_18680)),hAPP(hAPP(c_COMBB(tc_fun(U_18680,tc_prod(U_18681,U_18680)),tc_fun(U_18680,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_18681),hAPP(c_COMBB(tc_prod(U_18681,U_18680),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_18680),U_18682)),c_Product__Type_OPair(U_18681,U_18680)))),U_18683)),U_18683)
    | ~ class_Smallcheck_Osmall(U_18681)
    | ~ class_Smallcheck_Osmall(U_18680) ),
    inference(clausify,[status(thm)],[f_4510_2]) ).

fof(f_4511_1,plain,
    ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2))
      | ? [B_f,B_d,B_i] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i))
          & ( hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(B_f,B_i) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_small_H_Opinduct]) ).

fof(f_4511_2,plain,
    ! [U_18690,U_18689,U_18688,U_18687] :
      ( hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
      | ? [U_18686,U_18685,U_18684] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_18690,U_18686),U_18685),U_18684))
          & ( hBOOL(hAPP(hAPP(hAPP(U_18690,U_18686),U_18685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(U_18686,U_18684) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18685),U_18684)) )
          & 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_18686),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18685),U_18684)))) )
      | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

fof(f_4511_3,plain,
    ! [U_18690,U_18689,U_18688,U_18687] :
      ( hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
      | ? [U_18685,U_18684] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),U_18685),U_18684))
          & ( hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),U_18685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK464(U_18690,U_18689,U_18688,U_18687),U_18684) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18685),U_18684)) )
          & 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)),sK464(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18685),U_18684)))) )
      | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18686,sK464(U_18690,U_18689,U_18688,U_18687))],[f_4511_2]) ).

fof(f_4511_4,plain,
    ! [U_18690,U_18689,U_18688,U_18687] :
      ( hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
      | ? [U_18684] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),U_18684))
          & ( hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18684),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK464(U_18690,U_18689,U_18688,U_18687),U_18684) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),U_18684)) )
          & 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)),sK464(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),U_18684)))) )
      | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18685,sK465(U_18690,U_18689,U_18688,U_18687))],[f_4511_3]) ).

fof(f_4511_5,plain,
    ! [U_18690,U_18689,U_18688,U_18687] :
      ( hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687)))
        & ( hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK466(U_18690,U_18689,U_18688,U_18687)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hAPP(sK464(U_18690,U_18689,U_18688,U_18687),sK466(U_18690,U_18689,U_18688,U_18687)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687))) )
        & 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)),sK464(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687))))) )
      | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18684,sK466(U_18690,U_18689,U_18688,U_18687))],[f_4511_4]) ).

cnf(f_4511_6,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)),sK464(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687)))))
    | hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
    | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(clausify,[status(thm)],[f_4511_5]) ).

cnf(f_4511_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK466(U_18690,U_18689,U_18688,U_18687)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hAPP(sK464(U_18690,U_18689,U_18688,U_18687),sK466(U_18690,U_18689,U_18688,U_18687)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687)))
    | hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
    | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(clausify,[status(thm)],[f_4511_5]) ).

cnf(f_4511_8,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_18690,sK464(U_18690,U_18689,U_18688,U_18687)),sK465(U_18690,U_18689,U_18688,U_18687)),sK466(U_18690,U_18689,U_18688,U_18687)))
    | hBOOL(hAPP(hAPP(hAPP(U_18690,U_18687),U_18688),U_18689))
    | ~ 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_18687),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_18688),U_18689)))) ),
    inference(clausify,[status(thm)],[f_4511_5]) ).

fof(f_4512_1,plain,
    ! [V_ys_2,V_xs_2,T_a,T_b] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) != hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__enum__inject]) ).

fof(f_4512_2,plain,
    ! [U_18694,U_18693,U_18692,U_18691] :
      ( U_18693 = U_18694
      | hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18692),U_18692,U_18691,c_Option_Othe(U_18692)),hAPP(c_Map_Omap__of(U_18691,U_18692),hAPP(hAPP(c_List_Ozip(U_18691,U_18692),c_Enum_Oenum__class_Oenum(U_18691)),U_18693))) != hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18692),U_18692,U_18691,c_Option_Othe(U_18692)),hAPP(c_Map_Omap__of(U_18691,U_18692),hAPP(hAPP(c_List_Ozip(U_18691,U_18692),c_Enum_Oenum__class_Oenum(U_18691)),U_18694)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18692)),U_18694) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18691)),c_Enum_Oenum__class_Oenum(U_18691))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18692)),U_18693) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18691)),c_Enum_Oenum__class_Oenum(U_18691))
      | ~ class_Enum_Oenum(U_18692)
      | ~ class_Enum_Oenum(U_18691) ),
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

cnf(f_4512_3,plain,
    ( U_18693 = U_18694
    | hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18692),U_18692,U_18691,c_Option_Othe(U_18692)),hAPP(c_Map_Omap__of(U_18691,U_18692),hAPP(hAPP(c_List_Ozip(U_18691,U_18692),c_Enum_Oenum__class_Oenum(U_18691)),U_18693))) != hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_18692),U_18692,U_18691,c_Option_Othe(U_18692)),hAPP(c_Map_Omap__of(U_18691,U_18692),hAPP(hAPP(c_List_Ozip(U_18691,U_18692),c_Enum_Oenum__class_Oenum(U_18691)),U_18694)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18692)),U_18694) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18691)),c_Enum_Oenum__class_Oenum(U_18691))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18692)),U_18693) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18691)),c_Enum_Oenum__class_Oenum(U_18691))
    | ~ class_Enum_Oenum(U_18692)
    | ~ class_Enum_Oenum(U_18691) ),
    inference(clausify,[status(thm)],[f_4512_2]) ).

fof(f_4513_1,plain,
    ! [T_b,T_a] :
      ( c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b))
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__prod__def]) ).

fof(f_4513_2,plain,
    ! [U_18696,U_18695] :
      ( c_Enum_Oenum__class_Oenum(tc_prod(U_18695,U_18696)) = c_Enum_Oproduct(U_18695,U_18696,c_Enum_Oenum__class_Oenum(U_18695),c_Enum_Oenum__class_Oenum(U_18696))
      | ~ class_Enum_Oenum(U_18696)
      | ~ class_Enum_Oenum(U_18695) ),
    inference(variable_rename,[status(thm)],[f_4513_1]) ).

cnf(f_4513_3,plain,
    ( c_Enum_Oenum__class_Oenum(tc_prod(U_18695,U_18696)) = c_Enum_Oproduct(U_18695,U_18696,c_Enum_Oenum__class_Oenum(U_18695),c_Enum_Oenum__class_Oenum(U_18696))
    | ~ class_Enum_Oenum(U_18696)
    | ~ class_Enum_Oenum(U_18695) ),
    inference(clausify,[status(thm)],[f_4513_2]) ).

fof(f_4514_1,plain,
    ! [T_a] :
      ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_UNIV__enum]) ).

fof(f_4514_2,plain,
    ! [U_18697] :
      ( c_Orderings_Otop__class_Otop(tc_fun(U_18697,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18697),c_Enum_Oenum__class_Oenum(U_18697))
      | ~ class_Enum_Oenum(U_18697) ),
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

cnf(f_4514_3,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(U_18697,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18697),c_Enum_Oenum__class_Oenum(U_18697))
    | ~ class_Enum_Oenum(U_18697) ),
    inference(clausify,[status(thm)],[f_4514_2]) ).

fof(f_4515_1,plain,
    ! [T_a] :
      ( hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__UNIV]) ).

fof(f_4515_2,plain,
    ! [U_18698] :
      ( hAPP(c_List_Oset(U_18698),c_Enum_Oenum__class_Oenum(U_18698)) = c_Orderings_Otop__class_Otop(tc_fun(U_18698,tc_HOL_Obool))
      | ~ class_Enum_Oenum(U_18698) ),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

cnf(f_4515_3,plain,
    ( hAPP(c_List_Oset(U_18698),c_Enum_Oenum__class_Oenum(U_18698)) = c_Orderings_Otop__class_Otop(tc_fun(U_18698,tc_HOL_Obool))
    | ~ class_Enum_Oenum(U_18698) ),
    inference(clausify,[status(thm)],[f_4515_2]) ).

fof(f_4516_1,plain,
    ! [V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_in__enum]) ).

fof(f_4516_2,plain,
    ! [U_18700,U_18699] :
      ( hBOOL(hAPP(hAPP(c_member(U_18699),U_18700),hAPP(c_List_Oset(U_18699),c_Enum_Oenum__class_Oenum(U_18699))))
      | ~ class_Enum_Oenum(U_18699) ),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

cnf(f_4516_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18699),U_18700),hAPP(c_List_Oset(U_18699),c_Enum_Oenum__class_Oenum(U_18699))))
    | ~ class_Enum_Oenum(U_18699) ),
    inference(clausify,[status(thm)],[f_4516_2]) ).

fof(f_4517_1,plain,
    ! [T_a] :
      ( c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a)))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__option__def]) ).

fof(f_4517_2,plain,
    ! [U_18701] :
      ( c_Enum_Oenum__class_Oenum(tc_Option_Ooption(U_18701)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(U_18701)),c_Option_Ooption_ONone(U_18701)),hAPP(hAPP(c_List_Omap(U_18701,tc_Option_Ooption(U_18701)),c_Option_Ooption_OSome(U_18701)),c_Enum_Oenum__class_Oenum(U_18701)))
      | ~ class_Enum_Oenum(U_18701) ),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

cnf(f_4517_3,plain,
    ( c_Enum_Oenum__class_Oenum(tc_Option_Ooption(U_18701)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(U_18701)),c_Option_Ooption_ONone(U_18701)),hAPP(hAPP(c_List_Omap(U_18701,tc_Option_Ooption(U_18701)),c_Option_Ooption_OSome(U_18701)),c_Enum_Oenum__class_Oenum(U_18701)))
    | ~ class_Enum_Oenum(U_18701) ),
    inference(clausify,[status(thm)],[f_4517_2]) ).

fof(f_4518_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a)))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__distinct]) ).

fof(f_4518_2,plain,
    ! [U_18702] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18702),c_Enum_Oenum__class_Oenum(U_18702)))
      | ~ class_Enum_Oenum(U_18702) ),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

cnf(f_4518_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18702),c_Enum_Oenum__class_Oenum(U_18702)))
    | ~ class_Enum_Oenum(U_18702) ),
    inference(clausify,[status(thm)],[f_4518_2]) ).

fof(f_4519_1,plain,
    ! [T_b,T_a] :
      ( c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b)))
      | ~ class_Enum_Oenum(T_b)
      | ~ class_HOL_Oequal(T_a)
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__fun__code]) ).

fof(f_4519_2,plain,
    ! [U_18704,U_18703] :
      ( c_Enum_Oenum__class_Oenum(tc_fun(U_18703,U_18704)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18704),tc_fun(U_18703,U_18704)),hAPP(hAPP(c_COMBB(tc_fun(U_18703,tc_Option_Ooption(U_18704)),tc_fun(U_18703,U_18704),tc_List_Olist(U_18704)),c_Fun_Ocomp(tc_Option_Ooption(U_18704),U_18704,U_18703,c_Option_Othe(U_18704))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18703,U_18704)),tc_fun(U_18703,tc_Option_Ooption(U_18704)),tc_List_Olist(U_18704)),c_Map_Omap__of(U_18703,U_18704)),hAPP(c_List_Ozip(U_18703,U_18704),c_Enum_Oenum__class_Oenum(U_18703))))),c_Enum_On__lists(U_18704,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18703)),c_Enum_Oenum__class_Oenum(U_18703)),c_Enum_Oenum__class_Oenum(U_18704)))
      | ~ class_Enum_Oenum(U_18704)
      | ~ class_HOL_Oequal(U_18703)
      | ~ class_Enum_Oenum(U_18703) ),
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

cnf(f_4519_3,plain,
    ( c_Enum_Oenum__class_Oenum(tc_fun(U_18703,U_18704)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18704),tc_fun(U_18703,U_18704)),hAPP(hAPP(c_COMBB(tc_fun(U_18703,tc_Option_Ooption(U_18704)),tc_fun(U_18703,U_18704),tc_List_Olist(U_18704)),c_Fun_Ocomp(tc_Option_Ooption(U_18704),U_18704,U_18703,c_Option_Othe(U_18704))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18703,U_18704)),tc_fun(U_18703,tc_Option_Ooption(U_18704)),tc_List_Olist(U_18704)),c_Map_Omap__of(U_18703,U_18704)),hAPP(c_List_Ozip(U_18703,U_18704),c_Enum_Oenum__class_Oenum(U_18703))))),c_Enum_On__lists(U_18704,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18703)),c_Enum_Oenum__class_Oenum(U_18703)),c_Enum_Oenum__class_Oenum(U_18704)))
    | ~ class_Enum_Oenum(U_18704)
    | ~ class_HOL_Oequal(U_18703)
    | ~ class_Enum_Oenum(U_18703) ),
    inference(clausify,[status(thm)],[f_4519_2]) ).

fof(f_4520_1,plain,
    ! [T_b,T_a] :
      ( c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b)))
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__fun__def]) ).

fof(f_4520_2,plain,
    ! [U_18706,U_18705] :
      ( c_Enum_Oenum__class_Oenum(tc_fun(U_18705,U_18706)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18706),tc_fun(U_18705,U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18705,tc_Option_Ooption(U_18706)),tc_fun(U_18705,U_18706),tc_List_Olist(U_18706)),c_Fun_Ocomp(tc_Option_Ooption(U_18706),U_18706,U_18705,c_Option_Othe(U_18706))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18705,U_18706)),tc_fun(U_18705,tc_Option_Ooption(U_18706)),tc_List_Olist(U_18706)),c_Map_Omap__of(U_18705,U_18706)),hAPP(c_List_Ozip(U_18705,U_18706),c_Enum_Oenum__class_Oenum(U_18705))))),c_Enum_On__lists(U_18706,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18705)),c_Enum_Oenum__class_Oenum(U_18705)),c_Enum_Oenum__class_Oenum(U_18706)))
      | ~ class_Enum_Oenum(U_18706)
      | ~ class_Enum_Oenum(U_18705) ),
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

cnf(f_4520_3,plain,
    ( c_Enum_Oenum__class_Oenum(tc_fun(U_18705,U_18706)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18706),tc_fun(U_18705,U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18705,tc_Option_Ooption(U_18706)),tc_fun(U_18705,U_18706),tc_List_Olist(U_18706)),c_Fun_Ocomp(tc_Option_Ooption(U_18706),U_18706,U_18705,c_Option_Othe(U_18706))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18705,U_18706)),tc_fun(U_18705,tc_Option_Ooption(U_18706)),tc_List_Olist(U_18706)),c_Map_Omap__of(U_18705,U_18706)),hAPP(c_List_Ozip(U_18705,U_18706),c_Enum_Oenum__class_Oenum(U_18705))))),c_Enum_On__lists(U_18706,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18705)),c_Enum_Oenum__class_Oenum(U_18705)),c_Enum_Oenum__class_Oenum(U_18706)))
    | ~ class_Enum_Oenum(U_18706)
    | ~ class_Enum_Oenum(U_18705) ),
    inference(clausify,[status(thm)],[f_4520_2]) ).

fof(f_4521_1,plain,
    ! [V_n_2,V_P_2,T_a] :
      ( ( ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
          | ? [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) )
          | ~ c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_all__n__lists__def]) ).

fof(f_4521_2,plain,
    ! [U_18711,U_18710,U_18709] :
      ( ( ( c_Enum_Oall__n__lists(U_18709,U_18710,U_18711)
          | ? [U_18708] :
              ( ~ hBOOL(hAPP(U_18710,U_18708))
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),U_18708),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709))))) ) )
        & ( ! [U_18707] :
              ( hBOOL(hAPP(U_18710,U_18707))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),U_18707),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709))))) )
          | ~ c_Enum_Oall__n__lists(U_18709,U_18710,U_18711) ) )
      | ~ class_Enum_Oenum(U_18709) ),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

fof(f_4521_3,plain,
    ! [U_18711,U_18710,U_18709] :
      ( ( ( c_Enum_Oall__n__lists(U_18709,U_18710,U_18711)
          | ( ~ hBOOL(hAPP(U_18710,sK467(U_18711,U_18710,U_18709)))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),sK467(U_18711,U_18710,U_18709)),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709))))) ) )
        & ( ! [U_18707] :
              ( hBOOL(hAPP(U_18710,U_18707))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),U_18707),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709))))) )
          | ~ c_Enum_Oall__n__lists(U_18709,U_18710,U_18711) ) )
      | ~ class_Enum_Oenum(U_18709) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18708,sK467(U_18711,U_18710,U_18709))],[f_4521_2]) ).

cnf(f_4521_4,plain,
    ( hBOOL(hAPP(U_18710,U_18707))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),U_18707),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709)))))
    | ~ c_Enum_Oall__n__lists(U_18709,U_18710,U_18711)
    | ~ class_Enum_Oenum(U_18709) ),
    inference(clausify,[status(thm)],[f_4521_3]) ).

cnf(f_4521_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18709)),sK467(U_18711,U_18710,U_18709)),hAPP(c_List_Oset(tc_List_Olist(U_18709)),c_Enum_On__lists(U_18709,U_18711,c_Enum_Oenum__class_Oenum(U_18709)))))
    | c_Enum_Oall__n__lists(U_18709,U_18710,U_18711)
    | ~ class_Enum_Oenum(U_18709) ),
    inference(clausify,[status(thm)],[f_4521_3]) ).

cnf(f_4521_6,plain,
    ( ~ hBOOL(hAPP(U_18710,sK467(U_18711,U_18710,U_18709)))
    | c_Enum_Oall__n__lists(U_18709,U_18710,U_18711)
    | ~ class_Enum_Oenum(U_18709) ),
    inference(clausify,[status(thm)],[f_4521_3]) ).

fof(f_4522_1,plain,
    ! [V_n_2,V_P_2,T_a] :
      ( ( ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) )
          | ~ c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ex__n__lists__def]) ).

fof(f_4522_2,plain,
    ! [U_18716,U_18715,U_18714] :
      ( ( ( c_Enum_Oex__n__lists(U_18714,U_18715,U_18716)
          | ! [U_18713] :
              ( ~ hBOOL(hAPP(U_18715,U_18713))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),U_18713),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714))))) ) )
        & ( ? [U_18712] :
              ( hBOOL(hAPP(U_18715,U_18712))
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),U_18712),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714))))) )
          | ~ c_Enum_Oex__n__lists(U_18714,U_18715,U_18716) ) )
      | ~ class_Enum_Oenum(U_18714) ),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

fof(f_4522_3,plain,
    ! [U_18716,U_18715,U_18714] :
      ( ( ( c_Enum_Oex__n__lists(U_18714,U_18715,U_18716)
          | ! [U_18713] :
              ( ~ hBOOL(hAPP(U_18715,U_18713))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),U_18713),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714))))) ) )
        & ( ( hBOOL(hAPP(U_18715,sK468(U_18716,U_18715,U_18714)))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),sK468(U_18716,U_18715,U_18714)),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714))))) )
          | ~ c_Enum_Oex__n__lists(U_18714,U_18715,U_18716) ) )
      | ~ class_Enum_Oenum(U_18714) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18712,sK468(U_18716,U_18715,U_18714))],[f_4522_2]) ).

cnf(f_4522_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),sK468(U_18716,U_18715,U_18714)),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714)))))
    | ~ c_Enum_Oex__n__lists(U_18714,U_18715,U_18716)
    | ~ class_Enum_Oenum(U_18714) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

cnf(f_4522_5,plain,
    ( hBOOL(hAPP(U_18715,sK468(U_18716,U_18715,U_18714)))
    | ~ c_Enum_Oex__n__lists(U_18714,U_18715,U_18716)
    | ~ class_Enum_Oenum(U_18714) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

cnf(f_4522_6,plain,
    ( c_Enum_Oex__n__lists(U_18714,U_18715,U_18716)
    | ~ hBOOL(hAPP(U_18715,U_18713))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18714)),U_18713),hAPP(c_List_Oset(tc_List_Olist(U_18714)),c_Enum_On__lists(U_18714,U_18716,c_Enum_Oenum__class_Oenum(U_18714)))))
    | ~ class_Enum_Oenum(U_18714) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

fof(f_4523_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
          | ~ c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) )
        & ( c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__fun__def]) ).

fof(f_4523_2,plain,
    ! [U_18719,U_18718,U_18717] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18718,U_18717)),U_18719))
          | ~ c_Enum_Oall__n__lists(U_18717,hAPP(hAPP(c_COMBB(tc_fun(U_18718,U_18717),tc_HOL_Obool,tc_List_Olist(U_18717)),U_18719),hAPP(hAPP(c_COMBB(tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_fun(U_18718,U_18717),tc_List_Olist(U_18717)),c_Fun_Ocomp(tc_Option_Ooption(U_18717),U_18717,U_18718,c_Option_Othe(U_18717))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18718,U_18717)),tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_List_Olist(U_18717)),c_Map_Omap__of(U_18718,U_18717)),hAPP(c_List_Ozip(U_18718,U_18717),c_Enum_Oenum__class_Oenum(U_18718))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18718)),c_Enum_Oenum__class_Oenum(U_18718))) )
        & ( c_Enum_Oall__n__lists(U_18717,hAPP(hAPP(c_COMBB(tc_fun(U_18718,U_18717),tc_HOL_Obool,tc_List_Olist(U_18717)),U_18719),hAPP(hAPP(c_COMBB(tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_fun(U_18718,U_18717),tc_List_Olist(U_18717)),c_Fun_Ocomp(tc_Option_Ooption(U_18717),U_18717,U_18718,c_Option_Othe(U_18717))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18718,U_18717)),tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_List_Olist(U_18717)),c_Map_Omap__of(U_18718,U_18717)),hAPP(c_List_Ozip(U_18718,U_18717),c_Enum_Oenum__class_Oenum(U_18718))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18718)),c_Enum_Oenum__class_Oenum(U_18718)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18718,U_18717)),U_18719)) ) )
      | ~ class_Enum_Oenum(U_18718)
      | ~ class_Enum_Oenum(U_18717) ),
    inference(variable_rename,[status(thm)],[f_4523_1]) ).

cnf(f_4523_3,plain,
    ( c_Enum_Oall__n__lists(U_18717,hAPP(hAPP(c_COMBB(tc_fun(U_18718,U_18717),tc_HOL_Obool,tc_List_Olist(U_18717)),U_18719),hAPP(hAPP(c_COMBB(tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_fun(U_18718,U_18717),tc_List_Olist(U_18717)),c_Fun_Ocomp(tc_Option_Ooption(U_18717),U_18717,U_18718,c_Option_Othe(U_18717))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18718,U_18717)),tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_List_Olist(U_18717)),c_Map_Omap__of(U_18718,U_18717)),hAPP(c_List_Ozip(U_18718,U_18717),c_Enum_Oenum__class_Oenum(U_18718))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18718)),c_Enum_Oenum__class_Oenum(U_18718)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18718,U_18717)),U_18719))
    | ~ class_Enum_Oenum(U_18718)
    | ~ class_Enum_Oenum(U_18717) ),
    inference(clausify,[status(thm)],[f_4523_2]) ).

cnf(f_4523_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18718,U_18717)),U_18719))
    | ~ c_Enum_Oall__n__lists(U_18717,hAPP(hAPP(c_COMBB(tc_fun(U_18718,U_18717),tc_HOL_Obool,tc_List_Olist(U_18717)),U_18719),hAPP(hAPP(c_COMBB(tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_fun(U_18718,U_18717),tc_List_Olist(U_18717)),c_Fun_Ocomp(tc_Option_Ooption(U_18717),U_18717,U_18718,c_Option_Othe(U_18717))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18718,U_18717)),tc_fun(U_18718,tc_Option_Ooption(U_18717)),tc_List_Olist(U_18717)),c_Map_Omap__of(U_18718,U_18717)),hAPP(c_List_Ozip(U_18718,U_18717),c_Enum_Oenum__class_Oenum(U_18718))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18718)),c_Enum_Oenum__class_Oenum(U_18718)))
    | ~ class_Enum_Oenum(U_18718)
    | ~ class_Enum_Oenum(U_18717) ),
    inference(clausify,[status(thm)],[f_4523_2]) ).

fof(f_4524_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
          | ~ c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) )
        & ( c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__fun__def]) ).

fof(f_4524_2,plain,
    ! [U_18722,U_18721,U_18720] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18721,U_18720)),U_18722))
          | ~ c_Enum_Oex__n__lists(U_18720,hAPP(hAPP(c_COMBB(tc_fun(U_18721,U_18720),tc_HOL_Obool,tc_List_Olist(U_18720)),U_18722),hAPP(hAPP(c_COMBB(tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_fun(U_18721,U_18720),tc_List_Olist(U_18720)),c_Fun_Ocomp(tc_Option_Ooption(U_18720),U_18720,U_18721,c_Option_Othe(U_18720))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18721,U_18720)),tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_List_Olist(U_18720)),c_Map_Omap__of(U_18721,U_18720)),hAPP(c_List_Ozip(U_18721,U_18720),c_Enum_Oenum__class_Oenum(U_18721))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),c_Enum_Oenum__class_Oenum(U_18721))) )
        & ( c_Enum_Oex__n__lists(U_18720,hAPP(hAPP(c_COMBB(tc_fun(U_18721,U_18720),tc_HOL_Obool,tc_List_Olist(U_18720)),U_18722),hAPP(hAPP(c_COMBB(tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_fun(U_18721,U_18720),tc_List_Olist(U_18720)),c_Fun_Ocomp(tc_Option_Ooption(U_18720),U_18720,U_18721,c_Option_Othe(U_18720))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18721,U_18720)),tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_List_Olist(U_18720)),c_Map_Omap__of(U_18721,U_18720)),hAPP(c_List_Ozip(U_18721,U_18720),c_Enum_Oenum__class_Oenum(U_18721))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),c_Enum_Oenum__class_Oenum(U_18721)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18721,U_18720)),U_18722)) ) )
      | ~ class_Enum_Oenum(U_18721)
      | ~ class_Enum_Oenum(U_18720) ),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

cnf(f_4524_3,plain,
    ( c_Enum_Oex__n__lists(U_18720,hAPP(hAPP(c_COMBB(tc_fun(U_18721,U_18720),tc_HOL_Obool,tc_List_Olist(U_18720)),U_18722),hAPP(hAPP(c_COMBB(tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_fun(U_18721,U_18720),tc_List_Olist(U_18720)),c_Fun_Ocomp(tc_Option_Ooption(U_18720),U_18720,U_18721,c_Option_Othe(U_18720))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18721,U_18720)),tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_List_Olist(U_18720)),c_Map_Omap__of(U_18721,U_18720)),hAPP(c_List_Ozip(U_18721,U_18720),c_Enum_Oenum__class_Oenum(U_18721))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),c_Enum_Oenum__class_Oenum(U_18721)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18721,U_18720)),U_18722))
    | ~ class_Enum_Oenum(U_18721)
    | ~ class_Enum_Oenum(U_18720) ),
    inference(clausify,[status(thm)],[f_4524_2]) ).

cnf(f_4524_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18721,U_18720)),U_18722))
    | ~ c_Enum_Oex__n__lists(U_18720,hAPP(hAPP(c_COMBB(tc_fun(U_18721,U_18720),tc_HOL_Obool,tc_List_Olist(U_18720)),U_18722),hAPP(hAPP(c_COMBB(tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_fun(U_18721,U_18720),tc_List_Olist(U_18720)),c_Fun_Ocomp(tc_Option_Ooption(U_18720),U_18720,U_18721,c_Option_Othe(U_18720))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18721,U_18720)),tc_fun(U_18721,tc_Option_Ooption(U_18720)),tc_List_Olist(U_18720)),c_Map_Omap__of(U_18721,U_18720)),hAPP(c_List_Ozip(U_18721,U_18720),c_Enum_Oenum__class_Oenum(U_18721))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),c_Enum_Oenum__class_Oenum(U_18721)))
    | ~ class_Enum_Oenum(U_18721)
    | ~ class_Enum_Oenum(U_18720) ),
    inference(clausify,[status(thm)],[f_4524_2]) ).

fof(f_4525_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def]) ).

fof(f_4525_2,plain,
    ! [U_18725,U_18724,U_18723] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18724,U_18723)),U_18725))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18724),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_HOL_Obool),tc_HOL_Obool,U_18724),c_Enum_Oenum__class_Oenum__all(U_18723)),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_prod(U_18724,U_18723)),tc_fun(U_18723,tc_HOL_Obool),U_18724),hAPP(c_COMBB(tc_prod(U_18724,U_18723),tc_HOL_Obool,U_18723),U_18725)),c_Product__Type_OPair(U_18724,U_18723))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18724),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_HOL_Obool),tc_HOL_Obool,U_18724),c_Enum_Oenum__class_Oenum__all(U_18723)),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_prod(U_18724,U_18723)),tc_fun(U_18723,tc_HOL_Obool),U_18724),hAPP(c_COMBB(tc_prod(U_18724,U_18723),tc_HOL_Obool,U_18723),U_18725)),c_Product__Type_OPair(U_18724,U_18723)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18724,U_18723)),U_18725)) ) )
      | ~ class_Enum_Oenum(U_18724)
      | ~ class_Enum_Oenum(U_18723) ),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

cnf(f_4525_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18724),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_HOL_Obool),tc_HOL_Obool,U_18724),c_Enum_Oenum__class_Oenum__all(U_18723)),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_prod(U_18724,U_18723)),tc_fun(U_18723,tc_HOL_Obool),U_18724),hAPP(c_COMBB(tc_prod(U_18724,U_18723),tc_HOL_Obool,U_18723),U_18725)),c_Product__Type_OPair(U_18724,U_18723)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18724,U_18723)),U_18725))
    | ~ class_Enum_Oenum(U_18724)
    | ~ class_Enum_Oenum(U_18723) ),
    inference(clausify,[status(thm)],[f_4525_2]) ).

cnf(f_4525_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18724,U_18723)),U_18725))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18724),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_HOL_Obool),tc_HOL_Obool,U_18724),c_Enum_Oenum__class_Oenum__all(U_18723)),hAPP(hAPP(c_COMBB(tc_fun(U_18723,tc_prod(U_18724,U_18723)),tc_fun(U_18723,tc_HOL_Obool),U_18724),hAPP(c_COMBB(tc_prod(U_18724,U_18723),tc_HOL_Obool,U_18723),U_18725)),c_Product__Type_OPair(U_18724,U_18723)))))
    | ~ class_Enum_Oenum(U_18724)
    | ~ class_Enum_Oenum(U_18723) ),
    inference(clausify,[status(thm)],[f_4525_2]) ).

fof(f_4526_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def]) ).

fof(f_4526_2,plain,
    ! [U_18728,U_18727,U_18726] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18727,U_18726)),U_18728))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18727),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_HOL_Obool),tc_HOL_Obool,U_18727),c_Enum_Oenum__class_Oenum__ex(U_18726)),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_prod(U_18727,U_18726)),tc_fun(U_18726,tc_HOL_Obool),U_18727),hAPP(c_COMBB(tc_prod(U_18727,U_18726),tc_HOL_Obool,U_18726),U_18728)),c_Product__Type_OPair(U_18727,U_18726))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18727),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_HOL_Obool),tc_HOL_Obool,U_18727),c_Enum_Oenum__class_Oenum__ex(U_18726)),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_prod(U_18727,U_18726)),tc_fun(U_18726,tc_HOL_Obool),U_18727),hAPP(c_COMBB(tc_prod(U_18727,U_18726),tc_HOL_Obool,U_18726),U_18728)),c_Product__Type_OPair(U_18727,U_18726)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18727,U_18726)),U_18728)) ) )
      | ~ class_Enum_Oenum(U_18727)
      | ~ class_Enum_Oenum(U_18726) ),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

cnf(f_4526_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18727),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_HOL_Obool),tc_HOL_Obool,U_18727),c_Enum_Oenum__class_Oenum__ex(U_18726)),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_prod(U_18727,U_18726)),tc_fun(U_18726,tc_HOL_Obool),U_18727),hAPP(c_COMBB(tc_prod(U_18727,U_18726),tc_HOL_Obool,U_18726),U_18728)),c_Product__Type_OPair(U_18727,U_18726)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18727,U_18726)),U_18728))
    | ~ class_Enum_Oenum(U_18727)
    | ~ class_Enum_Oenum(U_18726) ),
    inference(clausify,[status(thm)],[f_4526_2]) ).

cnf(f_4526_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18727,U_18726)),U_18728))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18727),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_HOL_Obool),tc_HOL_Obool,U_18727),c_Enum_Oenum__class_Oenum__ex(U_18726)),hAPP(hAPP(c_COMBB(tc_fun(U_18726,tc_prod(U_18727,U_18726)),tc_fun(U_18726,tc_HOL_Obool),U_18727),hAPP(c_COMBB(tc_prod(U_18727,U_18726),tc_HOL_Obool,U_18726),U_18728)),c_Product__Type_OPair(U_18727,U_18726)))))
    | ~ class_Enum_Oenum(U_18727)
    | ~ class_Enum_Oenum(U_18726) ),
    inference(clausify,[status(thm)],[f_4526_2]) ).

fof(f_4527_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_all__code]) ).

fof(f_4527_2,plain,
    ! [U_18732,U_18731] :
      ( ( ( ! [U_18730] : hBOOL(hAPP(U_18732,U_18730))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732))
          | ? [U_18729] : ~ hBOOL(hAPP(U_18732,U_18729)) ) )
      | ~ class_Enum_Oenum(U_18731) ),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

fof(f_4527_3,plain,
    ! [U_18732,U_18731] :
      ( ( ( ! [U_18730] : hBOOL(hAPP(U_18732,U_18730))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732))
          | ~ hBOOL(hAPP(U_18732,sK469(U_18732,U_18731))) ) )
      | ~ class_Enum_Oenum(U_18731) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18729,sK469(U_18732,U_18731))],[f_4527_2]) ).

cnf(f_4527_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732))
    | ~ hBOOL(hAPP(U_18732,sK469(U_18732,U_18731)))
    | ~ class_Enum_Oenum(U_18731) ),
    inference(clausify,[status(thm)],[f_4527_3]) ).

cnf(f_4527_5,plain,
    ( hBOOL(hAPP(U_18732,U_18730))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18731),U_18732))
    | ~ class_Enum_Oenum(U_18731) ),
    inference(clausify,[status(thm)],[f_4527_3]) ).

fof(f_4528_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_exists__code]) ).

fof(f_4528_2,plain,
    ! [U_18736,U_18735] :
      ( ( ( ? [U_18734] : hBOOL(hAPP(U_18736,U_18734))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736))
          | ! [U_18733] : ~ hBOOL(hAPP(U_18736,U_18733)) ) )
      | ~ class_Enum_Oenum(U_18735) ),
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

fof(f_4528_3,plain,
    ! [U_18736,U_18735] :
      ( ( ( hBOOL(hAPP(U_18736,sK470(U_18736,U_18735)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736))
          | ! [U_18733] : ~ hBOOL(hAPP(U_18736,U_18733)) ) )
      | ~ class_Enum_Oenum(U_18735) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_18734,sK470(U_18736,U_18735))],[f_4528_2]) ).

cnf(f_4528_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736))
    | ~ hBOOL(hAPP(U_18736,U_18733))
    | ~ class_Enum_Oenum(U_18735) ),
    inference(clausify,[status(thm)],[f_4528_3]) ).

cnf(f_4528_5,plain,
    ( hBOOL(hAPP(U_18736,sK470(U_18736,U_18735)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18735),U_18736))
    | ~ class_Enum_Oenum(U_18735) ),
    inference(clausify,[status(thm)],[f_4528_3]) ).

fof(f_4529_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
        & ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all]) ).

fof(f_4529_2,plain,
    ! [U_18740,U_18739] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740))
          | ? [U_18738] : ~ hBOOL(hAPP(U_18740,U_18738)) )
        & ( ! [U_18737] : hBOOL(hAPP(U_18740,U_18737))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740)) ) )
      | ~ class_Enum_Oenum(U_18739) ),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

fof(f_4529_3,plain,
    ! [U_18740,U_18739] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740))
          | ~ hBOOL(hAPP(U_18740,sK471(U_18740,U_18739))) )
        & ( ! [U_18737] : hBOOL(hAPP(U_18740,U_18737))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740)) ) )
      | ~ class_Enum_Oenum(U_18739) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_18738,sK471(U_18740,U_18739))],[f_4529_2]) ).

cnf(f_4529_4,plain,
    ( hBOOL(hAPP(U_18740,U_18737))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740))
    | ~ class_Enum_Oenum(U_18739) ),
    inference(clausify,[status(thm)],[f_4529_3]) ).

cnf(f_4529_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18739),U_18740))
    | ~ hBOOL(hAPP(U_18740,sK471(U_18740,U_18739)))
    | ~ class_Enum_Oenum(U_18739) ),
    inference(clausify,[status(thm)],[f_4529_3]) ).

fof(f_4530_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
        & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex]) ).

fof(f_4530_2,plain,
    ! [U_18744,U_18743] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744))
          | ! [U_18742] : ~ hBOOL(hAPP(U_18744,U_18742)) )
        & ( ? [U_18741] : hBOOL(hAPP(U_18744,U_18741))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744)) ) )
      | ~ class_Enum_Oenum(U_18743) ),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

fof(f_4530_3,plain,
    ! [U_18744,U_18743] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744))
          | ! [U_18742] : ~ hBOOL(hAPP(U_18744,U_18742)) )
        & ( hBOOL(hAPP(U_18744,sK472(U_18744,U_18743)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744)) ) )
      | ~ class_Enum_Oenum(U_18743) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_18741,sK472(U_18744,U_18743))],[f_4530_2]) ).

cnf(f_4530_4,plain,
    ( hBOOL(hAPP(U_18744,sK472(U_18744,U_18743)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744))
    | ~ class_Enum_Oenum(U_18743) ),
    inference(clausify,[status(thm)],[f_4530_3]) ).

cnf(f_4530_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18743),U_18744))
    | ~ hBOOL(hAPP(U_18744,U_18742))
    | ~ class_Enum_Oenum(U_18743) ),
    inference(clausify,[status(thm)],[f_4530_3]) ).

fof(f_4531_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
          | ~ hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
            & hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) )
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__option__def]) ).

fof(f_4531_2,plain,
    ! [U_18746,U_18745] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(U_18745)),U_18746))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18745),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18745),tc_HOL_Obool,U_18745),U_18746),c_Option_Ooption_OSome(U_18745))))
          | ~ hBOOL(hAPP(U_18746,c_Option_Ooption_ONone(U_18745))) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18745),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18745),tc_HOL_Obool,U_18745),U_18746),c_Option_Ooption_OSome(U_18745))))
            & hBOOL(hAPP(U_18746,c_Option_Ooption_ONone(U_18745))) )
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(U_18745)),U_18746)) ) )
      | ~ class_Enum_Oenum(U_18745) ),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

cnf(f_4531_3,plain,
    ( hBOOL(hAPP(U_18746,c_Option_Ooption_ONone(U_18745)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(U_18745)),U_18746))
    | ~ class_Enum_Oenum(U_18745) ),
    inference(clausify,[status(thm)],[f_4531_2]) ).

cnf(f_4531_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18745),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18745),tc_HOL_Obool,U_18745),U_18746),c_Option_Ooption_OSome(U_18745))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(U_18745)),U_18746))
    | ~ class_Enum_Oenum(U_18745) ),
    inference(clausify,[status(thm)],[f_4531_2]) ).

cnf(f_4531_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(U_18745)),U_18746))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18745),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18745),tc_HOL_Obool,U_18745),U_18746),c_Option_Ooption_OSome(U_18745))))
    | ~ hBOOL(hAPP(U_18746,c_Option_Ooption_ONone(U_18745)))
    | ~ class_Enum_Oenum(U_18745) ),
    inference(clausify,[status(thm)],[f_4531_2]) ).

fof(f_4532_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
          | ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
            & ~ hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) ) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a))))
          | hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__option__def]) ).

fof(f_4532_2,plain,
    ! [U_18748,U_18747] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(U_18747)),U_18748))
          | ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18747),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18747),tc_HOL_Obool,U_18747),U_18748),c_Option_Ooption_OSome(U_18747))))
            & ~ hBOOL(hAPP(U_18748,c_Option_Ooption_ONone(U_18747))) ) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18747),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18747),tc_HOL_Obool,U_18747),U_18748),c_Option_Ooption_OSome(U_18747))))
          | hBOOL(hAPP(U_18748,c_Option_Ooption_ONone(U_18747)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(U_18747)),U_18748)) ) )
      | ~ class_Enum_Oenum(U_18747) ),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

cnf(f_4532_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18747),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18747),tc_HOL_Obool,U_18747),U_18748),c_Option_Ooption_OSome(U_18747))))
    | hBOOL(hAPP(U_18748,c_Option_Ooption_ONone(U_18747)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(U_18747)),U_18748))
    | ~ class_Enum_Oenum(U_18747) ),
    inference(clausify,[status(thm)],[f_4532_2]) ).

cnf(f_4532_4,plain,
    ( ~ hBOOL(hAPP(U_18748,c_Option_Ooption_ONone(U_18747)))
    | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(U_18747)),U_18748))
    | ~ class_Enum_Oenum(U_18747) ),
    inference(clausify,[status(thm)],[f_4532_2]) ).

cnf(f_4532_5,plain,
    ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18747),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_18747),tc_HOL_Obool,U_18747),U_18748),c_Option_Ooption_OSome(U_18747))))
    | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(U_18747)),U_18748))
    | ~ class_Enum_Oenum(U_18747) ),
    inference(clausify,[status(thm)],[f_4532_2]) ).

fof(f_4533_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J]) ).

fof(f_4533_2,plain,
    ! [U_18752,U_18751,U_18750,U_18749] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18750,U_18749)),U_18751),U_18752))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18750),hAPP(hAPP(c_COMBS(U_18750,U_18749,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18749,tc_fun(U_18749,tc_HOL_Obool),U_18750),c_Orderings_Oord__class_Oless__eq(U_18749)),U_18751)),U_18752))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18750),hAPP(hAPP(c_COMBS(U_18750,U_18749,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18749,tc_fun(U_18749,tc_HOL_Obool),U_18750),c_Orderings_Oord__class_Oless__eq(U_18749)),U_18751)),U_18752)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18750,U_18749)),U_18751),U_18752)) ) )
      | ~ class_Enum_Oenum(U_18750)
      | ~ class_Orderings_Oorder(U_18749) ),
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

cnf(f_4533_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18750),hAPP(hAPP(c_COMBS(U_18750,U_18749,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18749,tc_fun(U_18749,tc_HOL_Obool),U_18750),c_Orderings_Oord__class_Oless__eq(U_18749)),U_18751)),U_18752)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18750,U_18749)),U_18751),U_18752))
    | ~ class_Enum_Oenum(U_18750)
    | ~ class_Orderings_Oorder(U_18749) ),
    inference(clausify,[status(thm)],[f_4533_2]) ).

cnf(f_4533_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18750,U_18749)),U_18751),U_18752))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18750),hAPP(hAPP(c_COMBS(U_18750,U_18749,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18749,tc_fun(U_18749,tc_HOL_Obool),U_18750),c_Orderings_Oord__class_Oless__eq(U_18749)),U_18751)),U_18752)))
    | ~ class_Enum_Oenum(U_18750)
    | ~ class_Orderings_Oorder(U_18749) ),
    inference(clausify,[status(thm)],[f_4533_2]) ).

fof(f_4534_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J]) ).

fof(f_4534_2,plain,
    ! [U_18756,U_18755,U_18754,U_18753] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18754,U_18753)),U_18755),U_18756))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18754),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18754),c_fNot),hAPP(hAPP(c_COMBS(U_18754,U_18753,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18753,tc_fun(U_18753,tc_HOL_Obool),U_18754),c_fequal),U_18755)),U_18756))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18754,U_18753)),U_18755),U_18756)) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18754),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18754),c_fNot),hAPP(hAPP(c_COMBS(U_18754,U_18753,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18753,tc_fun(U_18753,tc_HOL_Obool),U_18754),c_fequal),U_18755)),U_18756))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18754,U_18753)),U_18755),U_18756)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18754,U_18753)),U_18755),U_18756)) ) )
      | ~ class_Enum_Oenum(U_18754)
      | ~ class_Orderings_Oorder(U_18753) ),
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

cnf(f_4534_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18754,U_18753)),U_18755),U_18756))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18754,U_18753)),U_18755),U_18756))
    | ~ class_Enum_Oenum(U_18754)
    | ~ class_Orderings_Oorder(U_18753) ),
    inference(clausify,[status(thm)],[f_4534_2]) ).

cnf(f_4534_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18754),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18754),c_fNot),hAPP(hAPP(c_COMBS(U_18754,U_18753,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18753,tc_fun(U_18753,tc_HOL_Obool),U_18754),c_fequal),U_18755)),U_18756))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18754,U_18753)),U_18755),U_18756))
    | ~ class_Enum_Oenum(U_18754)
    | ~ class_Orderings_Oorder(U_18753) ),
    inference(clausify,[status(thm)],[f_4534_2]) ).

cnf(f_4534_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18754,U_18753)),U_18755),U_18756))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18754),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18754),c_fNot),hAPP(hAPP(c_COMBS(U_18754,U_18753,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18753,tc_fun(U_18753,tc_HOL_Obool),U_18754),c_fequal),U_18755)),U_18756))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18754,U_18753)),U_18755),U_18756))
    | ~ class_Enum_Oenum(U_18754)
    | ~ class_Orderings_Oorder(U_18753) ),
    inference(clausify,[status(thm)],[f_4534_2]) ).

fof(f_4535_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
          | ~ c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) )
        & ( c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) ) )
      | ~ class_HOL_Oequal(T_a)
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__fun__code]) ).

fof(f_4535_2,plain,
    ! [U_18759,U_18758,U_18757] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18758,U_18757)),U_18759))
          | ~ c_Enum_Oex__n__lists(U_18757,hAPP(hAPP(c_COMBB(tc_fun(U_18758,U_18757),tc_HOL_Obool,tc_List_Olist(U_18757)),U_18759),hAPP(hAPP(c_COMBB(tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_fun(U_18758,U_18757),tc_List_Olist(U_18757)),c_Fun_Ocomp(tc_Option_Ooption(U_18757),U_18757,U_18758,c_Option_Othe(U_18757))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18758,U_18757)),tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_List_Olist(U_18757)),c_Map_Omap__of(U_18758,U_18757)),hAPP(c_List_Ozip(U_18758,U_18757),c_Enum_Oenum__class_Oenum(U_18758))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18758)),c_Enum_Oenum__class_Oenum(U_18758))) )
        & ( c_Enum_Oex__n__lists(U_18757,hAPP(hAPP(c_COMBB(tc_fun(U_18758,U_18757),tc_HOL_Obool,tc_List_Olist(U_18757)),U_18759),hAPP(hAPP(c_COMBB(tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_fun(U_18758,U_18757),tc_List_Olist(U_18757)),c_Fun_Ocomp(tc_Option_Ooption(U_18757),U_18757,U_18758,c_Option_Othe(U_18757))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18758,U_18757)),tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_List_Olist(U_18757)),c_Map_Omap__of(U_18758,U_18757)),hAPP(c_List_Ozip(U_18758,U_18757),c_Enum_Oenum__class_Oenum(U_18758))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18758)),c_Enum_Oenum__class_Oenum(U_18758)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18758,U_18757)),U_18759)) ) )
      | ~ class_HOL_Oequal(U_18758)
      | ~ class_Enum_Oenum(U_18758)
      | ~ class_Enum_Oenum(U_18757) ),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

cnf(f_4535_3,plain,
    ( c_Enum_Oex__n__lists(U_18757,hAPP(hAPP(c_COMBB(tc_fun(U_18758,U_18757),tc_HOL_Obool,tc_List_Olist(U_18757)),U_18759),hAPP(hAPP(c_COMBB(tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_fun(U_18758,U_18757),tc_List_Olist(U_18757)),c_Fun_Ocomp(tc_Option_Ooption(U_18757),U_18757,U_18758,c_Option_Othe(U_18757))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18758,U_18757)),tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_List_Olist(U_18757)),c_Map_Omap__of(U_18758,U_18757)),hAPP(c_List_Ozip(U_18758,U_18757),c_Enum_Oenum__class_Oenum(U_18758))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18758)),c_Enum_Oenum__class_Oenum(U_18758)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18758,U_18757)),U_18759))
    | ~ class_HOL_Oequal(U_18758)
    | ~ class_Enum_Oenum(U_18758)
    | ~ class_Enum_Oenum(U_18757) ),
    inference(clausify,[status(thm)],[f_4535_2]) ).

cnf(f_4535_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(U_18758,U_18757)),U_18759))
    | ~ c_Enum_Oex__n__lists(U_18757,hAPP(hAPP(c_COMBB(tc_fun(U_18758,U_18757),tc_HOL_Obool,tc_List_Olist(U_18757)),U_18759),hAPP(hAPP(c_COMBB(tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_fun(U_18758,U_18757),tc_List_Olist(U_18757)),c_Fun_Ocomp(tc_Option_Ooption(U_18757),U_18757,U_18758,c_Option_Othe(U_18757))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18758,U_18757)),tc_fun(U_18758,tc_Option_Ooption(U_18757)),tc_List_Olist(U_18757)),c_Map_Omap__of(U_18758,U_18757)),hAPP(c_List_Ozip(U_18758,U_18757),c_Enum_Oenum__class_Oenum(U_18758))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18758)),c_Enum_Oenum__class_Oenum(U_18758)))
    | ~ class_HOL_Oequal(U_18758)
    | ~ class_Enum_Oenum(U_18758)
    | ~ class_Enum_Oenum(U_18757) ),
    inference(clausify,[status(thm)],[f_4535_2]) ).

fof(f_4536_1,plain,
    ! [V_P_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
          | ~ c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) )
        & ( c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) ) )
      | ~ class_HOL_Oequal(T_a)
      | ~ class_Enum_Oenum(T_a)
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__fun__code]) ).

fof(f_4536_2,plain,
    ! [U_18762,U_18761,U_18760] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18761,U_18760)),U_18762))
          | ~ c_Enum_Oall__n__lists(U_18760,hAPP(hAPP(c_COMBB(tc_fun(U_18761,U_18760),tc_HOL_Obool,tc_List_Olist(U_18760)),U_18762),hAPP(hAPP(c_COMBB(tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_fun(U_18761,U_18760),tc_List_Olist(U_18760)),c_Fun_Ocomp(tc_Option_Ooption(U_18760),U_18760,U_18761,c_Option_Othe(U_18760))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18761,U_18760)),tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_List_Olist(U_18760)),c_Map_Omap__of(U_18761,U_18760)),hAPP(c_List_Ozip(U_18761,U_18760),c_Enum_Oenum__class_Oenum(U_18761))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18761)),c_Enum_Oenum__class_Oenum(U_18761))) )
        & ( c_Enum_Oall__n__lists(U_18760,hAPP(hAPP(c_COMBB(tc_fun(U_18761,U_18760),tc_HOL_Obool,tc_List_Olist(U_18760)),U_18762),hAPP(hAPP(c_COMBB(tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_fun(U_18761,U_18760),tc_List_Olist(U_18760)),c_Fun_Ocomp(tc_Option_Ooption(U_18760),U_18760,U_18761,c_Option_Othe(U_18760))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18761,U_18760)),tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_List_Olist(U_18760)),c_Map_Omap__of(U_18761,U_18760)),hAPP(c_List_Ozip(U_18761,U_18760),c_Enum_Oenum__class_Oenum(U_18761))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18761)),c_Enum_Oenum__class_Oenum(U_18761)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18761,U_18760)),U_18762)) ) )
      | ~ class_HOL_Oequal(U_18761)
      | ~ class_Enum_Oenum(U_18761)
      | ~ class_Enum_Oenum(U_18760) ),
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

cnf(f_4536_3,plain,
    ( c_Enum_Oall__n__lists(U_18760,hAPP(hAPP(c_COMBB(tc_fun(U_18761,U_18760),tc_HOL_Obool,tc_List_Olist(U_18760)),U_18762),hAPP(hAPP(c_COMBB(tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_fun(U_18761,U_18760),tc_List_Olist(U_18760)),c_Fun_Ocomp(tc_Option_Ooption(U_18760),U_18760,U_18761,c_Option_Othe(U_18760))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18761,U_18760)),tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_List_Olist(U_18760)),c_Map_Omap__of(U_18761,U_18760)),hAPP(c_List_Ozip(U_18761,U_18760),c_Enum_Oenum__class_Oenum(U_18761))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18761)),c_Enum_Oenum__class_Oenum(U_18761)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18761,U_18760)),U_18762))
    | ~ class_HOL_Oequal(U_18761)
    | ~ class_Enum_Oenum(U_18761)
    | ~ class_Enum_Oenum(U_18760) ),
    inference(clausify,[status(thm)],[f_4536_2]) ).

cnf(f_4536_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(U_18761,U_18760)),U_18762))
    | ~ c_Enum_Oall__n__lists(U_18760,hAPP(hAPP(c_COMBB(tc_fun(U_18761,U_18760),tc_HOL_Obool,tc_List_Olist(U_18760)),U_18762),hAPP(hAPP(c_COMBB(tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_fun(U_18761,U_18760),tc_List_Olist(U_18760)),c_Fun_Ocomp(tc_Option_Ooption(U_18760),U_18760,U_18761,c_Option_Othe(U_18760))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(U_18761,U_18760)),tc_fun(U_18761,tc_Option_Ooption(U_18760)),tc_List_Olist(U_18760)),c_Map_Omap__of(U_18761,U_18760)),hAPP(c_List_Ozip(U_18761,U_18760),c_Enum_Oenum__class_Oenum(U_18761))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18761)),c_Enum_Oenum__class_Oenum(U_18761)))
    | ~ class_HOL_Oequal(U_18761)
    | ~ class_Enum_Oenum(U_18761)
    | ~ class_Enum_Oenum(U_18760) ),
    inference(clausify,[status(thm)],[f_4536_2]) ).

fof(f_4537_1,plain,
    ! [V_x,V_ys,T_b,T_a] :
      ( ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__zip__enum__is__Some]) ).

fof(f_4537_2,plain,
    ! [U_18767,U_18766,U_18765,U_18764] :
      ( ? [U_18763] : hAPP(hAPP(c_Map_Omap__of(U_18764,U_18765),hAPP(hAPP(c_List_Ozip(U_18764,U_18765),c_Enum_Oenum__class_Oenum(U_18764)),U_18766)),U_18767) = hAPP(c_Option_Ooption_OSome(U_18765),U_18763)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18765)),U_18766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18764)),c_Enum_Oenum__class_Oenum(U_18764))
      | ~ class_Enum_Oenum(U_18764) ),
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

fof(f_4537_3,plain,
    ! [U_18767,U_18766,U_18765,U_18764] :
      ( hAPP(hAPP(c_Map_Omap__of(U_18764,U_18765),hAPP(hAPP(c_List_Ozip(U_18764,U_18765),c_Enum_Oenum__class_Oenum(U_18764)),U_18766)),U_18767) = hAPP(c_Option_Ooption_OSome(U_18765),sK473(U_18767,U_18766,U_18765,U_18764))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18765)),U_18766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18764)),c_Enum_Oenum__class_Oenum(U_18764))
      | ~ class_Enum_Oenum(U_18764) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_18763,sK473(U_18767,U_18766,U_18765,U_18764))],[f_4537_2]) ).

cnf(f_4537_4,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_18764,U_18765),hAPP(hAPP(c_List_Ozip(U_18764,U_18765),c_Enum_Oenum__class_Oenum(U_18764)),U_18766)),U_18767) = hAPP(c_Option_Ooption_OSome(U_18765),sK473(U_18767,U_18766,U_18765,U_18764))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18765)),U_18766) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18764)),c_Enum_Oenum__class_Oenum(U_18764))
    | ~ class_Enum_Oenum(U_18764) ),
    inference(clausify,[status(thm)],[f_4537_3]) ).

fof(f_4538_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_a,T_b,tc_HOL_Obool),V_P_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__def]) ).

fof(f_4538_2,plain,
    ! [U_18774,U_18773,U_18772,U_18771,U_18770] :
      ( ( c_List_Olist__all2(U_18770,U_18771,U_18772,U_18773,U_18774)
        | ? [U_18769] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18770,U_18771,tc_HOL_Obool),U_18772),U_18769))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18770,U_18771)),U_18769),hAPP(c_List_Oset(tc_prod(U_18770,U_18771)),hAPP(hAPP(c_List_Ozip(U_18770,U_18771),U_18773),U_18774)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18770)),U_18773) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18771)),U_18774) )
      & ( ( ! [U_18768] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18770,U_18771,tc_HOL_Obool),U_18772),U_18768))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18770,U_18771)),U_18768),hAPP(c_List_Oset(tc_prod(U_18770,U_18771)),hAPP(hAPP(c_List_Ozip(U_18770,U_18771),U_18773),U_18774)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18770)),U_18773) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18771)),U_18774) )
        | ~ c_List_Olist__all2(U_18770,U_18771,U_18772,U_18773,U_18774) ) ),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

fof(f_4538_3,plain,
    ( ! [U_18784,U_18782,U_18780,U_18778,U_18776] :
        ( c_List_Olist__all2(U_18776,U_18778,U_18780,U_18782,U_18784)
        | ? [U_18769] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18776,U_18778,tc_HOL_Obool),U_18780),U_18769))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18776,U_18778)),U_18769),hAPP(c_List_Oset(tc_prod(U_18776,U_18778)),hAPP(hAPP(c_List_Ozip(U_18776,U_18778),U_18782),U_18784)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18776)),U_18782) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18784) )
    & ! [U_18783,U_18781,U_18779,U_18777,U_18775] :
        ( ( ! [U_18768] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18775,U_18777,tc_HOL_Obool),U_18779),U_18768))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18775,U_18777)),U_18768),hAPP(c_List_Oset(tc_prod(U_18775,U_18777)),hAPP(hAPP(c_List_Ozip(U_18775,U_18777),U_18781),U_18783)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18775)),U_18781) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18777)),U_18783) )
        | ~ c_List_Olist__all2(U_18775,U_18777,U_18779,U_18781,U_18783) ) ),
    inference(miniscope,[status(thm)],[f_4538_2]) ).

fof(f_4538_4,plain,
    ( ! [U_18784,U_18782,U_18780,U_18778,U_18776] :
        ( c_List_Olist__all2(U_18776,U_18778,U_18780,U_18782,U_18784)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18776,U_18778,tc_HOL_Obool),U_18780),sK474(U_18784,U_18782,U_18780,U_18778,U_18776)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18776,U_18778)),sK474(U_18784,U_18782,U_18780,U_18778,U_18776)),hAPP(c_List_Oset(tc_prod(U_18776,U_18778)),hAPP(hAPP(c_List_Ozip(U_18776,U_18778),U_18782),U_18784)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18776)),U_18782) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18784) )
    & ! [U_18783,U_18781,U_18779,U_18777,U_18775] :
        ( ( ! [U_18768] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18775,U_18777,tc_HOL_Obool),U_18779),U_18768))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18775,U_18777)),U_18768),hAPP(c_List_Oset(tc_prod(U_18775,U_18777)),hAPP(hAPP(c_List_Ozip(U_18775,U_18777),U_18781),U_18783)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18775)),U_18781) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18777)),U_18783) )
        | ~ c_List_Olist__all2(U_18775,U_18777,U_18779,U_18781,U_18783) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_18769,sK474(U_18784,U_18782,U_18780,U_18778,U_18776))],[f_4538_3]) ).

cnf(f_4538_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18775)),U_18781) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18777)),U_18783)
    | ~ c_List_Olist__all2(U_18775,U_18777,U_18779,U_18781,U_18783) ),
    inference(clausify,[status(thm)],[f_4538_4]) ).

cnf(f_4538_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18775,U_18777,tc_HOL_Obool),U_18779),U_18768))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18775,U_18777)),U_18768),hAPP(c_List_Oset(tc_prod(U_18775,U_18777)),hAPP(hAPP(c_List_Ozip(U_18775,U_18777),U_18781),U_18783))))
    | ~ c_List_Olist__all2(U_18775,U_18777,U_18779,U_18781,U_18783) ),
    inference(clausify,[status(thm)],[f_4538_4]) ).

cnf(f_4538_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18776,U_18778)),sK474(U_18784,U_18782,U_18780,U_18778,U_18776)),hAPP(c_List_Oset(tc_prod(U_18776,U_18778)),hAPP(hAPP(c_List_Ozip(U_18776,U_18778),U_18782),U_18784))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18776)),U_18782) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18784)
    | c_List_Olist__all2(U_18776,U_18778,U_18780,U_18782,U_18784) ),
    inference(clausify,[status(thm)],[f_4538_4]) ).

cnf(f_4538_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18776,U_18778,tc_HOL_Obool),U_18780),sK474(U_18784,U_18782,U_18780,U_18778,U_18776)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18776)),U_18782) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18778)),U_18784)
    | c_List_Olist__all2(U_18776,U_18778,U_18780,U_18782,U_18784) ),
    inference(clausify,[status(thm)],[f_4538_4]) ).

fof(f_4539_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD]) ).

fof(f_4539_2,plain,
    ! [U_18789,U_18788,U_18787,U_18786,U_18785] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18785)),U_18788) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18786)),U_18789)
      | ~ c_List_Olist__all2(U_18785,U_18786,U_18787,U_18788,U_18789) ),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

cnf(f_4539_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18785)),U_18788) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18786)),U_18789)
    | ~ c_List_Olist__all2(U_18785,U_18786,U_18787,U_18788,U_18789) ),
    inference(clausify,[status(thm)],[f_4539_2]) ).

fof(f_4540_1,plain,
    ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__dropI]) ).

fof(f_4540_2,plain,
    ! [U_18795,U_18794,U_18793,U_18792,U_18791,U_18790] :
      ( c_List_Olist__all2(U_18790,U_18791,U_18792,hAPP(hAPP(c_List_Odrop(U_18790),U_18795),U_18793),hAPP(hAPP(c_List_Odrop(U_18791),U_18795),U_18794))
      | ~ c_List_Olist__all2(U_18790,U_18791,U_18792,U_18793,U_18794) ),
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

cnf(f_4540_3,plain,
    ( c_List_Olist__all2(U_18790,U_18791,U_18792,hAPP(hAPP(c_List_Odrop(U_18790),U_18795),U_18793),hAPP(hAPP(c_List_Odrop(U_18791),U_18795),U_18794))
    | ~ c_List_Olist__all2(U_18790,U_18791,U_18792,U_18793,U_18794) ),
    inference(clausify,[status(thm)],[f_4540_2]) ).

fof(f_4541_1,plain,
    ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__takeI]) ).

fof(f_4541_2,plain,
    ! [U_18801,U_18800,U_18799,U_18798,U_18797,U_18796] :
      ( c_List_Olist__all2(U_18796,U_18797,U_18798,hAPP(hAPP(c_List_Otake(U_18796),U_18801),U_18799),hAPP(hAPP(c_List_Otake(U_18797),U_18801),U_18800))
      | ~ c_List_Olist__all2(U_18796,U_18797,U_18798,U_18799,U_18800) ),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

cnf(f_4541_3,plain,
    ( c_List_Olist__all2(U_18796,U_18797,U_18798,hAPP(hAPP(c_List_Otake(U_18796),U_18801),U_18799),hAPP(hAPP(c_List_Otake(U_18797),U_18801),U_18800))
    | ~ c_List_Olist__all2(U_18796,U_18797,U_18798,U_18799,U_18800) ),
    inference(clausify,[status(thm)],[f_4541_2]) ).

fof(f_4542_1,plain,
    ! [T_a,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ~ c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) )
      & ( c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2)
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__eq]) ).

fof(f_4542_2,plain,
    ! [U_18804,U_18803,U_18802] :
      ( ( U_18802 = U_18803
        | ~ c_List_Olist__all2(U_18804,U_18804,c_fequal,U_18802,U_18803) )
      & ( c_List_Olist__all2(U_18804,U_18804,c_fequal,U_18802,U_18803)
        | U_18802 != U_18803 ) ),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

fof(f_4542_3,plain,
    ( ! [U_18810,U_18808,U_18806] :
        ( U_18806 = U_18808
        | ~ c_List_Olist__all2(U_18810,U_18810,c_fequal,U_18806,U_18808) )
    & ! [U_18809,U_18807,U_18805] :
        ( c_List_Olist__all2(U_18809,U_18809,c_fequal,U_18805,U_18807)
        | U_18805 != U_18807 ) ),
    inference(miniscope,[status(thm)],[f_4542_2]) ).

cnf(f_4542_4,plain,
    ( c_List_Olist__all2(U_18809,U_18809,c_fequal,U_18805,U_18807)
    | U_18805 != U_18807 ),
    inference(clausify,[status(thm)],[f_4542_3]) ).

cnf(f_4542_5,plain,
    ( U_18806 = U_18808
    | ~ c_List_Olist__all2(U_18810,U_18810,c_fequal,U_18806,U_18808) ),
    inference(clausify,[status(thm)],[f_4542_3]) ).

fof(f_4543_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2)
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__appendI]) ).

fof(f_4543_2,plain,
    ! [U_18817,U_18816,U_18815,U_18814,U_18813,U_18812,U_18811] :
      ( c_List_Olist__all2(U_18811,U_18812,U_18813,hAPP(hAPP(c_List_Oappend(U_18811),U_18814),U_18816),hAPP(hAPP(c_List_Oappend(U_18812),U_18815),U_18817))
      | ~ c_List_Olist__all2(U_18811,U_18812,U_18813,U_18816,U_18817)
      | ~ c_List_Olist__all2(U_18811,U_18812,U_18813,U_18814,U_18815) ),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

cnf(f_4543_3,plain,
    ( c_List_Olist__all2(U_18811,U_18812,U_18813,hAPP(hAPP(c_List_Oappend(U_18811),U_18814),U_18816),hAPP(hAPP(c_List_Oappend(U_18812),U_18815),U_18817))
    | ~ c_List_Olist__all2(U_18811,U_18812,U_18813,U_18816,U_18817)
    | ~ c_List_Olist__all2(U_18811,U_18812,U_18813,U_18814,U_18815) ),
    inference(clausify,[status(thm)],[f_4543_2]) ).

fof(f_4544_1,plain,
    ! [V_ys_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_b) )
      & ( V_ys_2 = c_List_Olist_ONil(T_b)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil]) ).

fof(f_4544_2,plain,
    ! [U_18821,U_18820,U_18819,U_18818] :
      ( ( c_List_Olist__all2(U_18818,U_18819,U_18820,c_List_Olist_ONil(U_18818),U_18821)
        | U_18821 != c_List_Olist_ONil(U_18819) )
      & ( U_18821 = c_List_Olist_ONil(U_18819)
        | ~ c_List_Olist__all2(U_18818,U_18819,U_18820,c_List_Olist_ONil(U_18818),U_18821) ) ),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

fof(f_4544_3,plain,
    ( ! [U_18829,U_18827,U_18825] :
        ( ! [U_18823] : c_List_Olist__all2(U_18823,U_18825,U_18827,c_List_Olist_ONil(U_18823),U_18829)
        | U_18829 != c_List_Olist_ONil(U_18825) )
    & ! [U_18828,U_18826,U_18824] :
        ( ! [U_18822] : ~ c_List_Olist__all2(U_18822,U_18824,U_18826,c_List_Olist_ONil(U_18822),U_18828)
        | U_18828 = c_List_Olist_ONil(U_18824) ) ),
    inference(miniscope,[status(thm)],[f_4544_2]) ).

cnf(f_4544_4,plain,
    ( ~ c_List_Olist__all2(U_18822,U_18824,U_18826,c_List_Olist_ONil(U_18822),U_18828)
    | U_18828 = c_List_Olist_ONil(U_18824) ),
    inference(clausify,[status(thm)],[f_4544_3]) ).

cnf(f_4544_5,plain,
    ( c_List_Olist__all2(U_18823,U_18825,U_18827,c_List_Olist_ONil(U_18823),U_18829)
    | U_18829 != c_List_Olist_ONil(U_18825) ),
    inference(clausify,[status(thm)],[f_4544_3]) ).

fof(f_4545_1,plain,
    ! [V_xs_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2]) ).

fof(f_4545_2,plain,
    ! [U_18833,U_18832,U_18831,U_18830] :
      ( ( c_List_Olist__all2(U_18830,U_18831,U_18832,U_18833,c_List_Olist_ONil(U_18831))
        | U_18833 != c_List_Olist_ONil(U_18830) )
      & ( U_18833 = c_List_Olist_ONil(U_18830)
        | ~ c_List_Olist__all2(U_18830,U_18831,U_18832,U_18833,c_List_Olist_ONil(U_18831)) ) ),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

fof(f_4545_3,plain,
    ( ! [U_18841,U_18839,U_18837,U_18835] :
        ( c_List_Olist__all2(U_18835,U_18837,U_18839,U_18841,c_List_Olist_ONil(U_18837))
        | U_18841 != c_List_Olist_ONil(U_18835) )
    & ! [U_18840,U_18838,U_18836,U_18834] :
        ( U_18840 = c_List_Olist_ONil(U_18834)
        | ~ c_List_Olist__all2(U_18834,U_18836,U_18838,U_18840,c_List_Olist_ONil(U_18836)) ) ),
    inference(miniscope,[status(thm)],[f_4545_2]) ).

cnf(f_4545_4,plain,
    ( U_18840 = c_List_Olist_ONil(U_18834)
    | ~ c_List_Olist__all2(U_18834,U_18836,U_18838,U_18840,c_List_Olist_ONil(U_18836)) ),
    inference(clausify,[status(thm)],[f_4545_3]) ).

cnf(f_4545_5,plain,
    ( c_List_Olist__all2(U_18835,U_18837,U_18839,U_18841,c_List_Olist_ONil(U_18837))
    | U_18841 != c_List_Olist_ONil(U_18835) ),
    inference(clausify,[status(thm)],[f_4545_3]) ).

fof(f_4546_1,plain,
    ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( ( ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))
          | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2)
          | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) )
        & ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2)
            & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) )
          | ~ c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2)) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__append]) ).

fof(f_4546_2,plain,
    ! [U_18848,U_18847,U_18846,U_18845,U_18844,U_18843,U_18842] :
      ( ( ( c_List_Olist__all2(U_18842,U_18844,U_18846,hAPP(hAPP(c_List_Oappend(U_18842),U_18843),U_18847),hAPP(hAPP(c_List_Oappend(U_18844),U_18845),U_18848))
          | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,U_18847,U_18848)
          | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,U_18843,U_18845) )
        & ( ( c_List_Olist__all2(U_18842,U_18844,U_18846,U_18847,U_18848)
            & c_List_Olist__all2(U_18842,U_18844,U_18846,U_18843,U_18845) )
          | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,hAPP(hAPP(c_List_Oappend(U_18842),U_18843),U_18847),hAPP(hAPP(c_List_Oappend(U_18844),U_18845),U_18848)) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18842)),U_18843) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18844)),U_18845) ),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

cnf(f_4546_3,plain,
    ( c_List_Olist__all2(U_18842,U_18844,U_18846,U_18843,U_18845)
    | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,hAPP(hAPP(c_List_Oappend(U_18842),U_18843),U_18847),hAPP(hAPP(c_List_Oappend(U_18844),U_18845),U_18848))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18842)),U_18843) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18844)),U_18845) ),
    inference(clausify,[status(thm)],[f_4546_2]) ).

cnf(f_4546_4,plain,
    ( c_List_Olist__all2(U_18842,U_18844,U_18846,U_18847,U_18848)
    | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,hAPP(hAPP(c_List_Oappend(U_18842),U_18843),U_18847),hAPP(hAPP(c_List_Oappend(U_18844),U_18845),U_18848))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18842)),U_18843) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18844)),U_18845) ),
    inference(clausify,[status(thm)],[f_4546_2]) ).

cnf(f_4546_5,plain,
    ( c_List_Olist__all2(U_18842,U_18844,U_18846,hAPP(hAPP(c_List_Oappend(U_18842),U_18843),U_18847),hAPP(hAPP(c_List_Oappend(U_18844),U_18845),U_18848))
    | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,U_18847,U_18848)
    | ~ c_List_Olist__all2(U_18842,U_18844,U_18846,U_18843,U_18845)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18842)),U_18843) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18844)),U_18845) ),
    inference(clausify,[status(thm)],[f_4546_2]) ).

fof(f_4547_1,plain,
    ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2))
        | ~ c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) )
      & ( c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__map2]) ).

fof(f_4547_2,plain,
    ! [U_18855,U_18854,U_18853,U_18852,U_18851,U_18850,U_18849] :
      ( ( c_List_Olist__all2(U_18849,U_18850,U_18851,U_18852,hAPP(hAPP(c_List_Omap(U_18853,U_18850),U_18854),U_18855))
        | ~ c_List_Olist__all2(U_18849,U_18853,hAPP(hAPP(c_COMBC(U_18849,tc_fun(U_18853,U_18850),tc_fun(U_18853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18850,tc_HOL_Obool),tc_fun(tc_fun(U_18853,U_18850),tc_fun(U_18853,tc_HOL_Obool)),U_18849),c_COMBB(U_18850,tc_HOL_Obool,U_18853)),U_18851)),U_18854),U_18852,U_18855) )
      & ( c_List_Olist__all2(U_18849,U_18853,hAPP(hAPP(c_COMBC(U_18849,tc_fun(U_18853,U_18850),tc_fun(U_18853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18850,tc_HOL_Obool),tc_fun(tc_fun(U_18853,U_18850),tc_fun(U_18853,tc_HOL_Obool)),U_18849),c_COMBB(U_18850,tc_HOL_Obool,U_18853)),U_18851)),U_18854),U_18852,U_18855)
        | ~ c_List_Olist__all2(U_18849,U_18850,U_18851,U_18852,hAPP(hAPP(c_List_Omap(U_18853,U_18850),U_18854),U_18855)) ) ),
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

fof(f_4547_3,plain,
    ( ! [U_18869,U_18867,U_18865,U_18863,U_18861,U_18859,U_18857] :
        ( c_List_Olist__all2(U_18857,U_18859,U_18861,U_18863,hAPP(hAPP(c_List_Omap(U_18865,U_18859),U_18867),U_18869))
        | ~ c_List_Olist__all2(U_18857,U_18865,hAPP(hAPP(c_COMBC(U_18857,tc_fun(U_18865,U_18859),tc_fun(U_18865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18859,tc_HOL_Obool),tc_fun(tc_fun(U_18865,U_18859),tc_fun(U_18865,tc_HOL_Obool)),U_18857),c_COMBB(U_18859,tc_HOL_Obool,U_18865)),U_18861)),U_18867),U_18863,U_18869) )
    & ! [U_18868,U_18866,U_18864,U_18862,U_18860,U_18858,U_18856] :
        ( c_List_Olist__all2(U_18856,U_18864,hAPP(hAPP(c_COMBC(U_18856,tc_fun(U_18864,U_18858),tc_fun(U_18864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18858,tc_HOL_Obool),tc_fun(tc_fun(U_18864,U_18858),tc_fun(U_18864,tc_HOL_Obool)),U_18856),c_COMBB(U_18858,tc_HOL_Obool,U_18864)),U_18860)),U_18866),U_18862,U_18868)
        | ~ c_List_Olist__all2(U_18856,U_18858,U_18860,U_18862,hAPP(hAPP(c_List_Omap(U_18864,U_18858),U_18866),U_18868)) ) ),
    inference(miniscope,[status(thm)],[f_4547_2]) ).

cnf(f_4547_4,plain,
    ( c_List_Olist__all2(U_18856,U_18864,hAPP(hAPP(c_COMBC(U_18856,tc_fun(U_18864,U_18858),tc_fun(U_18864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18858,tc_HOL_Obool),tc_fun(tc_fun(U_18864,U_18858),tc_fun(U_18864,tc_HOL_Obool)),U_18856),c_COMBB(U_18858,tc_HOL_Obool,U_18864)),U_18860)),U_18866),U_18862,U_18868)
    | ~ c_List_Olist__all2(U_18856,U_18858,U_18860,U_18862,hAPP(hAPP(c_List_Omap(U_18864,U_18858),U_18866),U_18868)) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

cnf(f_4547_5,plain,
    ( c_List_Olist__all2(U_18857,U_18859,U_18861,U_18863,hAPP(hAPP(c_List_Omap(U_18865,U_18859),U_18867),U_18869))
    | ~ c_List_Olist__all2(U_18857,U_18865,hAPP(hAPP(c_COMBC(U_18857,tc_fun(U_18865,U_18859),tc_fun(U_18865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18859,tc_HOL_Obool),tc_fun(tc_fun(U_18865,U_18859),tc_fun(U_18865,tc_HOL_Obool)),U_18857),c_COMBB(U_18859,tc_HOL_Obool,U_18865)),U_18861)),U_18867),U_18863,U_18869) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

fof(f_4548_1,plain,
    ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2)
        | ~ c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) )
      & ( c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__map1]) ).

fof(f_4548_2,plain,
    ! [U_18876,U_18875,U_18874,U_18873,U_18872,U_18871,U_18870] :
      ( ( c_List_Olist__all2(U_18870,U_18871,U_18872,hAPP(hAPP(c_List_Omap(U_18873,U_18870),U_18874),U_18875),U_18876)
        | ~ c_List_Olist__all2(U_18873,U_18871,hAPP(hAPP(c_COMBB(U_18870,tc_fun(U_18871,tc_HOL_Obool),U_18873),U_18872),U_18874),U_18875,U_18876) )
      & ( c_List_Olist__all2(U_18873,U_18871,hAPP(hAPP(c_COMBB(U_18870,tc_fun(U_18871,tc_HOL_Obool),U_18873),U_18872),U_18874),U_18875,U_18876)
        | ~ c_List_Olist__all2(U_18870,U_18871,U_18872,hAPP(hAPP(c_List_Omap(U_18873,U_18870),U_18874),U_18875),U_18876) ) ),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

fof(f_4548_3,plain,
    ( ! [U_18890,U_18888,U_18886,U_18884,U_18882,U_18880,U_18878] :
        ( c_List_Olist__all2(U_18878,U_18880,U_18882,hAPP(hAPP(c_List_Omap(U_18884,U_18878),U_18886),U_18888),U_18890)
        | ~ c_List_Olist__all2(U_18884,U_18880,hAPP(hAPP(c_COMBB(U_18878,tc_fun(U_18880,tc_HOL_Obool),U_18884),U_18882),U_18886),U_18888,U_18890) )
    & ! [U_18889,U_18887,U_18885,U_18883,U_18881,U_18879,U_18877] :
        ( c_List_Olist__all2(U_18883,U_18879,hAPP(hAPP(c_COMBB(U_18877,tc_fun(U_18879,tc_HOL_Obool),U_18883),U_18881),U_18885),U_18887,U_18889)
        | ~ c_List_Olist__all2(U_18877,U_18879,U_18881,hAPP(hAPP(c_List_Omap(U_18883,U_18877),U_18885),U_18887),U_18889) ) ),
    inference(miniscope,[status(thm)],[f_4548_2]) ).

cnf(f_4548_4,plain,
    ( c_List_Olist__all2(U_18883,U_18879,hAPP(hAPP(c_COMBB(U_18877,tc_fun(U_18879,tc_HOL_Obool),U_18883),U_18881),U_18885),U_18887,U_18889)
    | ~ c_List_Olist__all2(U_18877,U_18879,U_18881,hAPP(hAPP(c_List_Omap(U_18883,U_18877),U_18885),U_18887),U_18889) ),
    inference(clausify,[status(thm)],[f_4548_3]) ).

cnf(f_4548_5,plain,
    ( c_List_Olist__all2(U_18878,U_18880,U_18882,hAPP(hAPP(c_List_Omap(U_18884,U_18878),U_18886),U_18888),U_18890)
    | ~ c_List_Olist__all2(U_18884,U_18880,hAPP(hAPP(c_COMBB(U_18878,tc_fun(U_18880,tc_HOL_Obool),U_18884),U_18882),U_18886),U_18888,U_18890) ),
    inference(clausify,[status(thm)],[f_4548_3]) ).

fof(f_4549_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
        | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) )
      & ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
          & hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) )
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Cons]) ).

fof(f_4549_2,plain,
    ! [U_18897,U_18896,U_18895,U_18894,U_18893,U_18892,U_18891] :
      ( ( c_List_Olist__all2(U_18891,U_18892,U_18893,hAPP(hAPP(c_List_Olist_OCons(U_18891),U_18894),U_18895),hAPP(hAPP(c_List_Olist_OCons(U_18892),U_18896),U_18897))
        | ~ c_List_Olist__all2(U_18891,U_18892,U_18893,U_18895,U_18897)
        | ~ hBOOL(hAPP(hAPP(U_18893,U_18894),U_18896)) )
      & ( ( c_List_Olist__all2(U_18891,U_18892,U_18893,U_18895,U_18897)
          & hBOOL(hAPP(hAPP(U_18893,U_18894),U_18896)) )
        | ~ c_List_Olist__all2(U_18891,U_18892,U_18893,hAPP(hAPP(c_List_Olist_OCons(U_18891),U_18894),U_18895),hAPP(hAPP(c_List_Olist_OCons(U_18892),U_18896),U_18897)) ) ),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

fof(f_4549_3,plain,
    ( ! [U_18911,U_18909,U_18907,U_18905,U_18903,U_18901,U_18899] :
        ( c_List_Olist__all2(U_18899,U_18901,U_18903,hAPP(hAPP(c_List_Olist_OCons(U_18899),U_18905),U_18907),hAPP(hAPP(c_List_Olist_OCons(U_18901),U_18909),U_18911))
        | ~ c_List_Olist__all2(U_18899,U_18901,U_18903,U_18907,U_18911)
        | ~ hBOOL(hAPP(hAPP(U_18903,U_18905),U_18909)) )
    & ! [U_18910,U_18908,U_18906,U_18904,U_18902,U_18900,U_18898] :
        ( ( c_List_Olist__all2(U_18898,U_18900,U_18902,U_18906,U_18910)
          & hBOOL(hAPP(hAPP(U_18902,U_18904),U_18908)) )
        | ~ c_List_Olist__all2(U_18898,U_18900,U_18902,hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18904),U_18906),hAPP(hAPP(c_List_Olist_OCons(U_18900),U_18908),U_18910)) ) ),
    inference(miniscope,[status(thm)],[f_4549_2]) ).

cnf(f_4549_4,plain,
    ( hBOOL(hAPP(hAPP(U_18902,U_18904),U_18908))
    | ~ c_List_Olist__all2(U_18898,U_18900,U_18902,hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18904),U_18906),hAPP(hAPP(c_List_Olist_OCons(U_18900),U_18908),U_18910)) ),
    inference(clausify,[status(thm)],[f_4549_3]) ).

cnf(f_4549_5,plain,
    ( c_List_Olist__all2(U_18898,U_18900,U_18902,U_18906,U_18910)
    | ~ c_List_Olist__all2(U_18898,U_18900,U_18902,hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18904),U_18906),hAPP(hAPP(c_List_Olist_OCons(U_18900),U_18908),U_18910)) ),
    inference(clausify,[status(thm)],[f_4549_3]) ).

cnf(f_4549_6,plain,
    ( c_List_Olist__all2(U_18899,U_18901,U_18903,hAPP(hAPP(c_List_Olist_OCons(U_18899),U_18905),U_18907),hAPP(hAPP(c_List_Olist_OCons(U_18901),U_18909),U_18911))
    | ~ c_List_Olist__all2(U_18899,U_18901,U_18903,U_18907,U_18911)
    | ~ hBOOL(hAPP(hAPP(U_18903,U_18905),U_18909)) ),
    inference(clausify,[status(thm)],[f_4549_3]) ).

fof(f_4550_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2]) ).

fof(f_4550_2,plain,
    ! [U_18917,U_18916,U_18915,U_18914,U_18913,U_18912] :
      ( hBOOL(hAPP(hAPP(U_18914,hAPP(hAPP(c_List_Onth(U_18912),U_18915),U_18917)),hAPP(hAPP(c_List_Onth(U_18913),U_18916),U_18917)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18917),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18913)),U_18916)))
      | ~ c_List_Olist__all2(U_18912,U_18913,U_18914,U_18915,U_18916) ),
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

cnf(f_4550_3,plain,
    ( hBOOL(hAPP(hAPP(U_18914,hAPP(hAPP(c_List_Onth(U_18912),U_18915),U_18917)),hAPP(hAPP(c_List_Onth(U_18913),U_18916),U_18917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18917),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18913)),U_18916)))
    | ~ c_List_Olist__all2(U_18912,U_18913,U_18914,U_18915,U_18916) ),
    inference(clausify,[status(thm)],[f_4550_2]) ).

fof(f_4551_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD]) ).

fof(f_4551_2,plain,
    ! [U_18923,U_18922,U_18921,U_18920,U_18919,U_18918] :
      ( hBOOL(hAPP(hAPP(U_18920,hAPP(hAPP(c_List_Onth(U_18918),U_18921),U_18923)),hAPP(hAPP(c_List_Onth(U_18919),U_18922),U_18923)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18923),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18918)),U_18921)))
      | ~ c_List_Olist__all2(U_18918,U_18919,U_18920,U_18921,U_18922) ),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

cnf(f_4551_3,plain,
    ( hBOOL(hAPP(hAPP(U_18920,hAPP(hAPP(c_List_Onth(U_18918),U_18921),U_18923)),hAPP(hAPP(c_List_Onth(U_18919),U_18922),U_18923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18923),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18918)),U_18921)))
    | ~ c_List_Olist__all2(U_18918,U_18919,U_18920,U_18921,U_18922) ),
    inference(clausify,[status(thm)],[f_4551_2]) ).

fof(f_4552_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
        | ? [B_i] :
            ( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__conv__all__nth]) ).

fof(f_4552_2,plain,
    ! [U_18930,U_18929,U_18928,U_18927,U_18926] :
      ( ( c_List_Olist__all2(U_18926,U_18927,U_18928,U_18929,U_18930)
        | ? [U_18925] :
            ( ~ hBOOL(hAPP(hAPP(U_18928,hAPP(hAPP(c_List_Onth(U_18926),U_18929),U_18925)),hAPP(hAPP(c_List_Onth(U_18927),U_18930),U_18925)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18925),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18926)),U_18929))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18926)),U_18929) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18927)),U_18930) )
      & ( ( ! [U_18924] :
              ( hBOOL(hAPP(hAPP(U_18928,hAPP(hAPP(c_List_Onth(U_18926),U_18929),U_18924)),hAPP(hAPP(c_List_Onth(U_18927),U_18930),U_18924)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18924),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18926)),U_18929))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18926)),U_18929) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18927)),U_18930) )
        | ~ c_List_Olist__all2(U_18926,U_18927,U_18928,U_18929,U_18930) ) ),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

fof(f_4552_3,plain,
    ( ! [U_18940,U_18938,U_18936,U_18934,U_18932] :
        ( c_List_Olist__all2(U_18932,U_18934,U_18936,U_18938,U_18940)
        | ? [U_18925] :
            ( ~ hBOOL(hAPP(hAPP(U_18936,hAPP(hAPP(c_List_Onth(U_18932),U_18938),U_18925)),hAPP(hAPP(c_List_Onth(U_18934),U_18940),U_18925)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18925),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18934)),U_18940) )
    & ! [U_18939,U_18937,U_18935,U_18933,U_18931] :
        ( ( ! [U_18924] :
              ( hBOOL(hAPP(hAPP(U_18935,hAPP(hAPP(c_List_Onth(U_18931),U_18937),U_18924)),hAPP(hAPP(c_List_Onth(U_18933),U_18939),U_18924)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18924),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18933)),U_18939) )
        | ~ c_List_Olist__all2(U_18931,U_18933,U_18935,U_18937,U_18939) ) ),
    inference(miniscope,[status(thm)],[f_4552_2]) ).

fof(f_4552_4,plain,
    ( ! [U_18940,U_18938,U_18936,U_18934,U_18932] :
        ( c_List_Olist__all2(U_18932,U_18934,U_18936,U_18938,U_18940)
        | ( ~ hBOOL(hAPP(hAPP(U_18936,hAPP(hAPP(c_List_Onth(U_18932),U_18938),sK475(U_18940,U_18938,U_18936,U_18934,U_18932))),hAPP(hAPP(c_List_Onth(U_18934),U_18940),sK475(U_18940,U_18938,U_18936,U_18934,U_18932))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK475(U_18940,U_18938,U_18936,U_18934,U_18932)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18934)),U_18940) )
    & ! [U_18939,U_18937,U_18935,U_18933,U_18931] :
        ( ( ! [U_18924] :
              ( hBOOL(hAPP(hAPP(U_18935,hAPP(hAPP(c_List_Onth(U_18931),U_18937),U_18924)),hAPP(hAPP(c_List_Onth(U_18933),U_18939),U_18924)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18924),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18933)),U_18939) )
        | ~ c_List_Olist__all2(U_18931,U_18933,U_18935,U_18937,U_18939) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_18925,sK475(U_18940,U_18938,U_18936,U_18934,U_18932))],[f_4552_3]) ).

cnf(f_4552_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18933)),U_18939)
    | ~ c_List_Olist__all2(U_18931,U_18933,U_18935,U_18937,U_18939) ),
    inference(clausify,[status(thm)],[f_4552_4]) ).

cnf(f_4552_6,plain,
    ( hBOOL(hAPP(hAPP(U_18935,hAPP(hAPP(c_List_Onth(U_18931),U_18937),U_18924)),hAPP(hAPP(c_List_Onth(U_18933),U_18939),U_18924)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18924),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18931)),U_18937)))
    | ~ c_List_Olist__all2(U_18931,U_18933,U_18935,U_18937,U_18939) ),
    inference(clausify,[status(thm)],[f_4552_4]) ).

cnf(f_4552_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK475(U_18940,U_18938,U_18936,U_18934,U_18932)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18934)),U_18940)
    | c_List_Olist__all2(U_18932,U_18934,U_18936,U_18938,U_18940) ),
    inference(clausify,[status(thm)],[f_4552_4]) ).

cnf(f_4552_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_18936,hAPP(hAPP(c_List_Onth(U_18932),U_18938),sK475(U_18940,U_18938,U_18936,U_18934,U_18932))),hAPP(hAPP(c_List_Onth(U_18934),U_18940),sK475(U_18940,U_18938,U_18936,U_18934,U_18932))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18932)),U_18938) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18934)),U_18940)
    | c_List_Olist__all2(U_18932,U_18934,U_18936,U_18938,U_18940) ),
    inference(clausify,[status(thm)],[f_4552_4]) ).

fof(f_4553_1,plain,
    ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_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_ys_2)))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2]) ).

fof(f_4553_2,plain,
    ! [U_18948,U_18947,U_18946,U_18945,U_18944,U_18943,U_18942,U_18941] :
      ( c_List_Olist__all2(U_18941,U_18942,U_18943,hAPP(hAPP(c_List_Olist__update(U_18941,U_18944),U_18948),U_18946),hAPP(hAPP(c_List_Olist__update(U_18942,U_18945),U_18948),U_18947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18948),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18942)),U_18945)))
      | ~ hBOOL(hAPP(hAPP(U_18943,U_18946),U_18947))
      | ~ c_List_Olist__all2(U_18941,U_18942,U_18943,U_18944,U_18945) ),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

cnf(f_4553_3,plain,
    ( c_List_Olist__all2(U_18941,U_18942,U_18943,hAPP(hAPP(c_List_Olist__update(U_18941,U_18944),U_18948),U_18946),hAPP(hAPP(c_List_Olist__update(U_18942,U_18945),U_18948),U_18947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18948),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18942)),U_18945)))
    | ~ hBOOL(hAPP(hAPP(U_18943,U_18946),U_18947))
    | ~ c_List_Olist__all2(U_18941,U_18942,U_18943,U_18944,U_18945) ),
    inference(clausify,[status(thm)],[f_4553_2]) ).

fof(f_4554_1,plain,
    ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_a,T_b,V_P_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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong]) ).

fof(f_4554_2,plain,
    ! [U_18956,U_18955,U_18954,U_18953,U_18952,U_18951,U_18950,U_18949] :
      ( c_List_Olist__all2(U_18950,U_18952,U_18953,hAPP(hAPP(c_List_Olist__update(U_18950,U_18951),U_18949),U_18955),hAPP(hAPP(c_List_Olist__update(U_18952,U_18954),U_18949),U_18956))
      | ~ hBOOL(hAPP(hAPP(U_18953,U_18955),U_18956))
      | ~ c_List_Olist__all2(U_18950,U_18952,U_18953,U_18951,U_18954)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18949),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18950)),U_18951))) ),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

cnf(f_4554_3,plain,
    ( c_List_Olist__all2(U_18950,U_18952,U_18953,hAPP(hAPP(c_List_Olist__update(U_18950,U_18951),U_18949),U_18955),hAPP(hAPP(c_List_Olist__update(U_18952,U_18954),U_18949),U_18956))
    | ~ hBOOL(hAPP(hAPP(U_18953,U_18955),U_18956))
    | ~ c_List_Olist__all2(U_18950,U_18952,U_18953,U_18951,U_18954)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18949),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18950)),U_18951))) ),
    inference(clausify,[status(thm)],[f_4554_2]) ).

fof(f_4555_1,plain,
    ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2I]) ).

fof(f_4555_2,plain,
    ! [U_18962,U_18961,U_18960,U_18959,U_18958] :
      ( c_List_Olist__all2(U_18958,U_18959,U_18962,U_18960,U_18961)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18958)),U_18960) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18959)),U_18961)
      | ? [U_18957] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18958,U_18959,tc_HOL_Obool),U_18962),U_18957))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18958,U_18959)),U_18957),hAPP(c_List_Oset(tc_prod(U_18958,U_18959)),hAPP(hAPP(c_List_Ozip(U_18958,U_18959),U_18960),U_18961)))) ) ),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

fof(f_4555_3,plain,
    ! [U_18962,U_18961,U_18960,U_18959,U_18958] :
      ( c_List_Olist__all2(U_18958,U_18959,U_18962,U_18960,U_18961)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18958)),U_18960) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18959)),U_18961)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18958,U_18959,tc_HOL_Obool),U_18962),sK476(U_18962,U_18961,U_18960,U_18959,U_18958)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18958,U_18959)),sK476(U_18962,U_18961,U_18960,U_18959,U_18958)),hAPP(c_List_Oset(tc_prod(U_18958,U_18959)),hAPP(hAPP(c_List_Ozip(U_18958,U_18959),U_18960),U_18961)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_18957,sK476(U_18962,U_18961,U_18960,U_18959,U_18958))],[f_4555_2]) ).

cnf(f_4555_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18958,U_18959)),sK476(U_18962,U_18961,U_18960,U_18959,U_18958)),hAPP(c_List_Oset(tc_prod(U_18958,U_18959)),hAPP(hAPP(c_List_Ozip(U_18958,U_18959),U_18960),U_18961))))
    | c_List_Olist__all2(U_18958,U_18959,U_18962,U_18960,U_18961)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18958)),U_18960) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18959)),U_18961) ),
    inference(clausify,[status(thm)],[f_4555_3]) ).

cnf(f_4555_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18958,U_18959,tc_HOL_Obool),U_18962),sK476(U_18962,U_18961,U_18960,U_18959,U_18958)))
    | c_List_Olist__all2(U_18958,U_18959,U_18962,U_18960,U_18961)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18958)),U_18960) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18959)),U_18961) ),
    inference(clausify,[status(thm)],[f_4555_3]) ).

fof(f_4556_1,plain,
    ! [V_x_2,V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set]) ).

fof(f_4556_2,plain,
    ! [U_18967,U_18966,U_18965,U_18964] :
      ( hBOOL(hAPP(U_18966,U_18967))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18964),U_18967),hAPP(c_List_Oset(U_18964),U_18965)))
      | ? [U_18963] :
          ( ~ hBOOL(hAPP(U_18966,hAPP(hAPP(c_List_Onth(U_18964),U_18965),U_18963)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18963),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18964)),U_18965))) ) ),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

fof(f_4556_3,plain,
    ! [U_18967,U_18966,U_18965,U_18964] :
      ( hBOOL(hAPP(U_18966,U_18967))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18964),U_18967),hAPP(c_List_Oset(U_18964),U_18965)))
      | ( ~ hBOOL(hAPP(U_18966,hAPP(hAPP(c_List_Onth(U_18964),U_18965),sK477(U_18967,U_18966,U_18965,U_18964))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK477(U_18967,U_18966,U_18965,U_18964)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18964)),U_18965))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_18963,sK477(U_18967,U_18966,U_18965,U_18964))],[f_4556_2]) ).

cnf(f_4556_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK477(U_18967,U_18966,U_18965,U_18964)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18964)),U_18965)))
    | hBOOL(hAPP(U_18966,U_18967))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18964),U_18967),hAPP(c_List_Oset(U_18964),U_18965))) ),
    inference(clausify,[status(thm)],[f_4556_3]) ).

cnf(f_4556_5,plain,
    ( ~ hBOOL(hAPP(U_18966,hAPP(hAPP(c_List_Onth(U_18964),U_18965),sK477(U_18967,U_18966,U_18965,U_18964))))
    | hBOOL(hAPP(U_18966,U_18967))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18964),U_18967),hAPP(c_List_Oset(U_18964),U_18965))) ),
    inference(clausify,[status(thm)],[f_4556_3]) ).

fof(f_4557_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups]) ).

fof(f_4557_2,plain,
    ! [U_18972,U_18971,U_18970,U_18969,U_18968] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_18968,U_18969,U_18970),U_18971),hAPP(c_List_Oset(U_18968),U_18972)) = hAPP(c_List_Ofoldl(U_18969,U_18968,hAPP(c_COMBC(U_18968,U_18969,U_18969),U_18970),U_18971),c_List_Oremdups(U_18968,U_18972))
      | ~ c_Finite__Set_Ofun__left__comm(U_18968,U_18969,U_18970) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

cnf(f_4557_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_18968,U_18969,U_18970),U_18971),hAPP(c_List_Oset(U_18968),U_18972)) = hAPP(c_List_Ofoldl(U_18969,U_18968,hAPP(c_COMBC(U_18968,U_18969,U_18969),U_18970),U_18971),c_List_Oremdups(U_18968,U_18972))
    | ~ c_Finite__Set_Ofun__left__comm(U_18968,U_18969,U_18970) ),
    inference(clausify,[status(thm)],[f_4557_2]) ).

fof(f_4558_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on]) ).

fof(f_4558_2,plain,
    ! [U_18977,U_18976,U_18975,U_18974,U_18973] :
      ( hAPP(hAPP(c_List_Omap(U_18973,U_18974),U_18975),hAPP(c_List_OremoveAll(U_18973,U_18976),U_18977)) = hAPP(c_List_OremoveAll(U_18974,hAPP(U_18975,U_18976)),hAPP(hAPP(c_List_Omap(U_18973,U_18974),U_18975),U_18977))
      | ~ c_Fun_Oinj__on(U_18973,U_18974,U_18975,hAPP(hAPP(c_Set_Oinsert(U_18973),U_18976),hAPP(c_List_Oset(U_18973),U_18977))) ),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

cnf(f_4558_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_18973,U_18974),U_18975),hAPP(c_List_OremoveAll(U_18973,U_18976),U_18977)) = hAPP(c_List_OremoveAll(U_18974,hAPP(U_18975,U_18976)),hAPP(hAPP(c_List_Omap(U_18973,U_18974),U_18975),U_18977))
    | ~ c_Fun_Oinj__on(U_18973,U_18974,U_18975,hAPP(hAPP(c_Set_Oinsert(U_18973),U_18976),hAPP(c_List_Oset(U_18973),U_18977))) ),
    inference(clausify,[status(thm)],[f_4558_2]) ).

fof(f_4559_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_4559_2,plain,
    ! [U_18979,U_18978] : hBOOL(hAPP(c_List_Odistinct(U_18978),c_List_Oremdups(U_18978,U_18979))),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

cnf(f_4559_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_18978),c_List_Oremdups(U_18978,U_18979))),
    inference(clausify,[status(thm)],[f_4559_2]) ).

fof(f_4560_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_4560_2,plain,
    ! [U_18981,U_18980] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18980)),c_List_Oremdups(U_18980,U_18981))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18980)),U_18981))),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

cnf(f_4560_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18980)),c_List_Oremdups(U_18980,U_18981))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18980)),U_18981))),
    inference(clausify,[status(thm)],[f_4560_2]) ).

fof(f_4561_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll__id]) ).

fof(f_4561_2,plain,
    ! [U_18984,U_18983,U_18982] :
      ( hAPP(c_List_OremoveAll(U_18982,U_18983),U_18984) = U_18984
      | hBOOL(hAPP(hAPP(c_member(U_18982),U_18983),hAPP(c_List_Oset(U_18982),U_18984))) ),
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

cnf(f_4561_3,plain,
    ( hAPP(c_List_OremoveAll(U_18982,U_18983),U_18984) = U_18984
    | hBOOL(hAPP(hAPP(c_member(U_18982),U_18983),hAPP(c_List_Oset(U_18982),U_18984))) ),
    inference(clausify,[status(thm)],[f_4561_2]) ).

fof(f_4562_1,plain,
    ! [V_xs_2,T_a] :
      ( ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | c_List_Oremdups(T_a,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct]) ).

fof(f_4562_2,plain,
    ! [U_18986,U_18985] :
      ( ( c_List_Oremdups(U_18985,U_18986) = U_18986
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18985),U_18986)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_18985),U_18986))
        | c_List_Oremdups(U_18985,U_18986) != U_18986 ) ),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

fof(f_4562_3,plain,
    ( ! [U_18990,U_18988] :
        ( c_List_Oremdups(U_18988,U_18990) = U_18990
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18988),U_18990)) )
    & ! [U_18989,U_18987] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18987),U_18989))
        | c_List_Oremdups(U_18987,U_18989) != U_18989 ) ),
    inference(miniscope,[status(thm)],[f_4562_2]) ).

cnf(f_4562_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18987),U_18989))
    | c_List_Oremdups(U_18987,U_18989) != U_18989 ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

cnf(f_4562_5,plain,
    ( c_List_Oremdups(U_18988,U_18990) = U_18990
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18988),U_18990)) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

fof(f_4563_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__removeAll]) ).

fof(f_4563_2,plain,
    ! [U_18993,U_18992,U_18991] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18991),hAPP(c_List_OremoveAll(U_18991,U_18993),U_18992)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18992)) ),
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

cnf(f_4563_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18991),hAPP(c_List_OremoveAll(U_18991,U_18993),U_18992)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18992)) ),
    inference(clausify,[status(thm)],[f_4563_2]) ).

fof(f_4564_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_4564_2,plain,
    ! [U_18995,U_18994] :
      ( c_List_Oremdups(U_18994,U_18995) = U_18995
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18994),U_18995)) ),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

cnf(f_4564_3,plain,
    ( c_List_Oremdups(U_18994,U_18995) = U_18995
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18994),U_18995)) ),
    inference(clausify,[status(thm)],[f_4564_2]) ).

fof(f_4565_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_4565_2,plain,
    ! [U_18998,U_18997,U_18996] :
      ( c_List_Oremove1(U_18996,U_18998,c_List_Oremdups(U_18996,U_18997)) = c_List_Oremdups(U_18996,c_List_Oremove1(U_18996,U_18998,U_18997))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18996),U_18997)) ),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

cnf(f_4565_3,plain,
    ( c_List_Oremove1(U_18996,U_18998,c_List_Oremdups(U_18996,U_18997)) = c_List_Oremdups(U_18996,c_List_Oremove1(U_18996,U_18998,U_18997))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18996),U_18997)) ),
    inference(clausify,[status(thm)],[f_4565_2]) ).

fof(f_4566_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
        | c_List_Oremdups(T_a,V_xs_2) != V_xs_2 )
      & ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__eq]) ).

fof(f_4566_2,plain,
    ! [U_19000,U_18999] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18999)),c_List_Oremdups(U_18999,U_19000)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18999)),U_19000)
        | c_List_Oremdups(U_18999,U_19000) != U_19000 )
      & ( c_List_Oremdups(U_18999,U_19000) = U_19000
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18999)),c_List_Oremdups(U_18999,U_19000)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18999)),U_19000) ) ),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

fof(f_4566_3,plain,
    ( ! [U_19004,U_19002] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),c_List_Oremdups(U_19002,U_19004)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),U_19004)
        | c_List_Oremdups(U_19002,U_19004) != U_19004 )
    & ! [U_19003,U_19001] :
        ( c_List_Oremdups(U_19001,U_19003) = U_19003
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19001)),c_List_Oremdups(U_19001,U_19003)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19001)),U_19003) ) ),
    inference(miniscope,[status(thm)],[f_4566_2]) ).

cnf(f_4566_4,plain,
    ( c_List_Oremdups(U_19001,U_19003) = U_19003
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19001)),c_List_Oremdups(U_19001,U_19003)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19001)),U_19003) ),
    inference(clausify,[status(thm)],[f_4566_3]) ).

cnf(f_4566_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),c_List_Oremdups(U_19002,U_19004)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),U_19004)
    | c_List_Oremdups(U_19002,U_19004) != U_19004 ),
    inference(clausify,[status(thm)],[f_4566_3]) ).

fof(f_4567_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__remdups]) ).

fof(f_4567_2,plain,
    ! [U_19006,U_19005] : hAPP(c_List_Oset(U_19005),c_List_Oremdups(U_19005,U_19006)) = hAPP(c_List_Oset(U_19005),U_19006),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

cnf(f_4567_3,plain,
    hAPP(c_List_Oset(U_19005),c_List_Oremdups(U_19005,U_19006)) = hAPP(c_List_Oset(U_19005),U_19006),
    inference(clausify,[status(thm)],[f_4567_2]) ).

fof(f_4568_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_4568_2,plain,
    ! [U_19008,U_19007] : c_List_Oremdups(U_19007,c_List_Oremdups(U_19007,U_19008)) = c_List_Oremdups(U_19007,U_19008),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

cnf(f_4568_3,plain,
    c_List_Oremdups(U_19007,c_List_Oremdups(U_19007,U_19008)) = c_List_Oremdups(U_19007,U_19008),
    inference(clausify,[status(thm)],[f_4568_2]) ).

fof(f_4569_1,plain,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_removeAll__append]) ).

fof(f_4569_2,plain,
    ! [U_19012,U_19011,U_19010,U_19009] : hAPP(c_List_OremoveAll(U_19009,U_19010),hAPP(hAPP(c_List_Oappend(U_19009),U_19011),U_19012)) = hAPP(hAPP(c_List_Oappend(U_19009),hAPP(c_List_OremoveAll(U_19009,U_19010),U_19011)),hAPP(c_List_OremoveAll(U_19009,U_19010),U_19012)),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

cnf(f_4569_3,plain,
    hAPP(c_List_OremoveAll(U_19009,U_19010),hAPP(hAPP(c_List_Oappend(U_19009),U_19011),U_19012)) = hAPP(hAPP(c_List_Oappend(U_19009),hAPP(c_List_OremoveAll(U_19009,U_19010),U_19011)),hAPP(c_List_OremoveAll(U_19009,U_19010),U_19012)),
    inference(clausify,[status(thm)],[f_4569_2]) ).

fof(f_4570_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_4570_2,plain,
    ! [U_19013] : c_List_Oremdups(U_19013,c_List_Olist_ONil(U_19013)) = c_List_Olist_ONil(U_19013),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

cnf(f_4570_3,plain,
    c_List_Oremdups(U_19013,c_List_Olist_ONil(U_19013)) = c_List_Olist_ONil(U_19013),
    inference(clausify,[status(thm)],[f_4570_2]) ).

fof(f_4571_1,plain,
    ! [V_x_2,T_a] :
      ( ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
        | V_x_2 != c_List_Olist_ONil(T_a) )
      & ( V_x_2 = c_List_Olist_ONil(T_a)
        | c_List_Olist_ONil(T_a) != c_List_Oremdups(T_a,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff]) ).

fof(f_4571_2,plain,
    ! [U_19015,U_19014] :
      ( ( c_List_Olist_ONil(U_19014) = c_List_Oremdups(U_19014,U_19015)
        | U_19015 != c_List_Olist_ONil(U_19014) )
      & ( U_19015 = c_List_Olist_ONil(U_19014)
        | c_List_Olist_ONil(U_19014) != c_List_Oremdups(U_19014,U_19015) ) ),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

fof(f_4571_3,plain,
    ( ! [U_19019,U_19017] :
        ( c_List_Olist_ONil(U_19017) = c_List_Oremdups(U_19017,U_19019)
        | U_19019 != c_List_Olist_ONil(U_19017) )
    & ! [U_19018,U_19016] :
        ( U_19018 = c_List_Olist_ONil(U_19016)
        | c_List_Olist_ONil(U_19016) != c_List_Oremdups(U_19016,U_19018) ) ),
    inference(miniscope,[status(thm)],[f_4571_2]) ).

cnf(f_4571_4,plain,
    ( U_19018 = c_List_Olist_ONil(U_19016)
    | c_List_Olist_ONil(U_19016) != c_List_Oremdups(U_19016,U_19018) ),
    inference(clausify,[status(thm)],[f_4571_3]) ).

cnf(f_4571_5,plain,
    ( c_List_Olist_ONil(U_19017) = c_List_Oremdups(U_19017,U_19019)
    | U_19019 != c_List_Olist_ONil(U_19017) ),
    inference(clausify,[status(thm)],[f_4571_3]) ).

fof(f_4572_1,plain,
    ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(f_4572_2,plain,
    ! [U_19021,U_19020] : hAPP(c_List_OremoveAll(U_19020,U_19021),c_List_Olist_ONil(U_19020)) = c_List_Olist_ONil(U_19020),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

cnf(f_4572_3,plain,
    hAPP(c_List_OremoveAll(U_19020,U_19021),c_List_Olist_ONil(U_19020)) = c_List_Olist_ONil(U_19020),
    inference(clausify,[status(thm)],[f_4572_2]) ).

fof(f_4573_1,plain,
    ! [V_x_2,T_a] :
      ( ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
        | V_x_2 != c_List_Olist_ONil(T_a) )
      & ( V_x_2 = c_List_Olist_ONil(T_a)
        | c_List_Oremdups(T_a,V_x_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff]) ).

fof(f_4573_2,plain,
    ! [U_19023,U_19022] :
      ( ( c_List_Oremdups(U_19022,U_19023) = c_List_Olist_ONil(U_19022)
        | U_19023 != c_List_Olist_ONil(U_19022) )
      & ( U_19023 = c_List_Olist_ONil(U_19022)
        | c_List_Oremdups(U_19022,U_19023) != c_List_Olist_ONil(U_19022) ) ),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

fof(f_4573_3,plain,
    ( ! [U_19027,U_19025] :
        ( c_List_Oremdups(U_19025,U_19027) = c_List_Olist_ONil(U_19025)
        | U_19027 != c_List_Olist_ONil(U_19025) )
    & ! [U_19026,U_19024] :
        ( U_19026 = c_List_Olist_ONil(U_19024)
        | c_List_Oremdups(U_19024,U_19026) != c_List_Olist_ONil(U_19024) ) ),
    inference(miniscope,[status(thm)],[f_4573_2]) ).

cnf(f_4573_4,plain,
    ( U_19026 = c_List_Olist_ONil(U_19024)
    | c_List_Oremdups(U_19024,U_19026) != c_List_Olist_ONil(U_19024) ),
    inference(clausify,[status(thm)],[f_4573_3]) ).

cnf(f_4573_5,plain,
    ( c_List_Oremdups(U_19025,U_19027) = c_List_Olist_ONil(U_19025)
    | U_19027 != c_List_Olist_ONil(U_19025) ),
    inference(clausify,[status(thm)],[f_4573_3]) ).

fof(f_4574_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__map__remdups]) ).

fof(f_4574_2,plain,
    ! [U_19031,U_19030,U_19029,U_19028] : c_List_Oremdups(U_19028,hAPP(hAPP(c_List_Omap(U_19029,U_19028),U_19030),c_List_Oremdups(U_19029,U_19031))) = c_List_Oremdups(U_19028,hAPP(hAPP(c_List_Omap(U_19029,U_19028),U_19030),U_19031)),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

cnf(f_4574_3,plain,
    c_List_Oremdups(U_19028,hAPP(hAPP(c_List_Omap(U_19029,U_19028),U_19030),c_List_Oremdups(U_19029,U_19031))) = c_List_Oremdups(U_19028,hAPP(hAPP(c_List_Omap(U_19029,U_19028),U_19030),U_19031)),
    inference(clausify,[status(thm)],[f_4574_2]) ).

fof(f_4575_1,plain,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( hAPP(c_List_OremoveAll(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),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))
        | V_x = V_y )
      & ( hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs)
        | V_x != V_y ) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J]) ).

fof(f_4575_2,plain,
    ! [U_19035,U_19034,U_19033,U_19032] :
      ( ( hAPP(c_List_OremoveAll(U_19034,U_19032),hAPP(hAPP(c_List_Olist_OCons(U_19034),U_19033),U_19035)) = hAPP(hAPP(c_List_Olist_OCons(U_19034),U_19033),hAPP(c_List_OremoveAll(U_19034,U_19032),U_19035))
        | U_19032 = U_19033 )
      & ( hAPP(c_List_OremoveAll(U_19034,U_19032),hAPP(hAPP(c_List_Olist_OCons(U_19034),U_19033),U_19035)) = hAPP(c_List_OremoveAll(U_19034,U_19032),U_19035)
        | U_19032 != U_19033 ) ),
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

fof(f_4575_3,plain,
    ( ! [U_19043,U_19041,U_19039,U_19037] :
        ( hAPP(c_List_OremoveAll(U_19041,U_19037),hAPP(hAPP(c_List_Olist_OCons(U_19041),U_19039),U_19043)) = hAPP(hAPP(c_List_Olist_OCons(U_19041),U_19039),hAPP(c_List_OremoveAll(U_19041,U_19037),U_19043))
        | U_19037 = U_19039 )
    & ! [U_19042,U_19040,U_19038,U_19036] :
        ( hAPP(c_List_OremoveAll(U_19040,U_19036),hAPP(hAPP(c_List_Olist_OCons(U_19040),U_19038),U_19042)) = hAPP(c_List_OremoveAll(U_19040,U_19036),U_19042)
        | U_19036 != U_19038 ) ),
    inference(miniscope,[status(thm)],[f_4575_2]) ).

cnf(f_4575_4,plain,
    ( hAPP(c_List_OremoveAll(U_19040,U_19036),hAPP(hAPP(c_List_Olist_OCons(U_19040),U_19038),U_19042)) = hAPP(c_List_OremoveAll(U_19040,U_19036),U_19042)
    | U_19036 != U_19038 ),
    inference(clausify,[status(thm)],[f_4575_3]) ).

cnf(f_4575_5,plain,
    ( hAPP(c_List_OremoveAll(U_19041,U_19037),hAPP(hAPP(c_List_Olist_OCons(U_19041),U_19039),U_19043)) = hAPP(hAPP(c_List_Olist_OCons(U_19041),U_19039),hAPP(c_List_OremoveAll(U_19041,U_19037),U_19043))
    | U_19037 = U_19039 ),
    inference(clausify,[status(thm)],[f_4575_3]) ).

fof(f_4576_1,plain,
    ! [V_x,V_xs,T_a] :
      ( c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll]) ).

fof(f_4576_2,plain,
    ! [U_19046,U_19045,U_19044] :
      ( c_List_Oremove1(U_19044,U_19046,U_19045) = hAPP(c_List_OremoveAll(U_19044,U_19046),U_19045)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19044),U_19045)) ),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

cnf(f_4576_3,plain,
    ( c_List_Oremove1(U_19044,U_19046,U_19045) = hAPP(c_List_OremoveAll(U_19044,U_19046),U_19045)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19044),U_19045)) ),
    inference(clausify,[status(thm)],[f_4576_2]) ).

fof(f_4577_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(f_4577_2,plain,
    ! [U_19049,U_19048,U_19047] :
      ( ( c_List_Oremdups(U_19047,hAPP(hAPP(c_List_Olist_OCons(U_19047),U_19048),U_19049)) = hAPP(hAPP(c_List_Olist_OCons(U_19047),U_19048),c_List_Oremdups(U_19047,U_19049))
        | hBOOL(hAPP(hAPP(c_member(U_19047),U_19048),hAPP(c_List_Oset(U_19047),U_19049))) )
      & ( c_List_Oremdups(U_19047,hAPP(hAPP(c_List_Olist_OCons(U_19047),U_19048),U_19049)) = c_List_Oremdups(U_19047,U_19049)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19047),U_19048),hAPP(c_List_Oset(U_19047),U_19049))) ) ),
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ( ! [U_19055,U_19053,U_19051] :
        ( c_List_Oremdups(U_19051,hAPP(hAPP(c_List_Olist_OCons(U_19051),U_19053),U_19055)) = hAPP(hAPP(c_List_Olist_OCons(U_19051),U_19053),c_List_Oremdups(U_19051,U_19055))
        | hBOOL(hAPP(hAPP(c_member(U_19051),U_19053),hAPP(c_List_Oset(U_19051),U_19055))) )
    & ! [U_19054,U_19052,U_19050] :
        ( c_List_Oremdups(U_19050,hAPP(hAPP(c_List_Olist_OCons(U_19050),U_19052),U_19054)) = c_List_Oremdups(U_19050,U_19054)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19050),U_19052),hAPP(c_List_Oset(U_19050),U_19054))) ) ),
    inference(miniscope,[status(thm)],[f_4577_2]) ).

cnf(f_4577_4,plain,
    ( c_List_Oremdups(U_19050,hAPP(hAPP(c_List_Olist_OCons(U_19050),U_19052),U_19054)) = c_List_Oremdups(U_19050,U_19054)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19050),U_19052),hAPP(c_List_Oset(U_19050),U_19054))) ),
    inference(clausify,[status(thm)],[f_4577_3]) ).

cnf(f_4577_5,plain,
    ( c_List_Oremdups(U_19051,hAPP(hAPP(c_List_Olist_OCons(U_19051),U_19053),U_19055)) = hAPP(hAPP(c_List_Olist_OCons(U_19051),U_19053),c_List_Oremdups(U_19051,U_19055))
    | hBOOL(hAPP(hAPP(c_member(U_19051),U_19053),hAPP(c_List_Oset(U_19051),U_19055))) ),
    inference(clausify,[status(thm)],[f_4577_3]) ).

fof(f_4578_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(f_4578_2,plain,
    ! [U_19057,U_19056] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19056)),c_List_Oremdups(U_19056,U_19057)) = hAPP(c_Finite__Set_Ocard(U_19056),hAPP(c_List_Oset(U_19056),U_19057)),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

cnf(f_4578_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19056)),c_List_Oremdups(U_19056,U_19057)) = hAPP(c_Finite__Set_Ocard(U_19056),hAPP(c_List_Oset(U_19056),U_19057)),
    inference(clausify,[status(thm)],[f_4578_2]) ).

fof(f_4579_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj]) ).

fof(f_4579_2,plain,
    ! [U_19062,U_19061,U_19060,U_19059,U_19058] :
      ( hAPP(hAPP(c_List_Omap(U_19058,U_19059),U_19060),hAPP(c_List_OremoveAll(U_19058,U_19061),U_19062)) = hAPP(c_List_OremoveAll(U_19059,hAPP(U_19060,U_19061)),hAPP(hAPP(c_List_Omap(U_19058,U_19059),U_19060),U_19062))
      | ~ c_Fun_Oinj__on(U_19058,U_19059,U_19060,c_Orderings_Otop__class_Otop(tc_fun(U_19058,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

cnf(f_4579_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_19058,U_19059),U_19060),hAPP(c_List_OremoveAll(U_19058,U_19061),U_19062)) = hAPP(c_List_OremoveAll(U_19059,hAPP(U_19060,U_19061)),hAPP(hAPP(c_List_Omap(U_19058,U_19059),U_19060),U_19062))
    | ~ c_Fun_Oinj__on(U_19058,U_19059,U_19060,c_Orderings_Otop__class_Otop(tc_fun(U_19058,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4579_2]) ).

fof(f_4580_1,plain,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_set__removeAll]) ).

fof(f_4580_2,plain,
    ! [U_19065,U_19064,U_19063] : hAPP(c_List_Oset(U_19063),hAPP(c_List_OremoveAll(U_19063,U_19064),U_19065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19063,tc_HOL_Obool)),hAPP(c_List_Oset(U_19063),U_19065)),hAPP(hAPP(c_Set_Oinsert(U_19063),U_19064),c_Orderings_Obot__class_Obot(tc_fun(U_19063,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

cnf(f_4580_3,plain,
    hAPP(c_List_Oset(U_19063),hAPP(c_List_OremoveAll(U_19063,U_19064),U_19065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19063,tc_HOL_Obool)),hAPP(c_List_Oset(U_19063),U_19065)),hAPP(hAPP(c_Set_Oinsert(U_19063),U_19064),c_Orderings_Obot__class_Obot(tc_fun(U_19063,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4580_2]) ).

fof(f_4581_1,plain,
    ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__concat]) ).

fof(f_4581_2,plain,
    ! [U_19067,U_19066] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19066)),c_List_Oremdups(U_19066,c_List_Oconcat(U_19066,U_19067))) = hAPP(c_Finite__Set_Ocard(U_19066),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_19066),tc_fun(U_19066,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_19066)),U_19067)),c_List_Oset(U_19066))),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

cnf(f_4581_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19066)),c_List_Oremdups(U_19066,c_List_Oconcat(U_19066,U_19067))) = hAPP(c_Finite__Set_Ocard(U_19066),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_19066),tc_fun(U_19066,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_19066)),U_19067)),c_List_Oset(U_19066))),
    inference(clausify,[status(thm)],[f_4581_2]) ).

fof(f_4582_1,plain,
    ! [V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups]) ).

fof(f_4582_2,plain,
    ! [U_19069,U_19068] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_19068,hAPP(c_List_Oset(U_19068),U_19069)) = c_List_Olinorder__class_Osort__key(U_19068,U_19068,c_COMBI(U_19068),c_List_Oremdups(U_19068,U_19069))
      | ~ class_Orderings_Olinorder(U_19068) ),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

cnf(f_4582_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_19068,hAPP(c_List_Oset(U_19068),U_19069)) = c_List_Olinorder__class_Osort__key(U_19068,U_19068,c_COMBI(U_19068),c_List_Oremdups(U_19068,U_19069))
    | ~ class_Orderings_Olinorder(U_19068) ),
    inference(clausify,[status(thm)],[f_4582_2]) ).

fof(f_4583_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_4583_2,plain,
    ! [U_19072,U_19071,U_19070] : c_List_Oconcat(U_19070,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19070)),U_19071),U_19072)) = hAPP(hAPP(c_List_Oappend(U_19070),U_19071),c_List_Oconcat(U_19070,U_19072)),
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

cnf(f_4583_3,plain,
    c_List_Oconcat(U_19070,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19070)),U_19071),U_19072)) = hAPP(hAPP(c_List_Oappend(U_19070),U_19071),c_List_Oconcat(U_19070,U_19072)),
    inference(clausify,[status(thm)],[f_4583_2]) ).

fof(f_4584_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__concat]) ).

fof(f_4584_2,plain,
    ! [U_19076,U_19075,U_19074,U_19073] : hAPP(hAPP(c_List_Omap(U_19073,U_19074),U_19075),c_List_Oconcat(U_19073,U_19076)) = c_List_Oconcat(U_19074,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19073),tc_List_Olist(U_19074)),hAPP(c_List_Omap(U_19073,U_19074),U_19075)),U_19076)),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

cnf(f_4584_3,plain,
    hAPP(hAPP(c_List_Omap(U_19073,U_19074),U_19075),c_List_Oconcat(U_19073,U_19076)) = c_List_Oconcat(U_19074,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19073),tc_List_Olist(U_19074)),hAPP(c_List_Omap(U_19073,U_19074),U_19075)),U_19076)),
    inference(clausify,[status(thm)],[f_4584_2]) ).

fof(f_4585_1,plain,
    ! [V_xss_2,T_a] :
      ( ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_a)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_a)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) )
        | c_List_Olist_ONil(T_a) != c_List_Oconcat(T_a,V_xss_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__eq__concat__conv]) ).

fof(f_4585_2,plain,
    ! [U_19080,U_19079] :
      ( ( c_List_Olist_ONil(U_19079) = c_List_Oconcat(U_19079,U_19080)
        | ? [U_19078] :
            ( U_19078 != c_List_Olist_ONil(U_19079)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19079)),U_19078),hAPP(c_List_Oset(tc_List_Olist(U_19079)),U_19080))) ) )
      & ( ! [U_19077] :
            ( U_19077 = c_List_Olist_ONil(U_19079)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19079)),U_19077),hAPP(c_List_Oset(tc_List_Olist(U_19079)),U_19080))) )
        | c_List_Olist_ONil(U_19079) != c_List_Oconcat(U_19079,U_19080) ) ),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

fof(f_4585_3,plain,
    ( ! [U_19084,U_19082] :
        ( c_List_Olist_ONil(U_19082) = c_List_Oconcat(U_19082,U_19084)
        | ? [U_19078] :
            ( U_19078 != c_List_Olist_ONil(U_19082)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19082)),U_19078),hAPP(c_List_Oset(tc_List_Olist(U_19082)),U_19084))) ) )
    & ! [U_19083,U_19081] :
        ( ! [U_19077] :
            ( U_19077 = c_List_Olist_ONil(U_19081)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19081)),U_19077),hAPP(c_List_Oset(tc_List_Olist(U_19081)),U_19083))) )
        | c_List_Olist_ONil(U_19081) != c_List_Oconcat(U_19081,U_19083) ) ),
    inference(miniscope,[status(thm)],[f_4585_2]) ).

fof(f_4585_4,plain,
    ( ! [U_19084,U_19082] :
        ( c_List_Olist_ONil(U_19082) = c_List_Oconcat(U_19082,U_19084)
        | ( sK478(U_19084,U_19082) != c_List_Olist_ONil(U_19082)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19082)),sK478(U_19084,U_19082)),hAPP(c_List_Oset(tc_List_Olist(U_19082)),U_19084))) ) )
    & ! [U_19083,U_19081] :
        ( ! [U_19077] :
            ( U_19077 = c_List_Olist_ONil(U_19081)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19081)),U_19077),hAPP(c_List_Oset(tc_List_Olist(U_19081)),U_19083))) )
        | c_List_Olist_ONil(U_19081) != c_List_Oconcat(U_19081,U_19083) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_19078,sK478(U_19084,U_19082))],[f_4585_3]) ).

cnf(f_4585_5,plain,
    ( U_19077 = c_List_Olist_ONil(U_19081)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19081)),U_19077),hAPP(c_List_Oset(tc_List_Olist(U_19081)),U_19083)))
    | c_List_Olist_ONil(U_19081) != c_List_Oconcat(U_19081,U_19083) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19082)),sK478(U_19084,U_19082)),hAPP(c_List_Oset(tc_List_Olist(U_19082)),U_19084)))
    | c_List_Olist_ONil(U_19082) = c_List_Oconcat(U_19082,U_19084) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

cnf(f_4585_7,plain,
    ( sK478(U_19084,U_19082) != c_List_Olist_ONil(U_19082)
    | c_List_Olist_ONil(U_19082) = c_List_Oconcat(U_19082,U_19084) ),
    inference(clausify,[status(thm)],[f_4585_4]) ).

fof(f_4586_1,plain,
    ! [V_xss_2,T_a] :
      ( ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_a)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_a)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) )
        | c_List_Oconcat(T_a,V_xss_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__Nil__conv]) ).

fof(f_4586_2,plain,
    ! [U_19088,U_19087] :
      ( ( c_List_Oconcat(U_19087,U_19088) = c_List_Olist_ONil(U_19087)
        | ? [U_19086] :
            ( U_19086 != c_List_Olist_ONil(U_19087)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19087)),U_19086),hAPP(c_List_Oset(tc_List_Olist(U_19087)),U_19088))) ) )
      & ( ! [U_19085] :
            ( U_19085 = c_List_Olist_ONil(U_19087)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19087)),U_19085),hAPP(c_List_Oset(tc_List_Olist(U_19087)),U_19088))) )
        | c_List_Oconcat(U_19087,U_19088) != c_List_Olist_ONil(U_19087) ) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

fof(f_4586_3,plain,
    ( ! [U_19092,U_19090] :
        ( c_List_Oconcat(U_19090,U_19092) = c_List_Olist_ONil(U_19090)
        | ? [U_19086] :
            ( U_19086 != c_List_Olist_ONil(U_19090)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19090)),U_19086),hAPP(c_List_Oset(tc_List_Olist(U_19090)),U_19092))) ) )
    & ! [U_19091,U_19089] :
        ( ! [U_19085] :
            ( U_19085 = c_List_Olist_ONil(U_19089)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19089)),U_19085),hAPP(c_List_Oset(tc_List_Olist(U_19089)),U_19091))) )
        | c_List_Oconcat(U_19089,U_19091) != c_List_Olist_ONil(U_19089) ) ),
    inference(miniscope,[status(thm)],[f_4586_2]) ).

fof(f_4586_4,plain,
    ( ! [U_19092,U_19090] :
        ( c_List_Oconcat(U_19090,U_19092) = c_List_Olist_ONil(U_19090)
        | ( sK479(U_19092,U_19090) != c_List_Olist_ONil(U_19090)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19090)),sK479(U_19092,U_19090)),hAPP(c_List_Oset(tc_List_Olist(U_19090)),U_19092))) ) )
    & ! [U_19091,U_19089] :
        ( ! [U_19085] :
            ( U_19085 = c_List_Olist_ONil(U_19089)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19089)),U_19085),hAPP(c_List_Oset(tc_List_Olist(U_19089)),U_19091))) )
        | c_List_Oconcat(U_19089,U_19091) != c_List_Olist_ONil(U_19089) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_19086,sK479(U_19092,U_19090))],[f_4586_3]) ).

cnf(f_4586_5,plain,
    ( U_19085 = c_List_Olist_ONil(U_19089)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19089)),U_19085),hAPP(c_List_Oset(tc_List_Olist(U_19089)),U_19091)))
    | c_List_Oconcat(U_19089,U_19091) != c_List_Olist_ONil(U_19089) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

cnf(f_4586_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19090)),sK479(U_19092,U_19090)),hAPP(c_List_Oset(tc_List_Olist(U_19090)),U_19092)))
    | c_List_Oconcat(U_19090,U_19092) = c_List_Olist_ONil(U_19090) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

cnf(f_4586_7,plain,
    ( sK479(U_19092,U_19090) != c_List_Olist_ONil(U_19090)
    | c_List_Oconcat(U_19090,U_19092) = c_List_Olist_ONil(U_19090) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

fof(f_4587_1,plain,
    ! [V_f_2,T_a,T_b] :
      ( c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J]) ).

fof(f_4587_2,plain,
    ! [U_19095,U_19094,U_19093] :
      ( c_List_Olinorder__class_Osort__key(U_19094,U_19093,U_19095,c_List_Olist_ONil(U_19094)) = c_List_Olist_ONil(U_19094)
      | ~ class_Orderings_Olinorder(U_19093) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

cnf(f_4587_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_19094,U_19093,U_19095,c_List_Olist_ONil(U_19094)) = c_List_Olist_ONil(U_19094)
    | ~ class_Orderings_Olinorder(U_19093) ),
    inference(clausify,[status(thm)],[f_4587_2]) ).

fof(f_4588_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_4588_2,plain,
    ! [U_19096] : c_List_Oconcat(U_19096,c_List_Olist_ONil(tc_List_Olist(U_19096))) = c_List_Olist_ONil(U_19096),
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

cnf(f_4588_3,plain,
    c_List_Oconcat(U_19096,c_List_Olist_ONil(tc_List_Olist(U_19096))) = c_List_Olist_ONil(U_19096),
    inference(clausify,[status(thm)],[f_4588_2]) ).

fof(f_4589_1,plain,
    ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2),
    inference(fof_nnf,[status(thm)],[fact_concat__conv__foldl]) ).

fof(f_4589_2,plain,
    ! [U_19098,U_19097] : c_List_Oconcat(U_19097,U_19098) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19097),tc_List_Olist(U_19097),c_List_Oappend(U_19097),c_List_Olist_ONil(U_19097)),U_19098),
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

cnf(f_4589_3,plain,
    c_List_Oconcat(U_19097,U_19098) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19097),tc_List_Olist(U_19097),c_List_Oappend(U_19097),c_List_Olist_ONil(U_19097)),U_19098),
    inference(clausify,[status(thm)],[f_4589_2]) ).

fof(f_4590_1,plain,
    ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_foldl__conv__concat]) ).

fof(f_4590_2,plain,
    ! [U_19101,U_19100,U_19099] : hAPP(c_List_Ofoldl(tc_List_Olist(U_19099),tc_List_Olist(U_19099),c_List_Oappend(U_19099),U_19100),U_19101) = hAPP(hAPP(c_List_Oappend(U_19099),U_19100),c_List_Oconcat(U_19099,U_19101)),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

cnf(f_4590_3,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_19099),tc_List_Olist(U_19099),c_List_Oappend(U_19099),U_19100),U_19101) = hAPP(hAPP(c_List_Oappend(U_19099),U_19100),c_List_Oconcat(U_19099,U_19101)),
    inference(clausify,[status(thm)],[f_4590_2]) ).

fof(f_4591_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_set__sort]) ).

fof(f_4591_2,plain,
    ! [U_19105,U_19104,U_19103,U_19102] :
      ( hAPP(c_List_Oset(U_19103),c_List_Olinorder__class_Osort__key(U_19103,U_19102,U_19104,U_19105)) = hAPP(c_List_Oset(U_19103),U_19105)
      | ~ class_Orderings_Olinorder(U_19102) ),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

cnf(f_4591_3,plain,
    ( hAPP(c_List_Oset(U_19103),c_List_Olinorder__class_Osort__key(U_19103,U_19102,U_19104,U_19105)) = hAPP(c_List_Oset(U_19103),U_19105)
    | ~ class_Orderings_Olinorder(U_19102) ),
    inference(clausify,[status(thm)],[f_4591_2]) ).

fof(f_4592_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_length__sort]) ).

fof(f_4592_2,plain,
    ! [U_19109,U_19108,U_19107,U_19106] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19107)),c_List_Olinorder__class_Osort__key(U_19107,U_19106,U_19108,U_19109)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19107)),U_19109)
      | ~ class_Orderings_Olinorder(U_19106) ),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

cnf(f_4592_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19107)),c_List_Olinorder__class_Osort__key(U_19107,U_19106,U_19108,U_19109)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19107)),U_19109)
    | ~ class_Orderings_Olinorder(U_19106) ),
    inference(clausify,[status(thm)],[f_4592_2]) ).

fof(f_4593_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
        & ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__sort]) ).

fof(f_4593_2,plain,
    ! [U_19113,U_19112,U_19111,U_19110] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_19111),c_List_Olinorder__class_Osort__key(U_19111,U_19110,U_19112,U_19113)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_19111),U_19113)) )
        & ( hBOOL(hAPP(c_List_Odistinct(U_19111),U_19113))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_19111),c_List_Olinorder__class_Osort__key(U_19111,U_19110,U_19112,U_19113))) ) )
      | ~ class_Orderings_Olinorder(U_19110) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

cnf(f_4593_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19111),U_19113))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19111),c_List_Olinorder__class_Osort__key(U_19111,U_19110,U_19112,U_19113)))
    | ~ class_Orderings_Olinorder(U_19110) ),
    inference(clausify,[status(thm)],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19111),c_List_Olinorder__class_Osort__key(U_19111,U_19110,U_19112,U_19113)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19111),U_19113))
    | ~ class_Orderings_Olinorder(U_19110) ),
    inference(clausify,[status(thm)],[f_4593_2]) ).

fof(f_4594_1,plain,
    ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_length__concat]) ).

fof(f_4594_2,plain,
    ! [U_19115,U_19114] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19114)),c_List_Oconcat(U_19114,U_19115)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19114),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19114))),U_19115)),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

cnf(f_4594_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19114)),c_List_Oconcat(U_19114,U_19115)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19114),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19114))),U_19115)),
    inference(clausify,[status(thm)],[f_4594_2]) ).

fof(f_4595_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)),
    inference(fof_nnf,[status(thm)],[fact_set__concat]) ).

fof(f_4595_2,plain,
    ! [U_19117,U_19116] : hAPP(c_List_Oset(U_19116),c_List_Oconcat(U_19116,U_19117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_19116),tc_fun(U_19116,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_19116)),U_19117)),c_List_Oset(U_19116)),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

cnf(f_4595_3,plain,
    hAPP(c_List_Oset(U_19116),c_List_Oconcat(U_19116,U_19117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_19116),tc_fun(U_19116,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_19116)),U_19117)),c_List_Oset(U_19116)),
    inference(clausify,[status(thm)],[f_4595_2]) ).

fof(f_4596_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
      ( c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J]) ).

fof(f_4596_2,plain,
    ! [U_19122,U_19121,U_19120,U_19119,U_19118] :
      ( c_List_Olinorder__class_Osort__key(U_19119,U_19118,U_19120,hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19121),U_19122)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19119,U_19118,U_19120),U_19121),c_List_Olinorder__class_Osort__key(U_19119,U_19118,U_19120,U_19122))
      | ~ class_Orderings_Olinorder(U_19118) ),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

cnf(f_4596_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_19119,U_19118,U_19120,hAPP(hAPP(c_List_Olist_OCons(U_19119),U_19121),U_19122)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19119,U_19118,U_19120),U_19121),c_List_Olinorder__class_Osort__key(U_19119,U_19118,U_19120,U_19122))
    | ~ class_Orderings_Olinorder(U_19118) ),
    inference(clausify,[status(thm)],[f_4596_2]) ).

fof(f_4597_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_4597_2,plain,
    ! [U_19125,U_19124,U_19123] : c_List_Oconcat(U_19123,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_19123)),U_19124),U_19125)) = hAPP(hAPP(c_List_Oappend(U_19123),c_List_Oconcat(U_19123,U_19124)),c_List_Oconcat(U_19123,U_19125)),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

cnf(f_4597_3,plain,
    c_List_Oconcat(U_19123,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_19123)),U_19124),U_19125)) = hAPP(hAPP(c_List_Oappend(U_19123),c_List_Oconcat(U_19123,U_19124)),c_List_Oconcat(U_19123,U_19125)),
    inference(clausify,[status(thm)],[f_4597_2]) ).

fof(f_4598_1,plain,
    ! [V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort]) ).

fof(f_4598_2,plain,
    ! [U_19127,U_19126] :
      ( c_List_Olinorder__class_Osort__key(U_19126,U_19126,c_COMBI(U_19126),U_19127) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19126),U_19126,hAPP(c_COMBC(U_19126,tc_List_Olist(U_19126),tc_List_Olist(U_19126)),c_List_Olinorder__class_Oinsort__key(U_19126,U_19126,c_COMBI(U_19126))),c_List_Olist_ONil(U_19126)),U_19127)
      | ~ class_Orderings_Olinorder(U_19126) ),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

cnf(f_4598_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_19126,U_19126,c_COMBI(U_19126),U_19127) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19126),U_19126,hAPP(c_COMBC(U_19126,tc_List_Olist(U_19126),tc_List_Olist(U_19126)),c_List_Olinorder__class_Oinsort__key(U_19126,U_19126,c_COMBI(U_19126))),c_List_Olist_ONil(U_19126)),U_19127)
    | ~ class_Orderings_Olinorder(U_19126) ),
    inference(clausify,[status(thm)],[f_4598_2]) ).

fof(f_4599_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | c_List_Oconcat(T_a,V_xs_2) != c_List_Oconcat(T_a,V_ys_2) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__concat__iff]) ).

fof(f_4599_2,plain,
    ! [U_19131,U_19130,U_19129] :
      ( ( ( c_List_Oconcat(U_19129,U_19130) = c_List_Oconcat(U_19129,U_19131)
          | U_19130 != U_19131 )
        & ( U_19130 = U_19131
          | c_List_Oconcat(U_19129,U_19130) != c_List_Oconcat(U_19129,U_19131) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
      | ? [U_19128] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19129),tc_List_Olist(U_19129),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19129),tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),tc_List_Olist(U_19129)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19129))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19129)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129)))),U_19128))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),U_19128),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19129),tc_List_Olist(U_19129)),U_19130),U_19131)))) ) ),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ! [U_19131,U_19130,U_19129] :
      ( ( ( c_List_Oconcat(U_19129,U_19130) = c_List_Oconcat(U_19129,U_19131)
          | U_19130 != U_19131 )
        & ( U_19130 = U_19131
          | c_List_Oconcat(U_19129,U_19130) != c_List_Oconcat(U_19129,U_19131) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19129),tc_List_Olist(U_19129),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19129),tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),tc_List_Olist(U_19129)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19129))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19129)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129)))),sK480(U_19131,U_19130,U_19129)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),sK480(U_19131,U_19130,U_19129)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19129),tc_List_Olist(U_19129)),U_19130),U_19131)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_19128,sK480(U_19131,U_19130,U_19129))],[f_4599_2]) ).

cnf(f_4599_4,plain,
    ( U_19130 = U_19131
    | c_List_Oconcat(U_19129,U_19130) != c_List_Oconcat(U_19129,U_19131)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),sK480(U_19131,U_19130,U_19129)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19129),tc_List_Olist(U_19129)),U_19130),U_19131)))) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_5,plain,
    ( c_List_Oconcat(U_19129,U_19130) = c_List_Oconcat(U_19129,U_19131)
    | U_19130 != U_19131
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),sK480(U_19131,U_19130,U_19129)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19129),tc_List_Olist(U_19129))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19129),tc_List_Olist(U_19129)),U_19130),U_19131)))) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_6,plain,
    ( U_19130 = U_19131
    | c_List_Oconcat(U_19129,U_19130) != c_List_Oconcat(U_19129,U_19131)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19129),tc_List_Olist(U_19129),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19129),tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),tc_List_Olist(U_19129)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19129))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19129)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129)))),sK480(U_19131,U_19130,U_19129))) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_7,plain,
    ( c_List_Oconcat(U_19129,U_19130) = c_List_Oconcat(U_19129,U_19131)
    | U_19130 != U_19131
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19130) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19129))),U_19131)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19129),tc_List_Olist(U_19129),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19129),tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19129),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19129),tc_HOL_Obool)),tc_List_Olist(U_19129)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19129))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19129)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19129)))),sK480(U_19131,U_19130,U_19129))) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

fof(f_4600_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( V_xs_2 = V_ys_2
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
      | c_List_Oconcat(T_a,V_xs_2) != c_List_Oconcat(T_a,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_concat__injective]) ).

fof(f_4600_2,plain,
    ! [U_19135,U_19134,U_19133] :
      ( U_19134 = U_19135
      | ? [U_19132] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19133),tc_List_Olist(U_19133),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19133),tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),tc_List_Olist(U_19133)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19133))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19133)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133)))),U_19132))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),U_19132),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19133),tc_List_Olist(U_19133)),U_19134),U_19135)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19135)
      | c_List_Oconcat(U_19133,U_19134) != c_List_Oconcat(U_19133,U_19135) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ! [U_19135,U_19134,U_19133] :
      ( U_19134 = U_19135
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19133),tc_List_Olist(U_19133),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19133),tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),tc_List_Olist(U_19133)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19133))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19133)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133)))),sK481(U_19135,U_19134,U_19133)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),sK481(U_19135,U_19134,U_19133)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19133),tc_List_Olist(U_19133)),U_19134),U_19135)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19135)
      | c_List_Oconcat(U_19133,U_19134) != c_List_Oconcat(U_19133,U_19135) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_19132,sK481(U_19135,U_19134,U_19133))],[f_4600_2]) ).

cnf(f_4600_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),sK481(U_19135,U_19134,U_19133)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_19133),tc_List_Olist(U_19133))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_19133),tc_List_Olist(U_19133)),U_19134),U_19135))))
    | U_19134 = U_19135
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19135)
    | c_List_Oconcat(U_19133,U_19134) != c_List_Oconcat(U_19133,U_19135) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

cnf(f_4600_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19133),tc_List_Olist(U_19133),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19133),tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_19133),tc_Nat_Onat),tc_fun(tc_List_Olist(U_19133),tc_HOL_Obool)),tc_List_Olist(U_19133)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19133))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_19133)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_19133)))),sK481(U_19135,U_19134,U_19133)))
    | U_19134 = U_19135
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19133))),U_19135)
    | c_List_Oconcat(U_19133,U_19134) != c_List_Oconcat(U_19133,U_19135) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

fof(f_4601_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_concat__map__singleton]) ).

fof(f_4601_2,plain,
    ! [U_19139,U_19138,U_19137,U_19136] : c_List_Oconcat(U_19136,hAPP(hAPP(c_List_Omap(U_19137,tc_List_Olist(U_19136)),hAPP(hAPP(c_COMBC(U_19137,tc_List_Olist(U_19136),tc_List_Olist(U_19136)),hAPP(hAPP(c_COMBB(U_19136,tc_fun(tc_List_Olist(U_19136),tc_List_Olist(U_19136)),U_19137),c_List_Olist_OCons(U_19136)),U_19138)),c_List_Olist_ONil(U_19136))),U_19139)) = hAPP(hAPP(c_List_Omap(U_19137,U_19136),U_19138),U_19139),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

cnf(f_4601_3,plain,
    c_List_Oconcat(U_19136,hAPP(hAPP(c_List_Omap(U_19137,tc_List_Olist(U_19136)),hAPP(hAPP(c_COMBC(U_19137,tc_List_Olist(U_19136),tc_List_Olist(U_19136)),hAPP(hAPP(c_COMBB(U_19136,tc_fun(tc_List_Olist(U_19136),tc_List_Olist(U_19136)),U_19137),c_List_Olist_OCons(U_19136)),U_19138)),c_List_Olist_ONil(U_19136))),U_19139)) = hAPP(hAPP(c_List_Omap(U_19137,U_19136),U_19138),U_19139),
    inference(clausify,[status(thm)],[f_4601_2]) ).

fof(f_4602_1,plain,
    ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(f_4602_2,plain,
    ! [U_19142,U_19141,U_19140] : c_Enum_On__lists(U_19140,hAPP(c_Nat_OSuc,U_19141),U_19142) = c_List_Oconcat(tc_List_Olist(U_19140),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19140),tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),hAPP(hAPP(c_COMBB(tc_fun(U_19140,tc_List_Olist(U_19140)),tc_fun(tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),tc_List_Olist(U_19140)),c_List_Omap(U_19140,tc_List_Olist(U_19140))),hAPP(c_COMBC(U_19140,tc_List_Olist(U_19140),tc_List_Olist(U_19140)),c_List_Olist_OCons(U_19140)))),U_19142)),c_Enum_On__lists(U_19140,U_19141,U_19142))),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

cnf(f_4602_3,plain,
    c_Enum_On__lists(U_19140,hAPP(c_Nat_OSuc,U_19141),U_19142) = c_List_Oconcat(tc_List_Olist(U_19140),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19140),tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),hAPP(hAPP(c_COMBB(tc_fun(U_19140,tc_List_Olist(U_19140)),tc_fun(tc_List_Olist(U_19140),tc_List_Olist(tc_List_Olist(U_19140))),tc_List_Olist(U_19140)),c_List_Omap(U_19140,tc_List_Olist(U_19140))),hAPP(c_COMBC(U_19140,tc_List_Olist(U_19140),tc_List_Olist(U_19140)),c_List_Olist_OCons(U_19140)))),U_19142)),c_Enum_On__lists(U_19140,U_19141,U_19142))),
    inference(clausify,[status(thm)],[f_4602_2]) ).

fof(f_4603_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(f_4603_2,plain,
    ! [U_19146,U_19145,U_19144,U_19143] : c_List_Otranspose(U_19143,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),U_19145)),U_19146)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),c_List_Oconcat(U_19143,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19143),tc_List_Olist(U_19143)),c_List_Olist_Olist__case(tc_List_Olist(U_19143),U_19143,c_List_Olist_ONil(U_19143),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19143),tc_fun(tc_List_Olist(U_19143),tc_List_Olist(U_19143)),U_19143),c_COMBK(tc_List_Olist(U_19143),tc_List_Olist(U_19143))),hAPP(hAPP(c_COMBC(U_19143,tc_List_Olist(U_19143),tc_List_Olist(U_19143)),c_List_Olist_OCons(U_19143)),c_List_Olist_ONil(U_19143))))),U_19146)))),c_List_Otranspose(U_19143,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),U_19145),c_List_Oconcat(tc_List_Olist(U_19143),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19143)),U_19143,c_List_Olist_ONil(tc_List_Olist(U_19143)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143))),U_19143),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143)),tc_List_Olist(tc_List_Olist(U_19143))),c_List_Olist_OCons(tc_List_Olist(U_19143))),c_List_Olist_ONil(tc_List_Olist(U_19143)))))),U_19146))))),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

cnf(f_4603_3,plain,
    c_List_Otranspose(U_19143,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),U_19145)),U_19146)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),hAPP(hAPP(c_List_Olist_OCons(U_19143),U_19144),c_List_Oconcat(U_19143,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19143),tc_List_Olist(U_19143)),c_List_Olist_Olist__case(tc_List_Olist(U_19143),U_19143,c_List_Olist_ONil(U_19143),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19143),tc_fun(tc_List_Olist(U_19143),tc_List_Olist(U_19143)),U_19143),c_COMBK(tc_List_Olist(U_19143),tc_List_Olist(U_19143))),hAPP(hAPP(c_COMBC(U_19143,tc_List_Olist(U_19143),tc_List_Olist(U_19143)),c_List_Olist_OCons(U_19143)),c_List_Olist_ONil(U_19143))))),U_19146)))),c_List_Otranspose(U_19143,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19143)),U_19145),c_List_Oconcat(tc_List_Olist(U_19143),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19143)),U_19143,c_List_Olist_ONil(tc_List_Olist(U_19143)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143))),U_19143),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19143),tc_List_Olist(tc_List_Olist(U_19143)),tc_List_Olist(tc_List_Olist(U_19143))),c_List_Olist_OCons(tc_List_Olist(U_19143))),c_List_Olist_ONil(tc_List_Olist(U_19143)))))),U_19146))))),
    inference(clausify,[status(thm)],[f_4603_2]) ).

fof(f_4604_1,plain,
    ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(f_4604_2,plain,
    ! [U_19148,U_19147] : c_List_Oconcat(U_19147,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olist_Olist__case(tc_List_Olist(U_19147),U_19147,c_List_Olist_ONil(U_19147),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19147),tc_fun(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),U_19147),c_COMBK(tc_List_Olist(U_19147),tc_List_Olist(U_19147))),hAPP(hAPP(c_COMBC(U_19147,tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olist_OCons(U_19147)),c_List_Olist_ONil(U_19147))))),U_19148)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19147),U_19147),c_List_Ohd(U_19147)),hAPP(c_List_Ofilter(tc_List_Olist(U_19147),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19147)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19147),tc_List_Olist(U_19147),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19147)))),U_19148)),
    inference(variable_rename,[status(thm)],[f_4604_1]) ).

cnf(f_4604_3,plain,
    c_List_Oconcat(U_19147,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olist_Olist__case(tc_List_Olist(U_19147),U_19147,c_List_Olist_ONil(U_19147),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19147),tc_fun(tc_List_Olist(U_19147),tc_List_Olist(U_19147)),U_19147),c_COMBK(tc_List_Olist(U_19147),tc_List_Olist(U_19147))),hAPP(hAPP(c_COMBC(U_19147,tc_List_Olist(U_19147),tc_List_Olist(U_19147)),c_List_Olist_OCons(U_19147)),c_List_Olist_ONil(U_19147))))),U_19148)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19147),U_19147),c_List_Ohd(U_19147)),hAPP(c_List_Ofilter(tc_List_Olist(U_19147),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19147)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19147),tc_List_Olist(U_19147),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19147)))),U_19148)),
    inference(clausify,[status(thm)],[f_4604_2]) ).

fof(f_4605_1,plain,
    ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__concat]) ).

fof(f_4605_2,plain,
    ! [U_19151,U_19150,U_19149] : hAPP(c_List_Ofilter(U_19149,U_19150),c_List_Oconcat(U_19149,U_19151)) = c_List_Oconcat(U_19149,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19149),tc_List_Olist(U_19149)),c_List_Ofilter(U_19149,U_19150)),U_19151)),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

cnf(f_4605_3,plain,
    hAPP(c_List_Ofilter(U_19149,U_19150),c_List_Oconcat(U_19149,U_19151)) = c_List_Oconcat(U_19149,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19149),tc_List_Olist(U_19149)),c_List_Ofilter(U_19149,U_19150)),U_19151)),
    inference(clausify,[status(thm)],[f_4605_2]) ).

fof(f_4606_1,plain,
    ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
      ( hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__sort]) ).

fof(f_4606_2,plain,
    ! [U_19156,U_19155,U_19154,U_19153,U_19152] :
      ( hAPP(c_List_Ofilter(U_19153,U_19154),c_List_Olinorder__class_Osort__key(U_19153,U_19152,U_19155,U_19156)) = c_List_Olinorder__class_Osort__key(U_19153,U_19152,U_19155,hAPP(c_List_Ofilter(U_19153,U_19154),U_19156))
      | ~ class_Orderings_Olinorder(U_19152) ),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

cnf(f_4606_3,plain,
    ( hAPP(c_List_Ofilter(U_19153,U_19154),c_List_Olinorder__class_Osort__key(U_19153,U_19152,U_19155,U_19156)) = c_List_Olinorder__class_Osort__key(U_19153,U_19152,U_19155,hAPP(c_List_Ofilter(U_19153,U_19154),U_19156))
    | ~ class_Orderings_Olinorder(U_19152) ),
    inference(clausify,[status(thm)],[f_4606_2]) ).

fof(f_4607_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_4607_2,plain,
    ! [U_19158,U_19157] : c_List_Otranspose(U_19157,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19157)),c_List_Olist_ONil(U_19157)),U_19158)) = c_List_Otranspose(U_19157,U_19158),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

cnf(f_4607_3,plain,
    c_List_Otranspose(U_19157,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19157)),c_List_Olist_ONil(U_19157)),U_19158)) = c_List_Otranspose(U_19157,U_19158),
    inference(clausify,[status(thm)],[f_4607_2]) ).

fof(f_4608_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter2]) ).

fof(f_4608_2,plain,
    ! [U_19161,U_19160,U_19159] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_19159),tc_List_Olist(U_19159)),c_List_Opartition(U_19159,U_19160,U_19161)) = hAPP(c_List_Ofilter(U_19159,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19159,c_fNot),U_19160)),U_19161),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

cnf(f_4608_3,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_19159),tc_List_Olist(U_19159)),c_List_Opartition(U_19159,U_19160,U_19161)) = hAPP(c_List_Ofilter(U_19159,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19159,c_fNot),U_19160)),U_19161),
    inference(clausify,[status(thm)],[f_4608_2]) ).

fof(f_4609_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__filter]) ).

fof(f_4609_2,plain,
    ! [U_19164,U_19163,U_19162] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19162),hAPP(c_List_Ofilter(U_19162,U_19164),U_19163)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19162),U_19163)) ),
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

cnf(f_4609_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19162),hAPP(c_List_Ofilter(U_19162,U_19164),U_19163)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19162),U_19163)) ),
    inference(clausify,[status(thm)],[f_4609_2]) ).

fof(f_4610_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(f_4610_2,plain,
    ! [U_19167,U_19166,U_19165] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),hAPP(c_List_Ofilter(U_19165,U_19166),U_19167))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),hAPP(c_List_Ofilter(U_19165,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19165),c_fNot),U_19166)),U_19167))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),U_19167),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

cnf(f_4610_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),hAPP(c_List_Ofilter(U_19165,U_19166),U_19167))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),hAPP(c_List_Ofilter(U_19165,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19165),c_fNot),U_19166)),U_19167))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19165)),U_19167),
    inference(clausify,[status(thm)],[f_4610_2]) ).

fof(f_4611_1,plain,
    ! [V_xs_2,V_P_2,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)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__le]) ).

fof(f_4611_2,plain,
    ! [U_19170,U_19169,U_19168] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),hAPP(c_List_Ofilter(U_19168,U_19169),U_19170))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19170))),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

cnf(f_4611_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),hAPP(c_List_Ofilter(U_19168,U_19169),U_19170))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19168)),U_19170))),
    inference(clausify,[status(thm)],[f_4611_2]) ).

fof(f_4612_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_filter__is__subset]) ).

fof(f_4612_2,plain,
    ! [U_19173,U_19172,U_19171] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19171,tc_HOL_Obool)),hAPP(c_List_Oset(U_19171),hAPP(c_List_Ofilter(U_19171,U_19172),U_19173))),hAPP(c_List_Oset(U_19171),U_19173))),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

cnf(f_4612_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19171,tc_HOL_Obool)),hAPP(c_List_Oset(U_19171),hAPP(c_List_Ofilter(U_19171,U_19172),U_19173))),hAPP(c_List_Oset(U_19171),U_19173))),
    inference(clausify,[status(thm)],[f_4612_2]) ).

fof(f_4613_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__id__conv]) ).

fof(f_4613_2,plain,
    ! [U_19178,U_19177,U_19176] :
      ( ( hAPP(c_List_Ofilter(U_19176,U_19177),U_19178) = U_19178
        | ? [U_19175] :
            ( ~ hBOOL(hAPP(U_19177,U_19175))
            & hBOOL(hAPP(hAPP(c_member(U_19176),U_19175),hAPP(c_List_Oset(U_19176),U_19178))) ) )
      & ( ! [U_19174] :
            ( hBOOL(hAPP(U_19177,U_19174))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19176),U_19174),hAPP(c_List_Oset(U_19176),U_19178))) )
        | hAPP(c_List_Ofilter(U_19176,U_19177),U_19178) != U_19178 ) ),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

fof(f_4613_3,plain,
    ( ! [U_19184,U_19182,U_19180] :
        ( hAPP(c_List_Ofilter(U_19180,U_19182),U_19184) = U_19184
        | ? [U_19175] :
            ( ~ hBOOL(hAPP(U_19182,U_19175))
            & hBOOL(hAPP(hAPP(c_member(U_19180),U_19175),hAPP(c_List_Oset(U_19180),U_19184))) ) )
    & ! [U_19183,U_19181,U_19179] :
        ( ! [U_19174] :
            ( hBOOL(hAPP(U_19181,U_19174))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19179),U_19174),hAPP(c_List_Oset(U_19179),U_19183))) )
        | hAPP(c_List_Ofilter(U_19179,U_19181),U_19183) != U_19183 ) ),
    inference(miniscope,[status(thm)],[f_4613_2]) ).

fof(f_4613_4,plain,
    ( ! [U_19184,U_19182,U_19180] :
        ( hAPP(c_List_Ofilter(U_19180,U_19182),U_19184) = U_19184
        | ( ~ hBOOL(hAPP(U_19182,sK482(U_19184,U_19182,U_19180)))
          & hBOOL(hAPP(hAPP(c_member(U_19180),sK482(U_19184,U_19182,U_19180)),hAPP(c_List_Oset(U_19180),U_19184))) ) )
    & ! [U_19183,U_19181,U_19179] :
        ( ! [U_19174] :
            ( hBOOL(hAPP(U_19181,U_19174))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19179),U_19174),hAPP(c_List_Oset(U_19179),U_19183))) )
        | hAPP(c_List_Ofilter(U_19179,U_19181),U_19183) != U_19183 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_19175,sK482(U_19184,U_19182,U_19180))],[f_4613_3]) ).

cnf(f_4613_5,plain,
    ( hBOOL(hAPP(U_19181,U_19174))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19179),U_19174),hAPP(c_List_Oset(U_19179),U_19183)))
    | hAPP(c_List_Ofilter(U_19179,U_19181),U_19183) != U_19183 ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

cnf(f_4613_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19180),sK482(U_19184,U_19182,U_19180)),hAPP(c_List_Oset(U_19180),U_19184)))
    | hAPP(c_List_Ofilter(U_19180,U_19182),U_19184) = U_19184 ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

cnf(f_4613_7,plain,
    ( ~ hBOOL(hAPP(U_19182,sK482(U_19184,U_19182,U_19180)))
    | hAPP(c_List_Ofilter(U_19180,U_19182),U_19184) = U_19184 ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

fof(f_4614_1,plain,
    ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort__triv]) ).

fof(f_4614_2,plain,
    ! [U_19190,U_19189,U_19188,U_19187,U_19186,U_19185] :
      ( hAPP(c_List_Ofilter(U_19188,U_19186),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19188,U_19185,U_19189),U_19187),U_19190)) = hAPP(c_List_Ofilter(U_19188,U_19186),U_19190)
      | hBOOL(hAPP(U_19186,U_19187))
      | ~ class_Orderings_Olinorder(U_19185) ),
    inference(variable_rename,[status(thm)],[f_4614_1]) ).

cnf(f_4614_3,plain,
    ( hAPP(c_List_Ofilter(U_19188,U_19186),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19188,U_19185,U_19189),U_19187),U_19190)) = hAPP(c_List_Ofilter(U_19188,U_19186),U_19190)
    | hBOOL(hAPP(U_19186,U_19187))
    | ~ class_Orderings_Olinorder(U_19185) ),
    inference(clausify,[status(thm)],[f_4614_2]) ).

fof(f_4615_1,plain,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__filter__not]) ).

fof(f_4615_2,plain,
    ! [U_19194,U_19193,U_19192,U_19191] :
      ( c_List_Oremove1(U_19193,U_19192,hAPP(c_List_Ofilter(U_19193,U_19191),U_19194)) = hAPP(c_List_Ofilter(U_19193,U_19191),U_19194)
      | hBOOL(hAPP(U_19191,U_19192)) ),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

cnf(f_4615_3,plain,
    ( c_List_Oremove1(U_19193,U_19192,hAPP(c_List_Ofilter(U_19193,U_19191),U_19194)) = hAPP(c_List_Ofilter(U_19193,U_19191),U_19194)
    | hBOOL(hAPP(U_19191,U_19192)) ),
    inference(clausify,[status(thm)],[f_4615_2]) ).

fof(f_4616_1,plain,
    ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__remove1]) ).

fof(f_4616_2,plain,
    ! [U_19198,U_19197,U_19196,U_19195] : hAPP(c_List_Ofilter(U_19195,U_19196),c_List_Oremove1(U_19195,U_19197,U_19198)) = c_List_Oremove1(U_19195,U_19197,hAPP(c_List_Ofilter(U_19195,U_19196),U_19198)),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

cnf(f_4616_3,plain,
    hAPP(c_List_Ofilter(U_19195,U_19196),c_List_Oremove1(U_19195,U_19197,U_19198)) = c_List_Oremove1(U_19195,U_19197,hAPP(c_List_Ofilter(U_19195,U_19196),U_19198)),
    inference(clausify,[status(thm)],[f_4616_2]) ).

fof(f_4617_1,plain,
    ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_filter__filter]) ).

fof(f_4617_2,plain,
    ! [U_19202,U_19201,U_19200,U_19199] : hAPP(c_List_Ofilter(U_19199,U_19200),hAPP(c_List_Ofilter(U_19199,U_19201),U_19202)) = hAPP(c_List_Ofilter(U_19199,hAPP(hAPP(c_COMBS(U_19199,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19199),c_fconj),U_19201)),U_19200)),U_19202),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

cnf(f_4617_3,plain,
    hAPP(c_List_Ofilter(U_19199,U_19200),hAPP(c_List_Ofilter(U_19199,U_19201),U_19202)) = hAPP(c_List_Ofilter(U_19199,hAPP(hAPP(c_COMBS(U_19199,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19199),c_fconj),U_19201)),U_19200)),U_19202),
    inference(clausify,[status(thm)],[f_4617_2]) ).

fof(f_4618_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter1]) ).

fof(f_4618_2,plain,
    ! [U_19205,U_19204,U_19203] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_19203),tc_List_Olist(U_19203)),c_List_Opartition(U_19203,U_19204,U_19205)) = hAPP(c_List_Ofilter(U_19203,U_19204),U_19205),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

cnf(f_4618_3,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_19203),tc_List_Olist(U_19203)),c_List_Opartition(U_19203,U_19204,U_19205)) = hAPP(c_List_Ofilter(U_19203,U_19204),U_19205),
    inference(clausify,[status(thm)],[f_4618_2]) ).

fof(f_4619_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__append]) ).

fof(f_4619_2,plain,
    ! [U_19209,U_19208,U_19207,U_19206] : hAPP(c_List_Ofilter(U_19206,U_19207),hAPP(hAPP(c_List_Oappend(U_19206),U_19208),U_19209)) = hAPP(hAPP(c_List_Oappend(U_19206),hAPP(c_List_Ofilter(U_19206,U_19207),U_19208)),hAPP(c_List_Ofilter(U_19206,U_19207),U_19209)),
    inference(variable_rename,[status(thm)],[f_4619_1]) ).

cnf(f_4619_3,plain,
    hAPP(c_List_Ofilter(U_19206,U_19207),hAPP(hAPP(c_List_Oappend(U_19206),U_19208),U_19209)) = hAPP(hAPP(c_List_Oappend(U_19206),hAPP(c_List_Ofilter(U_19206,U_19207),U_19208)),hAPP(c_List_Ofilter(U_19206,U_19207),U_19209)),
    inference(clausify,[status(thm)],[f_4619_2]) ).

fof(f_4620_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_4620_2,plain,
    ! [U_19210] : c_List_Otranspose(U_19210,c_List_Olist_ONil(tc_List_Olist(U_19210))) = c_List_Olist_ONil(tc_List_Olist(U_19210)),
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

cnf(f_4620_3,plain,
    c_List_Otranspose(U_19210,c_List_Olist_ONil(tc_List_Olist(U_19210))) = c_List_Olist_ONil(tc_List_Olist(U_19210)),
    inference(clausify,[status(thm)],[f_4620_2]) ).

fof(f_4621_1,plain,
    ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(f_4621_2,plain,
    ! [U_19212,U_19211] : hAPP(c_List_Ofilter(U_19211,U_19212),c_List_Olist_ONil(U_19211)) = c_List_Olist_ONil(U_19211),
    inference(variable_rename,[status(thm)],[f_4621_1]) ).

cnf(f_4621_3,plain,
    hAPP(c_List_Ofilter(U_19211,U_19212),c_List_Olist_ONil(U_19211)) = c_List_Olist_ONil(U_19211),
    inference(clausify,[status(thm)],[f_4621_2]) ).

fof(f_4622_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__empty__conv]) ).

fof(f_4622_2,plain,
    ! [U_19217,U_19216,U_19215] :
      ( ( hAPP(c_List_Ofilter(U_19215,U_19216),U_19217) = c_List_Olist_ONil(U_19215)
        | ? [U_19214] :
            ( hBOOL(hAPP(U_19216,U_19214))
            & hBOOL(hAPP(hAPP(c_member(U_19215),U_19214),hAPP(c_List_Oset(U_19215),U_19217))) ) )
      & ( ! [U_19213] :
            ( ~ hBOOL(hAPP(U_19216,U_19213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19215),U_19213),hAPP(c_List_Oset(U_19215),U_19217))) )
        | hAPP(c_List_Ofilter(U_19215,U_19216),U_19217) != c_List_Olist_ONil(U_19215) ) ),
    inference(variable_rename,[status(thm)],[f_4622_1]) ).

fof(f_4622_3,plain,
    ( ! [U_19223,U_19221,U_19219] :
        ( hAPP(c_List_Ofilter(U_19219,U_19221),U_19223) = c_List_Olist_ONil(U_19219)
        | ? [U_19214] :
            ( hBOOL(hAPP(U_19221,U_19214))
            & hBOOL(hAPP(hAPP(c_member(U_19219),U_19214),hAPP(c_List_Oset(U_19219),U_19223))) ) )
    & ! [U_19222,U_19220,U_19218] :
        ( ! [U_19213] :
            ( ~ hBOOL(hAPP(U_19220,U_19213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19218),U_19213),hAPP(c_List_Oset(U_19218),U_19222))) )
        | hAPP(c_List_Ofilter(U_19218,U_19220),U_19222) != c_List_Olist_ONil(U_19218) ) ),
    inference(miniscope,[status(thm)],[f_4622_2]) ).

fof(f_4622_4,plain,
    ( ! [U_19223,U_19221,U_19219] :
        ( hAPP(c_List_Ofilter(U_19219,U_19221),U_19223) = c_List_Olist_ONil(U_19219)
        | ( hBOOL(hAPP(U_19221,sK483(U_19223,U_19221,U_19219)))
          & hBOOL(hAPP(hAPP(c_member(U_19219),sK483(U_19223,U_19221,U_19219)),hAPP(c_List_Oset(U_19219),U_19223))) ) )
    & ! [U_19222,U_19220,U_19218] :
        ( ! [U_19213] :
            ( ~ hBOOL(hAPP(U_19220,U_19213))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19218),U_19213),hAPP(c_List_Oset(U_19218),U_19222))) )
        | hAPP(c_List_Ofilter(U_19218,U_19220),U_19222) != c_List_Olist_ONil(U_19218) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_19214,sK483(U_19223,U_19221,U_19219))],[f_4622_3]) ).

cnf(f_4622_5,plain,
    ( ~ hBOOL(hAPP(U_19220,U_19213))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19218),U_19213),hAPP(c_List_Oset(U_19218),U_19222)))
    | hAPP(c_List_Ofilter(U_19218,U_19220),U_19222) != c_List_Olist_ONil(U_19218) ),
    inference(clausify,[status(thm)],[f_4622_4]) ).

cnf(f_4622_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19219),sK483(U_19223,U_19221,U_19219)),hAPP(c_List_Oset(U_19219),U_19223)))
    | hAPP(c_List_Ofilter(U_19219,U_19221),U_19223) = c_List_Olist_ONil(U_19219) ),
    inference(clausify,[status(thm)],[f_4622_4]) ).

cnf(f_4622_7,plain,
    ( hBOOL(hAPP(U_19221,sK483(U_19223,U_19221,U_19219)))
    | hAPP(c_List_Ofilter(U_19219,U_19221),U_19223) = c_List_Olist_ONil(U_19219) ),
    inference(clausify,[status(thm)],[f_4622_4]) ).

fof(f_4623_1,plain,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(f_4623_2,plain,
    ! [U_19227,U_19226,U_19225,U_19224] :
      ( ( hAPP(c_List_Ofilter(U_19226,U_19224),hAPP(hAPP(c_List_Olist_OCons(U_19226),U_19225),U_19227)) = hAPP(c_List_Ofilter(U_19226,U_19224),U_19227)
        | hBOOL(hAPP(U_19224,U_19225)) )
      & ( hAPP(c_List_Ofilter(U_19226,U_19224),hAPP(hAPP(c_List_Olist_OCons(U_19226),U_19225),U_19227)) = hAPP(hAPP(c_List_Olist_OCons(U_19226),U_19225),hAPP(c_List_Ofilter(U_19226,U_19224),U_19227))
        | ~ hBOOL(hAPP(U_19224,U_19225)) ) ),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

fof(f_4623_3,plain,
    ( ! [U_19235,U_19233,U_19231,U_19229] :
        ( hAPP(c_List_Ofilter(U_19233,U_19229),hAPP(hAPP(c_List_Olist_OCons(U_19233),U_19231),U_19235)) = hAPP(c_List_Ofilter(U_19233,U_19229),U_19235)
        | hBOOL(hAPP(U_19229,U_19231)) )
    & ! [U_19234,U_19232,U_19230,U_19228] :
        ( hAPP(c_List_Ofilter(U_19232,U_19228),hAPP(hAPP(c_List_Olist_OCons(U_19232),U_19230),U_19234)) = hAPP(hAPP(c_List_Olist_OCons(U_19232),U_19230),hAPP(c_List_Ofilter(U_19232,U_19228),U_19234))
        | ~ hBOOL(hAPP(U_19228,U_19230)) ) ),
    inference(miniscope,[status(thm)],[f_4623_2]) ).

cnf(f_4623_4,plain,
    ( hAPP(c_List_Ofilter(U_19232,U_19228),hAPP(hAPP(c_List_Olist_OCons(U_19232),U_19230),U_19234)) = hAPP(hAPP(c_List_Olist_OCons(U_19232),U_19230),hAPP(c_List_Ofilter(U_19232,U_19228),U_19234))
    | ~ hBOOL(hAPP(U_19228,U_19230)) ),
    inference(clausify,[status(thm)],[f_4623_3]) ).

cnf(f_4623_5,plain,
    ( hAPP(c_List_Ofilter(U_19233,U_19229),hAPP(hAPP(c_List_Olist_OCons(U_19233),U_19231),U_19235)) = hAPP(c_List_Ofilter(U_19233,U_19229),U_19235)
    | hBOOL(hAPP(U_19229,U_19231)) ),
    inference(clausify,[status(thm)],[f_4623_3]) ).

fof(f_4624_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__map]) ).

fof(f_4624_2,plain,
    ! [U_19240,U_19239,U_19238,U_19237,U_19236] : hAPP(c_List_Ofilter(U_19236,U_19237),hAPP(hAPP(c_List_Omap(U_19238,U_19236),U_19239),U_19240)) = hAPP(hAPP(c_List_Omap(U_19238,U_19236),U_19239),hAPP(c_List_Ofilter(U_19238,hAPP(c_Fun_Ocomp(U_19236,tc_HOL_Obool,U_19238,U_19237),U_19239)),U_19240)),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

cnf(f_4624_3,plain,
    hAPP(c_List_Ofilter(U_19236,U_19237),hAPP(hAPP(c_List_Omap(U_19238,U_19236),U_19239),U_19240)) = hAPP(hAPP(c_List_Omap(U_19238,U_19236),U_19239),hAPP(c_List_Ofilter(U_19238,hAPP(c_Fun_Ocomp(U_19236,tc_HOL_Obool,U_19238,U_19237),U_19239)),U_19240)),
    inference(clausify,[status(thm)],[f_4624_2]) ).

fof(f_4625_1,plain,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll__filter__not]) ).

fof(f_4625_2,plain,
    ! [U_19244,U_19243,U_19242,U_19241] :
      ( hAPP(c_List_OremoveAll(U_19243,U_19242),hAPP(c_List_Ofilter(U_19243,U_19241),U_19244)) = hAPP(c_List_Ofilter(U_19243,U_19241),U_19244)
      | hBOOL(hAPP(U_19241,U_19242)) ),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

cnf(f_4625_3,plain,
    ( hAPP(c_List_OremoveAll(U_19243,U_19242),hAPP(c_List_Ofilter(U_19243,U_19241),U_19244)) = hAPP(c_List_Ofilter(U_19243,U_19241),U_19244)
    | hBOOL(hAPP(U_19241,U_19242)) ),
    inference(clausify,[status(thm)],[f_4625_2]) ).

fof(f_4626_1,plain,
    ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__filter]) ).

fof(f_4626_2,plain,
    ! [U_19247,U_19246,U_19245] : c_List_Oremdups(U_19245,hAPP(c_List_Ofilter(U_19245,U_19246),U_19247)) = hAPP(c_List_Ofilter(U_19245,U_19246),c_List_Oremdups(U_19245,U_19247)),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

cnf(f_4626_3,plain,
    c_List_Oremdups(U_19245,hAPP(c_List_Ofilter(U_19245,U_19246),U_19247)) = hAPP(c_List_Ofilter(U_19245,U_19246),c_List_Oremdups(U_19245,U_19247)),
    inference(clausify,[status(thm)],[f_4626_2]) ).

fof(f_4627_1,plain,
    ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(f_4627_2,plain,
    ! [U_19249,U_19248] : c_List_OremoveAll(U_19248,U_19249) = c_List_Ofilter(U_19248,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19248),c_fNot),hAPP(c_fequal,U_19249))),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

cnf(f_4627_3,plain,
    c_List_OremoveAll(U_19248,U_19249) = c_List_Ofilter(U_19248,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19248),c_fNot),hAPP(c_fequal,U_19249))),
    inference(clausify,[status(thm)],[f_4627_2]) ).

fof(f_4628_1,plain,
    ! [V_xs_2,T_a,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),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_a))),c_List_Otranspose(T_a,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__transpose]) ).

fof(f_4628_2,plain,
    ! [U_19252,U_19251,U_19250] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19251)),c_List_Otranspose(U_19251,U_19252)),U_19250) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19251),U_19251),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19251),tc_Nat_Onat,U_19251),c_List_Onth(U_19251)),U_19250)),hAPP(c_List_Ofilter(tc_List_Olist(U_19251),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19251)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19251)))),U_19252))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19251))),c_List_Otranspose(U_19251,U_19252)))) ),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

cnf(f_4628_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19251)),c_List_Otranspose(U_19251,U_19252)),U_19250) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19251),U_19251),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19251),tc_Nat_Onat,U_19251),c_List_Onth(U_19251)),U_19250)),hAPP(c_List_Ofilter(tc_List_Olist(U_19251),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19251)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19251)))),U_19252))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19250),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19251))),c_List_Otranspose(U_19251,U_19252)))) ),
    inference(clausify,[status(thm)],[f_4628_2]) ).

fof(f_4629_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__map__map]) ).

fof(f_4629_2,plain,
    ! [U_19256,U_19255,U_19254,U_19253] : c_List_Otranspose(U_19253,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19254),tc_List_Olist(U_19253)),hAPP(c_List_Omap(U_19254,U_19253),U_19255)),U_19256)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19254),tc_List_Olist(U_19253)),hAPP(c_List_Omap(U_19254,U_19253),U_19255)),c_List_Otranspose(U_19254,U_19256)),
    inference(variable_rename,[status(thm)],[f_4629_1]) ).

cnf(f_4629_3,plain,
    c_List_Otranspose(U_19253,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19254),tc_List_Olist(U_19253)),hAPP(c_List_Omap(U_19254,U_19253),U_19255)),U_19256)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19254),tc_List_Olist(U_19253)),hAPP(c_List_Omap(U_19254,U_19253),U_19255)),c_List_Otranspose(U_19254,U_19256)),
    inference(clausify,[status(thm)],[f_4629_2]) ).

fof(f_4630_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_set__filter]) ).

fof(f_4630_2,plain,
    ! [U_19259,U_19258,U_19257] : hAPP(c_List_Oset(U_19257),hAPP(c_List_Ofilter(U_19257,U_19258),U_19259)) = hAPP(c_Set_OCollect(U_19257),hAPP(hAPP(c_COMBS(U_19257,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19257),c_fconj),hAPP(hAPP(c_COMBC(U_19257,tc_fun(U_19257,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19257)),hAPP(c_List_Oset(U_19257),U_19259)))),U_19258)),
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

cnf(f_4630_3,plain,
    hAPP(c_List_Oset(U_19257),hAPP(c_List_Ofilter(U_19257,U_19258),U_19259)) = hAPP(c_Set_OCollect(U_19257),hAPP(hAPP(c_COMBS(U_19257,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19257),c_fconj),hAPP(hAPP(c_COMBC(U_19257,tc_fun(U_19257,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19257)),hAPP(c_List_Oset(U_19257),U_19259)))),U_19258)),
    inference(clausify,[status(thm)],[f_4630_2]) ).

fof(f_4631_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__filter__map]) ).

fof(f_4631_2,plain,
    ! [U_19264,U_19263,U_19262,U_19261,U_19260] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19260)),hAPP(c_List_Ofilter(U_19260,U_19261),hAPP(hAPP(c_List_Omap(U_19262,U_19260),U_19263),U_19264))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19262)),hAPP(c_List_Ofilter(U_19262,hAPP(c_Fun_Ocomp(U_19260,tc_HOL_Obool,U_19262,U_19261),U_19263)),U_19264)),
    inference(variable_rename,[status(thm)],[f_4631_1]) ).

cnf(f_4631_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19260)),hAPP(c_List_Ofilter(U_19260,U_19261),hAPP(hAPP(c_List_Omap(U_19262,U_19260),U_19263),U_19264))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19262)),hAPP(c_List_Ofilter(U_19262,hAPP(c_Fun_Ocomp(U_19260,tc_HOL_Obool,U_19262,U_19261),U_19263)),U_19264)),
    inference(clausify,[status(thm)],[f_4631_2]) ).

fof(f_4632_1,plain,
    ! [V_P_2,V_xs_2,V_x_2,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__filter__less]) ).

fof(f_4632_2,plain,
    ! [U_19268,U_19267,U_19266,U_19265] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19265)),hAPP(c_List_Ofilter(U_19265,U_19268),U_19267))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19265)),U_19267)))
      | hBOOL(hAPP(U_19268,U_19266))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19265),U_19266),hAPP(c_List_Oset(U_19265),U_19267))) ),
    inference(variable_rename,[status(thm)],[f_4632_1]) ).

cnf(f_4632_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19265)),hAPP(c_List_Ofilter(U_19265,U_19268),U_19267))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19265)),U_19267)))
    | hBOOL(hAPP(U_19268,U_19266))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19265),U_19266),hAPP(c_List_Oset(U_19265),U_19267))) ),
    inference(clausify,[status(thm)],[f_4632_2]) ).

fof(f_4633_1,plain,
    ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition__filter__conv]) ).

fof(f_4633_2,plain,
    ! [U_19271,U_19270,U_19269] : c_List_Opartition(U_19269,U_19270,U_19271) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19269),tc_List_Olist(U_19269)),hAPP(c_List_Ofilter(U_19269,U_19270),U_19271)),hAPP(c_List_Ofilter(U_19269,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19269,c_fNot),U_19270)),U_19271)),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

cnf(f_4633_3,plain,
    c_List_Opartition(U_19269,U_19270,U_19271) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19269),tc_List_Olist(U_19269)),hAPP(c_List_Ofilter(U_19269,U_19270),U_19271)),hAPP(c_List_Ofilter(U_19269,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19269,c_fNot),U_19270)),U_19271)),
    inference(clausify,[status(thm)],[f_4633_2]) ).

fof(f_4634_1,plain,
    ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__minus__filter__out]) ).

fof(f_4634_2,plain,
    ! [U_19274,U_19273,U_19272] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19272,tc_HOL_Obool)),hAPP(c_List_Oset(U_19272),U_19273)),hAPP(hAPP(c_Set_Oinsert(U_19272),U_19274),c_Orderings_Obot__class_Obot(tc_fun(U_19272,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_19272),hAPP(c_List_Ofilter(U_19272,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19272),c_fNot),hAPP(hAPP(c_COMBC(U_19272,U_19272,tc_HOL_Obool),c_fequal),U_19274))),U_19273)),
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

cnf(f_4634_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19272,tc_HOL_Obool)),hAPP(c_List_Oset(U_19272),U_19273)),hAPP(hAPP(c_Set_Oinsert(U_19272),U_19274),c_Orderings_Obot__class_Obot(tc_fun(U_19272,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_19272),hAPP(c_List_Ofilter(U_19272,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19272),c_fNot),hAPP(hAPP(c_COMBC(U_19272,U_19272,tc_HOL_Obool),c_fequal),U_19274))),U_19273)),
    inference(clausify,[status(thm)],[f_4634_2]) ).

fof(f_4635_1,plain,
    ! [V_s_2,V_xs_2,T_a] :
      ( hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_filter__in__sublist]) ).

fof(f_4635_2,plain,
    ! [U_19277,U_19276,U_19275] :
      ( hAPP(c_List_Ofilter(U_19275,hAPP(hAPP(c_COMBC(U_19275,tc_fun(U_19275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19275)),hAPP(c_List_Oset(U_19275),c_List_Osublist(U_19275,U_19276,U_19277)))),U_19276) = c_List_Osublist(U_19275,U_19276,U_19277)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19275),U_19276)) ),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

cnf(f_4635_3,plain,
    ( hAPP(c_List_Ofilter(U_19275,hAPP(hAPP(c_COMBC(U_19275,tc_fun(U_19275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19275)),hAPP(c_List_Oset(U_19275),c_List_Osublist(U_19275,U_19276,U_19277)))),U_19276) = c_List_Osublist(U_19275,U_19276,U_19277)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19275),U_19276)) ),
    inference(clausify,[status(thm)],[f_4635_2]) ).

fof(f_4636_1,plain,
    ! [V_xs_2,T_a] :
      ( ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_a)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_a)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) )
        | c_List_Otranspose(T_a,V_xs_2) != c_List_Olist_ONil(tc_List_Olist(T_a)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__empty]) ).

fof(f_4636_2,plain,
    ! [U_19281,U_19280] :
      ( ( c_List_Otranspose(U_19280,U_19281) = c_List_Olist_ONil(tc_List_Olist(U_19280))
        | ? [U_19279] :
            ( U_19279 != c_List_Olist_ONil(U_19280)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19280)),U_19279),hAPP(c_List_Oset(tc_List_Olist(U_19280)),U_19281))) ) )
      & ( ! [U_19278] :
            ( U_19278 = c_List_Olist_ONil(U_19280)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19280)),U_19278),hAPP(c_List_Oset(tc_List_Olist(U_19280)),U_19281))) )
        | c_List_Otranspose(U_19280,U_19281) != c_List_Olist_ONil(tc_List_Olist(U_19280)) ) ),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

fof(f_4636_3,plain,
    ( ! [U_19285,U_19283] :
        ( c_List_Otranspose(U_19283,U_19285) = c_List_Olist_ONil(tc_List_Olist(U_19283))
        | ? [U_19279] :
            ( U_19279 != c_List_Olist_ONil(U_19283)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19283)),U_19279),hAPP(c_List_Oset(tc_List_Olist(U_19283)),U_19285))) ) )
    & ! [U_19284,U_19282] :
        ( ! [U_19278] :
            ( U_19278 = c_List_Olist_ONil(U_19282)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19282)),U_19278),hAPP(c_List_Oset(tc_List_Olist(U_19282)),U_19284))) )
        | c_List_Otranspose(U_19282,U_19284) != c_List_Olist_ONil(tc_List_Olist(U_19282)) ) ),
    inference(miniscope,[status(thm)],[f_4636_2]) ).

fof(f_4636_4,plain,
    ( ! [U_19285,U_19283] :
        ( c_List_Otranspose(U_19283,U_19285) = c_List_Olist_ONil(tc_List_Olist(U_19283))
        | ( sK484(U_19285,U_19283) != c_List_Olist_ONil(U_19283)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19283)),sK484(U_19285,U_19283)),hAPP(c_List_Oset(tc_List_Olist(U_19283)),U_19285))) ) )
    & ! [U_19284,U_19282] :
        ( ! [U_19278] :
            ( U_19278 = c_List_Olist_ONil(U_19282)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19282)),U_19278),hAPP(c_List_Oset(tc_List_Olist(U_19282)),U_19284))) )
        | c_List_Otranspose(U_19282,U_19284) != c_List_Olist_ONil(tc_List_Olist(U_19282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_19279,sK484(U_19285,U_19283))],[f_4636_3]) ).

cnf(f_4636_5,plain,
    ( U_19278 = c_List_Olist_ONil(U_19282)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19282)),U_19278),hAPP(c_List_Oset(tc_List_Olist(U_19282)),U_19284)))
    | c_List_Otranspose(U_19282,U_19284) != c_List_Olist_ONil(tc_List_Olist(U_19282)) ),
    inference(clausify,[status(thm)],[f_4636_4]) ).

cnf(f_4636_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19283)),sK484(U_19285,U_19283)),hAPP(c_List_Oset(tc_List_Olist(U_19283)),U_19285)))
    | c_List_Otranspose(U_19283,U_19285) = c_List_Olist_ONil(tc_List_Olist(U_19283)) ),
    inference(clausify,[status(thm)],[f_4636_4]) ).

cnf(f_4636_7,plain,
    ( sK484(U_19285,U_19283) != c_List_Olist_ONil(U_19283)
    | c_List_Otranspose(U_19283,U_19285) = c_List_Olist_ONil(tc_List_Olist(U_19283)) ),
    inference(clausify,[status(thm)],[f_4636_4]) ).

fof(f_4637_1,plain,
    ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__conv__card]) ).

fof(f_4637_2,plain,
    ! [U_19288,U_19287,U_19286] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),hAPP(c_List_Ofilter(U_19286,U_19287),U_19288)) = 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_19286)),U_19288)))),hAPP(hAPP(c_COMBB(U_19286,tc_HOL_Obool,tc_Nat_Onat),U_19287),hAPP(c_List_Onth(U_19286),U_19288))))),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

cnf(f_4637_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),hAPP(c_List_Ofilter(U_19286,U_19287),U_19288)) = 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_19286)),U_19288)))),hAPP(hAPP(c_COMBB(U_19286,tc_HOL_Obool,tc_Nat_Onat),U_19287),hAPP(c_List_Onth(U_19286),U_19288))))),
    inference(clausify,[status(thm)],[f_4637_2]) ).

fof(f_4638_1,plain,
    ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(f_4638_2,plain,
    ! [U_19290,U_19289] : c_List_Oconcat(tc_List_Olist(U_19289),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19289)),U_19289,c_List_Olist_ONil(tc_List_Olist(U_19289)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289))),U_19289),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289)),tc_List_Olist(tc_List_Olist(U_19289))),c_List_Olist_OCons(tc_List_Olist(U_19289))),c_List_Olist_ONil(tc_List_Olist(U_19289)))))),U_19290)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19289),tc_List_Olist(U_19289)),c_List_Otl(U_19289)),hAPP(c_List_Ofilter(tc_List_Olist(U_19289),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19289)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19289),tc_List_Olist(U_19289),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19289)))),U_19290)),
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

cnf(f_4638_3,plain,
    c_List_Oconcat(tc_List_Olist(U_19289),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19289)),U_19289,c_List_Olist_ONil(tc_List_Olist(U_19289)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289))),U_19289),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19289),tc_List_Olist(tc_List_Olist(U_19289)),tc_List_Olist(tc_List_Olist(U_19289))),c_List_Olist_OCons(tc_List_Olist(U_19289))),c_List_Olist_ONil(tc_List_Olist(U_19289)))))),U_19290)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19289),tc_List_Olist(U_19289)),c_List_Otl(U_19289)),hAPP(c_List_Ofilter(tc_List_Olist(U_19289),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19289)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19289),tc_List_Olist(U_19289),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19289)))),U_19290)),
    inference(clausify,[status(thm)],[f_4638_2]) ).

fof(f_4639_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_a] :
      ( c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J]) ).

fof(f_4639_2,plain,
    ! [U_19294,U_19293,U_19292,U_19291] :
      ( c_List_Otranspose(U_19291,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),U_19293)),U_19294)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),c_List_Oconcat(U_19291,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19291),tc_List_Olist(U_19291)),c_List_Olist_Olist__case(tc_List_Olist(U_19291),U_19291,c_List_Olist_ONil(U_19291),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19291),tc_fun(tc_List_Olist(U_19291),tc_List_Olist(U_19291)),U_19291),c_COMBK(tc_List_Olist(U_19291),tc_List_Olist(U_19291))),hAPP(hAPP(c_COMBC(U_19291,tc_List_Olist(U_19291),tc_List_Olist(U_19291)),c_List_Olist_OCons(U_19291)),c_List_Olist_ONil(U_19291))))),U_19294)))),c_List_Otranspose(U_19291,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),U_19293),c_List_Oconcat(tc_List_Olist(U_19291),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19291)),U_19291,c_List_Olist_ONil(tc_List_Olist(U_19291)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291))),U_19291),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291)),tc_List_Olist(tc_List_Olist(U_19291))),c_List_Olist_OCons(tc_List_Olist(U_19291))),c_List_Olist_ONil(tc_List_Olist(U_19291)))))),U_19294)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19291)),c_List_Otranspose__rel(U_19291)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),U_19293)),U_19294))) ),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

cnf(f_4639_3,plain,
    ( c_List_Otranspose(U_19291,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),U_19293)),U_19294)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),c_List_Oconcat(U_19291,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19291),tc_List_Olist(U_19291)),c_List_Olist_Olist__case(tc_List_Olist(U_19291),U_19291,c_List_Olist_ONil(U_19291),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19291),tc_fun(tc_List_Olist(U_19291),tc_List_Olist(U_19291)),U_19291),c_COMBK(tc_List_Olist(U_19291),tc_List_Olist(U_19291))),hAPP(hAPP(c_COMBC(U_19291,tc_List_Olist(U_19291),tc_List_Olist(U_19291)),c_List_Olist_OCons(U_19291)),c_List_Olist_ONil(U_19291))))),U_19294)))),c_List_Otranspose(U_19291,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),U_19293),c_List_Oconcat(tc_List_Olist(U_19291),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_19291)),U_19291,c_List_Olist_ONil(tc_List_Olist(U_19291)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291))),U_19291),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19291),tc_List_Olist(tc_List_Olist(U_19291)),tc_List_Olist(tc_List_Olist(U_19291))),c_List_Olist_OCons(tc_List_Olist(U_19291))),c_List_Olist_ONil(tc_List_Olist(U_19291)))))),U_19294)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19291)),c_List_Otranspose__rel(U_19291)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19291)),hAPP(hAPP(c_List_Olist_OCons(U_19291),U_19292),U_19293)),U_19294))) ),
    inference(clausify,[status(thm)],[f_4639_2]) ).

fof(f_4640_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),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,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__filter__def]) ).

fof(f_4640_2,plain,
    ! [U_19298,U_19297,U_19296,U_19295] : c_List_Omap__filter(U_19295,U_19296,U_19297,U_19298) = hAPP(hAPP(c_List_Omap(U_19295,U_19296),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_19296),U_19296,U_19295,c_Option_Othe(U_19296)),U_19297)),hAPP(c_List_Ofilter(U_19295,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19295),c_fNot),hAPP(hAPP(c_COMBC(U_19295,tc_Option_Ooption(U_19296),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_19296),tc_fun(tc_Option_Ooption(U_19296),tc_HOL_Obool),U_19295),c_fequal),U_19297)),c_Option_Ooption_ONone(U_19296)))),U_19298)),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

cnf(f_4640_3,plain,
    c_List_Omap__filter(U_19295,U_19296,U_19297,U_19298) = hAPP(hAPP(c_List_Omap(U_19295,U_19296),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_19296),U_19296,U_19295,c_Option_Othe(U_19296)),U_19297)),hAPP(c_List_Ofilter(U_19295,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19295),c_fNot),hAPP(hAPP(c_COMBC(U_19295,tc_Option_Ooption(U_19296),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_19296),tc_fun(tc_Option_Ooption(U_19296),tc_HOL_Obool),U_19295),c_fequal),U_19297)),c_Option_Ooption_ONone(U_19296)))),U_19298)),
    inference(clausify,[status(thm)],[f_4640_2]) ).

fof(f_4641_1,plain,
    ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_map__filter__simps_I2_J]) ).

fof(f_4641_2,plain,
    ! [U_19301,U_19300,U_19299] : c_List_Omap__filter(U_19299,U_19300,U_19301,c_List_Olist_ONil(U_19299)) = c_List_Olist_ONil(U_19300),
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

cnf(f_4641_3,plain,
    c_List_Omap__filter(U_19299,U_19300,U_19301,c_List_Olist_ONil(U_19299)) = c_List_Olist_ONil(U_19300),
    inference(clausify,[status(thm)],[f_4641_2]) ).

fof(f_4642_1,plain,
    ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
      ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2)
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
      | hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__filter__in]) ).

fof(f_4642_2,plain,
    ! [U_19307,U_19306,U_19305,U_19304,U_19303,U_19302] :
      ( hAPP(hAPP(c_Map_Omap__of(U_19302,U_19303),hAPP(c_List_Ofilter(tc_prod(U_19302,U_19303),hAPP(c_Product__Type_Oprod_Oprod__case(U_19302,U_19303,tc_HOL_Obool),U_19307)),U_19304)),U_19305) = hAPP(c_Option_Ooption_OSome(U_19303),U_19306)
      | ~ hBOOL(hAPP(hAPP(U_19307,U_19305),U_19306))
      | hAPP(hAPP(c_Map_Omap__of(U_19302,U_19303),U_19304),U_19305) != hAPP(c_Option_Ooption_OSome(U_19303),U_19306) ),
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

cnf(f_4642_3,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_19302,U_19303),hAPP(c_List_Ofilter(tc_prod(U_19302,U_19303),hAPP(c_Product__Type_Oprod_Oprod__case(U_19302,U_19303,tc_HOL_Obool),U_19307)),U_19304)),U_19305) = hAPP(c_Option_Ooption_OSome(U_19303),U_19306)
    | ~ hBOOL(hAPP(hAPP(U_19307,U_19305),U_19306))
    | hAPP(hAPP(c_Map_Omap__of(U_19302,U_19303),U_19304),U_19305) != hAPP(c_Option_Ooption_OSome(U_19303),U_19306) ),
    inference(clausify,[status(thm)],[f_4642_2]) ).

fof(f_4643_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,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_4643_2,plain,
    ! [U_19312,U_19311,U_19310,U_19309,U_19308] : c_List_Omap__filter(U_19308,U_19309,U_19310,hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19311),U_19312)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_19309),U_19309,c_List_Omap__filter(U_19308,U_19309,U_19310,U_19312),hAPP(hAPP(c_COMBC(U_19309,tc_List_Olist(U_19309),tc_List_Olist(U_19309)),c_List_Olist_OCons(U_19309)),c_List_Omap__filter(U_19308,U_19309,U_19310,U_19312))),hAPP(U_19310,U_19311)),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

cnf(f_4643_3,plain,
    c_List_Omap__filter(U_19308,U_19309,U_19310,hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19311),U_19312)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_19309),U_19309,c_List_Omap__filter(U_19308,U_19309,U_19310,U_19312),hAPP(hAPP(c_COMBC(U_19309,tc_List_Olist(U_19309),tc_List_Olist(U_19309)),c_List_Olist_OCons(U_19309)),c_List_Omap__filter(U_19308,U_19309,U_19310,U_19312))),hAPP(U_19310,U_19311)),
    inference(clausify,[status(thm)],[f_4643_2]) ).

fof(f_4644_1,plain,
    ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,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_4644_2,plain,
    ! [U_19316,U_19315,U_19314,U_19313] : hAPP(hAPP(c_List_Omap(tc_prod(U_19313,tc_Nat_Onat),U_19313),c_Product__Type_Ofst(U_19313,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19313,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_19313,tc_Nat_Onat)),U_19314),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_19313,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_19313,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_19313,tc_Nat_Onat),U_19315),U_19316))) = hAPP(hAPP(c_List_Omap(tc_prod(U_19313,tc_Nat_Onat),U_19313),c_Product__Type_Ofst(U_19313,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19313,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_19313,tc_Nat_Onat)),U_19314),c_Product__Type_Osnd(U_19313,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_19313,tc_Nat_Onat),U_19315),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_19316)))),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

cnf(f_4644_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_19313,tc_Nat_Onat),U_19313),c_Product__Type_Ofst(U_19313,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19313,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_19313,tc_Nat_Onat)),U_19314),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_19313,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_19313,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_19313,tc_Nat_Onat),U_19315),U_19316))) = hAPP(hAPP(c_List_Omap(tc_prod(U_19313,tc_Nat_Onat),U_19313),c_Product__Type_Ofst(U_19313,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19313,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_19313,tc_Nat_Onat)),U_19314),c_Product__Type_Osnd(U_19313,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_19313,tc_Nat_Onat),U_19315),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_19316)))),
    inference(clausify,[status(thm)],[f_4644_2]) ).

fof(f_4645_1,plain,
    ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(f_4645_2,plain,
    ! [U_19318,U_19317] : c_Random_Oselect__weight(U_19317,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_19317),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_19317,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_19317,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_19317)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_19318)) = c_Random_Oselect__weight(U_19317,U_19318),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

cnf(f_4645_3,plain,
    c_Random_Oselect__weight(U_19317,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_19317),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_19317,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_19317,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_19317)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_19318)) = c_Random_Oselect__weight(U_19317,U_19318),
    inference(clausify,[status(thm)],[f_4645_2]) ).

fof(f_4646_1,plain,
    ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_pick__drop__zero]) ).

fof(f_4646_2,plain,
    ! [U_19320,U_19319] : c_Random_Opick(U_19319,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_19319),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_19319,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_19319,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_19319)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_19320)) = c_Random_Opick(U_19319,U_19320),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

cnf(f_4646_3,plain,
    c_Random_Opick(U_19319,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_19319),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_19319,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_19319,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_19319)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_19320)) = c_Random_Opick(U_19319,U_19320),
    inference(clausify,[status(thm)],[f_4646_2]) ).

fof(f_4647_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))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J]) ).

fof(f_4647_2,plain,
    ! [U_19321] :
      ( c_List_Otranspose(U_19321,c_List_Olist_ONil(tc_List_Olist(U_19321))) = c_List_Olist_ONil(tc_List_Olist(U_19321))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19321)),c_List_Otranspose__rel(U_19321)),c_List_Olist_ONil(tc_List_Olist(U_19321)))) ),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

cnf(f_4647_3,plain,
    ( c_List_Otranspose(U_19321,c_List_Olist_ONil(tc_List_Olist(U_19321))) = c_List_Olist_ONil(tc_List_Olist(U_19321))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19321)),c_List_Otranspose__rel(U_19321)),c_List_Olist_ONil(tc_List_Olist(U_19321)))) ),
    inference(clausify,[status(thm)],[f_4647_2]) ).

fof(f_4648_1,plain,
    ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_map__filter__map__filter]) ).

fof(f_4648_2,plain,
    ! [U_19326,U_19325,U_19324,U_19323,U_19322] : hAPP(hAPP(c_List_Omap(U_19322,U_19323),U_19324),hAPP(c_List_Ofilter(U_19322,U_19325),U_19326)) = c_List_Omap__filter(U_19322,U_19323,hAPP(hAPP(c_COMBC(U_19322,tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323)),hAPP(hAPP(c_COMBS(U_19322,tc_Option_Ooption(U_19323),tc_fun(tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_19323),tc_fun(tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323))),U_19322),c_If(tc_Option_Ooption(U_19323))),U_19325)),hAPP(hAPP(c_COMBB(U_19323,tc_Option_Ooption(U_19323),U_19322),c_Option_Ooption_OSome(U_19323)),U_19324))),c_Option_Ooption_ONone(U_19323)),U_19326),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

cnf(f_4648_3,plain,
    hAPP(hAPP(c_List_Omap(U_19322,U_19323),U_19324),hAPP(c_List_Ofilter(U_19322,U_19325),U_19326)) = c_List_Omap__filter(U_19322,U_19323,hAPP(hAPP(c_COMBC(U_19322,tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323)),hAPP(hAPP(c_COMBS(U_19322,tc_Option_Ooption(U_19323),tc_fun(tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_19323),tc_fun(tc_Option_Ooption(U_19323),tc_Option_Ooption(U_19323))),U_19322),c_If(tc_Option_Ooption(U_19323))),U_19325)),hAPP(hAPP(c_COMBB(U_19323,tc_Option_Ooption(U_19323),U_19322),c_Option_Ooption_OSome(U_19323)),U_19324))),c_Option_Ooption_ONone(U_19323)),U_19326),
    inference(clausify,[status(thm)],[f_4648_2]) ).

fof(f_4649_1,plain,
    ! [V_xss_2,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_2)) = c_List_Otranspose(T_a,V_xss_2)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J]) ).

fof(f_4649_2,plain,
    ! [U_19328,U_19327] :
      ( c_List_Otranspose(U_19327,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19327)),c_List_Olist_ONil(U_19327)),U_19328)) = c_List_Otranspose(U_19327,U_19328)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19327)),c_List_Otranspose__rel(U_19327)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19327)),c_List_Olist_ONil(U_19327)),U_19328))) ),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

cnf(f_4649_3,plain,
    ( c_List_Otranspose(U_19327,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19327)),c_List_Olist_ONil(U_19327)),U_19328)) = c_List_Otranspose(U_19327,U_19328)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_19327)),c_List_Otranspose__rel(U_19327)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_19327)),c_List_Olist_ONil(U_19327)),U_19328))) ),
    inference(clausify,[status(thm)],[f_4649_2]) ).

fof(f_4650_1,plain,
    ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__max__length]) ).

fof(f_4650_2,plain,
    ! [U_19330,U_19329] : c_List_Ofoldr(tc_List_Olist(U_19329),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19329)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19329))),c_List_Otranspose(U_19329,U_19330),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19329))),hAPP(c_List_Ofilter(tc_List_Olist(U_19329),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19329)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19329),tc_List_Olist(U_19329),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19329)))),U_19330)),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

cnf(f_4650_3,plain,
    c_List_Ofoldr(tc_List_Olist(U_19329),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19329)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19329))),c_List_Otranspose(U_19329,U_19330),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19329))),hAPP(c_List_Ofilter(tc_List_Olist(U_19329),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19329)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19329),tc_List_Olist(U_19329),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19329)))),U_19330)),
    inference(clausify,[status(thm)],[f_4650_2]) ).

fof(f_4651_1,plain,
    ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_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_a)),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)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__max]) ).

fof(f_4651_2,plain,
    ! [U_19334,U_19333,U_19332,U_19331] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19331)),U_19332))),c_List_Ofoldr(tc_List_Olist(U_19333),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19333)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19333))),U_19334,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_19331)),U_19332)),c_List_Ofoldr(tc_List_Olist(U_19333),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19333)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19333),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_19333)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19333)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19333),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19333)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19333),tc_List_Olist(U_19333),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19333)))),U_19334),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

cnf(f_4651_3,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_19331)),U_19332))),c_List_Ofoldr(tc_List_Olist(U_19333),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19333)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19333))),U_19334,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_19331)),U_19332)),c_List_Ofoldr(tc_List_Olist(U_19333),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19333)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19333),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_19333)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19333)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19333),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19333)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19333),tc_List_Olist(U_19333),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19333)))),U_19334),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4651_2]) ).

fof(f_4652_1,plain,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__append]) ).

fof(f_4652_2,plain,
    ! [U_19340,U_19339,U_19338,U_19337,U_19336,U_19335] : c_List_Ofoldr(U_19335,U_19336,U_19337,hAPP(hAPP(c_List_Oappend(U_19335),U_19338),U_19339),U_19340) = c_List_Ofoldr(U_19335,U_19336,U_19337,U_19338,c_List_Ofoldr(U_19335,U_19336,U_19337,U_19339,U_19340)),
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

cnf(f_4652_3,plain,
    c_List_Ofoldr(U_19335,U_19336,U_19337,hAPP(hAPP(c_List_Oappend(U_19335),U_19338),U_19339),U_19340) = c_List_Ofoldr(U_19335,U_19336,U_19337,U_19338,c_List_Ofoldr(U_19335,U_19336,U_19337,U_19339,U_19340)),
    inference(clausify,[status(thm)],[f_4652_2]) ).

fof(f_4653_1,plain,
    ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(f_4653_2,plain,
    ! [U_19344,U_19343,U_19342,U_19341] : c_List_Ofoldr(U_19341,U_19342,U_19343,c_List_Olist_ONil(U_19341),U_19344) = U_19344,
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

cnf(f_4653_3,plain,
    c_List_Ofoldr(U_19341,U_19342,U_19343,c_List_Olist_ONil(U_19341),U_19344) = U_19344,
    inference(clausify,[status(thm)],[f_4653_2]) ).

fof(f_4654_1,plain,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(f_4654_2,plain,
    ! [U_19350,U_19349,U_19348,U_19347,U_19346,U_19345] : c_List_Ofoldr(U_19345,U_19346,U_19347,hAPP(hAPP(c_List_Olist_OCons(U_19345),U_19348),U_19349),U_19350) = hAPP(hAPP(U_19347,U_19348),c_List_Ofoldr(U_19345,U_19346,U_19347,U_19349,U_19350)),
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

cnf(f_4654_3,plain,
    c_List_Ofoldr(U_19345,U_19346,U_19347,hAPP(hAPP(c_List_Olist_OCons(U_19345),U_19348),U_19349),U_19350) = hAPP(hAPP(U_19347,U_19348),c_List_Ofoldr(U_19345,U_19346,U_19347,U_19349,U_19350)),
    inference(clausify,[status(thm)],[f_4654_2]) ).

fof(f_4655_1,plain,
    ! [V_a_2,V_xs_2,T_a] :
      ( c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2)
      | ~ class_Groups_Oab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl]) ).

fof(f_4655_2,plain,
    ! [U_19353,U_19352,U_19351] :
      ( c_List_Ofoldr(U_19351,U_19351,c_Groups_Oplus__class_Oplus(U_19351),U_19352,U_19353) = hAPP(c_List_Ofoldl(U_19351,U_19351,c_Groups_Oplus__class_Oplus(U_19351),U_19353),U_19352)
      | ~ class_Groups_Oab__semigroup__add(U_19351) ),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

cnf(f_4655_3,plain,
    ( c_List_Ofoldr(U_19351,U_19351,c_Groups_Oplus__class_Oplus(U_19351),U_19352,U_19353) = hAPP(c_List_Ofoldl(U_19351,U_19351,c_Groups_Oplus__class_Oplus(U_19351),U_19353),U_19352)
    | ~ class_Groups_Oab__semigroup__add(U_19351) ),
    inference(clausify,[status(thm)],[f_4655_2]) ).

fof(f_4656_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldr__map]) ).

fof(f_4656_2,plain,
    ! [U_19360,U_19359,U_19358,U_19357,U_19356,U_19355,U_19354] : c_List_Ofoldr(U_19354,U_19355,U_19356,hAPP(hAPP(c_List_Omap(U_19357,U_19354),U_19358),U_19359),U_19360) = c_List_Ofoldr(U_19357,U_19355,hAPP(c_Fun_Ocomp(U_19354,tc_fun(U_19355,U_19355),U_19357,U_19356),U_19358),U_19359,U_19360),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

cnf(f_4656_3,plain,
    c_List_Ofoldr(U_19354,U_19355,U_19356,hAPP(hAPP(c_List_Omap(U_19357,U_19354),U_19358),U_19359),U_19360) = c_List_Ofoldr(U_19357,U_19355,hAPP(c_Fun_Ocomp(U_19354,tc_fun(U_19355,U_19355),U_19357,U_19356),U_19358),U_19359,U_19360),
    inference(clausify,[status(thm)],[f_4656_2]) ).

fof(f_4657_1,plain,
    ! [V_xs_2,T_a] :
      ( hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1]) ).

fof(f_4657_2,plain,
    ! [U_19362,U_19361] :
      ( hAPP(c_List_Ofoldl(U_19361,U_19361,c_Groups_Oplus__class_Oplus(U_19361),c_Groups_Ozero__class_Ozero(U_19361)),U_19362) = c_List_Ofoldr(U_19361,U_19361,c_Groups_Oplus__class_Oplus(U_19361),U_19362,c_Groups_Ozero__class_Ozero(U_19361))
      | ~ class_Groups_Omonoid__add(U_19361) ),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

cnf(f_4657_3,plain,
    ( hAPP(c_List_Ofoldl(U_19361,U_19361,c_Groups_Oplus__class_Oplus(U_19361),c_Groups_Ozero__class_Ozero(U_19361)),U_19362) = c_List_Ofoldr(U_19361,U_19361,c_Groups_Oplus__class_Oplus(U_19361),U_19362,c_Groups_Ozero__class_Ozero(U_19361))
    | ~ class_Groups_Omonoid__add(U_19361) ),
    inference(clausify,[status(thm)],[f_4657_2]) ).

fof(f_4658_1,plain,
    ! [V_xs_2,V_a_2,T_a] :
      ( hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma]) ).

fof(f_4658_2,plain,
    ! [U_19365,U_19364,U_19363] :
      ( hAPP(c_List_Ofoldl(U_19363,U_19363,c_Groups_Oplus__class_Oplus(U_19363),U_19364),U_19365) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19363),U_19364),c_List_Ofoldr(U_19363,U_19363,c_Groups_Oplus__class_Oplus(U_19363),U_19365,c_Groups_Ozero__class_Ozero(U_19363)))
      | ~ class_Groups_Omonoid__add(U_19363) ),
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

cnf(f_4658_3,plain,
    ( hAPP(c_List_Ofoldl(U_19363,U_19363,c_Groups_Oplus__class_Oplus(U_19363),U_19364),U_19365) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19363),U_19364),c_List_Ofoldr(U_19363,U_19363,c_Groups_Oplus__class_Oplus(U_19363),U_19365,c_Groups_Ozero__class_Ozero(U_19363)))
    | ~ class_Groups_Omonoid__add(U_19363) ),
    inference(clausify,[status(thm)],[f_4658_2]) ).

fof(f_4659_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__transpose]) ).

fof(f_4659_2,plain,
    ! [U_19367,U_19366] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19366))),c_List_Otranspose(U_19366,U_19367)) = c_List_Ofoldr(tc_List_Olist(U_19366),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19366)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19366))),U_19367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

cnf(f_4659_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19366))),c_List_Otranspose(U_19366,U_19367)) = c_List_Ofoldr(tc_List_Olist(U_19366),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19366)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19366))),U_19367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4659_2]) ).

fof(f_4660_1,plain,
    ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__def]) ).

fof(f_4660_2,plain,
    ! [U_19370,U_19369,U_19368] : c_List_Osublist(U_19368,U_19369,U_19370) = hAPP(hAPP(c_List_Omap(tc_prod(U_19368,tc_Nat_Onat),U_19368),c_Product__Type_Ofst(U_19368,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19368,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19368,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_19368,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_19368,tc_Nat_Onat))),U_19370)),hAPP(hAPP(c_List_Ozip(U_19368,tc_Nat_Onat),U_19369),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369))))),
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

cnf(f_4660_3,plain,
    c_List_Osublist(U_19368,U_19369,U_19370) = hAPP(hAPP(c_List_Omap(tc_prod(U_19368,tc_Nat_Onat),U_19368),c_Product__Type_Ofst(U_19368,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19368,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19368,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_19368,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_19368,tc_Nat_Onat))),U_19370)),hAPP(hAPP(c_List_Ozip(U_19368,tc_Nat_Onat),U_19369),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19368)),U_19369))))),
    inference(clausify,[status(thm)],[f_4660_2]) ).

fof(f_4661_1,plain,
    ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(f_4661_2,plain,
    ! [U_19374,U_19373,U_19372,U_19371] : hAPP(hAPP(c_List_Omap(tc_prod(U_19371,tc_Nat_Onat),U_19371),c_Product__Type_Ofst(U_19371,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19371,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_19371,tc_Nat_Onat))),U_19372)),hAPP(hAPP(c_List_Ozip(U_19371,tc_Nat_Onat),U_19373),c_List_Oupt(U_19374,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19374),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19371)),U_19373)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_19371,tc_Nat_Onat),U_19371),c_Product__Type_Ofst(U_19371,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19371,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_19371,tc_Nat_Onat))),U_19374))),U_19372)),hAPP(hAPP(c_List_Ozip(U_19371,tc_Nat_Onat),U_19373),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19371)),U_19373))))),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

cnf(f_4661_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_19371,tc_Nat_Onat),U_19371),c_Product__Type_Ofst(U_19371,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19371,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_19371,tc_Nat_Onat))),U_19372)),hAPP(hAPP(c_List_Ozip(U_19371,tc_Nat_Onat),U_19373),c_List_Oupt(U_19374,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19374),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19371)),U_19373)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_19371,tc_Nat_Onat),U_19371),c_Product__Type_Ofst(U_19371,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_19371,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_19371,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_19371,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_19371,tc_Nat_Onat))),U_19374))),U_19372)),hAPP(hAPP(c_List_Ozip(U_19371,tc_Nat_Onat),U_19373),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19371)),U_19373))))),
    inference(clausify,[status(thm)],[f_4661_2]) ).

fof(f_4662_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_4662_2,plain,
    ! [U_19376,U_19375] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19375),U_19376) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19375,U_19376)),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

cnf(f_4662_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19375),U_19376) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19375,U_19376)),
    inference(clausify,[status(thm)],[f_4662_2]) ).

fof(f_4663_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_4663_2,plain,
    ! [U_19378,U_19377] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19377,U_19378)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19377),U_19378),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

cnf(f_4663_3,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19377,U_19378)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19377),U_19378),
    inference(clausify,[status(thm)],[f_4663_2]) ).

fof(f_4664_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_4664_2,plain,
    ! [U_19380,U_19379] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_19379,U_19380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19380),U_19379),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

cnf(f_4664_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_19379,U_19380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19380),U_19379),
    inference(clausify,[status(thm)],[f_4664_2]) ).

fof(f_4665_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_4665_2,plain,
    ! [U_19382,U_19381] :
      ( c_List_Oupt(U_19381,hAPP(c_Nat_OSuc,U_19382)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19381,U_19382)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19382),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19381),U_19382)) ),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

cnf(f_4665_3,plain,
    ( c_List_Oupt(U_19381,hAPP(c_Nat_OSuc,U_19382)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19381,U_19382)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19382),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19381),U_19382)) ),
    inference(clausify,[status(thm)],[f_4665_2]) ).

fof(f_4666_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_4666_2,plain,
    ! [U_19384,U_19383] :
      ( ( c_List_Oupt(U_19383,hAPP(c_Nat_OSuc,U_19384)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19383),U_19384)) )
      & ( c_List_Oupt(U_19383,hAPP(c_Nat_OSuc,U_19384)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19383,U_19384)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19384),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19383),U_19384)) ) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

fof(f_4666_3,plain,
    ( ! [U_19388,U_19386] :
        ( c_List_Oupt(U_19386,hAPP(c_Nat_OSuc,U_19388)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19386),U_19388)) )
    & ! [U_19387,U_19385] :
        ( c_List_Oupt(U_19385,hAPP(c_Nat_OSuc,U_19387)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19385,U_19387)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19387),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19385),U_19387)) ) ),
    inference(miniscope,[status(thm)],[f_4666_2]) ).

cnf(f_4666_4,plain,
    ( c_List_Oupt(U_19385,hAPP(c_Nat_OSuc,U_19387)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19385,U_19387)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19387),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19385),U_19387)) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

cnf(f_4666_5,plain,
    ( c_List_Oupt(U_19386,hAPP(c_Nat_OSuc,U_19388)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19386),U_19388)) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

fof(f_4667_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_4667_2,plain,
    ! [U_19390,U_19389] :
      ( ( c_List_Oupt(U_19389,U_19390) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19389),U_19390)) )
      & ( c_List_Oupt(U_19389,U_19390) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19389),c_List_Oupt(hAPP(c_Nat_OSuc,U_19389),U_19390))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19389),U_19390)) ) ),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

fof(f_4667_3,plain,
    ( ! [U_19394,U_19392] :
        ( c_List_Oupt(U_19392,U_19394) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19392),U_19394)) )
    & ! [U_19393,U_19391] :
        ( c_List_Oupt(U_19391,U_19393) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19391),c_List_Oupt(hAPP(c_Nat_OSuc,U_19391),U_19393))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19391),U_19393)) ) ),
    inference(miniscope,[status(thm)],[f_4667_2]) ).

cnf(f_4667_4,plain,
    ( c_List_Oupt(U_19391,U_19393) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19391),c_List_Oupt(hAPP(c_Nat_OSuc,U_19391),U_19393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19391),U_19393)) ),
    inference(clausify,[status(thm)],[f_4667_3]) ).

cnf(f_4667_5,plain,
    ( c_List_Oupt(U_19392,U_19394) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19392),U_19394)) ),
    inference(clausify,[status(thm)],[f_4667_3]) ).

fof(f_4668_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_4668_2,plain,
    ! [U_19396,U_19395] :
      ( c_List_Oupt(U_19395,U_19396) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19395),c_List_Oupt(hAPP(c_Nat_OSuc,U_19395),U_19396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19395),U_19396)) ),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

cnf(f_4668_3,plain,
    ( c_List_Oupt(U_19395,U_19396) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19395),c_List_Oupt(hAPP(c_Nat_OSuc,U_19395),U_19396))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19395),U_19396)) ),
    inference(clausify,[status(thm)],[f_4668_2]) ).

fof(f_4669_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_4669_2,plain,
    ! [U_19398,U_19397] :
      ( c_List_Oupt(U_19398,U_19397) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19397),U_19398)) ),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

cnf(f_4669_3,plain,
    ( c_List_Oupt(U_19398,U_19397) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19397),U_19398)) ),
    inference(clausify,[status(thm)],[f_4669_2]) ).

fof(f_4670_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_4670_2,plain,
    ! [U_19400,U_19399] :
      ( ( c_List_Oupt(U_19399,U_19400) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19400),U_19399))
          & U_19400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19400),U_19399))
        | U_19400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_19399,U_19400) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

fof(f_4670_3,plain,
    ( ! [U_19404,U_19402] :
        ( c_List_Oupt(U_19402,U_19404) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19404),U_19402))
          & U_19404 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_19403,U_19401] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19403),U_19401))
        | U_19403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_19401,U_19403) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4670_2]) ).

cnf(f_4670_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19403),U_19401))
    | U_19403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_19401,U_19403) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4670_3]) ).

cnf(f_4670_5,plain,
    ( U_19404 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_19402,U_19404) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4670_3]) ).

cnf(f_4670_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19404),U_19402))
    | c_List_Oupt(U_19402,U_19404) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4670_3]) ).

fof(f_4671_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_4671_2,plain,
    ! [U_19405] : c_List_Oupt(U_19405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

cnf(f_4671_3,plain,
    c_List_Oupt(U_19405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4671_2]) ).

fof(f_4672_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_4672_2,plain,
    ! [U_19408,U_19407,U_19406] :
      ( c_List_Oupt(U_19406,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19407),U_19408)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19406,U_19407)),c_List_Oupt(U_19407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19407),U_19408)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19406),U_19407)) ),
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

cnf(f_4672_3,plain,
    ( c_List_Oupt(U_19406,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19407),U_19408)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_19406,U_19407)),c_List_Oupt(U_19407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19407),U_19408)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19406),U_19407)) ),
    inference(clausify,[status(thm)],[f_4672_2]) ).

fof(f_4673_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_4673_2,plain,
    ! [U_19410,U_19409] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19409),U_19410)) = c_List_Oupt(U_19409,U_19410),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

cnf(f_4673_3,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_19409),U_19410)) = c_List_Oupt(U_19409,U_19410),
    inference(clausify,[status(thm)],[f_4673_2]) ).

fof(f_4674_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_4674_2,plain,
    ! [U_19413,U_19412,U_19411] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_19412),c_List_Oupt(U_19411,U_19413)) = c_List_Oupt(U_19411,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19411),U_19412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19411),U_19412)),U_19413)) ),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

cnf(f_4674_3,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_19412),c_List_Oupt(U_19411,U_19413)) = c_List_Oupt(U_19411,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19411),U_19412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19411),U_19412)),U_19413)) ),
    inference(clausify,[status(thm)],[f_4674_2]) ).

fof(f_4675_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_4675_2,plain,
    ! [U_19415,U_19414] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_19414,U_19415)) = U_19414
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19414),U_19415)) ),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

cnf(f_4675_3,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_19414,U_19415)) = U_19414
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19414),U_19415)) ),
    inference(clausify,[status(thm)],[f_4675_2]) ).

fof(f_4676_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_4676_2,plain,
    ! [U_19418,U_19417,U_19416] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_19416),c_List_Oupt(U_19417,U_19418)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19417),U_19416),U_19418),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

cnf(f_4676_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_19416),c_List_Oupt(U_19417,U_19418)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19417),U_19416),U_19418),
    inference(clausify,[status(thm)],[f_4676_2]) ).

fof(f_4677_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_4677_2,plain,
    ! [U_19420,U_19419] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_19419,U_19420))),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

cnf(f_4677_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_19419,U_19420))),
    inference(clausify,[status(thm)],[f_4677_2]) ).

fof(f_4678_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_4678_2,plain,
    ! [U_19422,U_19421] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)) = 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_19421)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19421)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19421)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19421)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19422))) ) ),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

fof(f_4678_3,plain,
    ( ! [U_19426,U_19424] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19424),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426)) = 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_19424)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426))) )
    & ! [U_19425,U_19423] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425))) ) ),
    inference(miniscope,[status(thm)],[f_4678_2]) ).

cnf(f_4678_4,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19423)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19425))) ),
    inference(clausify,[status(thm)],[f_4678_3]) ).

cnf(f_4678_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19424),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426)) = 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_19424)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19426))) ),
    inference(clausify,[status(thm)],[f_4678_3]) ).

fof(f_4679_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_4679_2,plain,
    ! [U_19430,U_19429,U_19428,U_19427] :
      ( ( c_List_Oupt(U_19427,U_19428) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19429),U_19430)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19427),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19428) != U_19430
        | U_19427 != U_19429
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19427),U_19428)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19427),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19428) = U_19430
          & U_19427 = U_19429
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19427),U_19428)) )
        | c_List_Oupt(U_19427,U_19428) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19429),U_19430) ) ),
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

fof(f_4679_3,plain,
    ( ! [U_19438,U_19436,U_19434,U_19432] :
        ( c_List_Oupt(U_19432,U_19434) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19436),U_19438)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19432),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19434) != U_19438
        | U_19432 != U_19436
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19432),U_19434)) )
    & ! [U_19437,U_19435,U_19433,U_19431] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19431),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19433) = U_19437
          & U_19431 = U_19435
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19431),U_19433)) )
        | c_List_Oupt(U_19431,U_19433) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19435),U_19437) ) ),
    inference(miniscope,[status(thm)],[f_4679_2]) ).

cnf(f_4679_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19431),U_19433))
    | c_List_Oupt(U_19431,U_19433) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19435),U_19437) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

cnf(f_4679_5,plain,
    ( U_19431 = U_19435
    | c_List_Oupt(U_19431,U_19433) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19435),U_19437) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

cnf(f_4679_6,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19431),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19433) = U_19437
    | c_List_Oupt(U_19431,U_19433) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19435),U_19437) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

cnf(f_4679_7,plain,
    ( c_List_Oupt(U_19432,U_19434) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_19436),U_19438)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19432),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19434) != U_19438
    | U_19432 != U_19436
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19432),U_19434)) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

fof(f_4680_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_4680_2,plain,
    ! [U_19440,U_19439] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_19439,U_19440)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19440),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19439),U_19440)) ),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

cnf(f_4680_3,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_19439,U_19440)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19440),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19439),U_19440)) ),
    inference(clausify,[status(thm)],[f_4680_2]) ).

fof(f_4681_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_4681_2,plain,
    ! [U_19442,U_19441] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_19441,U_19442)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_19441),hAPP(c_Nat_OSuc,U_19442)),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

cnf(f_4681_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_19441,U_19442)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_19441),hAPP(c_Nat_OSuc,U_19442)),
    inference(clausify,[status(thm)],[f_4681_2]) ).

fof(f_4682_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_4682_2,plain,
    ! [U_19444,U_19443] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_19443,U_19444) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19443,hAPP(c_Nat_OSuc,U_19444))),
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

cnf(f_4682_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_19443,U_19444) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19443,hAPP(c_Nat_OSuc,U_19444))),
    inference(clausify,[status(thm)],[f_4682_2]) ).

fof(f_4683_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_4683_2,plain,
    ! [U_19445] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_19445) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19445)),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

cnf(f_4683_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_19445) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19445)),
    inference(clausify,[status(thm)],[f_4683_2]) ).

fof(f_4684_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_4684_2,plain,
    ! [U_19448,U_19447,U_19446] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_19446,U_19448)),U_19447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19446),U_19447)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19446),U_19447)),U_19448)) ),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

cnf(f_4684_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_19446,U_19448)),U_19447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19446),U_19447)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19446),U_19447)),U_19448)) ),
    inference(clausify,[status(thm)],[f_4684_2]) ).

fof(f_4685_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_4685_2,plain,
    ! [U_19450,U_19449] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_19449,U_19450) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_19449),hAPP(c_Nat_OSuc,U_19450))),
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

cnf(f_4685_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_19449,U_19450) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_19449),hAPP(c_Nat_OSuc,U_19450))),
    inference(clausify,[status(thm)],[f_4685_2]) ).

fof(f_4686_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_4686_2,plain,
    ! [U_19452,U_19451] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_19451,U_19452) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_19451),U_19452)),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

cnf(f_4686_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_19451,U_19452) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_19451),U_19452)),
    inference(clausify,[status(thm)],[f_4686_2]) ).

fof(f_4687_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_4687_2,plain,
    ! [U_19453] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_19453) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_19453))),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

cnf(f_4687_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_19453) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_19453))),
    inference(clausify,[status(thm)],[f_4687_2]) ).

fof(f_4688_1,plain,
    ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__nth]) ).

fof(f_4688_2,plain,
    ! [U_19455,U_19454] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19454),hAPP(c_List_Onth(U_19454),U_19455)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19455))) = U_19455,
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

cnf(f_4688_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19454),hAPP(c_List_Onth(U_19454),U_19455)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19455))) = U_19455,
    inference(clausify,[status(thm)],[f_4688_2]) ).

fof(f_4689_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_a),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_a) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat]) ).

fof(f_4689_2,plain,
    ! [U_19459,U_19458,U_19457,U_19456] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19456),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19456),U_19457),c_List_Oupt(U_19458,U_19459))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_19456),U_19457),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19458,U_19459)))
      | ~ class_Groups_Ocomm__monoid__add(U_19456) ),
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

cnf(f_4689_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19456),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19456),U_19457),c_List_Oupt(U_19458,U_19459))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_19456),U_19457),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19458,U_19459)))
    | ~ class_Groups_Ocomm__monoid__add(U_19456) ),
    inference(clausify,[status(thm)],[f_4689_2]) ).

fof(f_4690_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_a] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat]) ).

fof(f_4690_2,plain,
    ! [U_19463,U_19462,U_19461,U_19460] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_19460),U_19461),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19462,U_19463))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19460),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19460),U_19461),c_List_Oupt(U_19462,U_19463)))
      | ~ class_Groups_Ocomm__monoid__add(U_19460) ),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

cnf(f_4690_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_19460),U_19461),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_19462,U_19463))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19460),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19460),U_19461),c_List_Oupt(U_19462,U_19463)))
    | ~ class_Groups_Ocomm__monoid__add(U_19460) ),
    inference(clausify,[status(thm)],[f_4690_2]) ).

fof(f_4691_1,plain,
    ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_4691_2,plain,
    ! [U_19468,U_19467,U_19466,U_19465,U_19464] :
      ( hAPP(hAPP(c_List_Onth(U_19467),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19467),U_19468),c_List_Oupt(U_19466,U_19465))),U_19464) = hAPP(U_19468,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19466),U_19464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19465),U_19466))) ),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

cnf(f_4691_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19467),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19467),U_19468),c_List_Oupt(U_19466,U_19465))),U_19464) = hAPP(U_19468,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19466),U_19464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19465),U_19466))) ),
    inference(clausify,[status(thm)],[f_4691_2]) ).

fof(f_4692_1,plain,
    ! [V_n_2,T_a,V_xs_2] :
      ( c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),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_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),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_a)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__rectangle]) ).

fof(f_4692_2,plain,
    ! [U_19472,U_19471,U_19470] :
      ( c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
      | ? [U_19469] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19471)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470),U_19469)) != U_19472
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470))) )
      | ( U_19472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_19470 = c_List_Olist_ONil(tc_List_Olist(U_19471)) ) ),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

fof(f_4692_3,plain,
    ! [U_19472,U_19471,U_19470] :
      ( c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19471)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470),sK485(U_19472,U_19471,U_19470))) != U_19472
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK485(U_19472,U_19471,U_19470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470))) )
      | ( U_19472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_19470 = c_List_Olist_ONil(tc_List_Olist(U_19471)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_19469,sK485(U_19472,U_19471,U_19470))],[f_4692_2]) ).

cnf(f_4692_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK485(U_19472,U_19471,U_19470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))
    | c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
    | U_19470 = c_List_Olist_ONil(tc_List_Olist(U_19471)) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

cnf(f_4692_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19471)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470),sK485(U_19472,U_19471,U_19470))) != U_19472
    | c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
    | U_19470 = c_List_Olist_ONil(tc_List_Olist(U_19471)) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

cnf(f_4692_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK485(U_19472,U_19471,U_19470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))
    | c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
    | U_19472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

cnf(f_4692_7,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19471)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470),sK485(U_19472,U_19471,U_19470))) != U_19472
    | c_List_Otranspose(U_19471,U_19470) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_19471),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_19471)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_19471)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_19471),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19471),tc_fun(tc_Nat_Onat,U_19471),tc_Nat_Onat),c_List_Onth(U_19471)),hAPP(c_List_Onth(tc_List_Olist(U_19471)),U_19470))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19471))),U_19470)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19472))
    | U_19472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

fof(f_4693_1,plain,
    ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2
      | hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),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_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__remove1]) ).

fof(f_4693_2,plain,
    ! [U_19477,U_19476,U_19475,U_19474,U_19473] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19474,U_19473,U_19477),U_19475),c_List_Oremove1(U_19474,U_19475,U_19476)) = U_19476
      | hAPP(c_List_Ohd(U_19474),hAPP(c_List_Ofilter(U_19474,hAPP(hAPP(c_COMBB(U_19473,tc_HOL_Obool,U_19474),hAPP(c_fequal,hAPP(U_19477,U_19475))),U_19477)),U_19476)) != U_19475
      | ~ c_List_Olinorder__class_Osorted(U_19473,hAPP(hAPP(c_List_Omap(U_19474,U_19473),U_19477),U_19476))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19474),U_19475),hAPP(c_List_Oset(U_19474),U_19476)))
      | ~ class_Orderings_Olinorder(U_19473) ),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

cnf(f_4693_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19474,U_19473,U_19477),U_19475),c_List_Oremove1(U_19474,U_19475,U_19476)) = U_19476
    | hAPP(c_List_Ohd(U_19474),hAPP(c_List_Ofilter(U_19474,hAPP(hAPP(c_COMBB(U_19473,tc_HOL_Obool,U_19474),hAPP(c_fequal,hAPP(U_19477,U_19475))),U_19477)),U_19476)) != U_19475
    | ~ c_List_Olinorder__class_Osorted(U_19473,hAPP(hAPP(c_List_Omap(U_19474,U_19473),U_19477),U_19476))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19474),U_19475),hAPP(c_List_Oset(U_19474),U_19476)))
    | ~ class_Orderings_Olinorder(U_19473) ),
    inference(clausify,[status(thm)],[f_4693_2]) ).

fof(f_4694_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_4694_2,plain,
    ! [U_19478] :
      ( c_List_Olinorder__class_Osorted(U_19478,c_List_Olist_ONil(U_19478))
      | ~ class_Orderings_Olinorder(U_19478) ),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

cnf(f_4694_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19478,c_List_Olist_ONil(U_19478))
    | ~ class_Orderings_Olinorder(U_19478) ),
    inference(clausify,[status(thm)],[f_4694_2]) ).

fof(f_4695_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_4695_2,plain,
    ! [U_19480,U_19479] :
      ( c_List_Olinorder__class_Osorted(U_19479,hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19480),c_List_Olist_ONil(U_19479)))
      | ~ class_Orderings_Olinorder(U_19479) ),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

cnf(f_4695_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19479,hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19480),c_List_Olist_ONil(U_19479)))
    | ~ class_Orderings_Olinorder(U_19479) ),
    inference(clausify,[status(thm)],[f_4695_2]) ).

fof(f_4696_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_4696_2,plain,
    ! [U_19482,U_19481] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_19481,U_19482)),
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

cnf(f_4696_3,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_19481,U_19482)),
    inference(clausify,[status(thm)],[f_4696_2]) ).

fof(f_4697_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2) )
        & ( ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_a,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__Cons]) ).

fof(f_4697_2,plain,
    ! [U_19487,U_19486,U_19485] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
          | ? [U_19484] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),U_19484))
              & hBOOL(hAPP(hAPP(c_member(U_19485),U_19484),hAPP(c_List_Oset(U_19485),U_19487))) )
          | ~ c_List_Olinorder__class_Osorted(U_19485,U_19487) )
        & ( ( ! [U_19483] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),U_19483))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19485),U_19483),hAPP(c_List_Oset(U_19485),U_19487))) )
            & c_List_Olinorder__class_Osorted(U_19485,U_19487) )
          | ~ c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487)) ) )
      | ~ class_Orderings_Olinorder(U_19485) ),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

fof(f_4697_3,plain,
    ! [U_19487,U_19486,U_19485] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),sK486(U_19487,U_19486,U_19485)))
            & hBOOL(hAPP(hAPP(c_member(U_19485),sK486(U_19487,U_19486,U_19485)),hAPP(c_List_Oset(U_19485),U_19487))) )
          | ~ c_List_Olinorder__class_Osorted(U_19485,U_19487) )
        & ( ( ! [U_19483] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),U_19483))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19485),U_19483),hAPP(c_List_Oset(U_19485),U_19487))) )
            & c_List_Olinorder__class_Osorted(U_19485,U_19487) )
          | ~ c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487)) ) )
      | ~ class_Orderings_Olinorder(U_19485) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_19484,sK486(U_19487,U_19486,U_19485))],[f_4697_2]) ).

cnf(f_4697_4,plain,
    ( c_List_Olinorder__class_Osorted(U_19485,U_19487)
    | ~ c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
    | ~ class_Orderings_Olinorder(U_19485) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

cnf(f_4697_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),U_19483))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19485),U_19483),hAPP(c_List_Oset(U_19485),U_19487)))
    | ~ c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
    | ~ class_Orderings_Olinorder(U_19485) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

cnf(f_4697_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19485),sK486(U_19487,U_19486,U_19485)),hAPP(c_List_Oset(U_19485),U_19487)))
    | ~ c_List_Olinorder__class_Osorted(U_19485,U_19487)
    | c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
    | ~ class_Orderings_Olinorder(U_19485) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

cnf(f_4697_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19485),U_19486),sK486(U_19487,U_19486,U_19485)))
    | ~ c_List_Olinorder__class_Osorted(U_19485,U_19487)
    | c_List_Olinorder__class_Osorted(U_19485,hAPP(hAPP(c_List_Olist_OCons(U_19485),U_19486),U_19487))
    | ~ class_Orderings_Olinorder(U_19485) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

fof(f_4698_1,plain,
    ! [V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__sort]) ).

fof(f_4698_2,plain,
    ! [U_19489,U_19488] :
      ( c_List_Olinorder__class_Osorted(U_19488,c_List_Olinorder__class_Osort__key(U_19488,U_19488,c_COMBI(U_19488),U_19489))
      | ~ class_Orderings_Olinorder(U_19488) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

cnf(f_4698_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19488,c_List_Olinorder__class_Osort__key(U_19488,U_19488,c_COMBI(U_19488),U_19489))
    | ~ class_Orderings_Olinorder(U_19488) ),
    inference(clausify,[status(thm)],[f_4698_2]) ).

fof(f_4699_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2) )
        & ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort]) ).

fof(f_4699_2,plain,
    ! [U_19492,U_19491,U_19490] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19490,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19490,U_19490,c_COMBI(U_19490)),U_19491),U_19492))
          | ~ c_List_Olinorder__class_Osorted(U_19490,U_19492) )
        & ( c_List_Olinorder__class_Osorted(U_19490,U_19492)
          | ~ c_List_Olinorder__class_Osorted(U_19490,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19490,U_19490,c_COMBI(U_19490)),U_19491),U_19492)) ) )
      | ~ class_Orderings_Olinorder(U_19490) ),
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

cnf(f_4699_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19490,U_19492)
    | ~ c_List_Olinorder__class_Osorted(U_19490,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19490,U_19490,c_COMBI(U_19490)),U_19491),U_19492))
    | ~ class_Orderings_Olinorder(U_19490) ),
    inference(clausify,[status(thm)],[f_4699_2]) ).

cnf(f_4699_4,plain,
    ( c_List_Olinorder__class_Osorted(U_19490,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19490,U_19490,c_COMBI(U_19490)),U_19491),U_19492))
    | ~ c_List_Olinorder__class_Osorted(U_19490,U_19492)
    | ~ class_Orderings_Olinorder(U_19490) ),
    inference(clausify,[status(thm)],[f_4699_2]) ).

fof(f_4700_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_4700_2,plain,
    ! [U_19495,U_19494,U_19493] :
      ( c_List_Olinorder__class_Osorted(U_19493,hAPP(hAPP(c_List_Odrop(U_19493),U_19495),U_19494))
      | ~ c_List_Olinorder__class_Osorted(U_19493,U_19494)
      | ~ class_Orderings_Olinorder(U_19493) ),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

cnf(f_4700_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19493,hAPP(hAPP(c_List_Odrop(U_19493),U_19495),U_19494))
    | ~ c_List_Olinorder__class_Osorted(U_19493,U_19494)
    | ~ class_Orderings_Olinorder(U_19493) ),
    inference(clausify,[status(thm)],[f_4700_2]) ).

fof(f_4701_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_4701_2,plain,
    ! [U_19498,U_19497,U_19496] :
      ( c_List_Olinorder__class_Osorted(U_19496,c_List_Oremove1(U_19496,U_19498,U_19497))
      | ~ c_List_Olinorder__class_Osorted(U_19496,U_19497)
      | ~ class_Orderings_Olinorder(U_19496) ),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

cnf(f_4701_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19496,c_List_Oremove1(U_19496,U_19498,U_19497))
    | ~ c_List_Olinorder__class_Osorted(U_19496,U_19497)
    | ~ class_Orderings_Olinorder(U_19496) ),
    inference(clausify,[status(thm)],[f_4701_2]) ).

fof(f_4702_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_4702_2,plain,
    ! [U_19500,U_19499] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_19499,U_19500)),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

cnf(f_4702_3,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_19499,U_19500)),
    inference(clausify,[status(thm)],[f_4702_2]) ).

fof(f_4703_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_4703_2,plain,
    ! [U_19503,U_19502,U_19501] :
      ( c_List_Olinorder__class_Osorted(U_19501,hAPP(hAPP(c_List_Otake(U_19501),U_19503),U_19502))
      | ~ c_List_Olinorder__class_Osorted(U_19501,U_19502)
      | ~ class_Orderings_Olinorder(U_19501) ),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

cnf(f_4703_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19501,hAPP(hAPP(c_List_Otake(U_19501),U_19503),U_19502))
    | ~ c_List_Olinorder__class_Osorted(U_19501,U_19502)
    | ~ class_Orderings_Olinorder(U_19501) ),
    inference(clausify,[status(thm)],[f_4703_2]) ).

fof(f_4704_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_4704_2,plain,
    ! [U_19505,U_19504] :
      ( c_List_Olinorder__class_Osorted(U_19504,hAPP(c_List_Otl(U_19504),U_19505))
      | ~ c_List_Olinorder__class_Osorted(U_19504,U_19505)
      | ~ class_Orderings_Olinorder(U_19504) ),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

cnf(f_4704_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19504,hAPP(c_List_Otl(U_19504),U_19505))
    | ~ c_List_Olinorder__class_Osorted(U_19504,U_19505)
    | ~ class_Orderings_Olinorder(U_19504) ),
    inference(clausify,[status(thm)],[f_4704_2]) ).

fof(f_4705_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert]) ).

fof(f_4705_2,plain,
    ! [U_19508,U_19507,U_19506] :
      ( c_List_Olinorder__class_Osorted(U_19506,c_List_Olinorder__class_Oinsort__insert__key(U_19506,U_19506,c_COMBI(U_19506),U_19508,U_19507))
      | ~ c_List_Olinorder__class_Osorted(U_19506,U_19507)
      | ~ class_Orderings_Olinorder(U_19506) ),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

cnf(f_4705_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19506,c_List_Olinorder__class_Oinsort__insert__key(U_19506,U_19506,c_COMBI(U_19506),U_19508,U_19507))
    | ~ c_List_Olinorder__class_Osorted(U_19506,U_19507)
    | ~ class_Orderings_Olinorder(U_19506) ),
    inference(clausify,[status(thm)],[f_4705_2]) ).

fof(f_4706_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_4706_2,plain,
    ! [U_19510,U_19509] :
      ( c_List_Olinorder__class_Osorted(U_19509,c_List_Obutlast(U_19509,U_19510))
      | ~ c_List_Olinorder__class_Osorted(U_19509,U_19510)
      | U_19510 = c_List_Olist_ONil(U_19509)
      | ~ class_Orderings_Olinorder(U_19509) ),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

cnf(f_4706_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19509,c_List_Obutlast(U_19509,U_19510))
    | ~ c_List_Olinorder__class_Osorted(U_19509,U_19510)
    | U_19510 = c_List_Olist_ONil(U_19509)
    | ~ class_Orderings_Olinorder(U_19509) ),
    inference(clausify,[status(thm)],[f_4706_2]) ).

fof(f_4707_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_4707_2,plain,
    ! [U_19511] :
      ( c_List_Olinorder__class_Osorted(U_19511,c_List_Olist_ONil(U_19511))
      | ~ class_Orderings_Olinorder(U_19511) ),
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

cnf(f_4707_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19511,c_List_Olist_ONil(U_19511))
    | ~ class_Orderings_Olinorder(U_19511) ),
    inference(clausify,[status(thm)],[f_4707_2]) ).

fof(f_4708_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_4708_2,plain,
    ! [U_19515,U_19514,U_19513,U_19512] :
      ( c_List_Olinorder__class_Osorted(U_19512,hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19513),hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19514),U_19515)))
      | ~ c_List_Olinorder__class_Osorted(U_19512,hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19514),U_19515))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19512),U_19513),U_19514))
      | ~ class_Orderings_Olinorder(U_19512) ),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

cnf(f_4708_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19512,hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19513),hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19514),U_19515)))
    | ~ c_List_Olinorder__class_Osorted(U_19512,hAPP(hAPP(c_List_Olist_OCons(U_19512),U_19514),U_19515))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19512),U_19513),U_19514))
    | ~ class_Orderings_Olinorder(U_19512) ),
    inference(clausify,[status(thm)],[f_4708_2]) ).

fof(f_4709_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
        & ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) )
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__many__eq]) ).

fof(f_4709_2,plain,
    ! [U_19519,U_19518,U_19517,U_19516] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19517),hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519)))
          | ~ c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19516),U_19517),U_19518)) )
        & ( ( c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19516),U_19517),U_19518)) )
          | ~ c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19517),hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519))) ) )
      | ~ class_Orderings_Olinorder(U_19516) ),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

cnf(f_4709_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19516),U_19517),U_19518))
    | ~ c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19517),hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519)))
    | ~ class_Orderings_Olinorder(U_19516) ),
    inference(clausify,[status(thm)],[f_4709_2]) ).

cnf(f_4709_4,plain,
    ( c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519))
    | ~ c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19517),hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519)))
    | ~ class_Orderings_Olinorder(U_19516) ),
    inference(clausify,[status(thm)],[f_4709_2]) ).

cnf(f_4709_5,plain,
    ( c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19517),hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519)))
    | ~ c_List_Olinorder__class_Osorted(U_19516,hAPP(hAPP(c_List_Olist_OCons(U_19516),U_19518),U_19519))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19516),U_19517),U_19518))
    | ~ class_Orderings_Olinorder(U_19516) ),
    inference(clausify,[status(thm)],[f_4709_2]) ).

fof(f_4710_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_4710_2,plain,
    ! [U_19521,U_19520] :
      ( c_List_Olinorder__class_Osorted(U_19520,c_List_Oremdups(U_19520,U_19521))
      | ~ c_List_Olinorder__class_Osorted(U_19520,U_19521)
      | ~ class_Orderings_Olinorder(U_19520) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

cnf(f_4710_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19520,c_List_Oremdups(U_19520,U_19521))
    | ~ c_List_Olinorder__class_Osorted(U_19520,U_19521)
    | ~ class_Orderings_Olinorder(U_19520) ),
    inference(clausify,[status(thm)],[f_4710_2]) ).

fof(f_4711_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_a),V_xs_2) != hAPP(c_List_Oset(T_a),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique]) ).

fof(f_4711_2,plain,
    ! [U_19524,U_19523,U_19522] :
      ( U_19523 = U_19524
      | hAPP(c_List_Oset(U_19522),U_19523) != hAPP(c_List_Oset(U_19522),U_19524)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19522),U_19524))
      | ~ c_List_Olinorder__class_Osorted(U_19522,U_19524)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19522),U_19523))
      | ~ c_List_Olinorder__class_Osorted(U_19522,U_19523)
      | ~ class_Orderings_Olinorder(U_19522) ),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

cnf(f_4711_3,plain,
    ( U_19523 = U_19524
    | hAPP(c_List_Oset(U_19522),U_19523) != hAPP(c_List_Oset(U_19522),U_19524)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19522),U_19524))
    | ~ c_List_Olinorder__class_Osorted(U_19522,U_19524)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19522),U_19523))
    | ~ c_List_Olinorder__class_Osorted(U_19522,U_19523)
    | ~ class_Orderings_Olinorder(U_19522) ),
    inference(clausify,[status(thm)],[f_4711_2]) ).

fof(f_4712_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__sort__key]) ).

fof(f_4712_2,plain,
    ! [U_19528,U_19527,U_19526,U_19525] :
      ( c_List_Olinorder__class_Osorted(U_19525,hAPP(hAPP(c_List_Omap(U_19526,U_19525),U_19527),c_List_Olinorder__class_Osort__key(U_19526,U_19525,U_19527,U_19528)))
      | ~ class_Orderings_Olinorder(U_19525) ),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

cnf(f_4712_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19525,hAPP(hAPP(c_List_Omap(U_19526,U_19525),U_19527),c_List_Olinorder__class_Osort__key(U_19526,U_19525,U_19527,U_19528)))
    | ~ class_Orderings_Olinorder(U_19525) ),
    inference(clausify,[status(thm)],[f_4712_2]) ).

fof(f_4713_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key]) ).

fof(f_4713_2,plain,
    ! [U_19533,U_19532,U_19531,U_19530,U_19529] :
      ( c_List_Olinorder__class_Osorted(U_19529,hAPP(hAPP(c_List_Omap(U_19530,U_19529),U_19531),c_List_Olinorder__class_Oinsort__insert__key(U_19530,U_19529,U_19531,U_19533,U_19532)))
      | ~ c_List_Olinorder__class_Osorted(U_19529,hAPP(hAPP(c_List_Omap(U_19530,U_19529),U_19531),U_19532))
      | ~ class_Orderings_Olinorder(U_19529) ),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

cnf(f_4713_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19529,hAPP(hAPP(c_List_Omap(U_19530,U_19529),U_19531),c_List_Olinorder__class_Oinsort__insert__key(U_19530,U_19529,U_19531,U_19533,U_19532)))
    | ~ c_List_Olinorder__class_Osorted(U_19529,hAPP(hAPP(c_List_Omap(U_19530,U_19529),U_19531),U_19532))
    | ~ class_Orderings_Olinorder(U_19529) ),
    inference(clausify,[status(thm)],[f_4713_2]) ).

fof(f_4714_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1]) ).

fof(f_4714_2,plain,
    ! [U_19538,U_19537,U_19536,U_19535,U_19534] :
      ( c_List_Olinorder__class_Osorted(U_19534,hAPP(hAPP(c_List_Omap(U_19535,U_19534),U_19536),c_List_Oremove1(U_19535,U_19538,U_19537)))
      | ~ c_List_Olinorder__class_Osorted(U_19534,hAPP(hAPP(c_List_Omap(U_19535,U_19534),U_19536),U_19537))
      | ~ class_Orderings_Olinorder(U_19534) ),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

cnf(f_4714_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19534,hAPP(hAPP(c_List_Omap(U_19535,U_19534),U_19536),c_List_Oremove1(U_19535,U_19538,U_19537)))
    | ~ c_List_Olinorder__class_Osorted(U_19534,hAPP(hAPP(c_List_Omap(U_19535,U_19534),U_19536),U_19537))
    | ~ class_Orderings_Olinorder(U_19534) ),
    inference(clausify,[status(thm)],[f_4714_2]) ).

fof(f_4715_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) )
        & ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__key]) ).

fof(f_4715_2,plain,
    ! [U_19543,U_19542,U_19541,U_19540,U_19539] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19540,U_19539,U_19541),U_19542),U_19543)))
          | ~ c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),U_19543)) )
        & ( c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),U_19543))
          | ~ c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19540,U_19539,U_19541),U_19542),U_19543))) ) )
      | ~ class_Orderings_Olinorder(U_19539) ),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

cnf(f_4715_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),U_19543))
    | ~ c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19540,U_19539,U_19541),U_19542),U_19543)))
    | ~ class_Orderings_Olinorder(U_19539) ),
    inference(clausify,[status(thm)],[f_4715_2]) ).

cnf(f_4715_4,plain,
    ( c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19540,U_19539,U_19541),U_19542),U_19543)))
    | ~ c_List_Olinorder__class_Osorted(U_19539,hAPP(hAPP(c_List_Omap(U_19540,U_19539),U_19541),U_19543))
    | ~ class_Orderings_Olinorder(U_19539) ),
    inference(clausify,[status(thm)],[f_4715_2]) ).

fof(f_4716_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__same]) ).

fof(f_4716_2,plain,
    ! [U_19548,U_19547,U_19546,U_19545,U_19544] :
      ( c_List_Olinorder__class_Osorted(U_19544,hAPP(hAPP(c_List_Omap(U_19545,U_19544),U_19546),hAPP(c_List_Ofilter(U_19545,hAPP(hAPP(c_COMBC(U_19545,U_19544,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_19544,tc_fun(U_19544,tc_HOL_Obool),U_19545),c_fequal),U_19546)),hAPP(U_19547,U_19548))),U_19548)))
      | ~ class_Orderings_Olinorder(U_19544) ),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

cnf(f_4716_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19544,hAPP(hAPP(c_List_Omap(U_19545,U_19544),U_19546),hAPP(c_List_Ofilter(U_19545,hAPP(hAPP(c_COMBC(U_19545,U_19544,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_19544,tc_fun(U_19544,tc_HOL_Obool),U_19545),c_fequal),U_19546)),hAPP(U_19547,U_19548))),U_19548)))
    | ~ class_Orderings_Olinorder(U_19544) ),
    inference(clausify,[status(thm)],[f_4716_2]) ).

fof(f_4717_1,plain,
    ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__filter]) ).

fof(f_4717_2,plain,
    ! [U_19553,U_19552,U_19551,U_19550,U_19549] :
      ( c_List_Olinorder__class_Osorted(U_19549,hAPP(hAPP(c_List_Omap(U_19550,U_19549),U_19551),hAPP(c_List_Ofilter(U_19550,U_19553),U_19552)))
      | ~ c_List_Olinorder__class_Osorted(U_19549,hAPP(hAPP(c_List_Omap(U_19550,U_19549),U_19551),U_19552))
      | ~ class_Orderings_Olinorder(U_19549) ),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

cnf(f_4717_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19549,hAPP(hAPP(c_List_Omap(U_19550,U_19549),U_19551),hAPP(c_List_Ofilter(U_19550,U_19553),U_19552)))
    | ~ c_List_Olinorder__class_Osorted(U_19549,hAPP(hAPP(c_List_Omap(U_19550,U_19549),U_19551),U_19552))
    | ~ class_Orderings_Olinorder(U_19549) ),
    inference(clausify,[status(thm)],[f_4717_2]) ).

fof(f_4718_1,plain,
    ! [V_xs_2,V_g_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__same]) ).

fof(f_4718_2,plain,
    ! [U_19556,U_19555,U_19554] :
      ( c_List_Olinorder__class_Osorted(U_19554,hAPP(c_List_Ofilter(U_19554,hAPP(hAPP(c_COMBC(U_19554,U_19554,tc_HOL_Obool),c_fequal),hAPP(U_19555,U_19556))),U_19556))
      | ~ class_Orderings_Olinorder(U_19554) ),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

cnf(f_4718_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19554,hAPP(c_List_Ofilter(U_19554,hAPP(hAPP(c_COMBC(U_19554,U_19554,tc_HOL_Obool),c_fequal),hAPP(U_19555,U_19556))),U_19556))
    | ~ class_Orderings_Olinorder(U_19554) ),
    inference(clausify,[status(thm)],[f_4718_2]) ).

fof(f_4719_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
          | ? [B_x] :
              ( ? [B_xa] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) )
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_a,V_ys_2)
          | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2) )
        & ( ( ! [B_x] :
                ( ! [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa))
                    | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
            & c_List_Olinorder__class_Osorted(T_a,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__append]) ).

fof(f_4719_2,plain,
    ! [U_19563,U_19562,U_19561] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
          | ? [U_19560] :
              ( ? [U_19559] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),U_19560),U_19559))
                  & hBOOL(hAPP(hAPP(c_member(U_19561),U_19559),hAPP(c_List_Oset(U_19561),U_19563))) )
              & hBOOL(hAPP(hAPP(c_member(U_19561),U_19560),hAPP(c_List_Oset(U_19561),U_19562))) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562) )
        & ( ( ! [U_19558] :
                ( ! [U_19557] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),U_19558),U_19557))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19557),hAPP(c_List_Oset(U_19561),U_19563))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19558),hAPP(c_List_Oset(U_19561),U_19562))) )
            & c_List_Olinorder__class_Osorted(U_19561,U_19563)
            & c_List_Olinorder__class_Osorted(U_19561,U_19562) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563)) ) )
      | ~ class_Orderings_Olinorder(U_19561) ),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

fof(f_4719_3,plain,
    ! [U_19563,U_19562,U_19561] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
          | ( ? [U_19559] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),sK487(U_19563,U_19562,U_19561)),U_19559))
                & hBOOL(hAPP(hAPP(c_member(U_19561),U_19559),hAPP(c_List_Oset(U_19561),U_19563))) )
            & hBOOL(hAPP(hAPP(c_member(U_19561),sK487(U_19563,U_19562,U_19561)),hAPP(c_List_Oset(U_19561),U_19562))) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562) )
        & ( ( ! [U_19558] :
                ( ! [U_19557] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),U_19558),U_19557))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19557),hAPP(c_List_Oset(U_19561),U_19563))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19558),hAPP(c_List_Oset(U_19561),U_19562))) )
            & c_List_Olinorder__class_Osorted(U_19561,U_19563)
            & c_List_Olinorder__class_Osorted(U_19561,U_19562) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563)) ) )
      | ~ class_Orderings_Olinorder(U_19561) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_19560,sK487(U_19563,U_19562,U_19561))],[f_4719_2]) ).

fof(f_4719_4,plain,
    ! [U_19563,U_19562,U_19561] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),sK487(U_19563,U_19562,U_19561)),sK488(U_19563,U_19562,U_19561)))
            & hBOOL(hAPP(hAPP(c_member(U_19561),sK488(U_19563,U_19562,U_19561)),hAPP(c_List_Oset(U_19561),U_19563)))
            & hBOOL(hAPP(hAPP(c_member(U_19561),sK487(U_19563,U_19562,U_19561)),hAPP(c_List_Oset(U_19561),U_19562))) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
          | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562) )
        & ( ( ! [U_19558] :
                ( ! [U_19557] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),U_19558),U_19557))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19557),hAPP(c_List_Oset(U_19561),U_19563))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19558),hAPP(c_List_Oset(U_19561),U_19562))) )
            & c_List_Olinorder__class_Osorted(U_19561,U_19563)
            & c_List_Olinorder__class_Osorted(U_19561,U_19562) )
          | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563)) ) )
      | ~ class_Orderings_Olinorder(U_19561) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_19559,sK488(U_19563,U_19562,U_19561))],[f_4719_3]) ).

cnf(f_4719_5,plain,
    ( c_List_Olinorder__class_Osorted(U_19561,U_19562)
    | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

cnf(f_4719_6,plain,
    ( c_List_Olinorder__class_Osorted(U_19561,U_19563)
    | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

cnf(f_4719_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),U_19558),U_19557))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19557),hAPP(c_List_Oset(U_19561),U_19563)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19561),U_19558),hAPP(c_List_Oset(U_19561),U_19562)))
    | ~ c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

cnf(f_4719_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19561),sK487(U_19563,U_19562,U_19561)),hAPP(c_List_Oset(U_19561),U_19562)))
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562)
    | c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

cnf(f_4719_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19561),sK488(U_19563,U_19562,U_19561)),hAPP(c_List_Oset(U_19561),U_19563)))
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562)
    | c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

cnf(f_4719_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19561),sK487(U_19563,U_19562,U_19561)),sK488(U_19563,U_19562,U_19561)))
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19563)
    | ~ c_List_Olinorder__class_Osorted(U_19561,U_19562)
    | c_List_Olinorder__class_Osorted(U_19561,hAPP(hAPP(c_List_Oappend(U_19561),U_19562),U_19563))
    | ~ class_Orderings_Olinorder(U_19561) ),
    inference(clausify,[status(thm)],[f_4719_4]) ).

fof(f_4720_1,plain,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort]) ).

fof(f_4720_2,plain,
    ! [U_19569,U_19568,U_19567,U_19566,U_19565,U_19564] :
      ( hAPP(c_List_Ofilter(U_19565,U_19568),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19565,U_19564,U_19566),U_19569),U_19567)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19565,U_19564,U_19566),U_19569),hAPP(c_List_Ofilter(U_19565,U_19568),U_19567))
      | ~ hBOOL(hAPP(U_19568,U_19569))
      | ~ c_List_Olinorder__class_Osorted(U_19564,hAPP(hAPP(c_List_Omap(U_19565,U_19564),U_19566),U_19567))
      | ~ class_Orderings_Olinorder(U_19564) ),
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

cnf(f_4720_3,plain,
    ( hAPP(c_List_Ofilter(U_19565,U_19568),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19565,U_19564,U_19566),U_19569),U_19567)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19565,U_19564,U_19566),U_19569),hAPP(c_List_Ofilter(U_19565,U_19568),U_19567))
    | ~ hBOOL(hAPP(U_19568,U_19569))
    | ~ c_List_Olinorder__class_Osorted(U_19564,hAPP(hAPP(c_List_Omap(U_19565,U_19564),U_19566),U_19567))
    | ~ class_Orderings_Olinorder(U_19564) ),
    inference(clausify,[status(thm)],[f_4720_2]) ).

fof(f_4721_1,plain,
    ! [V_a1_2,V_a2_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
          | ~ c_List_Olinorder__class_Osorted(T_a,V_a1_2)
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) ) )
        & ( ( c_List_Olinorder__class_Osorted(T_a,V_a1_2)
            & ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) ) )
          | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I2_J]) ).

fof(f_4721_2,plain,
    ! [U_19574,U_19573,U_19572] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
          | ~ c_List_Olinorder__class_Osorted(U_19572,U_19574)
          | ? [U_19571] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),U_19571))
              & hBOOL(hAPP(hAPP(c_member(U_19572),U_19571),hAPP(c_List_Oset(U_19572),U_19574))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_19572,U_19574)
            & ! [U_19570] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),U_19570))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19572),U_19570),hAPP(c_List_Oset(U_19572),U_19574))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574)) ) )
      | ~ class_Orderings_Olinorder(U_19572) ),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

fof(f_4721_3,plain,
    ! [U_19574,U_19573,U_19572] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
          | ~ c_List_Olinorder__class_Osorted(U_19572,U_19574)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),sK489(U_19574,U_19573,U_19572)))
            & hBOOL(hAPP(hAPP(c_member(U_19572),sK489(U_19574,U_19573,U_19572)),hAPP(c_List_Oset(U_19572),U_19574))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_19572,U_19574)
            & ! [U_19570] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),U_19570))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19572),U_19570),hAPP(c_List_Oset(U_19572),U_19574))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574)) ) )
      | ~ class_Orderings_Olinorder(U_19572) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_19571,sK489(U_19574,U_19573,U_19572))],[f_4721_2]) ).

cnf(f_4721_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),U_19570))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19572),U_19570),hAPP(c_List_Oset(U_19572),U_19574)))
    | ~ c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
    | ~ class_Orderings_Olinorder(U_19572) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

cnf(f_4721_5,plain,
    ( c_List_Olinorder__class_Osorted(U_19572,U_19574)
    | ~ c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
    | ~ class_Orderings_Olinorder(U_19572) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

cnf(f_4721_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19572),sK489(U_19574,U_19573,U_19572)),hAPP(c_List_Oset(U_19572),U_19574)))
    | ~ c_List_Olinorder__class_Osorted(U_19572,U_19574)
    | c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
    | ~ class_Orderings_Olinorder(U_19572) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

cnf(f_4721_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19572),U_19573),sK489(U_19574,U_19573,U_19572)))
    | ~ c_List_Olinorder__class_Osorted(U_19572,U_19574)
    | c_List_Olinorder__class_Osorted(U_19572,hAPP(hAPP(c_List_Olist_OCons(U_19572),U_19573),U_19574))
    | ~ class_Orderings_Olinorder(U_19572) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

fof(f_4722_1,plain,
    ! [V_A_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)))
        & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
        & hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set]) ).

fof(f_4722_2,plain,
    ! [U_19576,U_19575] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19575),c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576)))
        & c_List_Olinorder__class_Osorted(U_19575,c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576))
        & hAPP(c_List_Oset(U_19575),c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576)) = U_19576 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19575),U_19576))
      | ~ class_Orderings_Olinorder(U_19575) ),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

cnf(f_4722_3,plain,
    ( hAPP(c_List_Oset(U_19575),c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576)) = U_19576
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19575),U_19576))
    | ~ class_Orderings_Olinorder(U_19575) ),
    inference(clausify,[status(thm)],[f_4722_2]) ).

cnf(f_4722_4,plain,
    ( c_List_Olinorder__class_Osorted(U_19575,c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19575),U_19576))
    | ~ class_Orderings_Olinorder(U_19575) ),
    inference(clausify,[status(thm)],[f_4722_2]) ).

cnf(f_4722_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19575),c_List_Olinorder__class_Osorted__list__of__set(U_19575,U_19576)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19575),U_19576))
    | ~ class_Orderings_Olinorder(U_19575) ),
    inference(clausify,[status(thm)],[f_4722_2]) ).

fof(f_4723_1,plain,
    ! [V_xs_2,V_a_2,T_a] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_insort__remove1]) ).

fof(f_4723_2,plain,
    ! [U_19579,U_19578,U_19577] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19577,U_19577,c_COMBI(U_19577)),U_19578),c_List_Oremove1(U_19577,U_19578,U_19579)) = U_19579
      | ~ c_List_Olinorder__class_Osorted(U_19577,U_19579)
      | ~ hBOOL(hAPP(hAPP(c_member(U_19577),U_19578),hAPP(c_List_Oset(U_19577),U_19579)))
      | ~ class_Orderings_Olinorder(U_19577) ),
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

cnf(f_4723_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19577,U_19577,c_COMBI(U_19577)),U_19578),c_List_Oremove1(U_19577,U_19578,U_19579)) = U_19579
    | ~ c_List_Olinorder__class_Osorted(U_19577,U_19579)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19577),U_19578),hAPP(c_List_Oset(U_19577),U_19579)))
    | ~ class_Orderings_Olinorder(U_19577) ),
    inference(clausify,[status(thm)],[f_4723_2]) ).

fof(f_4724_1,plain,
    ! [V_xs_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
          | ? [B_j] :
              ( ? [B_i] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) )
        & ( ! [B_j] :
              ( ! [B_i] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__equals__nth__mono]) ).

fof(f_4724_2,plain,
    ! [U_19585,U_19584] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19584,U_19585)
          | ? [U_19583] :
              ( ? [U_19582] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19582)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19583)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19582),U_19583)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19583),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) ) )
        & ( ! [U_19581] :
              ( ! [U_19580] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19580)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19581)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19580),U_19581)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) )
          | ~ c_List_Olinorder__class_Osorted(U_19584,U_19585) ) )
      | ~ class_Orderings_Olinorder(U_19584) ),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ! [U_19585,U_19584] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19584,U_19585)
          | ( ? [U_19582] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19582)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),sK490(U_19585,U_19584))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19582),sK490(U_19585,U_19584))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK490(U_19585,U_19584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) ) )
        & ( ! [U_19581] :
              ( ! [U_19580] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19580)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19581)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19580),U_19581)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) )
          | ~ c_List_Olinorder__class_Osorted(U_19584,U_19585) ) )
      | ~ class_Orderings_Olinorder(U_19584) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_19583,sK490(U_19585,U_19584))],[f_4724_2]) ).

fof(f_4724_4,plain,
    ! [U_19585,U_19584] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19584,U_19585)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),sK491(U_19585,U_19584))),hAPP(hAPP(c_List_Onth(U_19584),U_19585),sK490(U_19585,U_19584))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK491(U_19585,U_19584)),sK490(U_19585,U_19584)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK490(U_19585,U_19584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) ) )
        & ( ! [U_19581] :
              ( ! [U_19580] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19580)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19581)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19580),U_19581)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585))) )
          | ~ c_List_Olinorder__class_Osorted(U_19584,U_19585) ) )
      | ~ class_Orderings_Olinorder(U_19584) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_19582,sK491(U_19585,U_19584))],[f_4724_3]) ).

cnf(f_4724_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19580)),hAPP(hAPP(c_List_Onth(U_19584),U_19585),U_19581)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19580),U_19581))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585)))
    | ~ c_List_Olinorder__class_Osorted(U_19584,U_19585)
    | ~ class_Orderings_Olinorder(U_19584) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

cnf(f_4724_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK490(U_19585,U_19584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19584)),U_19585)))
    | c_List_Olinorder__class_Osorted(U_19584,U_19585)
    | ~ class_Orderings_Olinorder(U_19584) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

cnf(f_4724_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK491(U_19585,U_19584)),sK490(U_19585,U_19584)))
    | c_List_Olinorder__class_Osorted(U_19584,U_19585)
    | ~ class_Orderings_Olinorder(U_19584) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

cnf(f_4724_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19584),hAPP(hAPP(c_List_Onth(U_19584),U_19585),sK491(U_19585,U_19584))),hAPP(hAPP(c_List_Onth(U_19584),U_19585),sK490(U_19585,U_19584))))
    | c_List_Olinorder__class_Osorted(U_19584,U_19585)
    | ~ class_Orderings_Olinorder(U_19584) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

fof(f_4725_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_4725_2,plain,
    ! [U_19589,U_19588,U_19587,U_19586] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19586),hAPP(hAPP(c_List_Onth(U_19586),U_19587),U_19588)),hAPP(hAPP(c_List_Onth(U_19586),U_19587),U_19589)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19586)),U_19587)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19588),U_19589))
      | ~ c_List_Olinorder__class_Osorted(U_19586,U_19587)
      | ~ class_Orderings_Olinorder(U_19586) ),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

cnf(f_4725_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19586),hAPP(hAPP(c_List_Onth(U_19586),U_19587),U_19588)),hAPP(hAPP(c_List_Onth(U_19586),U_19587),U_19589)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19586)),U_19587)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19588),U_19589))
    | ~ c_List_Olinorder__class_Osorted(U_19586,U_19587)
    | ~ class_Orderings_Olinorder(U_19586) ),
    inference(clausify,[status(thm)],[f_4725_2]) ).

fof(f_4726_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_a),V_xs_2) != hAPP(c_List_Oset(T_a),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique]) ).

fof(f_4726_2,plain,
    ! [U_19594,U_19593,U_19592,U_19591,U_19590] :
      ( U_19593 = U_19594
      | hAPP(c_List_Oset(U_19591),U_19593) != hAPP(c_List_Oset(U_19591),U_19594)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19590),hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19594)))
      | ~ c_List_Olinorder__class_Osorted(U_19590,hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19594))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19590),hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19593)))
      | ~ c_List_Olinorder__class_Osorted(U_19590,hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19593))
      | ~ c_Fun_Oinj__on(U_19591,U_19590,U_19592,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19591,tc_HOL_Obool)),hAPP(c_List_Oset(U_19591),U_19593)),hAPP(c_List_Oset(U_19591),U_19594)))
      | ~ class_Orderings_Olinorder(U_19590) ),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

cnf(f_4726_3,plain,
    ( U_19593 = U_19594
    | hAPP(c_List_Oset(U_19591),U_19593) != hAPP(c_List_Oset(U_19591),U_19594)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19590),hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19594)))
    | ~ c_List_Olinorder__class_Osorted(U_19590,hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19594))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19590),hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19593)))
    | ~ c_List_Olinorder__class_Osorted(U_19590,hAPP(hAPP(c_List_Omap(U_19591,U_19590),U_19592),U_19593))
    | ~ c_Fun_Oinj__on(U_19591,U_19590,U_19592,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19591,tc_HOL_Obool)),hAPP(c_List_Oset(U_19591),U_19593)),hAPP(c_List_Oset(U_19591),U_19594)))
    | ~ class_Orderings_Olinorder(U_19590) ),
    inference(clausify,[status(thm)],[f_4726_2]) ).

fof(f_4727_1,plain,
    ! [V_i_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),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_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column]) ).

fof(f_4727_2,plain,
    ! [U_19597,U_19596,U_19595] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19595),U_19595),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19595),tc_Nat_Onat,U_19595),c_List_Onth(U_19595)),U_19597)),hAPP(c_List_Ofilter(tc_List_Olist(U_19595),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19595)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19597)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19595)))),c_List_Otranspose(U_19595,U_19596))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19595)),U_19596),U_19597)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19595))),U_19596)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19595),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19595))),U_19596))) ),
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

cnf(f_4727_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19595),U_19595),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19595),tc_Nat_Onat,U_19595),c_List_Onth(U_19595)),U_19597)),hAPP(c_List_Ofilter(tc_List_Olist(U_19595),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19595)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19597)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19595)))),c_List_Otranspose(U_19595,U_19596))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19595)),U_19596),U_19597)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19595))),U_19596)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19595),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19595))),U_19596))) ),
    inference(clausify,[status(thm)],[f_4727_2]) ).

fof(f_4728_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_a] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),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_a))),c_List_Otranspose(T_a,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_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted]) ).

fof(f_4728_2,plain,
    ! [U_19601,U_19600,U_19599,U_19598] :
      ( hAPP(hAPP(c_List_Onth(U_19598),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19598)),c_List_Otranspose(U_19598,U_19599)),U_19600)),U_19601) = hAPP(hAPP(c_List_Onth(U_19598),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19598)),U_19599),U_19601)),U_19600)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19601),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19598))),hAPP(c_List_Ofilter(tc_List_Olist(U_19598),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19598)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19600)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19598)))),U_19599))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19598))),c_List_Otranspose(U_19598,U_19599))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19598),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19598))),U_19599))) ),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

cnf(f_4728_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19598),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19598)),c_List_Otranspose(U_19598,U_19599)),U_19600)),U_19601) = hAPP(hAPP(c_List_Onth(U_19598),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19598)),U_19599),U_19601)),U_19600)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19601),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19598))),hAPP(c_List_Ofilter(tc_List_Olist(U_19598),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19598)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19600)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19598)))),U_19599))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19598))),c_List_Otranspose(U_19598,U_19599))))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19598),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19598))),U_19599))) ),
    inference(clausify,[status(thm)],[f_4728_2]) ).

fof(f_4729_1,plain,
    ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__rev]) ).

fof(f_4729_2,plain,
    ! [U_19603,U_19602] : c_Fun_Oinj__on(tc_List_Olist(U_19602),tc_List_Olist(U_19602),c_List_Orev(U_19602),U_19603),
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

cnf(f_4729_3,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_19602),tc_List_Olist(U_19602),c_List_Orev(U_19602),U_19603),
    inference(clausify,[status(thm)],[f_4729_2]) ).

fof(f_4730_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rev]) ).

fof(f_4730_2,plain,
    ! [U_19605,U_19604] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19604),hAPP(c_List_Orev(U_19604),U_19605)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19604),U_19605)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19604),U_19605))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19604),hAPP(c_List_Orev(U_19604),U_19605))) ) ),
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

fof(f_4730_3,plain,
    ( ! [U_19609,U_19607] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19607),hAPP(c_List_Orev(U_19607),U_19609)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19607),U_19609)) )
    & ! [U_19608,U_19606] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19606),U_19608))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19606),hAPP(c_List_Orev(U_19606),U_19608))) ) ),
    inference(miniscope,[status(thm)],[f_4730_2]) ).

cnf(f_4730_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19606),U_19608))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19606),hAPP(c_List_Orev(U_19606),U_19608))) ),
    inference(clausify,[status(thm)],[f_4730_3]) ).

cnf(f_4730_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19607),hAPP(c_List_Orev(U_19607),U_19609)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19607),U_19609)) ),
    inference(clausify,[status(thm)],[f_4730_3]) ).

fof(f_4731_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_4731_2,plain,
    ! [U_19612,U_19611,U_19610] : hAPP(c_List_Orev(U_19610),hAPP(hAPP(c_List_Oappend(U_19610),U_19611),U_19612)) = hAPP(hAPP(c_List_Oappend(U_19610),hAPP(c_List_Orev(U_19610),U_19612)),hAPP(c_List_Orev(U_19610),U_19611)),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

cnf(f_4731_3,plain,
    hAPP(c_List_Orev(U_19610),hAPP(hAPP(c_List_Oappend(U_19610),U_19611),U_19612)) = hAPP(hAPP(c_List_Oappend(U_19610),hAPP(c_List_Orev(U_19610),U_19612)),hAPP(c_List_Orev(U_19610),U_19611)),
    inference(clausify,[status(thm)],[f_4731_2]) ).

fof(f_4732_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_4732_2,plain,
    ! [U_19613] : hAPP(c_List_Orev(U_19613),c_List_Olist_ONil(U_19613)) = c_List_Olist_ONil(U_19613),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

cnf(f_4732_3,plain,
    hAPP(c_List_Orev(U_19613),c_List_Olist_ONil(U_19613)) = c_List_Olist_ONil(U_19613),
    inference(clausify,[status(thm)],[f_4732_2]) ).

fof(f_4733_1,plain,
    ! [V_xs_2,T_a] :
      ( ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | c_List_Olist_ONil(T_a) != hAPP(c_List_Orev(T_a),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv]) ).

fof(f_4733_2,plain,
    ! [U_19615,U_19614] :
      ( ( c_List_Olist_ONil(U_19614) = hAPP(c_List_Orev(U_19614),U_19615)
        | U_19615 != c_List_Olist_ONil(U_19614) )
      & ( U_19615 = c_List_Olist_ONil(U_19614)
        | c_List_Olist_ONil(U_19614) != hAPP(c_List_Orev(U_19614),U_19615) ) ),
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

fof(f_4733_3,plain,
    ( ! [U_19619,U_19617] :
        ( c_List_Olist_ONil(U_19617) = hAPP(c_List_Orev(U_19617),U_19619)
        | U_19619 != c_List_Olist_ONil(U_19617) )
    & ! [U_19618,U_19616] :
        ( U_19618 = c_List_Olist_ONil(U_19616)
        | c_List_Olist_ONil(U_19616) != hAPP(c_List_Orev(U_19616),U_19618) ) ),
    inference(miniscope,[status(thm)],[f_4733_2]) ).

cnf(f_4733_4,plain,
    ( U_19618 = c_List_Olist_ONil(U_19616)
    | c_List_Olist_ONil(U_19616) != hAPP(c_List_Orev(U_19616),U_19618) ),
    inference(clausify,[status(thm)],[f_4733_3]) ).

cnf(f_4733_5,plain,
    ( c_List_Olist_ONil(U_19617) = hAPP(c_List_Orev(U_19617),U_19619)
    | U_19619 != c_List_Olist_ONil(U_19617) ),
    inference(clausify,[status(thm)],[f_4733_3]) ).

fof(f_4734_1,plain,
    ! [V_xs_2,T_a] :
      ( ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
        | V_xs_2 != c_List_Olist_ONil(T_a) )
      & ( V_xs_2 = c_List_Olist_ONil(T_a)
        | hAPP(c_List_Orev(T_a),V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv]) ).

fof(f_4734_2,plain,
    ! [U_19621,U_19620] :
      ( ( hAPP(c_List_Orev(U_19620),U_19621) = c_List_Olist_ONil(U_19620)
        | U_19621 != c_List_Olist_ONil(U_19620) )
      & ( U_19621 = c_List_Olist_ONil(U_19620)
        | hAPP(c_List_Orev(U_19620),U_19621) != c_List_Olist_ONil(U_19620) ) ),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ( ! [U_19625,U_19623] :
        ( hAPP(c_List_Orev(U_19623),U_19625) = c_List_Olist_ONil(U_19623)
        | U_19625 != c_List_Olist_ONil(U_19623) )
    & ! [U_19624,U_19622] :
        ( U_19624 = c_List_Olist_ONil(U_19622)
        | hAPP(c_List_Orev(U_19622),U_19624) != c_List_Olist_ONil(U_19622) ) ),
    inference(miniscope,[status(thm)],[f_4734_2]) ).

cnf(f_4734_4,plain,
    ( U_19624 = c_List_Olist_ONil(U_19622)
    | hAPP(c_List_Orev(U_19622),U_19624) != c_List_Olist_ONil(U_19622) ),
    inference(clausify,[status(thm)],[f_4734_3]) ).

cnf(f_4734_5,plain,
    ( hAPP(c_List_Orev(U_19623),U_19625) = c_List_Olist_ONil(U_19623)
    | U_19625 != c_List_Olist_ONil(U_19623) ),
    inference(clausify,[status(thm)],[f_4734_3]) ).

fof(f_4735_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
        | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) != hAPP(c_List_Orev(T_a),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv]) ).

fof(f_4735_2,plain,
    ! [U_19628,U_19627,U_19626] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_19626),U_19627),c_List_Olist_ONil(U_19626)) = hAPP(c_List_Orev(U_19626),U_19628)
        | U_19628 != hAPP(hAPP(c_List_Olist_OCons(U_19626),U_19627),c_List_Olist_ONil(U_19626)) )
      & ( U_19628 = hAPP(hAPP(c_List_Olist_OCons(U_19626),U_19627),c_List_Olist_ONil(U_19626))
        | hAPP(hAPP(c_List_Olist_OCons(U_19626),U_19627),c_List_Olist_ONil(U_19626)) != hAPP(c_List_Orev(U_19626),U_19628) ) ),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

fof(f_4735_3,plain,
    ( ! [U_19634,U_19632,U_19630] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19630),U_19632),c_List_Olist_ONil(U_19630)) = hAPP(c_List_Orev(U_19630),U_19634)
        | U_19634 != hAPP(hAPP(c_List_Olist_OCons(U_19630),U_19632),c_List_Olist_ONil(U_19630)) )
    & ! [U_19633,U_19631,U_19629] :
        ( U_19633 = hAPP(hAPP(c_List_Olist_OCons(U_19629),U_19631),c_List_Olist_ONil(U_19629))
        | hAPP(hAPP(c_List_Olist_OCons(U_19629),U_19631),c_List_Olist_ONil(U_19629)) != hAPP(c_List_Orev(U_19629),U_19633) ) ),
    inference(miniscope,[status(thm)],[f_4735_2]) ).

cnf(f_4735_4,plain,
    ( U_19633 = hAPP(hAPP(c_List_Olist_OCons(U_19629),U_19631),c_List_Olist_ONil(U_19629))
    | hAPP(hAPP(c_List_Olist_OCons(U_19629),U_19631),c_List_Olist_ONil(U_19629)) != hAPP(c_List_Orev(U_19629),U_19633) ),
    inference(clausify,[status(thm)],[f_4735_3]) ).

cnf(f_4735_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19630),U_19632),c_List_Olist_ONil(U_19630)) = hAPP(c_List_Orev(U_19630),U_19634)
    | U_19634 != hAPP(hAPP(c_List_Olist_OCons(U_19630),U_19632),c_List_Olist_ONil(U_19630)) ),
    inference(clausify,[status(thm)],[f_4735_3]) ).

fof(f_4736_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
        | hAPP(c_List_Orev(T_a),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv]) ).

fof(f_4736_2,plain,
    ! [U_19637,U_19636,U_19635] :
      ( ( hAPP(c_List_Orev(U_19635),U_19636) = hAPP(hAPP(c_List_Olist_OCons(U_19635),U_19637),c_List_Olist_ONil(U_19635))
        | U_19636 != hAPP(hAPP(c_List_Olist_OCons(U_19635),U_19637),c_List_Olist_ONil(U_19635)) )
      & ( U_19636 = hAPP(hAPP(c_List_Olist_OCons(U_19635),U_19637),c_List_Olist_ONil(U_19635))
        | hAPP(c_List_Orev(U_19635),U_19636) != hAPP(hAPP(c_List_Olist_OCons(U_19635),U_19637),c_List_Olist_ONil(U_19635)) ) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

fof(f_4736_3,plain,
    ( ! [U_19643,U_19641,U_19639] :
        ( hAPP(c_List_Orev(U_19639),U_19641) = hAPP(hAPP(c_List_Olist_OCons(U_19639),U_19643),c_List_Olist_ONil(U_19639))
        | U_19641 != hAPP(hAPP(c_List_Olist_OCons(U_19639),U_19643),c_List_Olist_ONil(U_19639)) )
    & ! [U_19642,U_19640,U_19638] :
        ( U_19640 = hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19642),c_List_Olist_ONil(U_19638))
        | hAPP(c_List_Orev(U_19638),U_19640) != hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19642),c_List_Olist_ONil(U_19638)) ) ),
    inference(miniscope,[status(thm)],[f_4736_2]) ).

cnf(f_4736_4,plain,
    ( U_19640 = hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19642),c_List_Olist_ONil(U_19638))
    | hAPP(c_List_Orev(U_19638),U_19640) != hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19642),c_List_Olist_ONil(U_19638)) ),
    inference(clausify,[status(thm)],[f_4736_3]) ).

cnf(f_4736_5,plain,
    ( hAPP(c_List_Orev(U_19639),U_19641) = hAPP(hAPP(c_List_Olist_OCons(U_19639),U_19643),c_List_Olist_ONil(U_19639))
    | U_19641 != hAPP(hAPP(c_List_Olist_OCons(U_19639),U_19643),c_List_Olist_ONil(U_19639)) ),
    inference(clausify,[status(thm)],[f_4736_3]) ).

fof(f_4737_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_4737_2,plain,
    ! [U_19646,U_19645,U_19644] : hAPP(c_List_Orev(U_19644),hAPP(hAPP(c_List_Olist_OCons(U_19644),U_19645),U_19646)) = hAPP(hAPP(c_List_Oappend(U_19644),hAPP(c_List_Orev(U_19644),U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19644),U_19645),c_List_Olist_ONil(U_19644))),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

cnf(f_4737_3,plain,
    hAPP(c_List_Orev(U_19644),hAPP(hAPP(c_List_Olist_OCons(U_19644),U_19645),U_19646)) = hAPP(hAPP(c_List_Oappend(U_19644),hAPP(c_List_Orev(U_19644),U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19644),U_19645),c_List_Olist_ONil(U_19644))),
    inference(clausify,[status(thm)],[f_4737_2]) ).

fof(f_4738_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_a] :
      ( ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))
        | hAPP(c_List_Orev(T_a),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff]) ).

fof(f_4738_2,plain,
    ! [U_19650,U_19649,U_19648,U_19647] :
      ( ( hAPP(c_List_Orev(U_19647),U_19648) = hAPP(hAPP(c_List_Olist_OCons(U_19647),U_19649),U_19650)
        | U_19648 != hAPP(hAPP(c_List_Oappend(U_19647),hAPP(c_List_Orev(U_19647),U_19650)),hAPP(hAPP(c_List_Olist_OCons(U_19647),U_19649),c_List_Olist_ONil(U_19647))) )
      & ( U_19648 = hAPP(hAPP(c_List_Oappend(U_19647),hAPP(c_List_Orev(U_19647),U_19650)),hAPP(hAPP(c_List_Olist_OCons(U_19647),U_19649),c_List_Olist_ONil(U_19647)))
        | hAPP(c_List_Orev(U_19647),U_19648) != hAPP(hAPP(c_List_Olist_OCons(U_19647),U_19649),U_19650) ) ),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ( ! [U_19658,U_19656,U_19654,U_19652] :
        ( hAPP(c_List_Orev(U_19652),U_19654) = hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19656),U_19658)
        | U_19654 != hAPP(hAPP(c_List_Oappend(U_19652),hAPP(c_List_Orev(U_19652),U_19658)),hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19656),c_List_Olist_ONil(U_19652))) )
    & ! [U_19657,U_19655,U_19653,U_19651] :
        ( U_19653 = hAPP(hAPP(c_List_Oappend(U_19651),hAPP(c_List_Orev(U_19651),U_19657)),hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19655),c_List_Olist_ONil(U_19651)))
        | hAPP(c_List_Orev(U_19651),U_19653) != hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19655),U_19657) ) ),
    inference(miniscope,[status(thm)],[f_4738_2]) ).

cnf(f_4738_4,plain,
    ( U_19653 = hAPP(hAPP(c_List_Oappend(U_19651),hAPP(c_List_Orev(U_19651),U_19657)),hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19655),c_List_Olist_ONil(U_19651)))
    | hAPP(c_List_Orev(U_19651),U_19653) != hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19655),U_19657) ),
    inference(clausify,[status(thm)],[f_4738_3]) ).

cnf(f_4738_5,plain,
    ( hAPP(c_List_Orev(U_19652),U_19654) = hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19656),U_19658)
    | U_19654 != hAPP(hAPP(c_List_Oappend(U_19652),hAPP(c_List_Orev(U_19652),U_19658)),hAPP(hAPP(c_List_Olist_OCons(U_19652),U_19656),c_List_Olist_ONil(U_19652))) ),
    inference(clausify,[status(thm)],[f_4738_3]) ).

fof(f_4739_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_rev__concat]) ).

fof(f_4739_2,plain,
    ! [U_19660,U_19659] : hAPP(c_List_Orev(U_19659),c_List_Oconcat(U_19659,U_19660)) = c_List_Oconcat(U_19659,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19659),tc_List_Olist(U_19659)),c_List_Orev(U_19659)),hAPP(c_List_Orev(tc_List_Olist(U_19659)),U_19660))),
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

cnf(f_4739_3,plain,
    hAPP(c_List_Orev(U_19659),c_List_Oconcat(U_19659,U_19660)) = c_List_Oconcat(U_19659,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19659),tc_List_Olist(U_19659)),c_List_Orev(U_19659)),hAPP(c_List_Orev(tc_List_Olist(U_19659)),U_19660))),
    inference(clausify,[status(thm)],[f_4739_2]) ).

fof(f_4740_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__map]) ).

fof(f_4740_2,plain,
    ! [U_19664,U_19663,U_19662,U_19661] : hAPP(c_List_Orev(U_19661),hAPP(hAPP(c_List_Omap(U_19662,U_19661),U_19663),U_19664)) = hAPP(hAPP(c_List_Omap(U_19662,U_19661),U_19663),hAPP(c_List_Orev(U_19662),U_19664)),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

cnf(f_4740_3,plain,
    hAPP(c_List_Orev(U_19661),hAPP(hAPP(c_List_Omap(U_19662,U_19661),U_19663),U_19664)) = hAPP(hAPP(c_List_Omap(U_19662,U_19661),U_19663),hAPP(c_List_Orev(U_19662),U_19664)),
    inference(clausify,[status(thm)],[f_4740_2]) ).

fof(f_4741_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__filter]) ).

fof(f_4741_2,plain,
    ! [U_19667,U_19666,U_19665] : hAPP(c_List_Orev(U_19665),hAPP(c_List_Ofilter(U_19665,U_19666),U_19667)) = hAPP(c_List_Ofilter(U_19665,U_19666),hAPP(c_List_Orev(U_19665),U_19667)),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

cnf(f_4741_3,plain,
    hAPP(c_List_Orev(U_19665),hAPP(c_List_Ofilter(U_19665,U_19666),U_19667)) = hAPP(c_List_Ofilter(U_19665,U_19666),hAPP(c_List_Orev(U_19665),U_19667)),
    inference(clausify,[status(thm)],[f_4741_2]) ).

fof(f_4742_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_4742_2,plain,
    ! [U_19671,U_19670,U_19669,U_19668] :
      ( hAPP(hAPP(c_List_Ozip(U_19668,U_19670),hAPP(c_List_Orev(U_19668),U_19669)),hAPP(c_List_Orev(U_19670),U_19671)) = hAPP(c_List_Orev(tc_prod(U_19668,U_19670)),hAPP(hAPP(c_List_Ozip(U_19668,U_19670),U_19669),U_19671))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19668)),U_19669) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19670)),U_19671) ),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

cnf(f_4742_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_19668,U_19670),hAPP(c_List_Orev(U_19668),U_19669)),hAPP(c_List_Orev(U_19670),U_19671)) = hAPP(c_List_Orev(tc_prod(U_19668,U_19670)),hAPP(hAPP(c_List_Ozip(U_19668,U_19670),U_19669),U_19671))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19668)),U_19669) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19670)),U_19671) ),
    inference(clausify,[status(thm)],[f_4742_2]) ).

fof(f_4743_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rev]) ).

fof(f_4743_2,plain,
    ! [U_19673,U_19672] : hAPP(c_List_Oset(U_19672),hAPP(c_List_Orev(U_19672),U_19673)) = hAPP(c_List_Oset(U_19672),U_19673),
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

cnf(f_4743_3,plain,
    hAPP(c_List_Oset(U_19672),hAPP(c_List_Orev(U_19672),U_19673)) = hAPP(c_List_Oset(U_19672),U_19673),
    inference(clausify,[status(thm)],[f_4743_2]) ).

fof(f_4744_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) )
      & ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2))
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__rev1]) ).

fof(f_4744_2,plain,
    ! [U_19678,U_19677,U_19676,U_19675,U_19674] :
      ( ( c_List_Olist__all2(U_19674,U_19675,U_19676,hAPP(c_List_Orev(U_19674),U_19677),U_19678)
        | ~ c_List_Olist__all2(U_19674,U_19675,U_19676,U_19677,hAPP(c_List_Orev(U_19675),U_19678)) )
      & ( c_List_Olist__all2(U_19674,U_19675,U_19676,U_19677,hAPP(c_List_Orev(U_19675),U_19678))
        | ~ c_List_Olist__all2(U_19674,U_19675,U_19676,hAPP(c_List_Orev(U_19674),U_19677),U_19678) ) ),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

fof(f_4744_3,plain,
    ( ! [U_19688,U_19686,U_19684,U_19682,U_19680] :
        ( c_List_Olist__all2(U_19680,U_19682,U_19684,hAPP(c_List_Orev(U_19680),U_19686),U_19688)
        | ~ c_List_Olist__all2(U_19680,U_19682,U_19684,U_19686,hAPP(c_List_Orev(U_19682),U_19688)) )
    & ! [U_19687,U_19685,U_19683,U_19681,U_19679] :
        ( c_List_Olist__all2(U_19679,U_19681,U_19683,U_19685,hAPP(c_List_Orev(U_19681),U_19687))
        | ~ c_List_Olist__all2(U_19679,U_19681,U_19683,hAPP(c_List_Orev(U_19679),U_19685),U_19687) ) ),
    inference(miniscope,[status(thm)],[f_4744_2]) ).

cnf(f_4744_4,plain,
    ( c_List_Olist__all2(U_19679,U_19681,U_19683,U_19685,hAPP(c_List_Orev(U_19681),U_19687))
    | ~ c_List_Olist__all2(U_19679,U_19681,U_19683,hAPP(c_List_Orev(U_19679),U_19685),U_19687) ),
    inference(clausify,[status(thm)],[f_4744_3]) ).

cnf(f_4744_5,plain,
    ( c_List_Olist__all2(U_19680,U_19682,U_19684,hAPP(c_List_Orev(U_19680),U_19686),U_19688)
    | ~ c_List_Olist__all2(U_19680,U_19682,U_19684,U_19686,hAPP(c_List_Orev(U_19682),U_19688)) ),
    inference(clausify,[status(thm)],[f_4744_3]) ).

fof(f_4745_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
      ( ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2))
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) )
      & ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
        | ~ c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__rev]) ).

fof(f_4745_2,plain,
    ! [U_19693,U_19692,U_19691,U_19690,U_19689] :
      ( ( c_List_Olist__all2(U_19689,U_19690,U_19691,hAPP(c_List_Orev(U_19689),U_19692),hAPP(c_List_Orev(U_19690),U_19693))
        | ~ c_List_Olist__all2(U_19689,U_19690,U_19691,U_19692,U_19693) )
      & ( c_List_Olist__all2(U_19689,U_19690,U_19691,U_19692,U_19693)
        | ~ c_List_Olist__all2(U_19689,U_19690,U_19691,hAPP(c_List_Orev(U_19689),U_19692),hAPP(c_List_Orev(U_19690),U_19693)) ) ),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

fof(f_4745_3,plain,
    ( ! [U_19703,U_19701,U_19699,U_19697,U_19695] :
        ( c_List_Olist__all2(U_19695,U_19697,U_19699,hAPP(c_List_Orev(U_19695),U_19701),hAPP(c_List_Orev(U_19697),U_19703))
        | ~ c_List_Olist__all2(U_19695,U_19697,U_19699,U_19701,U_19703) )
    & ! [U_19702,U_19700,U_19698,U_19696,U_19694] :
        ( c_List_Olist__all2(U_19694,U_19696,U_19698,U_19700,U_19702)
        | ~ c_List_Olist__all2(U_19694,U_19696,U_19698,hAPP(c_List_Orev(U_19694),U_19700),hAPP(c_List_Orev(U_19696),U_19702)) ) ),
    inference(miniscope,[status(thm)],[f_4745_2]) ).

cnf(f_4745_4,plain,
    ( c_List_Olist__all2(U_19694,U_19696,U_19698,U_19700,U_19702)
    | ~ c_List_Olist__all2(U_19694,U_19696,U_19698,hAPP(c_List_Orev(U_19694),U_19700),hAPP(c_List_Orev(U_19696),U_19702)) ),
    inference(clausify,[status(thm)],[f_4745_3]) ).

cnf(f_4745_5,plain,
    ( c_List_Olist__all2(U_19695,U_19697,U_19699,hAPP(c_List_Orev(U_19695),U_19701),hAPP(c_List_Orev(U_19697),U_19703))
    | ~ c_List_Olist__all2(U_19695,U_19697,U_19699,U_19701,U_19703) ),
    inference(clausify,[status(thm)],[f_4745_3]) ).

fof(f_4746_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_4746_2,plain,
    ! [U_19705,U_19704] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19704),hAPP(c_List_Orev(U_19704),U_19705)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19704),U_19705)
      | ~ class_Groups_Ocomm__monoid__add(U_19704) ),
    inference(variable_rename,[status(thm)],[f_4746_1]) ).

cnf(f_4746_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19704),hAPP(c_List_Orev(U_19704),U_19705)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19704),U_19705)
    | ~ class_Groups_Ocomm__monoid__add(U_19704) ),
    inference(clausify,[status(thm)],[f_4746_2]) ).

fof(f_4747_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
        | V_xs_2 != V_ys_2 )
      & ( V_xs_2 = V_ys_2
        | hAPP(c_List_Orev(T_a),V_xs_2) != hAPP(c_List_Orev(T_a),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv]) ).

fof(f_4747_2,plain,
    ! [U_19708,U_19707,U_19706] :
      ( ( hAPP(c_List_Orev(U_19706),U_19707) = hAPP(c_List_Orev(U_19706),U_19708)
        | U_19707 != U_19708 )
      & ( U_19707 = U_19708
        | hAPP(c_List_Orev(U_19706),U_19707) != hAPP(c_List_Orev(U_19706),U_19708) ) ),
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

fof(f_4747_3,plain,
    ( ! [U_19714,U_19712] :
        ( ! [U_19710] : hAPP(c_List_Orev(U_19710),U_19712) = hAPP(c_List_Orev(U_19710),U_19714)
        | U_19712 != U_19714 )
    & ! [U_19713,U_19711] :
        ( ! [U_19709] : hAPP(c_List_Orev(U_19709),U_19711) != hAPP(c_List_Orev(U_19709),U_19713)
        | U_19711 = U_19713 ) ),
    inference(miniscope,[status(thm)],[f_4747_2]) ).

cnf(f_4747_4,plain,
    ( hAPP(c_List_Orev(U_19709),U_19711) != hAPP(c_List_Orev(U_19709),U_19713)
    | U_19711 = U_19713 ),
    inference(clausify,[status(thm)],[f_4747_3]) ).

cnf(f_4747_5,plain,
    ( hAPP(c_List_Orev(U_19710),U_19712) = hAPP(c_List_Orev(U_19710),U_19714)
    | U_19712 != U_19714 ),
    inference(clausify,[status(thm)],[f_4747_3]) ).

fof(f_4748_1,plain,
    ! [V_ys_2,V_xs_2,T_a] :
      ( ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
        | V_xs_2 != hAPP(c_List_Orev(T_a),V_ys_2) )
      & ( V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2)
        | hAPP(c_List_Orev(T_a),V_xs_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__swap]) ).

fof(f_4748_2,plain,
    ! [U_19717,U_19716,U_19715] :
      ( ( hAPP(c_List_Orev(U_19715),U_19716) = U_19717
        | U_19716 != hAPP(c_List_Orev(U_19715),U_19717) )
      & ( U_19716 = hAPP(c_List_Orev(U_19715),U_19717)
        | hAPP(c_List_Orev(U_19715),U_19716) != U_19717 ) ),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

fof(f_4748_3,plain,
    ( ! [U_19723,U_19721,U_19719] :
        ( hAPP(c_List_Orev(U_19719),U_19721) = U_19723
        | U_19721 != hAPP(c_List_Orev(U_19719),U_19723) )
    & ! [U_19722,U_19720,U_19718] :
        ( U_19720 = hAPP(c_List_Orev(U_19718),U_19722)
        | hAPP(c_List_Orev(U_19718),U_19720) != U_19722 ) ),
    inference(miniscope,[status(thm)],[f_4748_2]) ).

cnf(f_4748_4,plain,
    ( U_19720 = hAPP(c_List_Orev(U_19718),U_19722)
    | hAPP(c_List_Orev(U_19718),U_19720) != U_19722 ),
    inference(clausify,[status(thm)],[f_4748_3]) ).

cnf(f_4748_5,plain,
    ( hAPP(c_List_Orev(U_19719),U_19721) = U_19723
    | U_19721 != hAPP(c_List_Orev(U_19719),U_19723) ),
    inference(clausify,[status(thm)],[f_4748_3]) ).

fof(f_4749_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_4749_2,plain,
    ! [U_19725,U_19724] : hAPP(c_List_Orev(U_19724),hAPP(c_List_Orev(U_19724),U_19725)) = U_19725,
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

cnf(f_4749_3,plain,
    hAPP(c_List_Orev(U_19724),hAPP(c_List_Orev(U_19724),U_19725)) = U_19725,
    inference(clausify,[status(thm)],[f_4749_2]) ).

fof(f_4750_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_4750_2,plain,
    ! [U_19727,U_19726] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19726)),hAPP(c_List_Orev(U_19726),U_19727)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19726)),U_19727),
    inference(variable_rename,[status(thm)],[f_4750_1]) ).

cnf(f_4750_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19726)),hAPP(c_List_Orev(U_19726),U_19727)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19726)),U_19727),
    inference(clausify,[status(thm)],[f_4750_2]) ).

fof(f_4751_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr]) ).

fof(f_4751_2,plain,
    ! [U_19732,U_19731,U_19730,U_19729,U_19728] : hAPP(c_List_Ofoldl(U_19728,U_19729,U_19730,U_19731),U_19732) = c_List_Ofoldr(U_19729,U_19728,hAPP(c_COMBC(U_19728,U_19729,U_19728),U_19730),hAPP(c_List_Orev(U_19729),U_19732),U_19731),
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

cnf(f_4751_3,plain,
    hAPP(c_List_Ofoldl(U_19728,U_19729,U_19730,U_19731),U_19732) = c_List_Ofoldr(U_19729,U_19728,hAPP(c_COMBC(U_19728,U_19729,U_19728),U_19730),hAPP(c_List_Orev(U_19729),U_19732),U_19731),
    inference(clausify,[status(thm)],[f_4751_2]) ).

fof(f_4752_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__foldl]) ).

fof(f_4752_2,plain,
    ! [U_19737,U_19736,U_19735,U_19734,U_19733] : c_List_Ofoldr(U_19733,U_19734,U_19735,U_19736,U_19737) = hAPP(c_List_Ofoldl(U_19734,U_19733,hAPP(c_COMBC(U_19733,U_19734,U_19734),U_19735),U_19737),hAPP(c_List_Orev(U_19733),U_19736)),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

cnf(f_4752_3,plain,
    c_List_Ofoldr(U_19733,U_19734,U_19735,U_19736,U_19737) = hAPP(c_List_Ofoldl(U_19734,U_19733,hAPP(c_COMBC(U_19733,U_19734,U_19734),U_19735),U_19737),hAPP(c_List_Orev(U_19733),U_19736)),
    inference(clausify,[status(thm)],[f_4752_2]) ).

fof(f_4753_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_4753_2,plain,
    ! [U_19739,U_19738] :
      ( c_List_Olast(U_19739,hAPP(c_List_Orev(U_19739),U_19738)) = hAPP(c_List_Ohd(U_19739),U_19738)
      | U_19738 = c_List_Olist_ONil(U_19739) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

cnf(f_4753_3,plain,
    ( c_List_Olast(U_19739,hAPP(c_List_Orev(U_19739),U_19738)) = hAPP(c_List_Ohd(U_19739),U_19738)
    | U_19738 = c_List_Olist_ONil(U_19739) ),
    inference(clausify,[status(thm)],[f_4753_2]) ).

fof(f_4754_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_4754_2,plain,
    ! [U_19741,U_19740] :
      ( hAPP(c_List_Ohd(U_19741),hAPP(c_List_Orev(U_19741),U_19740)) = c_List_Olast(U_19741,U_19740)
      | U_19740 = c_List_Olist_ONil(U_19741) ),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

cnf(f_4754_3,plain,
    ( hAPP(c_List_Ohd(U_19741),hAPP(c_List_Orev(U_19741),U_19740)) = c_List_Olast(U_19741,U_19740)
    | U_19740 = c_List_Olist_ONil(U_19741) ),
    inference(clausify,[status(thm)],[f_4754_2]) ).

fof(f_4755_1,plain,
    ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_sorted__transpose]) ).

fof(f_4755_2,plain,
    ! [U_19743,U_19742] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19742),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19742))),c_List_Otranspose(U_19742,U_19743)))),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

cnf(f_4755_3,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_19742),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19742))),c_List_Otranspose(U_19742,U_19743)))),
    inference(clausify,[status(thm)],[f_4755_2]) ).

fof(f_4756_1,plain,
    ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rev__foldl__cons]) ).

fof(f_4756_2,plain,
    ! [U_19745,U_19744] : hAPP(c_List_Orev(U_19744),U_19745) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19744),U_19744,hAPP(c_COMBC(U_19744,tc_List_Olist(U_19744),tc_List_Olist(U_19744)),c_List_Olist_OCons(U_19744)),c_List_Olist_ONil(U_19744)),U_19745),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

cnf(f_4756_3,plain,
    hAPP(c_List_Orev(U_19744),U_19745) = hAPP(c_List_Ofoldl(tc_List_Olist(U_19744),U_19744,hAPP(c_COMBC(U_19744,tc_List_Olist(U_19744),tc_List_Olist(U_19744)),c_List_Olist_OCons(U_19744)),c_List_Olist_ONil(U_19744)),U_19745),
    inference(clausify,[status(thm)],[f_4756_2]) ).

fof(f_4757_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_4757_2,plain,
    ! [U_19748,U_19747,U_19746] : hAPP(c_List_Orev(U_19746),hAPP(hAPP(c_List_Odrop(U_19746),U_19747),U_19748)) = hAPP(hAPP(c_List_Otake(U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19746)),U_19748)),U_19747)),hAPP(c_List_Orev(U_19746),U_19748)),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

cnf(f_4757_3,plain,
    hAPP(c_List_Orev(U_19746),hAPP(hAPP(c_List_Odrop(U_19746),U_19747),U_19748)) = hAPP(hAPP(c_List_Otake(U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19746)),U_19748)),U_19747)),hAPP(c_List_Orev(U_19746),U_19748)),
    inference(clausify,[status(thm)],[f_4757_2]) ).

fof(f_4758_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_4758_2,plain,
    ! [U_19751,U_19750,U_19749] : hAPP(c_List_Orev(U_19749),hAPP(hAPP(c_List_Otake(U_19749),U_19750),U_19751)) = hAPP(hAPP(c_List_Odrop(U_19749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19749)),U_19751)),U_19750)),hAPP(c_List_Orev(U_19749),U_19751)),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

cnf(f_4758_3,plain,
    hAPP(c_List_Orev(U_19749),hAPP(hAPP(c_List_Otake(U_19749),U_19750),U_19751)) = hAPP(hAPP(c_List_Odrop(U_19749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19749)),U_19751)),U_19750)),hAPP(c_List_Orev(U_19749),U_19751)),
    inference(clausify,[status(thm)],[f_4758_2]) ).

fof(f_4759_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_4759_2,plain,
    ! [U_19754,U_19753,U_19752] : hAPP(c_List_Orotate(U_19752,U_19753),hAPP(c_List_Orev(U_19752),U_19754)) = hAPP(c_List_Orev(U_19752),hAPP(c_List_Orotate(U_19752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19752)),U_19754)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19753,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19752)),U_19754)))),U_19754)),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

cnf(f_4759_3,plain,
    hAPP(c_List_Orotate(U_19752,U_19753),hAPP(c_List_Orev(U_19752),U_19754)) = hAPP(c_List_Orev(U_19752),hAPP(c_List_Orotate(U_19752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19752)),U_19754)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19753,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19752)),U_19754)))),U_19754)),
    inference(clausify,[status(thm)],[f_4759_2]) ).

fof(f_4760_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_4760_2,plain,
    ! [U_19757,U_19756,U_19755] :
      ( hAPP(hAPP(c_List_Onth(U_19756),hAPP(c_List_Orev(U_19756),U_19757)),U_19755) = hAPP(hAPP(c_List_Onth(U_19756),U_19757),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19756)),U_19757)),hAPP(c_Nat_OSuc,U_19755)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19755),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19756)),U_19757))) ),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

cnf(f_4760_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19756),hAPP(c_List_Orev(U_19756),U_19757)),U_19755) = hAPP(hAPP(c_List_Onth(U_19756),U_19757),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19756)),U_19757)),hAPP(c_Nat_OSuc,U_19755)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19755),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19756)),U_19757))) ),
    inference(clausify,[status(thm)],[f_4760_2]) ).

fof(f_4761_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_4761_2,plain,
    ! [U_19761,U_19760,U_19759,U_19758] :
      ( hAPP(c_List_Orev(U_19759),hAPP(hAPP(c_List_Olist__update(U_19759,U_19760),U_19758),U_19761)) = hAPP(hAPP(c_List_Olist__update(U_19759,hAPP(c_List_Orev(U_19759),U_19760)),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_19759)),U_19760)),U_19758)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19761)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19758),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19759)),U_19760))) ),
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

cnf(f_4761_3,plain,
    ( hAPP(c_List_Orev(U_19759),hAPP(hAPP(c_List_Olist__update(U_19759,U_19760),U_19758),U_19761)) = hAPP(hAPP(c_List_Olist__update(U_19759,hAPP(c_List_Orev(U_19759),U_19760)),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_19759)),U_19760)),U_19758)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19761)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19758),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19759)),U_19760))) ),
    inference(clausify,[status(thm)],[f_4761_2]) ).

fof(f_4762_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_4762_2,plain,
    ! [U_19765,U_19764,U_19763,U_19762] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19762),hAPP(hAPP(c_List_Onth(U_19762),U_19763),U_19765)),hAPP(hAPP(c_List_Onth(U_19762),U_19763),U_19764)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19765),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19762)),U_19763)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19764),U_19765))
      | ~ c_List_Olinorder__class_Osorted(U_19762,hAPP(c_List_Orev(U_19762),U_19763))
      | ~ class_Orderings_Olinorder(U_19762) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

cnf(f_4762_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19762),hAPP(hAPP(c_List_Onth(U_19762),U_19763),U_19765)),hAPP(hAPP(c_List_Onth(U_19762),U_19763),U_19764)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19765),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19762)),U_19763)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19764),U_19765))
    | ~ c_List_Olinorder__class_Osorted(U_19762,hAPP(c_List_Orev(U_19762),U_19763))
    | ~ class_Orderings_Olinorder(U_19762) ),
    inference(clausify,[status(thm)],[f_4762_2]) ).

fof(f_4763_1,plain,
    ! [V_y_2,V_xs_2,T_a] :
      ( ( ( c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2)
          | V_xs_2 = c_List_Olist_ONil(T_a) )
        & ( c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2
          | V_xs_2 != c_List_Olist_ONil(T_a) ) )
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted]) ).

fof(f_4763_2,plain,
    ! [U_19768,U_19767,U_19766] :
      ( ( ( c_List_Ofoldr(U_19766,U_19766,c_Orderings_Oord__class_Omax(U_19766),U_19767,U_19768) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_19766),hAPP(hAPP(c_List_Onth(U_19766),U_19767),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_19768)
          | U_19767 = c_List_Olist_ONil(U_19766) )
        & ( c_List_Ofoldr(U_19766,U_19766,c_Orderings_Oord__class_Omax(U_19766),U_19767,U_19768) = U_19768
          | U_19767 != c_List_Olist_ONil(U_19766) ) )
      | ~ c_List_Olinorder__class_Osorted(U_19766,hAPP(c_List_Orev(U_19766),U_19767))
      | ~ class_Orderings_Olinorder(U_19766) ),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

cnf(f_4763_3,plain,
    ( c_List_Ofoldr(U_19766,U_19766,c_Orderings_Oord__class_Omax(U_19766),U_19767,U_19768) = U_19768
    | U_19767 != c_List_Olist_ONil(U_19766)
    | ~ c_List_Olinorder__class_Osorted(U_19766,hAPP(c_List_Orev(U_19766),U_19767))
    | ~ class_Orderings_Olinorder(U_19766) ),
    inference(clausify,[status(thm)],[f_4763_2]) ).

cnf(f_4763_4,plain,
    ( c_List_Ofoldr(U_19766,U_19766,c_Orderings_Oord__class_Omax(U_19766),U_19767,U_19768) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_19766),hAPP(hAPP(c_List_Onth(U_19766),U_19767),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_19768)
    | U_19767 = c_List_Olist_ONil(U_19766)
    | ~ c_List_Olinorder__class_Osorted(U_19766,hAPP(c_List_Orev(U_19766),U_19767))
    | ~ class_Orderings_Olinorder(U_19766) ),
    inference(clausify,[status(thm)],[f_4763_2]) ).

fof(f_4764_1,plain,
    ! [V_xs_2,T_a] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted]) ).

fof(f_4764_2,plain,
    ! [U_19770,U_19769] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19769))),c_List_Otranspose(U_19769,U_19770)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19769)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19769)),U_19770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_19770 = c_List_Olist_ONil(tc_List_Olist(U_19769)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19769))),c_List_Otranspose(U_19769,U_19770)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_19770 != c_List_Olist_ONil(tc_List_Olist(U_19769)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19769),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19769))),U_19770))) ),
    inference(variable_rename,[status(thm)],[f_4764_1]) ).

cnf(f_4764_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19769))),c_List_Otranspose(U_19769,U_19770)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_19770 != c_List_Olist_ONil(tc_List_Olist(U_19769))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19769),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19769))),U_19770))) ),
    inference(clausify,[status(thm)],[f_4764_2]) ).

cnf(f_4764_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19769))),c_List_Otranspose(U_19769,U_19770)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19769)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19769)),U_19770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_19770 = c_List_Olist_ONil(tc_List_Olist(U_19769))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19769),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19769))),U_19770))) ),
    inference(clausify,[status(thm)],[f_4764_2]) ).

fof(f_4765_1,plain,
    ! [V_i_2,V_xs_2,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),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_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column__length]) ).

fof(f_4765_2,plain,
    ! [U_19773,U_19772,U_19771] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19771))),hAPP(c_List_Ofilter(tc_List_Olist(U_19771),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19771)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19773)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19771)))),c_List_Otranspose(U_19771,U_19772))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19771)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19771)),U_19772),U_19773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19773),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19771))),U_19772)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19771),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19771))),U_19772))) ),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

cnf(f_4765_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19771))),hAPP(c_List_Ofilter(tc_List_Olist(U_19771),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_19771)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19773)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19771)))),c_List_Otranspose(U_19771,U_19772))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19771)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_19771)),U_19772),U_19773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19773),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19771))),U_19772)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19771),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19771))),U_19772))) ),
    inference(clausify,[status(thm)],[f_4765_2]) ).

fof(f_4766_1,plain,
    ! [V_xs_2,T_a] :
      ( c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),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_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__transpose]) ).

fof(f_4766_2,plain,
    ! [U_19775,U_19774] :
      ( c_List_Otranspose(U_19774,c_List_Otranspose(U_19774,U_19775)) = c_List_OtakeWhile(tc_List_Olist(U_19774),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19774)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19774),tc_List_Olist(U_19774),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19774))),U_19775)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19774),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19774))),U_19775))) ),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

cnf(f_4766_3,plain,
    ( c_List_Otranspose(U_19774,c_List_Otranspose(U_19774,U_19775)) = c_List_OtakeWhile(tc_List_Olist(U_19774),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19774)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19774),tc_List_Olist(U_19774),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19774))),U_19775)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_19774),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_19774))),U_19775))) ),
    inference(clausify,[status(thm)],[f_4766_2]) ).

fof(f_4767_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]) ).

cnf(f_4767_2,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_4767_1]) ).

fof(f_4768_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile]) ).

fof(f_4768_2,plain,
    ! [U_19778,U_19777,U_19776] :
      ( c_List_Olinorder__class_Osorted(U_19776,c_List_OtakeWhile(U_19776,U_19778,U_19777))
      | ~ c_List_Olinorder__class_Osorted(U_19776,U_19777)
      | ~ class_Orderings_Olinorder(U_19776) ),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

cnf(f_4768_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19776,c_List_OtakeWhile(U_19776,U_19778,U_19777))
    | ~ c_List_Olinorder__class_Osorted(U_19776,U_19777)
    | ~ class_Orderings_Olinorder(U_19776) ),
    inference(clausify,[status(thm)],[f_4768_2]) ).

fof(f_4769_1,plain,
    ! [V_xs_2,V_P_2,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_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__le]) ).

fof(f_4769_2,plain,
    ! [U_19781,U_19780,U_19779] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19779)),c_List_OtakeWhile(U_19779,U_19780,U_19781))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19779)),U_19781))),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

cnf(f_4769_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19779)),c_List_OtakeWhile(U_19779,U_19780,U_19781))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19779)),U_19781))),
    inference(clausify,[status(thm)],[f_4769_2]) ).

fof(f_4770_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | c_List_OtakeWhile(T_a,V_P_2,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv]) ).

fof(f_4770_2,plain,
    ! [U_19786,U_19785,U_19784] :
      ( ( c_List_OtakeWhile(U_19784,U_19785,U_19786) = U_19786
        | ? [U_19783] :
            ( ~ hBOOL(hAPP(U_19785,U_19783))
            & hBOOL(hAPP(hAPP(c_member(U_19784),U_19783),hAPP(c_List_Oset(U_19784),U_19786))) ) )
      & ( ! [U_19782] :
            ( hBOOL(hAPP(U_19785,U_19782))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19784),U_19782),hAPP(c_List_Oset(U_19784),U_19786))) )
        | c_List_OtakeWhile(U_19784,U_19785,U_19786) != U_19786 ) ),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

fof(f_4770_3,plain,
    ( ! [U_19792,U_19790,U_19788] :
        ( c_List_OtakeWhile(U_19788,U_19790,U_19792) = U_19792
        | ? [U_19783] :
            ( ~ hBOOL(hAPP(U_19790,U_19783))
            & hBOOL(hAPP(hAPP(c_member(U_19788),U_19783),hAPP(c_List_Oset(U_19788),U_19792))) ) )
    & ! [U_19791,U_19789,U_19787] :
        ( ! [U_19782] :
            ( hBOOL(hAPP(U_19789,U_19782))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19787),U_19782),hAPP(c_List_Oset(U_19787),U_19791))) )
        | c_List_OtakeWhile(U_19787,U_19789,U_19791) != U_19791 ) ),
    inference(miniscope,[status(thm)],[f_4770_2]) ).

fof(f_4770_4,plain,
    ( ! [U_19792,U_19790,U_19788] :
        ( c_List_OtakeWhile(U_19788,U_19790,U_19792) = U_19792
        | ( ~ hBOOL(hAPP(U_19790,sK492(U_19792,U_19790,U_19788)))
          & hBOOL(hAPP(hAPP(c_member(U_19788),sK492(U_19792,U_19790,U_19788)),hAPP(c_List_Oset(U_19788),U_19792))) ) )
    & ! [U_19791,U_19789,U_19787] :
        ( ! [U_19782] :
            ( hBOOL(hAPP(U_19789,U_19782))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19787),U_19782),hAPP(c_List_Oset(U_19787),U_19791))) )
        | c_List_OtakeWhile(U_19787,U_19789,U_19791) != U_19791 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_19783,sK492(U_19792,U_19790,U_19788))],[f_4770_3]) ).

cnf(f_4770_5,plain,
    ( hBOOL(hAPP(U_19789,U_19782))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19787),U_19782),hAPP(c_List_Oset(U_19787),U_19791)))
    | c_List_OtakeWhile(U_19787,U_19789,U_19791) != U_19791 ),
    inference(clausify,[status(thm)],[f_4770_4]) ).

cnf(f_4770_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19788),sK492(U_19792,U_19790,U_19788)),hAPP(c_List_Oset(U_19788),U_19792)))
    | c_List_OtakeWhile(U_19788,U_19790,U_19792) = U_19792 ),
    inference(clausify,[status(thm)],[f_4770_4]) ).

cnf(f_4770_7,plain,
    ( ~ hBOOL(hAPP(U_19790,sK492(U_19792,U_19790,U_19788)))
    | c_List_OtakeWhile(U_19788,U_19790,U_19792) = U_19792 ),
    inference(clausify,[status(thm)],[f_4770_4]) ).

fof(f_4771_1,plain,
    ! [V_xs_2,V_P_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__takeWhileD]) ).

fof(f_4771_2,plain,
    ! [U_19796,U_19795,U_19794,U_19793] :
      ( ( hBOOL(hAPP(U_19795,U_19794))
        & hBOOL(hAPP(hAPP(c_member(U_19793),U_19794),hAPP(c_List_Oset(U_19793),U_19796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_19793),U_19794),hAPP(c_List_Oset(U_19793),c_List_OtakeWhile(U_19793,U_19795,U_19796)))) ),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

cnf(f_4771_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19793),U_19794),hAPP(c_List_Oset(U_19793),U_19796)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19793),U_19794),hAPP(c_List_Oset(U_19793),c_List_OtakeWhile(U_19793,U_19795,U_19796)))) ),
    inference(clausify,[status(thm)],[f_4771_2]) ).

cnf(f_4771_4,plain,
    ( hBOOL(hAPP(U_19795,U_19794))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19793),U_19794),hAPP(c_List_Oset(U_19793),c_List_OtakeWhile(U_19793,U_19795,U_19796)))) ),
    inference(clausify,[status(thm)],[f_4771_2]) ).

fof(f_4772_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__fst]) ).

fof(f_4772_2,plain,
    ! [U_19801,U_19800,U_19799,U_19798,U_19797] : hAPP(hAPP(c_List_Ozip(U_19797,U_19798),c_List_OtakeWhile(U_19797,U_19799,U_19800)),U_19801) = c_List_OtakeWhile(tc_prod(U_19797,U_19798),hAPP(c_Fun_Ocomp(U_19797,tc_HOL_Obool,tc_prod(U_19797,U_19798),U_19799),c_Product__Type_Ofst(U_19797,U_19798)),hAPP(hAPP(c_List_Ozip(U_19797,U_19798),U_19800),U_19801)),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

cnf(f_4772_3,plain,
    hAPP(hAPP(c_List_Ozip(U_19797,U_19798),c_List_OtakeWhile(U_19797,U_19799,U_19800)),U_19801) = c_List_OtakeWhile(tc_prod(U_19797,U_19798),hAPP(c_Fun_Ocomp(U_19797,tc_HOL_Obool,tc_prod(U_19797,U_19798),U_19799),c_Product__Type_Ofst(U_19797,U_19798)),hAPP(hAPP(c_List_Ozip(U_19797,U_19798),U_19800),U_19801)),
    inference(clausify,[status(thm)],[f_4772_2]) ).

fof(f_4773_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__snd]) ).

fof(f_4773_2,plain,
    ! [U_19806,U_19805,U_19804,U_19803,U_19802] : hAPP(hAPP(c_List_Ozip(U_19802,U_19803),U_19804),c_List_OtakeWhile(U_19803,U_19805,U_19806)) = c_List_OtakeWhile(tc_prod(U_19802,U_19803),hAPP(c_Fun_Ocomp(U_19803,tc_HOL_Obool,tc_prod(U_19802,U_19803),U_19805),c_Product__Type_Osnd(U_19802,U_19803)),hAPP(hAPP(c_List_Ozip(U_19802,U_19803),U_19804),U_19806)),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

cnf(f_4773_3,plain,
    hAPP(hAPP(c_List_Ozip(U_19802,U_19803),U_19804),c_List_OtakeWhile(U_19803,U_19805,U_19806)) = c_List_OtakeWhile(tc_prod(U_19802,U_19803),hAPP(c_Fun_Ocomp(U_19803,tc_HOL_Obool,tc_prod(U_19802,U_19803),U_19805),c_Product__Type_Osnd(U_19802,U_19803)),hAPP(hAPP(c_List_Ozip(U_19802,U_19803),U_19804),U_19806)),
    inference(clausify,[status(thm)],[f_4773_2]) ).

fof(f_4774_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__map]) ).

fof(f_4774_2,plain,
    ! [U_19811,U_19810,U_19809,U_19808,U_19807] : c_List_OtakeWhile(U_19807,U_19808,hAPP(hAPP(c_List_Omap(U_19809,U_19807),U_19810),U_19811)) = hAPP(hAPP(c_List_Omap(U_19809,U_19807),U_19810),c_List_OtakeWhile(U_19809,hAPP(c_Fun_Ocomp(U_19807,tc_HOL_Obool,U_19809,U_19808),U_19810),U_19811)),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

cnf(f_4774_3,plain,
    c_List_OtakeWhile(U_19807,U_19808,hAPP(hAPP(c_List_Omap(U_19809,U_19807),U_19810),U_19811)) = hAPP(hAPP(c_List_Omap(U_19809,U_19807),U_19810),c_List_OtakeWhile(U_19809,hAPP(c_Fun_Ocomp(U_19807,tc_HOL_Obool,U_19809,U_19808),U_19810),U_19811)),
    inference(clausify,[status(thm)],[f_4774_2]) ).

fof(f_4775_1,plain,
    ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
      ( c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__tail]) ).

fof(f_4775_2,plain,
    ! [U_19816,U_19815,U_19814,U_19813,U_19812] :
      ( c_List_OtakeWhile(U_19814,U_19812,hAPP(hAPP(c_List_Oappend(U_19814),U_19815),hAPP(hAPP(c_List_Olist_OCons(U_19814),U_19813),U_19816))) = c_List_OtakeWhile(U_19814,U_19812,U_19815)
      | hBOOL(hAPP(U_19812,U_19813)) ),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

cnf(f_4775_3,plain,
    ( c_List_OtakeWhile(U_19814,U_19812,hAPP(hAPP(c_List_Oappend(U_19814),U_19815),hAPP(hAPP(c_List_Olist_OCons(U_19814),U_19813),U_19816))) = c_List_OtakeWhile(U_19814,U_19812,U_19815)
    | hBOOL(hAPP(U_19812,U_19813)) ),
    inference(clausify,[status(thm)],[f_4775_2]) ).

fof(f_4776_1,plain,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(f_4776_2,plain,
    ! [U_19820,U_19819,U_19818,U_19817] :
      ( ( c_List_OtakeWhile(U_19819,U_19817,hAPP(hAPP(c_List_Olist_OCons(U_19819),U_19818),U_19820)) = c_List_Olist_ONil(U_19819)
        | hBOOL(hAPP(U_19817,U_19818)) )
      & ( c_List_OtakeWhile(U_19819,U_19817,hAPP(hAPP(c_List_Olist_OCons(U_19819),U_19818),U_19820)) = hAPP(hAPP(c_List_Olist_OCons(U_19819),U_19818),c_List_OtakeWhile(U_19819,U_19817,U_19820))
        | ~ hBOOL(hAPP(U_19817,U_19818)) ) ),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

fof(f_4776_3,plain,
    ( ! [U_19828,U_19826,U_19824,U_19822] :
        ( c_List_OtakeWhile(U_19826,U_19822,hAPP(hAPP(c_List_Olist_OCons(U_19826),U_19824),U_19828)) = c_List_Olist_ONil(U_19826)
        | hBOOL(hAPP(U_19822,U_19824)) )
    & ! [U_19827,U_19825,U_19823,U_19821] :
        ( c_List_OtakeWhile(U_19825,U_19821,hAPP(hAPP(c_List_Olist_OCons(U_19825),U_19823),U_19827)) = hAPP(hAPP(c_List_Olist_OCons(U_19825),U_19823),c_List_OtakeWhile(U_19825,U_19821,U_19827))
        | ~ hBOOL(hAPP(U_19821,U_19823)) ) ),
    inference(miniscope,[status(thm)],[f_4776_2]) ).

cnf(f_4776_4,plain,
    ( c_List_OtakeWhile(U_19825,U_19821,hAPP(hAPP(c_List_Olist_OCons(U_19825),U_19823),U_19827)) = hAPP(hAPP(c_List_Olist_OCons(U_19825),U_19823),c_List_OtakeWhile(U_19825,U_19821,U_19827))
    | ~ hBOOL(hAPP(U_19821,U_19823)) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

cnf(f_4776_5,plain,
    ( c_List_OtakeWhile(U_19826,U_19822,hAPP(hAPP(c_List_Olist_OCons(U_19826),U_19824),U_19828)) = c_List_Olist_ONil(U_19826)
    | hBOOL(hAPP(U_19822,U_19824)) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

fof(f_4777_1,plain,
    ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(f_4777_2,plain,
    ! [U_19830,U_19829] : c_List_OtakeWhile(U_19829,U_19830,c_List_Olist_ONil(U_19829)) = c_List_Olist_ONil(U_19829),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

cnf(f_4777_3,plain,
    c_List_OtakeWhile(U_19829,U_19830,c_List_Olist_ONil(U_19829)) = c_List_Olist_ONil(U_19829),
    inference(clausify,[status(thm)],[f_4777_2]) ).

fof(f_4778_1,plain,
    ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(f_4778_2,plain,
    ! [U_19833,U_19832,U_19831] : c_List_OtakeWhile(U_19831,U_19832,U_19833) = hAPP(hAPP(c_List_Otake(U_19831),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19831)),c_List_OtakeWhile(U_19831,U_19832,U_19833))),U_19833),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

cnf(f_4778_3,plain,
    c_List_OtakeWhile(U_19831,U_19832,U_19833) = hAPP(hAPP(c_List_Otake(U_19831),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19831)),c_List_OtakeWhile(U_19831,U_19832,U_19833))),U_19833),
    inference(clausify,[status(thm)],[f_4778_2]) ).

fof(f_4779_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile]) ).

fof(f_4779_2,plain,
    ! [U_19836,U_19835,U_19834] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19834),c_List_OtakeWhile(U_19834,U_19836,U_19835)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19834),U_19835)) ),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

cnf(f_4779_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19834),c_List_OtakeWhile(U_19834,U_19836,U_19835)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19834),U_19835)) ),
    inference(clausify,[status(thm)],[f_4779_2]) ).

fof(f_4780_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_4780_2,plain,
    ! [U_19837] : c_List_Oreturn__list(U_19837) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_19837),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

cnf(f_4780_3,plain,
    c_List_Oreturn__list(U_19837) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_19837),
    inference(clausify,[status(thm)],[f_4780_2]) ).

fof(f_4781_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append1]) ).

fof(f_4781_2,plain,
    ! [U_19842,U_19841,U_19840,U_19839,U_19838] :
      ( c_List_OtakeWhile(U_19838,U_19841,hAPP(hAPP(c_List_Oappend(U_19838),U_19840),U_19842)) = c_List_OtakeWhile(U_19838,U_19841,U_19840)
      | hBOOL(hAPP(U_19841,U_19839))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19838),U_19839),hAPP(c_List_Oset(U_19838),U_19840))) ),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

cnf(f_4781_3,plain,
    ( c_List_OtakeWhile(U_19838,U_19841,hAPP(hAPP(c_List_Oappend(U_19838),U_19840),U_19842)) = c_List_OtakeWhile(U_19838,U_19841,U_19840)
    | hBOOL(hAPP(U_19841,U_19839))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19838),U_19839),hAPP(c_List_Oset(U_19838),U_19840))) ),
    inference(clausify,[status(thm)],[f_4781_2]) ).

fof(f_4782_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(f_4782_2,plain,
    ! [U_19845,U_19844,U_19843] :
      ( ~ hBOOL(hAPP(U_19844,hAPP(hAPP(c_List_Onth(U_19843),U_19845),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),c_List_OtakeWhile(U_19843,U_19844,U_19845)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),c_List_OtakeWhile(U_19843,U_19844,U_19845))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),U_19845))) ),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

cnf(f_4782_3,plain,
    ( ~ hBOOL(hAPP(U_19844,hAPP(hAPP(c_List_Onth(U_19843),U_19845),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),c_List_OtakeWhile(U_19843,U_19844,U_19845)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),c_List_OtakeWhile(U_19843,U_19844,U_19845))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19843)),U_19845))) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

fof(f_4783_1,plain,
    ! [V_xs_2,V_P_2,T_a,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__nth]) ).

fof(f_4783_2,plain,
    ! [U_19849,U_19848,U_19847,U_19846] :
      ( hAPP(hAPP(c_List_Onth(U_19847),c_List_OtakeWhile(U_19847,U_19848,U_19849)),U_19846) = hAPP(hAPP(c_List_Onth(U_19847),U_19849),U_19846)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19846),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19847)),c_List_OtakeWhile(U_19847,U_19848,U_19849)))) ),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

cnf(f_4783_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19847),c_List_OtakeWhile(U_19847,U_19848,U_19849)),U_19846) = hAPP(hAPP(c_List_Onth(U_19847),U_19849),U_19846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19846),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19847)),c_List_OtakeWhile(U_19847,U_19848,U_19849)))) ),
    inference(clausify,[status(thm)],[f_4783_2]) ).

fof(f_4784_1,plain,
    ! [T_a,V_xs_2] :
      ( c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last]) ).

fof(f_4784_2,plain,
    ! [U_19851,U_19850] :
      ( c_List_OtakeWhile(U_19851,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19851),c_fNot),hAPP(hAPP(c_COMBC(U_19851,U_19851,tc_HOL_Obool),c_fequal),c_List_Olast(U_19851,U_19850))),U_19850) = c_List_Obutlast(U_19851,U_19850)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19851),U_19850))
      | U_19850 = c_List_Olist_ONil(U_19851) ),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

cnf(f_4784_3,plain,
    ( c_List_OtakeWhile(U_19851,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19851),c_fNot),hAPP(hAPP(c_COMBC(U_19851,U_19851,tc_HOL_Obool),c_fequal),c_List_Olast(U_19851,U_19850))),U_19850) = c_List_Obutlast(U_19851,U_19850)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19851),U_19850))
    | U_19850 = c_List_Olist_ONil(U_19851) ),
    inference(clausify,[status(thm)],[f_4784_2]) ).

fof(f_4785_1,plain,
    ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
      ( hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev]) ).

fof(f_4785_2,plain,
    ! [U_19856,U_19855,U_19854,U_19853,U_19852] :
      ( hAPP(c_List_Ofilter(U_19853,hAPP(hAPP(c_COMBB(U_19852,tc_HOL_Obool,U_19853),hAPP(c_Orderings_Oord__class_Oless(U_19852),U_19856)),U_19854)),U_19855) = c_List_OtakeWhile(U_19853,hAPP(hAPP(c_COMBB(U_19852,tc_HOL_Obool,U_19853),hAPP(c_Orderings_Oord__class_Oless(U_19852),U_19856)),U_19854),U_19855)
      | ~ c_List_Olinorder__class_Osorted(U_19852,hAPP(c_List_Orev(U_19852),hAPP(hAPP(c_List_Omap(U_19853,U_19852),U_19854),U_19855)))
      | ~ class_Orderings_Olinorder(U_19852) ),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

cnf(f_4785_3,plain,
    ( hAPP(c_List_Ofilter(U_19853,hAPP(hAPP(c_COMBB(U_19852,tc_HOL_Obool,U_19853),hAPP(c_Orderings_Oord__class_Oless(U_19852),U_19856)),U_19854)),U_19855) = c_List_OtakeWhile(U_19853,hAPP(hAPP(c_COMBB(U_19852,tc_HOL_Obool,U_19853),hAPP(c_Orderings_Oord__class_Oless(U_19852),U_19856)),U_19854),U_19855)
    | ~ c_List_Olinorder__class_Osorted(U_19852,hAPP(c_List_Orev(U_19852),hAPP(hAPP(c_List_Omap(U_19853,U_19852),U_19854),U_19855)))
    | ~ class_Orderings_Olinorder(U_19852) ),
    inference(clausify,[status(thm)],[f_4785_2]) ).

fof(f_4786_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_4786_2,plain,
    ! [U_19857] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_19857)) = U_19857
      | ~ c_List_Onat__list(U_19857) ),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

cnf(f_4786_3,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(U_19857)) = U_19857
    | ~ c_List_Onat__list(U_19857) ),
    inference(clausify,[status(thm)],[f_4786_2]) ).

fof(f_4787_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_4787_2,plain,
    ! [U_19859,U_19858] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_19858),U_19859) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_19858)),c_List_Oembed__list(U_19859))),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

cnf(f_4787_3,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_19858),U_19859) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_19858)),c_List_Oembed__list(U_19859))),
    inference(clausify,[status(thm)],[f_4787_2]) ).

fof(f_4788_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_4788_2,plain,
    ! [U_19860] : c_List_Oembed__list(U_19860) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_19860),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

cnf(f_4788_3,plain,
    c_List_Oembed__list(U_19860) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_19860),
    inference(clausify,[status(thm)],[f_4788_2]) ).

fof(f_4789_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev]) ).

fof(f_4789_2,plain,
    ! [U_19863,U_19862,U_19861] :
      ( c_List_OtakeWhile(U_19861,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19861),c_fNot),hAPP(hAPP(c_COMBC(U_19861,U_19861,tc_HOL_Obool),c_fequal),U_19863)),hAPP(c_List_Orev(U_19861),U_19862)) = hAPP(c_List_Orev(U_19861),hAPP(c_List_Otl(U_19861),c_List_OdropWhile(U_19861,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19861),c_fNot),hAPP(hAPP(c_COMBC(U_19861,U_19861,tc_HOL_Obool),c_fequal),U_19863)),U_19862)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19861),U_19863),hAPP(c_List_Oset(U_19861),U_19862)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19861),U_19862)) ),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

cnf(f_4789_3,plain,
    ( c_List_OtakeWhile(U_19861,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19861),c_fNot),hAPP(hAPP(c_COMBC(U_19861,U_19861,tc_HOL_Obool),c_fequal),U_19863)),hAPP(c_List_Orev(U_19861),U_19862)) = hAPP(c_List_Orev(U_19861),hAPP(c_List_Otl(U_19861),c_List_OdropWhile(U_19861,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19861),c_fNot),hAPP(hAPP(c_COMBC(U_19861,U_19861,tc_HOL_Obool),c_fequal),U_19863)),U_19862)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19861),U_19863),hAPP(c_List_Oset(U_19861),U_19862)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19861),U_19862)) ),
    inference(clausify,[status(thm)],[f_4789_2]) ).

fof(f_4790_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev]) ).

fof(f_4790_2,plain,
    ! [U_19866,U_19865,U_19864] :
      ( c_List_OdropWhile(U_19864,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19864),c_fNot),hAPP(hAPP(c_COMBC(U_19864,U_19864,tc_HOL_Obool),c_fequal),U_19866)),hAPP(c_List_Orev(U_19864),U_19865)) = hAPP(hAPP(c_List_Olist_OCons(U_19864),U_19866),hAPP(c_List_Orev(U_19864),c_List_OtakeWhile(U_19864,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19864),c_fNot),hAPP(hAPP(c_COMBC(U_19864,U_19864,tc_HOL_Obool),c_fequal),U_19866)),U_19865)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19864),U_19866),hAPP(c_List_Oset(U_19864),U_19865)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19864),U_19865)) ),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

cnf(f_4790_3,plain,
    ( c_List_OdropWhile(U_19864,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19864),c_fNot),hAPP(hAPP(c_COMBC(U_19864,U_19864,tc_HOL_Obool),c_fequal),U_19866)),hAPP(c_List_Orev(U_19864),U_19865)) = hAPP(hAPP(c_List_Olist_OCons(U_19864),U_19866),hAPP(c_List_Orev(U_19864),c_List_OtakeWhile(U_19864,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19864),c_fNot),hAPP(hAPP(c_COMBC(U_19864,U_19864,tc_HOL_Obool),c_fequal),U_19866)),U_19865)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19864),U_19866),hAPP(c_List_Oset(U_19864),U_19865)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19864),U_19865)) ),
    inference(clausify,[status(thm)],[f_4790_2]) ).

fof(f_4791_1,plain,
    ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(f_4791_2,plain,
    ! [U_19869,U_19868,U_19867] : hAPP(hAPP(c_List_Oappend(U_19867),c_List_OtakeWhile(U_19867,U_19868,U_19869)),c_List_OdropWhile(U_19867,U_19868,U_19869)) = U_19869,
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

cnf(f_4791_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19867),c_List_OtakeWhile(U_19867,U_19868,U_19869)),c_List_OdropWhile(U_19867,U_19868,U_19869)) = U_19869,
    inference(clausify,[status(thm)],[f_4791_2]) ).

fof(f_4792_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__map]) ).

fof(f_4792_2,plain,
    ! [U_19874,U_19873,U_19872,U_19871,U_19870] : c_List_OdropWhile(U_19870,U_19871,hAPP(hAPP(c_List_Omap(U_19872,U_19870),U_19873),U_19874)) = hAPP(hAPP(c_List_Omap(U_19872,U_19870),U_19873),c_List_OdropWhile(U_19872,hAPP(c_Fun_Ocomp(U_19870,tc_HOL_Obool,U_19872,U_19871),U_19873),U_19874)),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

cnf(f_4792_3,plain,
    c_List_OdropWhile(U_19870,U_19871,hAPP(hAPP(c_List_Omap(U_19872,U_19870),U_19873),U_19874)) = hAPP(hAPP(c_List_Omap(U_19872,U_19870),U_19873),c_List_OdropWhile(U_19872,hAPP(c_Fun_Ocomp(U_19870,tc_HOL_Obool,U_19872,U_19871),U_19873),U_19874)),
    inference(clausify,[status(thm)],[f_4792_2]) ).

fof(f_4793_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile]) ).

fof(f_4793_2,plain,
    ! [U_19877,U_19876,U_19875] :
      ( c_List_Olinorder__class_Osorted(U_19875,c_List_OdropWhile(U_19875,U_19877,U_19876))
      | ~ c_List_Olinorder__class_Osorted(U_19875,U_19876)
      | ~ class_Orderings_Olinorder(U_19875) ),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

cnf(f_4793_3,plain,
    ( c_List_Olinorder__class_Osorted(U_19875,c_List_OdropWhile(U_19875,U_19877,U_19876))
    | ~ c_List_Olinorder__class_Osorted(U_19875,U_19876)
    | ~ class_Orderings_Olinorder(U_19875) ),
    inference(clausify,[status(thm)],[f_4793_2]) ).

fof(f_4794_1,plain,
    ! [V_xs_2,V_P_2,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_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__dropWhile__le]) ).

fof(f_4794_2,plain,
    ! [U_19880,U_19879,U_19878] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19878)),c_List_OdropWhile(U_19878,U_19879,U_19880))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19878)),U_19880))),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

cnf(f_4794_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19878)),c_List_OdropWhile(U_19878,U_19879,U_19880))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19878)),U_19880))),
    inference(clausify,[status(thm)],[f_4794_2]) ).

fof(f_4795_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Nil__conv]) ).

fof(f_4795_2,plain,
    ! [U_19885,U_19884,U_19883] :
      ( ( c_List_OdropWhile(U_19883,U_19884,U_19885) = c_List_Olist_ONil(U_19883)
        | ? [U_19882] :
            ( ~ hBOOL(hAPP(U_19884,U_19882))
            & hBOOL(hAPP(hAPP(c_member(U_19883),U_19882),hAPP(c_List_Oset(U_19883),U_19885))) ) )
      & ( ! [U_19881] :
            ( hBOOL(hAPP(U_19884,U_19881))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19883),U_19881),hAPP(c_List_Oset(U_19883),U_19885))) )
        | c_List_OdropWhile(U_19883,U_19884,U_19885) != c_List_Olist_ONil(U_19883) ) ),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

fof(f_4795_3,plain,
    ( ! [U_19891,U_19889,U_19887] :
        ( c_List_OdropWhile(U_19887,U_19889,U_19891) = c_List_Olist_ONil(U_19887)
        | ? [U_19882] :
            ( ~ hBOOL(hAPP(U_19889,U_19882))
            & hBOOL(hAPP(hAPP(c_member(U_19887),U_19882),hAPP(c_List_Oset(U_19887),U_19891))) ) )
    & ! [U_19890,U_19888,U_19886] :
        ( ! [U_19881] :
            ( hBOOL(hAPP(U_19888,U_19881))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19886),U_19881),hAPP(c_List_Oset(U_19886),U_19890))) )
        | c_List_OdropWhile(U_19886,U_19888,U_19890) != c_List_Olist_ONil(U_19886) ) ),
    inference(miniscope,[status(thm)],[f_4795_2]) ).

fof(f_4795_4,plain,
    ( ! [U_19891,U_19889,U_19887] :
        ( c_List_OdropWhile(U_19887,U_19889,U_19891) = c_List_Olist_ONil(U_19887)
        | ( ~ hBOOL(hAPP(U_19889,sK493(U_19891,U_19889,U_19887)))
          & hBOOL(hAPP(hAPP(c_member(U_19887),sK493(U_19891,U_19889,U_19887)),hAPP(c_List_Oset(U_19887),U_19891))) ) )
    & ! [U_19890,U_19888,U_19886] :
        ( ! [U_19881] :
            ( hBOOL(hAPP(U_19888,U_19881))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19886),U_19881),hAPP(c_List_Oset(U_19886),U_19890))) )
        | c_List_OdropWhile(U_19886,U_19888,U_19890) != c_List_Olist_ONil(U_19886) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_19882,sK493(U_19891,U_19889,U_19887))],[f_4795_3]) ).

cnf(f_4795_5,plain,
    ( hBOOL(hAPP(U_19888,U_19881))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19886),U_19881),hAPP(c_List_Oset(U_19886),U_19890)))
    | c_List_OdropWhile(U_19886,U_19888,U_19890) != c_List_Olist_ONil(U_19886) ),
    inference(clausify,[status(thm)],[f_4795_4]) ).

cnf(f_4795_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19887),sK493(U_19891,U_19889,U_19887)),hAPP(c_List_Oset(U_19887),U_19891)))
    | c_List_OdropWhile(U_19887,U_19889,U_19891) = c_List_Olist_ONil(U_19887) ),
    inference(clausify,[status(thm)],[f_4795_4]) ).

cnf(f_4795_7,plain,
    ( ~ hBOOL(hAPP(U_19889,sK493(U_19891,U_19889,U_19887)))
    | c_List_OdropWhile(U_19887,U_19889,U_19891) = c_List_Olist_ONil(U_19887) ),
    inference(clausify,[status(thm)],[f_4795_4]) ).

fof(f_4796_1,plain,
    ! [V_xs_2,T_a,V_x_2,V_P_2] :
      ( ( c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(f_4796_2,plain,
    ! [U_19895,U_19894,U_19893,U_19892] :
      ( ( c_List_OdropWhile(U_19894,U_19892,hAPP(hAPP(c_List_Olist_OCons(U_19894),U_19893),U_19895)) = hAPP(hAPP(c_List_Olist_OCons(U_19894),U_19893),U_19895)
        | hBOOL(hAPP(U_19892,U_19893)) )
      & ( c_List_OdropWhile(U_19894,U_19892,hAPP(hAPP(c_List_Olist_OCons(U_19894),U_19893),U_19895)) = c_List_OdropWhile(U_19894,U_19892,U_19895)
        | ~ hBOOL(hAPP(U_19892,U_19893)) ) ),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

fof(f_4796_3,plain,
    ( ! [U_19903,U_19901,U_19899,U_19897] :
        ( c_List_OdropWhile(U_19901,U_19897,hAPP(hAPP(c_List_Olist_OCons(U_19901),U_19899),U_19903)) = hAPP(hAPP(c_List_Olist_OCons(U_19901),U_19899),U_19903)
        | hBOOL(hAPP(U_19897,U_19899)) )
    & ! [U_19902,U_19900,U_19898,U_19896] :
        ( c_List_OdropWhile(U_19900,U_19896,hAPP(hAPP(c_List_Olist_OCons(U_19900),U_19898),U_19902)) = c_List_OdropWhile(U_19900,U_19896,U_19902)
        | ~ hBOOL(hAPP(U_19896,U_19898)) ) ),
    inference(miniscope,[status(thm)],[f_4796_2]) ).

cnf(f_4796_4,plain,
    ( c_List_OdropWhile(U_19900,U_19896,hAPP(hAPP(c_List_Olist_OCons(U_19900),U_19898),U_19902)) = c_List_OdropWhile(U_19900,U_19896,U_19902)
    | ~ hBOOL(hAPP(U_19896,U_19898)) ),
    inference(clausify,[status(thm)],[f_4796_3]) ).

cnf(f_4796_5,plain,
    ( c_List_OdropWhile(U_19901,U_19897,hAPP(hAPP(c_List_Olist_OCons(U_19901),U_19899),U_19903)) = hAPP(hAPP(c_List_Olist_OCons(U_19901),U_19899),U_19903)
    | hBOOL(hAPP(U_19897,U_19899)) ),
    inference(clausify,[status(thm)],[f_4796_3]) ).

fof(f_4797_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
      | c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__dropWhile]) ).

fof(f_4797_2,plain,
    ! [U_19906,U_19905,U_19904] :
      ( ~ hBOOL(hAPP(U_19905,hAPP(c_List_Ohd(U_19904),c_List_OdropWhile(U_19904,U_19905,U_19906))))
      | c_List_OdropWhile(U_19904,U_19905,U_19906) = c_List_Olist_ONil(U_19904) ),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

cnf(f_4797_3,plain,
    ( ~ hBOOL(hAPP(U_19905,hAPP(c_List_Ohd(U_19904),c_List_OdropWhile(U_19904,U_19905,U_19906))))
    | c_List_OdropWhile(U_19904,U_19905,U_19906) = c_List_Olist_ONil(U_19904) ),
    inference(clausify,[status(thm)],[f_4797_2]) ).

fof(f_4798_1,plain,
    ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(f_4798_2,plain,
    ! [U_19908,U_19907] : c_List_OdropWhile(U_19907,U_19908,c_List_Olist_ONil(U_19907)) = c_List_Olist_ONil(U_19907),
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

cnf(f_4798_3,plain,
    c_List_OdropWhile(U_19907,U_19908,c_List_Olist_ONil(U_19907)) = c_List_Olist_ONil(U_19907),
    inference(clausify,[status(thm)],[f_4798_2]) ).

fof(f_4799_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile]) ).

fof(f_4799_2,plain,
    ! [U_19911,U_19910,U_19909] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19909),c_List_OdropWhile(U_19909,U_19911,U_19910)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19909),U_19910)) ),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

cnf(f_4799_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19909),c_List_OdropWhile(U_19909,U_19911,U_19910)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19909),U_19910)) ),
    inference(clausify,[status(thm)],[f_4799_2]) ).

fof(f_4800_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__append1]) ).

fof(f_4800_2,plain,
    ! [U_19916,U_19915,U_19914,U_19913,U_19912] :
      ( c_List_OdropWhile(U_19912,U_19915,hAPP(hAPP(c_List_Oappend(U_19912),U_19914),U_19916)) = hAPP(hAPP(c_List_Oappend(U_19912),c_List_OdropWhile(U_19912,U_19915,U_19914)),U_19916)
      | hBOOL(hAPP(U_19915,U_19913))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19912),U_19913),hAPP(c_List_Oset(U_19912),U_19914))) ),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

cnf(f_4800_3,plain,
    ( c_List_OdropWhile(U_19912,U_19915,hAPP(hAPP(c_List_Oappend(U_19912),U_19914),U_19916)) = hAPP(hAPP(c_List_Oappend(U_19912),c_List_OdropWhile(U_19912,U_19915,U_19914)),U_19916)
    | hBOOL(hAPP(U_19915,U_19913))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19912),U_19913),hAPP(c_List_Oset(U_19912),U_19914))) ),
    inference(clausify,[status(thm)],[f_4800_2]) ).

fof(f_4801_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
      ( ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
        | hBOOL(hAPP(V_P_2,V_y_2))
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) )
      & ( ( ~ hBOOL(hAPP(V_P_2,V_y_2))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) )
        | c_List_OdropWhile(T_a,V_P_2,V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(f_4801_2,plain,
    ! [U_19921,U_19920,U_19919,U_19918,U_19917] :
      ( ( c_List_OdropWhile(U_19917,U_19918,U_19919) = hAPP(hAPP(c_List_Olist_OCons(U_19917),U_19920),U_19921)
        | hBOOL(hAPP(U_19918,U_19920))
        | U_19919 != hAPP(hAPP(c_List_Oappend(U_19917),c_List_OtakeWhile(U_19917,U_19918,U_19919)),hAPP(hAPP(c_List_Olist_OCons(U_19917),U_19920),U_19921)) )
      & ( ( ~ hBOOL(hAPP(U_19918,U_19920))
          & U_19919 = hAPP(hAPP(c_List_Oappend(U_19917),c_List_OtakeWhile(U_19917,U_19918,U_19919)),hAPP(hAPP(c_List_Olist_OCons(U_19917),U_19920),U_19921)) )
        | c_List_OdropWhile(U_19917,U_19918,U_19919) != hAPP(hAPP(c_List_Olist_OCons(U_19917),U_19920),U_19921) ) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

fof(f_4801_3,plain,
    ( ! [U_19931,U_19929,U_19927,U_19925,U_19923] :
        ( c_List_OdropWhile(U_19923,U_19925,U_19927) = hAPP(hAPP(c_List_Olist_OCons(U_19923),U_19929),U_19931)
        | hBOOL(hAPP(U_19925,U_19929))
        | U_19927 != hAPP(hAPP(c_List_Oappend(U_19923),c_List_OtakeWhile(U_19923,U_19925,U_19927)),hAPP(hAPP(c_List_Olist_OCons(U_19923),U_19929),U_19931)) )
    & ! [U_19930,U_19928,U_19926,U_19924,U_19922] :
        ( ( ~ hBOOL(hAPP(U_19924,U_19928))
          & U_19926 = hAPP(hAPP(c_List_Oappend(U_19922),c_List_OtakeWhile(U_19922,U_19924,U_19926)),hAPP(hAPP(c_List_Olist_OCons(U_19922),U_19928),U_19930)) )
        | c_List_OdropWhile(U_19922,U_19924,U_19926) != hAPP(hAPP(c_List_Olist_OCons(U_19922),U_19928),U_19930) ) ),
    inference(miniscope,[status(thm)],[f_4801_2]) ).

cnf(f_4801_4,plain,
    ( U_19926 = hAPP(hAPP(c_List_Oappend(U_19922),c_List_OtakeWhile(U_19922,U_19924,U_19926)),hAPP(hAPP(c_List_Olist_OCons(U_19922),U_19928),U_19930))
    | c_List_OdropWhile(U_19922,U_19924,U_19926) != hAPP(hAPP(c_List_Olist_OCons(U_19922),U_19928),U_19930) ),
    inference(clausify,[status(thm)],[f_4801_3]) ).

cnf(f_4801_5,plain,
    ( ~ hBOOL(hAPP(U_19924,U_19928))
    | c_List_OdropWhile(U_19922,U_19924,U_19926) != hAPP(hAPP(c_List_Olist_OCons(U_19922),U_19928),U_19930) ),
    inference(clausify,[status(thm)],[f_4801_3]) ).

cnf(f_4801_6,plain,
    ( c_List_OdropWhile(U_19923,U_19925,U_19927) = hAPP(hAPP(c_List_Olist_OCons(U_19923),U_19929),U_19931)
    | hBOOL(hAPP(U_19925,U_19929))
    | U_19927 != hAPP(hAPP(c_List_Oappend(U_19923),c_List_OtakeWhile(U_19923,U_19925,U_19927)),hAPP(hAPP(c_List_Olist_OCons(U_19923),U_19929),U_19931)) ),
    inference(clausify,[status(thm)],[f_4801_3]) ).

fof(f_4802_1,plain,
    ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(f_4802_2,plain,
    ! [U_19934,U_19933,U_19932] : c_List_OdropWhile(U_19932,U_19933,U_19934) = hAPP(hAPP(c_List_Odrop(U_19932),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19932)),c_List_OtakeWhile(U_19932,U_19933,U_19934))),U_19934),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

cnf(f_4802_3,plain,
    c_List_OdropWhile(U_19932,U_19933,U_19934) = hAPP(hAPP(c_List_Odrop(U_19932),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19932)),c_List_OtakeWhile(U_19932,U_19933,U_19934))),U_19934),
    inference(clausify,[status(thm)],[f_4802_2]) ).

fof(f_4803_1,plain,
    ! [V_xs_2,V_P_2,T_a,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),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_a)),c_List_OtakeWhile(T_a,V_P_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_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__nth]) ).

fof(f_4803_2,plain,
    ! [U_19938,U_19937,U_19936,U_19935] :
      ( hAPP(hAPP(c_List_Onth(U_19936),c_List_OdropWhile(U_19936,U_19937,U_19938)),U_19935) = hAPP(hAPP(c_List_Onth(U_19936),U_19938),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19935),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),c_List_OtakeWhile(U_19936,U_19937,U_19938))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19935),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),c_List_OdropWhile(U_19936,U_19937,U_19938)))) ),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

cnf(f_4803_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19936),c_List_OdropWhile(U_19936,U_19937,U_19938)),U_19935) = hAPP(hAPP(c_List_Onth(U_19936),U_19938),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19935),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),c_List_OtakeWhile(U_19936,U_19937,U_19938))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19935),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),c_List_OdropWhile(U_19936,U_19937,U_19938)))) ),
    inference(clausify,[status(thm)],[f_4803_2]) ).

fof(f_4804_1,plain,
    ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b)
          & ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__filter]) ).

fof(f_4804_2,plain,
    ! [U_19944,U_19943,U_19942,U_19941,U_19940] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),hAPP(c_List_Ofilter(U_19941,U_19943),U_19942))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),U_19942))
      | ? [U_19939] :
          ( hAPP(U_19944,U_19939) != c_Groups_Ozero__class_Ozero(U_19940)
          & ~ hBOOL(hAPP(U_19943,U_19939))
          & hBOOL(hAPP(hAPP(c_member(U_19941),U_19939),hAPP(c_List_Oset(U_19941),U_19942))) )
      | ~ class_Groups_Omonoid__add(U_19940) ),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

fof(f_4804_3,plain,
    ! [U_19944,U_19943,U_19942,U_19941,U_19940] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),hAPP(c_List_Ofilter(U_19941,U_19943),U_19942))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),U_19942))
      | ( hAPP(U_19944,sK494(U_19944,U_19943,U_19942,U_19941,U_19940)) != c_Groups_Ozero__class_Ozero(U_19940)
        & ~ hBOOL(hAPP(U_19943,sK494(U_19944,U_19943,U_19942,U_19941,U_19940)))
        & hBOOL(hAPP(hAPP(c_member(U_19941),sK494(U_19944,U_19943,U_19942,U_19941,U_19940)),hAPP(c_List_Oset(U_19941),U_19942))) )
      | ~ class_Groups_Omonoid__add(U_19940) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_19939,sK494(U_19944,U_19943,U_19942,U_19941,U_19940))],[f_4804_2]) ).

cnf(f_4804_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19941),sK494(U_19944,U_19943,U_19942,U_19941,U_19940)),hAPP(c_List_Oset(U_19941),U_19942)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),hAPP(c_List_Ofilter(U_19941,U_19943),U_19942))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),U_19942))
    | ~ class_Groups_Omonoid__add(U_19940) ),
    inference(clausify,[status(thm)],[f_4804_3]) ).

cnf(f_4804_5,plain,
    ( ~ hBOOL(hAPP(U_19943,sK494(U_19944,U_19943,U_19942,U_19941,U_19940)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),hAPP(c_List_Ofilter(U_19941,U_19943),U_19942))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),U_19942))
    | ~ class_Groups_Omonoid__add(U_19940) ),
    inference(clausify,[status(thm)],[f_4804_3]) ).

cnf(f_4804_6,plain,
    ( hAPP(U_19944,sK494(U_19944,U_19943,U_19942,U_19941,U_19940)) != c_Groups_Ozero__class_Ozero(U_19940)
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),hAPP(c_List_Ofilter(U_19941,U_19943),U_19942))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_19940),hAPP(hAPP(c_List_Omap(U_19941,U_19940),U_19944),U_19942))
    | ~ class_Groups_Omonoid__add(U_19940) ),
    inference(clausify,[status(thm)],[f_4804_3]) ).

fof(f_4805_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_4805_2,plain,
    ! [U_19948,U_19947] :
      ( c_List_Olinorder__class_Osorted(U_19947,U_19948)
      | ? [U_19946,U_19945] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19947),hAPP(hAPP(c_List_Onth(U_19947),U_19948),U_19946)),hAPP(hAPP(c_List_Onth(U_19947),U_19948),U_19945)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19945),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19948)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19946),U_19945)) )
      | ~ class_Orderings_Olinorder(U_19947) ),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

fof(f_4805_3,plain,
    ! [U_19948,U_19947] :
      ( c_List_Olinorder__class_Osorted(U_19947,U_19948)
      | ? [U_19945] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19947),hAPP(hAPP(c_List_Onth(U_19947),U_19948),sK495(U_19948,U_19947))),hAPP(hAPP(c_List_Onth(U_19947),U_19948),U_19945)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19945),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19948)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK495(U_19948,U_19947)),U_19945)) )
      | ~ class_Orderings_Olinorder(U_19947) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_19946,sK495(U_19948,U_19947))],[f_4805_2]) ).

fof(f_4805_4,plain,
    ! [U_19948,U_19947] :
      ( c_List_Olinorder__class_Osorted(U_19947,U_19948)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19947),hAPP(hAPP(c_List_Onth(U_19947),U_19948),sK495(U_19948,U_19947))),hAPP(hAPP(c_List_Onth(U_19947),U_19948),sK496(U_19948,U_19947))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_19948,U_19947)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19948)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK495(U_19948,U_19947)),sK496(U_19948,U_19947))) )
      | ~ class_Orderings_Olinorder(U_19947) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_19945,sK496(U_19948,U_19947))],[f_4805_3]) ).

cnf(f_4805_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK495(U_19948,U_19947)),sK496(U_19948,U_19947)))
    | c_List_Olinorder__class_Osorted(U_19947,U_19948)
    | ~ class_Orderings_Olinorder(U_19947) ),
    inference(clausify,[status(thm)],[f_4805_4]) ).

cnf(f_4805_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_19948,U_19947)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19948)))
    | c_List_Olinorder__class_Osorted(U_19947,U_19948)
    | ~ class_Orderings_Olinorder(U_19947) ),
    inference(clausify,[status(thm)],[f_4805_4]) ).

cnf(f_4805_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19947),hAPP(hAPP(c_List_Onth(U_19947),U_19948),sK495(U_19948,U_19947))),hAPP(hAPP(c_List_Onth(U_19947),U_19948),sK496(U_19948,U_19947))))
    | c_List_Olinorder__class_Osorted(U_19947,U_19948)
    | ~ class_Orderings_Olinorder(U_19947) ),
    inference(clausify,[status(thm)],[f_4805_4]) ).

fof(f_4806_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)
      | ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(f_4806_2,plain,
    ! [U_19952,U_19951,U_19950] :
      ( c_List_OtakeWhile(U_19950,U_19951,U_19952) = hAPP(c_List_Ofilter(U_19950,U_19951),U_19952)
      | ? [U_19949] :
          ( hBOOL(hAPP(U_19951,U_19949))
          & hBOOL(hAPP(hAPP(c_member(U_19950),U_19949),hAPP(c_List_Oset(U_19950),c_List_OdropWhile(U_19950,U_19951,U_19952)))) ) ),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

fof(f_4806_3,plain,
    ! [U_19952,U_19951,U_19950] :
      ( c_List_OtakeWhile(U_19950,U_19951,U_19952) = hAPP(c_List_Ofilter(U_19950,U_19951),U_19952)
      | ( hBOOL(hAPP(U_19951,sK497(U_19952,U_19951,U_19950)))
        & hBOOL(hAPP(hAPP(c_member(U_19950),sK497(U_19952,U_19951,U_19950)),hAPP(c_List_Oset(U_19950),c_List_OdropWhile(U_19950,U_19951,U_19952)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_19949,sK497(U_19952,U_19951,U_19950))],[f_4806_2]) ).

cnf(f_4806_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19950),sK497(U_19952,U_19951,U_19950)),hAPP(c_List_Oset(U_19950),c_List_OdropWhile(U_19950,U_19951,U_19952))))
    | c_List_OtakeWhile(U_19950,U_19951,U_19952) = hAPP(c_List_Ofilter(U_19950,U_19951),U_19952) ),
    inference(clausify,[status(thm)],[f_4806_3]) ).

cnf(f_4806_5,plain,
    ( hBOOL(hAPP(U_19951,sK497(U_19952,U_19951,U_19950)))
    | c_List_OtakeWhile(U_19950,U_19951,U_19952) = hAPP(c_List_Ofilter(U_19950,U_19951),U_19952) ),
    inference(clausify,[status(thm)],[f_4806_3]) ).

fof(f_4807_1,plain,
    ! [V_P_2,V_xs_2,T_a,V_n_2] :
      ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)
      | ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) )
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),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_a)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(f_4807_2,plain,
    ! [U_19957,U_19956,U_19955,U_19954] :
      ( c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
      | ( hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19954)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19954),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956))) )
      | ? [U_19953] :
          ( ~ hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19953)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19953),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19953),U_19954)) ) ),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

fof(f_4807_3,plain,
    ! [U_19957,U_19956,U_19955,U_19954] :
      ( c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
      | ( hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19954)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19954),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956))) )
      | ( ~ hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),sK498(U_19957,U_19956,U_19955,U_19954))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),U_19954)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_19953,sK498(U_19957,U_19956,U_19955,U_19954))],[f_4807_2]) ).

cnf(f_4807_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19954),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),U_19954)) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

cnf(f_4807_5,plain,
    ( hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19954)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),U_19954)) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

cnf(f_4807_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19954),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956))) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

cnf(f_4807_7,plain,
    ( hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19954)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_19957,U_19956,U_19955,U_19954)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956))) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

cnf(f_4807_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19954),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19955)),U_19956)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | ~ hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),sK498(U_19957,U_19956,U_19955,U_19954)))) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

cnf(f_4807_9,plain,
    ( hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),U_19954)))
    | c_List_OtakeWhile(U_19955,U_19957,U_19956) = hAPP(hAPP(c_List_Otake(U_19955),U_19954),U_19956)
    | ~ hBOOL(hAPP(U_19957,hAPP(hAPP(c_List_Onth(U_19955),U_19956),sK498(U_19957,U_19956,U_19955,U_19954)))) ),
    inference(clausify,[status(thm)],[f_4807_3]) ).

fof(f_4808_1,plain,
    ! [V_xs_2,T_a,V_P_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__less__P__nth]) ).

fof(f_4808_2,plain,
    ! [U_19962,U_19961,U_19960,U_19959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),c_List_OtakeWhile(U_19961,U_19960,U_19962))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),U_19962)))
      | ? [U_19958] :
          ( ~ hBOOL(hAPP(U_19960,hAPP(hAPP(c_List_Onth(U_19961),U_19962),U_19958)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19958),U_19959)) ) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

fof(f_4808_3,plain,
    ! [U_19962,U_19961,U_19960,U_19959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),c_List_OtakeWhile(U_19961,U_19960,U_19962))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),U_19962)))
      | ( ~ hBOOL(hAPP(U_19960,hAPP(hAPP(c_List_Onth(U_19961),U_19962),sK499(U_19962,U_19961,U_19960,U_19959))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK499(U_19962,U_19961,U_19960,U_19959)),U_19959)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_19958,sK499(U_19962,U_19961,U_19960,U_19959))],[f_4808_2]) ).

cnf(f_4808_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK499(U_19962,U_19961,U_19960,U_19959)),U_19959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),c_List_OtakeWhile(U_19961,U_19960,U_19962))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),U_19962))) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

cnf(f_4808_5,plain,
    ( ~ hBOOL(hAPP(U_19960,hAPP(hAPP(c_List_Onth(U_19961),U_19962),sK499(U_19962,U_19961,U_19960,U_19959))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),c_List_OtakeWhile(U_19961,U_19960,U_19962))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19961)),U_19962))) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

fof(f_4809_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
          | ( ! [B_xs,B_x] :
                ( ~ c_List_Olinorder__class_Osorted(T_a,B_xs)
                | ? [B_xa] :
                    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa))
                    & hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) )
                | V_a_2 != hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) )
            & V_a_2 != c_List_Olist_ONil(T_a) ) )
        & ( ? [B_xs,B_x] :
              ( c_List_Olinorder__class_Osorted(T_a,B_xs)
              & ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa))
                  | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) )
              & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) )
          | V_a_2 = c_List_Olist_ONil(T_a)
          | ~ c_List_Olinorder__class_Osorted(T_a,V_a_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Osimps]) ).

fof(f_4809_2,plain,
    ! [U_19970,U_19969] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19969,U_19970)
          | ( ! [U_19968,U_19967] :
                ( ~ c_List_Olinorder__class_Osorted(U_19969,U_19968)
                | ? [U_19966] :
                    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),U_19966))
                    & hBOOL(hAPP(hAPP(c_member(U_19969),U_19966),hAPP(c_List_Oset(U_19969),U_19968))) )
                | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968) )
            & U_19970 != c_List_Olist_ONil(U_19969) ) )
        & ( ? [U_19965,U_19964] :
              ( c_List_Olinorder__class_Osorted(U_19969,U_19965)
              & ! [U_19963] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19964),U_19963))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),U_19965))) )
              & U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19964),U_19965) )
          | U_19970 = c_List_Olist_ONil(U_19969)
          | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970) ) )
      | ~ class_Orderings_Olinorder(U_19969) ),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

fof(f_4809_3,plain,
    ! [U_19970,U_19969] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19969,U_19970)
          | ( ! [U_19968] :
                ( ! [U_19967] :
                    ( ? [U_19966] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),U_19966))
                        & hBOOL(hAPP(hAPP(c_member(U_19969),U_19966),hAPP(c_List_Oset(U_19969),U_19968))) )
                    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968) )
                | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968) )
            & U_19970 != c_List_Olist_ONil(U_19969) ) )
        & ( ? [U_19965] :
              ( ? [U_19964] :
                  ( ! [U_19963] :
                      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19964),U_19963))
                      | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),U_19965))) )
                  & U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19964),U_19965) )
              & c_List_Olinorder__class_Osorted(U_19969,U_19965) )
          | U_19970 = c_List_Olist_ONil(U_19969)
          | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970) ) )
      | ~ class_Orderings_Olinorder(U_19969) ),
    inference(miniscope,[status(thm)],[f_4809_2]) ).

fof(f_4809_4,plain,
    ! [U_19970,U_19969] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19969,U_19970)
          | ( ! [U_19968] :
                ( ! [U_19967] :
                    ( ? [U_19966] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),U_19966))
                        & hBOOL(hAPP(hAPP(c_member(U_19969),U_19966),hAPP(c_List_Oset(U_19969),U_19968))) )
                    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968) )
                | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968) )
            & U_19970 != c_List_Olist_ONil(U_19969) ) )
        & ( ( ? [U_19964] :
                ( ! [U_19963] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19964),U_19963))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),sK500(U_19970,U_19969)))) )
                & U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19964),sK500(U_19970,U_19969)) )
            & c_List_Olinorder__class_Osorted(U_19969,sK500(U_19970,U_19969)) )
          | U_19970 = c_List_Olist_ONil(U_19969)
          | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970) ) )
      | ~ class_Orderings_Olinorder(U_19969) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_19965,sK500(U_19970,U_19969))],[f_4809_3]) ).

fof(f_4809_5,plain,
    ! [U_19970,U_19969] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19969,U_19970)
          | ( ! [U_19968] :
                ( ! [U_19967] :
                    ( ? [U_19966] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),U_19966))
                        & hBOOL(hAPP(hAPP(c_member(U_19969),U_19966),hAPP(c_List_Oset(U_19969),U_19968))) )
                    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968) )
                | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968) )
            & U_19970 != c_List_Olist_ONil(U_19969) ) )
        & ( ( ! [U_19963] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),sK501(U_19970,U_19969)),U_19963))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),sK500(U_19970,U_19969)))) )
            & U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),sK501(U_19970,U_19969)),sK500(U_19970,U_19969))
            & c_List_Olinorder__class_Osorted(U_19969,sK500(U_19970,U_19969)) )
          | U_19970 = c_List_Olist_ONil(U_19969)
          | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970) ) )
      | ~ class_Orderings_Olinorder(U_19969) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_19964,sK501(U_19970,U_19969))],[f_4809_4]) ).

fof(f_4809_6,plain,
    ! [U_19970,U_19969] :
      ( ( ( c_List_Olinorder__class_Osorted(U_19969,U_19970)
          | ( ! [U_19968] :
                ( ! [U_19967] :
                    ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),sK502(U_19970,U_19969,U_19968,U_19967)))
                      & hBOOL(hAPP(hAPP(c_member(U_19969),sK502(U_19970,U_19969,U_19968,U_19967)),hAPP(c_List_Oset(U_19969),U_19968))) )
                    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968) )
                | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968) )
            & U_19970 != c_List_Olist_ONil(U_19969) ) )
        & ( ( ! [U_19963] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),sK501(U_19970,U_19969)),U_19963))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),sK500(U_19970,U_19969)))) )
            & U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),sK501(U_19970,U_19969)),sK500(U_19970,U_19969))
            & c_List_Olinorder__class_Osorted(U_19969,sK500(U_19970,U_19969)) )
          | U_19970 = c_List_Olist_ONil(U_19969)
          | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970) ) )
      | ~ class_Orderings_Olinorder(U_19969) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_19966,sK502(U_19970,U_19969,U_19968,U_19967))],[f_4809_5]) ).

cnf(f_4809_7,plain,
    ( c_List_Olinorder__class_Osorted(U_19969,sK500(U_19970,U_19969))
    | U_19970 = c_List_Olist_ONil(U_19969)
    | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

cnf(f_4809_8,plain,
    ( U_19970 = hAPP(hAPP(c_List_Olist_OCons(U_19969),sK501(U_19970,U_19969)),sK500(U_19970,U_19969))
    | U_19970 = c_List_Olist_ONil(U_19969)
    | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

cnf(f_4809_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),sK501(U_19970,U_19969)),U_19963))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19969),U_19963),hAPP(c_List_Oset(U_19969),sK500(U_19970,U_19969))))
    | U_19970 = c_List_Olist_ONil(U_19969)
    | ~ c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

cnf(f_4809_10,plain,
    ( U_19970 != c_List_Olist_ONil(U_19969)
    | c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

cnf(f_4809_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19969),sK502(U_19970,U_19969,U_19968,U_19967)),hAPP(c_List_Oset(U_19969),U_19968)))
    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968)
    | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968)
    | c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

cnf(f_4809_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19969),U_19967),sK502(U_19970,U_19969,U_19968,U_19967)))
    | U_19970 != hAPP(hAPP(c_List_Olist_OCons(U_19969),U_19967),U_19968)
    | ~ c_List_Olinorder__class_Osorted(U_19969,U_19968)
    | c_List_Olinorder__class_Osorted(U_19969,U_19970)
    | ~ class_Orderings_Olinorder(U_19969) ),
    inference(clausify,[status(thm)],[f_4809_6]) ).

fof(f_4810_1,plain,
    ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))),
    inference(fof_nnf,[status(thm)],[fact_map__upds__def]) ).

fof(f_4810_2,plain,
    ! [U_19975,U_19974,U_19973,U_19972,U_19971] : c_Map_Omap__upds(U_19971,U_19972,U_19973,U_19974,U_19975) = c_Map_Omap__add(U_19971,U_19972,U_19973,hAPP(c_Map_Omap__of(U_19971,U_19972),hAPP(c_List_Orev(tc_prod(U_19971,U_19972)),hAPP(hAPP(c_List_Ozip(U_19971,U_19972),U_19974),U_19975)))),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

cnf(f_4810_3,plain,
    c_Map_Omap__upds(U_19971,U_19972,U_19973,U_19974,U_19975) = c_Map_Omap__add(U_19971,U_19972,U_19973,hAPP(c_Map_Omap__of(U_19971,U_19972),hAPP(c_List_Orev(tc_prod(U_19971,U_19972)),hAPP(hAPP(c_List_Ozip(U_19971,U_19972),U_19974),U_19975)))),
    inference(clausify,[status(thm)],[f_4810_2]) ).

fof(f_4811_1,plain,
    ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_map__comp__def]) ).

fof(f_4811_2,plain,
    ! [U_19981,U_19980,U_19979,U_19978,U_19977,U_19976] : c_Map_Omap__comp(U_19976,U_19977,U_19978,U_19979,U_19980,U_19981) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_19977),U_19976,c_Option_Ooption_ONone(U_19977),U_19979),hAPP(U_19980,U_19981)),
    inference(variable_rename,[status(thm)],[f_4811_1]) ).

cnf(f_4811_3,plain,
    c_Map_Omap__comp(U_19976,U_19977,U_19978,U_19979,U_19980,U_19981) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_19977),U_19976,c_Option_Ooption_ONone(U_19977),U_19979),hAPP(U_19980,U_19981)),
    inference(clausify,[status(thm)],[f_4811_2]) ).

fof(f_4812_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__of__append]) ).

fof(f_4812_2,plain,
    ! [U_19985,U_19984,U_19983,U_19982] : hAPP(c_Map_Omap__of(U_19982,U_19983),hAPP(hAPP(c_List_Oappend(tc_prod(U_19982,U_19983)),U_19984),U_19985)) = c_Map_Omap__add(U_19982,U_19983,hAPP(c_Map_Omap__of(U_19982,U_19983),U_19985),hAPP(c_Map_Omap__of(U_19982,U_19983),U_19984)),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

cnf(f_4812_3,plain,
    hAPP(c_Map_Omap__of(U_19982,U_19983),hAPP(hAPP(c_List_Oappend(tc_prod(U_19982,U_19983)),U_19984),U_19985)) = c_Map_Omap__add(U_19982,U_19983,hAPP(c_Map_Omap__of(U_19982,U_19983),U_19985),hAPP(c_Map_Omap__of(U_19982,U_19983),U_19984)),
    inference(clausify,[status(thm)],[f_4812_2]) ).

fof(f_4813_1,plain,
    ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_map__comp__empty_I1_J]) ).

fof(f_4813_2,plain,
    ! [U_19990,U_19989,U_19988,U_19987,U_19986] : c_Map_Omap__comp(U_19986,U_19987,U_19988,U_19989,hAPP(c_COMBK(tc_Option_Ooption(U_19986),U_19988),c_Option_Ooption_ONone(U_19986)),U_19990) = c_Option_Ooption_ONone(U_19987),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

cnf(f_4813_3,plain,
    c_Map_Omap__comp(U_19986,U_19987,U_19988,U_19989,hAPP(c_COMBK(tc_Option_Ooption(U_19986),U_19988),c_Option_Ooption_ONone(U_19986)),U_19990) = c_Option_Ooption_ONone(U_19987),
    inference(clausify,[status(thm)],[f_4813_2]) ).

fof(f_4814_1,plain,
    ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a),
    inference(fof_nnf,[status(thm)],[fact_map__comp__empty_I2_J]) ).

fof(f_4814_2,plain,
    ! [U_19995,U_19994,U_19993,U_19992,U_19991] : c_Map_Omap__comp(U_19991,U_19992,U_19993,hAPP(c_COMBK(tc_Option_Ooption(U_19992),U_19991),c_Option_Ooption_ONone(U_19992)),U_19994,U_19995) = c_Option_Ooption_ONone(U_19992),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

cnf(f_4814_3,plain,
    c_Map_Omap__comp(U_19991,U_19992,U_19993,hAPP(c_COMBK(tc_Option_Ooption(U_19992),U_19991),c_Option_Ooption_ONone(U_19992)),U_19994,U_19995) = c_Option_Ooption_ONone(U_19992),
    inference(clausify,[status(thm)],[f_4814_2]) ).

fof(f_4815_1,plain,
    ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
      ( c_Map_Omap__comp(T_a,T_c,T_b,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_a),V_k_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J]) ).

fof(f_4815_2,plain,
    ! [U_20002,U_20001,U_20000,U_19999,U_19998,U_19997,U_19996] :
      ( c_Map_Omap__comp(U_19998,U_20000,U_20001,U_20002,U_19996,U_19997) = hAPP(U_20002,U_19999)
      | hAPP(U_19996,U_19997) != hAPP(c_Option_Ooption_OSome(U_19998),U_19999) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

cnf(f_4815_3,plain,
    ( c_Map_Omap__comp(U_19998,U_20000,U_20001,U_20002,U_19996,U_19997) = hAPP(U_20002,U_19999)
    | hAPP(U_19996,U_19997) != hAPP(c_Option_Ooption_OSome(U_19998),U_19999) ),
    inference(clausify,[status(thm)],[f_4815_2]) ).

fof(f_4816_1,plain,
    ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
      ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
      | hAPP(V_n_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__find__right]) ).

fof(f_4816_2,plain,
    ! [U_20008,U_20007,U_20006,U_20005,U_20004,U_20003] :
      ( hAPP(c_Map_Omap__add(U_20007,U_20005,U_20008,U_20003),U_20004) = hAPP(c_Option_Ooption_OSome(U_20005),U_20006)
      | hAPP(U_20003,U_20004) != hAPP(c_Option_Ooption_OSome(U_20005),U_20006) ),
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

cnf(f_4816_3,plain,
    ( hAPP(c_Map_Omap__add(U_20007,U_20005,U_20008,U_20003),U_20004) = hAPP(c_Option_Ooption_OSome(U_20005),U_20006)
    | hAPP(U_20003,U_20004) != hAPP(c_Option_Ooption_OSome(U_20005),U_20006) ),
    inference(clausify,[status(thm)],[f_4816_2]) ).

fof(f_4817_1,plain,
    ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
      ( ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
        | ! [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) != hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
            | hAPP(V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),B_k_H) ) )
      & ( ? [B_k_H] :
            ( hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) )
        | c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__Some__iff]) ).

fof(f_4817_2,plain,
    ! [U_20017,U_20016,U_20015,U_20014,U_20013,U_20012,U_20011] :
      ( ( c_Map_Omap__comp(U_20011,U_20012,U_20013,U_20014,U_20015,U_20016) = hAPP(c_Option_Ooption_OSome(U_20012),U_20017)
        | ! [U_20010] :
            ( hAPP(U_20014,U_20010) != hAPP(c_Option_Ooption_OSome(U_20012),U_20017)
            | hAPP(U_20015,U_20016) != hAPP(c_Option_Ooption_OSome(U_20011),U_20010) ) )
      & ( ? [U_20009] :
            ( hAPP(U_20014,U_20009) = hAPP(c_Option_Ooption_OSome(U_20012),U_20017)
            & hAPP(U_20015,U_20016) = hAPP(c_Option_Ooption_OSome(U_20011),U_20009) )
        | c_Map_Omap__comp(U_20011,U_20012,U_20013,U_20014,U_20015,U_20016) != hAPP(c_Option_Ooption_OSome(U_20012),U_20017) ) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

fof(f_4817_3,plain,
    ( ! [U_20031,U_20029,U_20027,U_20025,U_20023,U_20021,U_20019] :
        ( c_Map_Omap__comp(U_20019,U_20021,U_20023,U_20025,U_20027,U_20029) = hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
        | ! [U_20010] :
            ( hAPP(U_20025,U_20010) != hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
            | hAPP(U_20027,U_20029) != hAPP(c_Option_Ooption_OSome(U_20019),U_20010) ) )
    & ! [U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018] :
        ( ? [U_20009] :
            ( hAPP(U_20024,U_20009) = hAPP(c_Option_Ooption_OSome(U_20020),U_20030)
            & hAPP(U_20026,U_20028) = hAPP(c_Option_Ooption_OSome(U_20018),U_20009) )
        | c_Map_Omap__comp(U_20018,U_20020,U_20022,U_20024,U_20026,U_20028) != hAPP(c_Option_Ooption_OSome(U_20020),U_20030) ) ),
    inference(miniscope,[status(thm)],[f_4817_2]) ).

fof(f_4817_4,plain,
    ( ! [U_20031,U_20029,U_20027,U_20025,U_20023,U_20021,U_20019] :
        ( c_Map_Omap__comp(U_20019,U_20021,U_20023,U_20025,U_20027,U_20029) = hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
        | ! [U_20010] :
            ( hAPP(U_20025,U_20010) != hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
            | hAPP(U_20027,U_20029) != hAPP(c_Option_Ooption_OSome(U_20019),U_20010) ) )
    & ! [U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018] :
        ( ( hAPP(U_20024,sK503(U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018)) = hAPP(c_Option_Ooption_OSome(U_20020),U_20030)
          & hAPP(U_20026,U_20028) = hAPP(c_Option_Ooption_OSome(U_20018),sK503(U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018)) )
        | c_Map_Omap__comp(U_20018,U_20020,U_20022,U_20024,U_20026,U_20028) != hAPP(c_Option_Ooption_OSome(U_20020),U_20030) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_20009,sK503(U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018))],[f_4817_3]) ).

cnf(f_4817_5,plain,
    ( hAPP(U_20026,U_20028) = hAPP(c_Option_Ooption_OSome(U_20018),sK503(U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018))
    | c_Map_Omap__comp(U_20018,U_20020,U_20022,U_20024,U_20026,U_20028) != hAPP(c_Option_Ooption_OSome(U_20020),U_20030) ),
    inference(clausify,[status(thm)],[f_4817_4]) ).

cnf(f_4817_6,plain,
    ( hAPP(U_20024,sK503(U_20030,U_20028,U_20026,U_20024,U_20022,U_20020,U_20018)) = hAPP(c_Option_Ooption_OSome(U_20020),U_20030)
    | c_Map_Omap__comp(U_20018,U_20020,U_20022,U_20024,U_20026,U_20028) != hAPP(c_Option_Ooption_OSome(U_20020),U_20030) ),
    inference(clausify,[status(thm)],[f_4817_4]) ).

cnf(f_4817_7,plain,
    ( c_Map_Omap__comp(U_20019,U_20021,U_20023,U_20025,U_20027,U_20029) = hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
    | hAPP(U_20025,U_20010) != hAPP(c_Option_Ooption_OSome(U_20021),U_20031)
    | hAPP(U_20027,U_20029) != hAPP(c_Option_Ooption_OSome(U_20019),U_20010) ),
    inference(clausify,[status(thm)],[f_4817_4]) ).

fof(f_4818_1,plain,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_map__add__upd]) ).

fof(f_4818_2,plain,
    ! [U_20037,U_20036,U_20035,U_20034,U_20033,U_20032] : c_Map_Omap__add(U_20032,U_20033,U_20034,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20032,tc_Option_Ooption(U_20033)),U_20035),U_20036),hAPP(c_Option_Ooption_OSome(U_20033),U_20037))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20032,tc_Option_Ooption(U_20033)),c_Map_Omap__add(U_20032,U_20033,U_20034,U_20035)),U_20036),hAPP(c_Option_Ooption_OSome(U_20033),U_20037)),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

cnf(f_4818_3,plain,
    c_Map_Omap__add(U_20032,U_20033,U_20034,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20032,tc_Option_Ooption(U_20033)),U_20035),U_20036),hAPP(c_Option_Ooption_OSome(U_20033),U_20037))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20032,tc_Option_Ooption(U_20033)),c_Map_Omap__add(U_20032,U_20033,U_20034,U_20035)),U_20036),hAPP(c_Option_Ooption_OSome(U_20033),U_20037)),
    inference(clausify,[status(thm)],[f_4818_2]) ).

fof(f_4819_1,plain,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
      ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
        & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) )
      | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
      | hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__SomeD]) ).

fof(f_4819_2,plain,
    ! [U_20043,U_20042,U_20041,U_20040,U_20039,U_20038] :
      ( ( hAPP(U_20040,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
        & hAPP(U_20041,U_20042) = c_Option_Ooption_ONone(U_20039) )
      | hAPP(U_20041,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
      | hAPP(c_Map_Omap__add(U_20038,U_20039,U_20040,U_20041),U_20042) != hAPP(c_Option_Ooption_OSome(U_20039),U_20043) ),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

fof(f_4819_3,plain,
    ! [U_20043,U_20042,U_20041,U_20040,U_20039] :
      ( ! [U_20038] : hAPP(c_Map_Omap__add(U_20038,U_20039,U_20040,U_20041),U_20042) != hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
      | ( hAPP(U_20040,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
        & hAPP(U_20041,U_20042) = c_Option_Ooption_ONone(U_20039) )
      | hAPP(U_20041,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043) ),
    inference(miniscope,[status(thm)],[f_4819_2]) ).

cnf(f_4819_4,plain,
    ( hAPP(U_20041,U_20042) = c_Option_Ooption_ONone(U_20039)
    | hAPP(U_20041,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
    | hAPP(c_Map_Omap__add(U_20038,U_20039,U_20040,U_20041),U_20042) != hAPP(c_Option_Ooption_OSome(U_20039),U_20043) ),
    inference(clausify,[status(thm)],[f_4819_3]) ).

cnf(f_4819_5,plain,
    ( hAPP(U_20040,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
    | hAPP(U_20041,U_20042) = hAPP(c_Option_Ooption_OSome(U_20039),U_20043)
    | hAPP(c_Map_Omap__add(U_20038,U_20039,U_20040,U_20041),U_20042) != hAPP(c_Option_Ooption_OSome(U_20039),U_20043) ),
    inference(clausify,[status(thm)],[f_4819_3]) ).

fof(f_4820_1,plain,
    ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
      ( ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
        | ( ( hAPP(V_m_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
            | hAPP(V_n_2,V_k_2) != c_Option_Ooption_ONone(T_a) )
          & hAPP(V_n_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) )
      & ( ( hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) )
        | hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
        | hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) != hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff]) ).

fof(f_4820_2,plain,
    ! [U_20049,U_20048,U_20047,U_20046,U_20045,U_20044] :
      ( ( hAPP(c_Map_Omap__add(U_20044,U_20045,U_20046,U_20047),U_20048) = hAPP(c_Option_Ooption_OSome(U_20045),U_20049)
        | ( ( hAPP(U_20046,U_20048) != hAPP(c_Option_Ooption_OSome(U_20045),U_20049)
            | hAPP(U_20047,U_20048) != c_Option_Ooption_ONone(U_20045) )
          & hAPP(U_20047,U_20048) != hAPP(c_Option_Ooption_OSome(U_20045),U_20049) ) )
      & ( ( hAPP(U_20046,U_20048) = hAPP(c_Option_Ooption_OSome(U_20045),U_20049)
          & hAPP(U_20047,U_20048) = c_Option_Ooption_ONone(U_20045) )
        | hAPP(U_20047,U_20048) = hAPP(c_Option_Ooption_OSome(U_20045),U_20049)
        | hAPP(c_Map_Omap__add(U_20044,U_20045,U_20046,U_20047),U_20048) != hAPP(c_Option_Ooption_OSome(U_20045),U_20049) ) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

fof(f_4820_3,plain,
    ( ! [U_20061,U_20059,U_20057,U_20055,U_20053] :
        ( ! [U_20051] : hAPP(c_Map_Omap__add(U_20051,U_20053,U_20055,U_20057),U_20059) = hAPP(c_Option_Ooption_OSome(U_20053),U_20061)
        | ( ( hAPP(U_20055,U_20059) != hAPP(c_Option_Ooption_OSome(U_20053),U_20061)
            | hAPP(U_20057,U_20059) != c_Option_Ooption_ONone(U_20053) )
          & hAPP(U_20057,U_20059) != hAPP(c_Option_Ooption_OSome(U_20053),U_20061) ) )
    & ! [U_20060,U_20058,U_20056,U_20054,U_20052] :
        ( ! [U_20050] : hAPP(c_Map_Omap__add(U_20050,U_20052,U_20054,U_20056),U_20058) != hAPP(c_Option_Ooption_OSome(U_20052),U_20060)
        | ( hAPP(U_20054,U_20058) = hAPP(c_Option_Ooption_OSome(U_20052),U_20060)
          & hAPP(U_20056,U_20058) = c_Option_Ooption_ONone(U_20052) )
        | hAPP(U_20056,U_20058) = hAPP(c_Option_Ooption_OSome(U_20052),U_20060) ) ),
    inference(miniscope,[status(thm)],[f_4820_2]) ).

cnf(f_4820_4,plain,
    ( hAPP(U_20056,U_20058) = c_Option_Ooption_ONone(U_20052)
    | hAPP(U_20056,U_20058) = hAPP(c_Option_Ooption_OSome(U_20052),U_20060)
    | hAPP(c_Map_Omap__add(U_20050,U_20052,U_20054,U_20056),U_20058) != hAPP(c_Option_Ooption_OSome(U_20052),U_20060) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

cnf(f_4820_5,plain,
    ( hAPP(U_20054,U_20058) = hAPP(c_Option_Ooption_OSome(U_20052),U_20060)
    | hAPP(U_20056,U_20058) = hAPP(c_Option_Ooption_OSome(U_20052),U_20060)
    | hAPP(c_Map_Omap__add(U_20050,U_20052,U_20054,U_20056),U_20058) != hAPP(c_Option_Ooption_OSome(U_20052),U_20060) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

cnf(f_4820_6,plain,
    ( hAPP(U_20057,U_20059) != hAPP(c_Option_Ooption_OSome(U_20053),U_20061)
    | hAPP(c_Map_Omap__add(U_20051,U_20053,U_20055,U_20057),U_20059) = hAPP(c_Option_Ooption_OSome(U_20053),U_20061) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

cnf(f_4820_7,plain,
    ( hAPP(U_20055,U_20059) != hAPP(c_Option_Ooption_OSome(U_20053),U_20061)
    | hAPP(U_20057,U_20059) != c_Option_Ooption_ONone(U_20053)
    | hAPP(c_Map_Omap__add(U_20051,U_20053,U_20055,U_20057),U_20059) = hAPP(c_Option_Ooption_OSome(U_20053),U_20061) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

fof(f_4821_1,plain,
    ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
      ( c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
      | hAPP(V_m2_2,V_k_2) != c_Option_Ooption_ONone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I1_J]) ).

fof(f_4821_2,plain,
    ! [U_20067,U_20066,U_20065,U_20064,U_20063,U_20062] :
      ( c_Map_Omap__comp(U_20064,U_20065,U_20066,U_20067,U_20062,U_20063) = c_Option_Ooption_ONone(U_20065)
      | hAPP(U_20062,U_20063) != c_Option_Ooption_ONone(U_20064) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

cnf(f_4821_3,plain,
    ( c_Map_Omap__comp(U_20064,U_20065,U_20066,U_20067,U_20062,U_20063) = c_Option_Ooption_ONone(U_20065)
    | hAPP(U_20062,U_20063) != c_Option_Ooption_ONone(U_20064) ),
    inference(clausify,[status(thm)],[f_4821_2]) ).

fof(f_4822_1,plain,
    ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
      ( ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
        | hAPP(V_m_2,V_k_2) != c_Option_Ooption_ONone(T_a)
        | hAPP(V_n_2,V_k_2) != c_Option_Ooption_ONone(T_a) )
      & ( ( hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a)
          & hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) )
        | hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) != c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__None]) ).

fof(f_4822_2,plain,
    ! [U_20072,U_20071,U_20070,U_20069,U_20068] :
      ( ( hAPP(c_Map_Omap__add(U_20068,U_20069,U_20070,U_20071),U_20072) = c_Option_Ooption_ONone(U_20069)
        | hAPP(U_20070,U_20072) != c_Option_Ooption_ONone(U_20069)
        | hAPP(U_20071,U_20072) != c_Option_Ooption_ONone(U_20069) )
      & ( ( hAPP(U_20070,U_20072) = c_Option_Ooption_ONone(U_20069)
          & hAPP(U_20071,U_20072) = c_Option_Ooption_ONone(U_20069) )
        | hAPP(c_Map_Omap__add(U_20068,U_20069,U_20070,U_20071),U_20072) != c_Option_Ooption_ONone(U_20069) ) ),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

fof(f_4822_3,plain,
    ( ! [U_20082,U_20080,U_20078,U_20076] :
        ( ! [U_20074] : hAPP(c_Map_Omap__add(U_20074,U_20076,U_20078,U_20080),U_20082) = c_Option_Ooption_ONone(U_20076)
        | hAPP(U_20078,U_20082) != c_Option_Ooption_ONone(U_20076)
        | hAPP(U_20080,U_20082) != c_Option_Ooption_ONone(U_20076) )
    & ! [U_20081,U_20079,U_20077,U_20075] :
        ( ! [U_20073] : hAPP(c_Map_Omap__add(U_20073,U_20075,U_20077,U_20079),U_20081) != c_Option_Ooption_ONone(U_20075)
        | ( hAPP(U_20077,U_20081) = c_Option_Ooption_ONone(U_20075)
          & hAPP(U_20079,U_20081) = c_Option_Ooption_ONone(U_20075) ) ) ),
    inference(miniscope,[status(thm)],[f_4822_2]) ).

cnf(f_4822_4,plain,
    ( hAPP(U_20079,U_20081) = c_Option_Ooption_ONone(U_20075)
    | hAPP(c_Map_Omap__add(U_20073,U_20075,U_20077,U_20079),U_20081) != c_Option_Ooption_ONone(U_20075) ),
    inference(clausify,[status(thm)],[f_4822_3]) ).

cnf(f_4822_5,plain,
    ( hAPP(U_20077,U_20081) = c_Option_Ooption_ONone(U_20075)
    | hAPP(c_Map_Omap__add(U_20073,U_20075,U_20077,U_20079),U_20081) != c_Option_Ooption_ONone(U_20075) ),
    inference(clausify,[status(thm)],[f_4822_3]) ).

cnf(f_4822_6,plain,
    ( hAPP(c_Map_Omap__add(U_20074,U_20076,U_20078,U_20080),U_20082) = c_Option_Ooption_ONone(U_20076)
    | hAPP(U_20078,U_20082) != c_Option_Ooption_ONone(U_20076)
    | hAPP(U_20080,U_20082) != c_Option_Ooption_ONone(U_20076) ),
    inference(clausify,[status(thm)],[f_4822_3]) ).

fof(f_4823_1,plain,
    ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_map__add__empty]) ).

fof(f_4823_2,plain,
    ! [U_20085,U_20084,U_20083] : c_Map_Omap__add(U_20083,U_20084,U_20085,hAPP(c_COMBK(tc_Option_Ooption(U_20084),U_20083),c_Option_Ooption_ONone(U_20084))) = U_20085,
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

cnf(f_4823_3,plain,
    c_Map_Omap__add(U_20083,U_20084,U_20085,hAPP(c_COMBK(tc_Option_Ooption(U_20084),U_20083),c_Option_Ooption_ONone(U_20084))) = U_20085,
    inference(clausify,[status(thm)],[f_4823_2]) ).

fof(f_4824_1,plain,
    ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2,
    inference(fof_nnf,[status(thm)],[fact_empty__map__add]) ).

fof(f_4824_2,plain,
    ! [U_20088,U_20087,U_20086] : c_Map_Omap__add(U_20086,U_20087,hAPP(c_COMBK(tc_Option_Ooption(U_20087),U_20086),c_Option_Ooption_ONone(U_20087)),U_20088) = U_20088,
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

cnf(f_4824_3,plain,
    c_Map_Omap__add(U_20086,U_20087,hAPP(c_COMBK(tc_Option_Ooption(U_20087),U_20086),c_Option_Ooption_ONone(U_20087)),U_20088) = U_20088,
    inference(clausify,[status(thm)],[f_4824_2]) ).

fof(f_4825_1,plain,
    ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__upds]) ).

fof(f_4825_2,plain,
    ! [U_20094,U_20093,U_20092,U_20091,U_20090,U_20089] : c_Map_Omap__add(U_20089,U_20090,U_20091,c_Map_Omap__upds(U_20089,U_20090,U_20092,U_20093,U_20094)) = c_Map_Omap__upds(U_20089,U_20090,c_Map_Omap__add(U_20089,U_20090,U_20091,U_20092),U_20093,U_20094),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

cnf(f_4825_3,plain,
    c_Map_Omap__add(U_20089,U_20090,U_20091,c_Map_Omap__upds(U_20089,U_20090,U_20092,U_20093,U_20094)) = c_Map_Omap__upds(U_20089,U_20090,c_Map_Omap__add(U_20089,U_20090,U_20091,U_20092),U_20093,U_20094),
    inference(clausify,[status(thm)],[f_4825_2]) ).

fof(f_4826_1,plain,
    ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_dom__map__add]) ).

fof(f_4826_2,plain,
    ! [U_20098,U_20097,U_20096,U_20095] : c_Map_Odom(U_20095,U_20096,c_Map_Omap__add(U_20095,U_20096,U_20097,U_20098)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20095,tc_HOL_Obool)),c_Map_Odom(U_20095,U_20096,U_20098)),c_Map_Odom(U_20095,U_20096,U_20097)),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

cnf(f_4826_3,plain,
    c_Map_Odom(U_20095,U_20096,c_Map_Omap__add(U_20095,U_20096,U_20097,U_20098)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20095,tc_HOL_Obool)),c_Map_Odom(U_20095,U_20096,U_20098)),c_Map_Odom(U_20095,U_20096,U_20097)),
    inference(clausify,[status(thm)],[f_4826_2]) ).

fof(f_4827_1,plain,
    ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
      ( hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I2_J]) ).

fof(f_4827_2,plain,
    ! [U_20103,U_20102,U_20101,U_20100,U_20099] :
      ( hAPP(c_Map_Omap__add(U_20099,U_20101,U_20102,U_20103),U_20100) = hAPP(U_20103,U_20100)
      | hBOOL(hAPP(hAPP(c_member(U_20099),U_20100),c_Map_Odom(U_20099,U_20101,U_20102))) ),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

cnf(f_4827_3,plain,
    ( hAPP(c_Map_Omap__add(U_20099,U_20101,U_20102,U_20103),U_20100) = hAPP(U_20103,U_20100)
    | hBOOL(hAPP(hAPP(c_member(U_20099),U_20100),c_Map_Odom(U_20099,U_20101,U_20102))) ),
    inference(clausify,[status(thm)],[f_4827_2]) ).

fof(f_4828_1,plain,
    ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
      ( hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I3_J]) ).

fof(f_4828_2,plain,
    ! [U_20108,U_20107,U_20106,U_20105,U_20104] :
      ( hAPP(c_Map_Omap__add(U_20104,U_20106,U_20108,U_20107),U_20105) = hAPP(U_20108,U_20105)
      | hBOOL(hAPP(hAPP(c_member(U_20104),U_20105),c_Map_Odom(U_20104,U_20106,U_20107))) ),
    inference(variable_rename,[status(thm)],[f_4828_1]) ).

cnf(f_4828_3,plain,
    ( hAPP(c_Map_Omap__add(U_20104,U_20106,U_20108,U_20107),U_20105) = hAPP(U_20108,U_20105)
    | hBOOL(hAPP(hAPP(c_member(U_20104),U_20105),c_Map_Odom(U_20104,U_20106,U_20107))) ),
    inference(clausify,[status(thm)],[f_4828_2]) ).

fof(f_4829_1,plain,
    ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
      ( hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J]) ).

fof(f_4829_2,plain,
    ! [U_20113,U_20112,U_20111,U_20110,U_20109] :
      ( hAPP(c_Map_Omap__add(U_20109,U_20111,U_20113,U_20112),U_20110) = hAPP(U_20112,U_20110)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20109),U_20110),c_Map_Odom(U_20109,U_20111,U_20112))) ),
    inference(variable_rename,[status(thm)],[f_4829_1]) ).

cnf(f_4829_3,plain,
    ( hAPP(c_Map_Omap__add(U_20109,U_20111,U_20113,U_20112),U_20110) = hAPP(U_20112,U_20110)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20109),U_20110),c_Map_Odom(U_20109,U_20111,U_20112))) ),
    inference(clausify,[status(thm)],[f_4829_2]) ).

fof(f_4830_1,plain,
    ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__assoc]) ).

fof(f_4830_2,plain,
    ! [U_20118,U_20117,U_20116,U_20115,U_20114] : c_Map_Omap__add(U_20114,U_20115,U_20116,c_Map_Omap__add(U_20114,U_20115,U_20117,U_20118)) = c_Map_Omap__add(U_20114,U_20115,c_Map_Omap__add(U_20114,U_20115,U_20116,U_20117),U_20118),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

cnf(f_4830_3,plain,
    c_Map_Omap__add(U_20114,U_20115,U_20116,c_Map_Omap__add(U_20114,U_20115,U_20117,U_20118)) = c_Map_Omap__add(U_20114,U_20115,c_Map_Omap__add(U_20114,U_20115,U_20116,U_20117),U_20118),
    inference(clausify,[status(thm)],[f_4830_2]) ).

fof(f_4831_1,plain,
    ! [V_m_H_2,V_m_2,T_b,T_a] :
      ( ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2))
        | ~ c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) )
      & ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2))
        | ~ c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom]) ).

fof(f_4831_2,plain,
    ! [U_20122,U_20121,U_20120,U_20119] :
      ( ( c_Fun_Oinj__on(U_20119,tc_Option_Ooption(U_20120),c_Map_Omap__add(U_20119,U_20120,U_20121,U_20122),c_Map_Odom(U_20119,U_20120,U_20122))
        | ~ c_Fun_Oinj__on(U_20119,tc_Option_Ooption(U_20120),U_20122,c_Map_Odom(U_20119,U_20120,U_20122)) )
      & ( c_Fun_Oinj__on(U_20119,tc_Option_Ooption(U_20120),U_20122,c_Map_Odom(U_20119,U_20120,U_20122))
        | ~ c_Fun_Oinj__on(U_20119,tc_Option_Ooption(U_20120),c_Map_Omap__add(U_20119,U_20120,U_20121,U_20122),c_Map_Odom(U_20119,U_20120,U_20122)) ) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

fof(f_4831_3,plain,
    ( ! [U_20130,U_20128,U_20126,U_20124] :
        ( c_Fun_Oinj__on(U_20124,tc_Option_Ooption(U_20126),c_Map_Omap__add(U_20124,U_20126,U_20128,U_20130),c_Map_Odom(U_20124,U_20126,U_20130))
        | ~ c_Fun_Oinj__on(U_20124,tc_Option_Ooption(U_20126),U_20130,c_Map_Odom(U_20124,U_20126,U_20130)) )
    & ! [U_20129,U_20127,U_20125,U_20123] :
        ( c_Fun_Oinj__on(U_20123,tc_Option_Ooption(U_20125),U_20129,c_Map_Odom(U_20123,U_20125,U_20129))
        | ~ c_Fun_Oinj__on(U_20123,tc_Option_Ooption(U_20125),c_Map_Omap__add(U_20123,U_20125,U_20127,U_20129),c_Map_Odom(U_20123,U_20125,U_20129)) ) ),
    inference(miniscope,[status(thm)],[f_4831_2]) ).

cnf(f_4831_4,plain,
    ( c_Fun_Oinj__on(U_20123,tc_Option_Ooption(U_20125),U_20129,c_Map_Odom(U_20123,U_20125,U_20129))
    | ~ c_Fun_Oinj__on(U_20123,tc_Option_Ooption(U_20125),c_Map_Omap__add(U_20123,U_20125,U_20127,U_20129),c_Map_Odom(U_20123,U_20125,U_20129)) ),
    inference(clausify,[status(thm)],[f_4831_3]) ).

cnf(f_4831_5,plain,
    ( c_Fun_Oinj__on(U_20124,tc_Option_Ooption(U_20126),c_Map_Omap__add(U_20124,U_20126,U_20128,U_20130),c_Map_Odom(U_20124,U_20126,U_20130))
    | ~ c_Fun_Oinj__on(U_20124,tc_Option_Ooption(U_20126),U_20130,c_Map_Odom(U_20124,U_20126,U_20130)) ),
    inference(clausify,[status(thm)],[f_4831_3]) ).

fof(f_4832_1,plain,
    ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_map__add__def]) ).

fof(f_4832_2,plain,
    ! [U_20135,U_20134,U_20133,U_20132,U_20131] : hAPP(c_Map_Omap__add(U_20131,U_20132,U_20133,U_20134),U_20135) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_20132),U_20132,hAPP(U_20133,U_20135),c_Option_Ooption_OSome(U_20132)),hAPP(U_20134,U_20135)),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

cnf(f_4832_3,plain,
    hAPP(c_Map_Omap__add(U_20131,U_20132,U_20133,U_20134),U_20135) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_20132),U_20132,hAPP(U_20133,U_20135),c_Option_Ooption_OSome(U_20132)),hAPP(U_20134,U_20135)),
    inference(clausify,[status(thm)],[f_4832_2]) ).

fof(f_4833_1,plain,
    ! [V_m2_2,V_m1_2,T_b,T_a] :
      ( c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__comm]) ).

fof(f_4833_2,plain,
    ! [U_20139,U_20138,U_20137,U_20136] :
      ( c_Map_Omap__add(U_20136,U_20137,U_20138,U_20139) = c_Map_Omap__add(U_20136,U_20137,U_20139,U_20138)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20136,tc_HOL_Obool)),c_Map_Odom(U_20136,U_20137,U_20138)),c_Map_Odom(U_20136,U_20137,U_20139)) != c_Orderings_Obot__class_Obot(tc_fun(U_20136,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

cnf(f_4833_3,plain,
    ( c_Map_Omap__add(U_20136,U_20137,U_20138,U_20139) = c_Map_Omap__add(U_20136,U_20137,U_20139,U_20138)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20136,tc_HOL_Obool)),c_Map_Odom(U_20136,U_20137,U_20138)),c_Map_Odom(U_20136,U_20137,U_20139)) != c_Orderings_Obot__class_Obot(tc_fun(U_20136,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4833_2]) ).

fof(f_4834_1,plain,
    ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
      ( ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
        | ( ! [B_k_H] :
              ( hAPP(V_m1_2,B_k_H) != c_Option_Ooption_ONone(T_a)
              | hAPP(V_m2_2,V_k_2) != hAPP(c_Option_Ooption_OSome(T_b),B_k_H) )
          & hAPP(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_a)
            & hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) )
        | hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
        | c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) != c_Option_Ooption_ONone(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__comp__None__iff]) ).

fof(f_4834_2,plain,
    ! [U_20147,U_20146,U_20145,U_20144,U_20143,U_20142] :
      ( ( c_Map_Omap__comp(U_20142,U_20143,U_20144,U_20145,U_20146,U_20147) = c_Option_Ooption_ONone(U_20143)
        | ( ! [U_20141] :
              ( hAPP(U_20145,U_20141) != c_Option_Ooption_ONone(U_20143)
              | hAPP(U_20146,U_20147) != hAPP(c_Option_Ooption_OSome(U_20142),U_20141) )
          & hAPP(U_20146,U_20147) != c_Option_Ooption_ONone(U_20142) ) )
      & ( ? [U_20140] :
            ( hAPP(U_20145,U_20140) = c_Option_Ooption_ONone(U_20143)
            & hAPP(U_20146,U_20147) = hAPP(c_Option_Ooption_OSome(U_20142),U_20140) )
        | hAPP(U_20146,U_20147) = c_Option_Ooption_ONone(U_20142)
        | c_Map_Omap__comp(U_20142,U_20143,U_20144,U_20145,U_20146,U_20147) != c_Option_Ooption_ONone(U_20143) ) ),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ( ! [U_20159,U_20157,U_20155,U_20153,U_20151,U_20149] :
        ( c_Map_Omap__comp(U_20149,U_20151,U_20153,U_20155,U_20157,U_20159) = c_Option_Ooption_ONone(U_20151)
        | ( ! [U_20141] :
              ( hAPP(U_20155,U_20141) != c_Option_Ooption_ONone(U_20151)
              | hAPP(U_20157,U_20159) != hAPP(c_Option_Ooption_OSome(U_20149),U_20141) )
          & hAPP(U_20157,U_20159) != c_Option_Ooption_ONone(U_20149) ) )
    & ! [U_20158,U_20156,U_20154,U_20152,U_20150,U_20148] :
        ( ? [U_20140] :
            ( hAPP(U_20154,U_20140) = c_Option_Ooption_ONone(U_20150)
            & hAPP(U_20156,U_20158) = hAPP(c_Option_Ooption_OSome(U_20148),U_20140) )
        | hAPP(U_20156,U_20158) = c_Option_Ooption_ONone(U_20148)
        | c_Map_Omap__comp(U_20148,U_20150,U_20152,U_20154,U_20156,U_20158) != c_Option_Ooption_ONone(U_20150) ) ),
    inference(miniscope,[status(thm)],[f_4834_2]) ).

fof(f_4834_4,plain,
    ( ! [U_20159,U_20157,U_20155,U_20153,U_20151,U_20149] :
        ( c_Map_Omap__comp(U_20149,U_20151,U_20153,U_20155,U_20157,U_20159) = c_Option_Ooption_ONone(U_20151)
        | ( ! [U_20141] :
              ( hAPP(U_20155,U_20141) != c_Option_Ooption_ONone(U_20151)
              | hAPP(U_20157,U_20159) != hAPP(c_Option_Ooption_OSome(U_20149),U_20141) )
          & hAPP(U_20157,U_20159) != c_Option_Ooption_ONone(U_20149) ) )
    & ! [U_20158,U_20156,U_20154,U_20152,U_20150,U_20148] :
        ( ( hAPP(U_20154,sK504(U_20158,U_20156,U_20154,U_20152,U_20150,U_20148)) = c_Option_Ooption_ONone(U_20150)
          & hAPP(U_20156,U_20158) = hAPP(c_Option_Ooption_OSome(U_20148),sK504(U_20158,U_20156,U_20154,U_20152,U_20150,U_20148)) )
        | hAPP(U_20156,U_20158) = c_Option_Ooption_ONone(U_20148)
        | c_Map_Omap__comp(U_20148,U_20150,U_20152,U_20154,U_20156,U_20158) != c_Option_Ooption_ONone(U_20150) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_20140,sK504(U_20158,U_20156,U_20154,U_20152,U_20150,U_20148))],[f_4834_3]) ).

cnf(f_4834_5,plain,
    ( hAPP(U_20156,U_20158) = hAPP(c_Option_Ooption_OSome(U_20148),sK504(U_20158,U_20156,U_20154,U_20152,U_20150,U_20148))
    | hAPP(U_20156,U_20158) = c_Option_Ooption_ONone(U_20148)
    | c_Map_Omap__comp(U_20148,U_20150,U_20152,U_20154,U_20156,U_20158) != c_Option_Ooption_ONone(U_20150) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

cnf(f_4834_6,plain,
    ( hAPP(U_20154,sK504(U_20158,U_20156,U_20154,U_20152,U_20150,U_20148)) = c_Option_Ooption_ONone(U_20150)
    | hAPP(U_20156,U_20158) = c_Option_Ooption_ONone(U_20148)
    | c_Map_Omap__comp(U_20148,U_20150,U_20152,U_20154,U_20156,U_20158) != c_Option_Ooption_ONone(U_20150) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

cnf(f_4834_7,plain,
    ( hAPP(U_20157,U_20159) != c_Option_Ooption_ONone(U_20149)
    | c_Map_Omap__comp(U_20149,U_20151,U_20153,U_20155,U_20157,U_20159) = c_Option_Ooption_ONone(U_20151) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

cnf(f_4834_8,plain,
    ( hAPP(U_20155,U_20141) != c_Option_Ooption_ONone(U_20151)
    | hAPP(U_20157,U_20159) != hAPP(c_Option_Ooption_OSome(U_20149),U_20141)
    | c_Map_Omap__comp(U_20149,U_20151,U_20153,U_20155,U_20157,U_20159) = c_Option_Ooption_ONone(U_20151) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

fof(f_4835_1,plain,
    ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2),
    inference(fof_nnf,[status(thm)],[fact_map__add__map__of__foldr]) ).

fof(f_4835_2,plain,
    ! [U_20163,U_20162,U_20161,U_20160] : c_Map_Omap__add(U_20160,U_20161,U_20162,hAPP(c_Map_Omap__of(U_20160,U_20161),U_20163)) = c_List_Ofoldr(tc_prod(U_20160,U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20160,U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),hAPP(hAPP(c_COMBC(U_20160,tc_fun(U_20161,tc_Option_Ooption(U_20161)),tc_fun(U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),tc_fun(tc_fun(U_20161,tc_Option_Ooption(U_20161)),tc_fun(U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))))),U_20160),c_COMBB(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))),U_20161)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),tc_fun(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),U_20160),c_COMBC(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),hAPP(c_COMBC(tc_fun(U_20160,tc_Option_Ooption(U_20161)),U_20160,tc_fun(tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),c_Fun_Ofun__upd(U_20160,tc_Option_Ooption(U_20161)))))),c_Option_Ooption_OSome(U_20161))),U_20163,U_20162),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

cnf(f_4835_3,plain,
    c_Map_Omap__add(U_20160,U_20161,U_20162,hAPP(c_Map_Omap__of(U_20160,U_20161),U_20163)) = c_List_Ofoldr(tc_prod(U_20160,U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20160,U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),hAPP(hAPP(c_COMBC(U_20160,tc_fun(U_20161,tc_Option_Ooption(U_20161)),tc_fun(U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),tc_fun(tc_fun(U_20161,tc_Option_Ooption(U_20161)),tc_fun(U_20161,tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))))),U_20160),c_COMBB(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161))),U_20161)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),tc_fun(tc_Option_Ooption(U_20161),tc_fun(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),U_20160),c_COMBC(tc_fun(U_20160,tc_Option_Ooption(U_20161)),tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),hAPP(c_COMBC(tc_fun(U_20160,tc_Option_Ooption(U_20161)),U_20160,tc_fun(tc_Option_Ooption(U_20161),tc_fun(U_20160,tc_Option_Ooption(U_20161)))),c_Fun_Ofun__upd(U_20160,tc_Option_Ooption(U_20161)))))),c_Option_Ooption_OSome(U_20161))),U_20163,U_20162),
    inference(clausify,[status(thm)],[f_4835_2]) ).

fof(f_4836_1,plain,
    ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
      ( c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2))
      | hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__add__upd__left]) ).

fof(f_4836_2,plain,
    ! [U_20169,U_20168,U_20167,U_20166,U_20165,U_20164] :
      ( c_Map_Omap__add(U_20164,U_20166,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20164,tc_Option_Ooption(U_20166)),U_20168),U_20165),hAPP(c_Option_Ooption_OSome(U_20166),U_20169)),U_20167) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20164,tc_Option_Ooption(U_20166)),c_Map_Omap__add(U_20164,U_20166,U_20168,U_20167)),U_20165),hAPP(c_Option_Ooption_OSome(U_20166),U_20169))
      | hBOOL(hAPP(hAPP(c_member(U_20164),U_20165),c_Map_Odom(U_20164,U_20166,U_20167))) ),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

cnf(f_4836_3,plain,
    ( c_Map_Omap__add(U_20164,U_20166,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20164,tc_Option_Ooption(U_20166)),U_20168),U_20165),hAPP(c_Option_Ooption_OSome(U_20166),U_20169)),U_20167) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_20164,tc_Option_Ooption(U_20166)),c_Map_Omap__add(U_20164,U_20166,U_20168,U_20167)),U_20165),hAPP(c_Option_Ooption_OSome(U_20166),U_20169))
    | hBOOL(hAPP(hAPP(c_member(U_20164),U_20165),c_Map_Odom(U_20164,U_20166,U_20167))) ),
    inference(clausify,[status(thm)],[f_4836_2]) ).

fof(f_4837_1,plain,
    ! [V_l_2,V_f_2,T_b,T_a] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__map__of__map__add]) ).

fof(f_4837_2,plain,
    ! [U_20173,U_20172,U_20171,U_20170] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_20170)),hAPP(c_Set_Oimage(U_20171,tc_Option_Ooption(U_20170),c_Map_Omap__add(U_20171,U_20170,U_20172,hAPP(c_Map_Omap__of(U_20171,U_20170),U_20173))),c_Orderings_Otop__class_Otop(tc_fun(U_20171,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_20170)),hAPP(c_Set_Oimage(U_20171,tc_Option_Ooption(U_20170),U_20172),c_Orderings_Otop__class_Otop(tc_fun(U_20171,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_4837_1]) ).

cnf(f_4837_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_20170)),hAPP(c_Set_Oimage(U_20171,tc_Option_Ooption(U_20170),c_Map_Omap__add(U_20171,U_20170,U_20172,hAPP(c_Map_Omap__of(U_20171,U_20170),U_20173))),c_Orderings_Otop__class_Otop(tc_fun(U_20171,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_20170)),hAPP(c_Set_Oimage(U_20171,tc_Option_Ooption(U_20170),U_20172),c_Orderings_Otop__class_Otop(tc_fun(U_20171,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_4837_2]) ).

fof(f_4838_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
        | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) )
      & ( c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_List_Oinsert__def]) ).

fof(f_4838_2,plain,
    ! [U_20176,U_20175,U_20174] :
      ( ( c_List_Oinsert(U_20174,U_20175,U_20176) = hAPP(hAPP(c_List_Olist_OCons(U_20174),U_20175),U_20176)
        | hBOOL(hAPP(hAPP(c_member(U_20174),U_20175),hAPP(c_List_Oset(U_20174),U_20176))) )
      & ( c_List_Oinsert(U_20174,U_20175,U_20176) = U_20176
        | ~ hBOOL(hAPP(hAPP(c_member(U_20174),U_20175),hAPP(c_List_Oset(U_20174),U_20176))) ) ),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

fof(f_4838_3,plain,
    ( ! [U_20182,U_20180,U_20178] :
        ( c_List_Oinsert(U_20178,U_20180,U_20182) = hAPP(hAPP(c_List_Olist_OCons(U_20178),U_20180),U_20182)
        | hBOOL(hAPP(hAPP(c_member(U_20178),U_20180),hAPP(c_List_Oset(U_20178),U_20182))) )
    & ! [U_20181,U_20179,U_20177] :
        ( c_List_Oinsert(U_20177,U_20179,U_20181) = U_20181
        | ~ hBOOL(hAPP(hAPP(c_member(U_20177),U_20179),hAPP(c_List_Oset(U_20177),U_20181))) ) ),
    inference(miniscope,[status(thm)],[f_4838_2]) ).

cnf(f_4838_4,plain,
    ( c_List_Oinsert(U_20177,U_20179,U_20181) = U_20181
    | ~ hBOOL(hAPP(hAPP(c_member(U_20177),U_20179),hAPP(c_List_Oset(U_20177),U_20181))) ),
    inference(clausify,[status(thm)],[f_4838_3]) ).

cnf(f_4838_5,plain,
    ( c_List_Oinsert(U_20178,U_20180,U_20182) = hAPP(hAPP(c_List_Olist_OCons(U_20178),U_20180),U_20182)
    | hBOOL(hAPP(hAPP(c_member(U_20178),U_20180),hAPP(c_List_Oset(U_20178),U_20182))) ),
    inference(clausify,[status(thm)],[f_4838_3]) ).

fof(f_4839_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_not__in__set__insert]) ).

fof(f_4839_2,plain,
    ! [U_20185,U_20184,U_20183] :
      ( c_List_Oinsert(U_20183,U_20184,U_20185) = hAPP(hAPP(c_List_Olist_OCons(U_20183),U_20184),U_20185)
      | hBOOL(hAPP(hAPP(c_member(U_20183),U_20184),hAPP(c_List_Oset(U_20183),U_20185))) ),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

cnf(f_4839_3,plain,
    ( c_List_Oinsert(U_20183,U_20184,U_20185) = hAPP(hAPP(c_List_Olist_OCons(U_20183),U_20184),U_20185)
    | hBOOL(hAPP(hAPP(c_member(U_20183),U_20184),hAPP(c_List_Oset(U_20183),U_20185))) ),
    inference(clausify,[status(thm)],[f_4839_2]) ).

fof(f_4840_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insert]) ).

fof(f_4840_2,plain,
    ! [U_20188,U_20187,U_20186] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20186),c_List_Oinsert(U_20186,U_20188,U_20187)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20186),U_20187)) ),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

cnf(f_4840_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20186),c_List_Oinsert(U_20186,U_20188,U_20187)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20186),U_20187)) ),
    inference(clausify,[status(thm)],[f_4840_2]) ).

fof(f_4841_1,plain,
    ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_insert__remdups]) ).

fof(f_4841_2,plain,
    ! [U_20191,U_20190,U_20189] : c_List_Oinsert(U_20189,U_20190,c_List_Oremdups(U_20189,U_20191)) = c_List_Oremdups(U_20189,c_List_Oinsert(U_20189,U_20190,U_20191)),
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

cnf(f_4841_3,plain,
    c_List_Oinsert(U_20189,U_20190,c_List_Oremdups(U_20189,U_20191)) = c_List_Oremdups(U_20189,c_List_Oinsert(U_20189,U_20190,U_20191)),
    inference(clausify,[status(thm)],[f_4841_2]) ).

fof(f_4842_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__insert]) ).

fof(f_4842_2,plain,
    ! [U_20194,U_20193,U_20192] :
      ( c_List_Oinsert(U_20192,U_20193,U_20194) = U_20194
      | ~ hBOOL(hAPP(hAPP(c_member(U_20192),U_20193),hAPP(c_List_Oset(U_20192),U_20194))) ),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

cnf(f_4842_3,plain,
    ( c_List_Oinsert(U_20192,U_20193,U_20194) = U_20194
    | ~ hBOOL(hAPP(hAPP(c_member(U_20192),U_20193),hAPP(c_List_Oset(U_20192),U_20194))) ),
    inference(clausify,[status(thm)],[f_4842_2]) ).

fof(f_4843_1,plain,
    ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset__insert]) ).

fof(f_4843_2,plain,
    ! [U_20197,U_20196,U_20195] : hAPP(c_List_Oset(U_20195),c_List_Oinsert(U_20195,U_20196,U_20197)) = hAPP(hAPP(c_Set_Oinsert(U_20195),U_20196),hAPP(c_List_Oset(U_20195),U_20197)),
    inference(variable_rename,[status(thm)],[f_4843_1]) ).

cnf(f_4843_3,plain,
    hAPP(c_List_Oset(U_20195),c_List_Oinsert(U_20195,U_20196,U_20197)) = hAPP(hAPP(c_Set_Oinsert(U_20195),U_20196),hAPP(c_List_Oset(U_20195),U_20197)),
    inference(clausify,[status(thm)],[f_4843_2]) ).

fof(f_4844_1,plain,
    ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_insert__Nil]) ).

fof(f_4844_2,plain,
    ! [U_20199,U_20198] : c_List_Oinsert(U_20198,U_20199,c_List_Olist_ONil(U_20198)) = hAPP(hAPP(c_List_Olist_OCons(U_20198),U_20199),c_List_Olist_ONil(U_20198)),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

cnf(f_4844_3,plain,
    c_List_Oinsert(U_20198,U_20199,c_List_Olist_ONil(U_20198)) = hAPP(hAPP(c_List_Olist_OCons(U_20198),U_20199),c_List_Olist_ONil(U_20198)),
    inference(clausify,[status(thm)],[f_4844_2]) ).

fof(f_4845_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_concat__map__maps]) ).

fof(f_4845_2,plain,
    ! [U_20203,U_20202,U_20201,U_20200] : c_List_Oconcat(U_20200,hAPP(hAPP(c_List_Omap(U_20201,tc_List_Olist(U_20200)),U_20202),U_20203)) = c_List_Omaps(U_20201,U_20200,U_20202,U_20203),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

cnf(f_4845_3,plain,
    c_List_Oconcat(U_20200,hAPP(hAPP(c_List_Omap(U_20201,tc_List_Olist(U_20200)),U_20202),U_20203)) = c_List_Omaps(U_20201,U_20200,U_20202,U_20203),
    inference(clausify,[status(thm)],[f_4845_2]) ).

fof(f_4846_1,plain,
    ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_maps__def]) ).

fof(f_4846_2,plain,
    ! [U_20207,U_20206,U_20205,U_20204] : c_List_Omaps(U_20204,U_20205,U_20206,U_20207) = c_List_Oconcat(U_20205,hAPP(hAPP(c_List_Omap(U_20204,tc_List_Olist(U_20205)),U_20206),U_20207)),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

cnf(f_4846_3,plain,
    c_List_Omaps(U_20204,U_20205,U_20206,U_20207) = c_List_Oconcat(U_20205,hAPP(hAPP(c_List_Omap(U_20204,tc_List_Olist(U_20205)),U_20206),U_20207)),
    inference(clausify,[status(thm)],[f_4846_2]) ).

fof(f_4847_1,plain,
    ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_maps__simps_I2_J]) ).

fof(f_4847_2,plain,
    ! [U_20210,U_20209,U_20208] : c_List_Omaps(U_20208,U_20209,U_20210,c_List_Olist_ONil(U_20208)) = c_List_Olist_ONil(U_20209),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

cnf(f_4847_3,plain,
    c_List_Omaps(U_20208,U_20209,U_20210,c_List_Olist_ONil(U_20208)) = c_List_Olist_ONil(U_20209),
    inference(clausify,[status(thm)],[f_4847_2]) ).

fof(f_4848_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_maps__simps_I1_J]) ).

fof(f_4848_2,plain,
    ! [U_20215,U_20214,U_20213,U_20212,U_20211] : c_List_Omaps(U_20211,U_20212,U_20213,hAPP(hAPP(c_List_Olist_OCons(U_20211),U_20214),U_20215)) = hAPP(hAPP(c_List_Oappend(U_20212),hAPP(U_20213,U_20214)),c_List_Omaps(U_20211,U_20212,U_20213,U_20215)),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

cnf(f_4848_3,plain,
    c_List_Omaps(U_20211,U_20212,U_20213,hAPP(hAPP(c_List_Olist_OCons(U_20211),U_20214),U_20215)) = hAPP(hAPP(c_List_Oappend(U_20212),hAPP(U_20213,U_20214)),c_List_Omaps(U_20211,U_20212,U_20213,U_20215)),
    inference(clausify,[status(thm)],[f_4848_2]) ).

fof(f_4849_1,plain,
    ! [V_xs_2,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2)))
      | ? [B_ys] :
          ( ? [B_zs] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
              & B_ys != B_zs
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) )
      | ? [B_ys] :
          ( ~ hBOOL(hAPP(c_List_Odistinct(T_a),B_ys))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__concat]) ).

fof(f_4849_2,plain,
    ! [U_20220,U_20219] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
      | ? [U_20218] :
          ( ? [U_20217] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),U_20218)),hAPP(c_List_Oset(U_20219),U_20217)) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
              & U_20218 != U_20217
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20217),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20218),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ? [U_20216] :
          ( ~ hBOOL(hAPP(c_List_Odistinct(U_20219),U_20216))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20216),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

fof(f_4849_3,plain,
    ! [U_20220,U_20219] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
      | ? [U_20218] :
          ( ? [U_20217] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),U_20218)),hAPP(c_List_Oset(U_20219),U_20217)) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
              & U_20218 != U_20217
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20217),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20218),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_20216,sK505(U_20220,U_20219))],[f_4849_2]) ).

fof(f_4849_4,plain,
    ! [U_20220,U_20219] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
      | ( ? [U_20217] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),sK506(U_20220,U_20219))),hAPP(c_List_Oset(U_20219),U_20217)) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
            & sK506(U_20220,U_20219) != U_20217
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),U_20217),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK506(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_20218,sK506(U_20220,U_20219))],[f_4849_3]) ).

fof(f_4849_5,plain,
    ! [U_20220,U_20219] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),sK506(U_20220,U_20219))),hAPP(c_List_Oset(U_20219),sK507(U_20220,U_20219))) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
        & sK506(U_20220,U_20219) != sK507(U_20220,U_20219)
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK507(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK506(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_20217,sK507(U_20220,U_20219))],[f_4849_4]) ).

cnf(f_4849_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK506(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK507(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_8,plain,
    ( sK506(U_20220,U_20219) != sK507(U_20220,U_20219)
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),sK506(U_20220,U_20219))),hAPP(c_List_Oset(U_20219),sK507(U_20220,U_20219))) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK505(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK506(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20219)),sK507(U_20220,U_20219)),hAPP(c_List_Oset(tc_List_Olist(U_20219)),U_20220)))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_12,plain,
    ( sK506(U_20220,U_20219) != sK507(U_20220,U_20219)
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

cnf(f_4849_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20219,tc_HOL_Obool)),hAPP(c_List_Oset(U_20219),sK506(U_20220,U_20219))),hAPP(c_List_Oset(U_20219),sK507(U_20220,U_20219))) != c_Orderings_Obot__class_Obot(tc_fun(U_20219,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_20219),c_List_Oconcat(U_20219,U_20220)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20219),sK505(U_20220,U_20219)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20219)),U_20220)) ),
    inference(clausify,[status(thm)],[f_4849_5]) ).

fof(f_4850_1,plain,
    ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
      ( ? [B_x] :
          ( hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_ran__restrictD]) ).

fof(f_4850_2,plain,
    ! [U_20226,U_20225,U_20224,U_20223,U_20222] :
      ( ? [U_20221] :
          ( hAPP(U_20225,U_20221) = hAPP(c_Option_Ooption_OSome(U_20222),U_20223)
          & hBOOL(hAPP(hAPP(c_member(U_20224),U_20221),U_20226)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_20222),U_20223),c_Map_Oran(U_20224,U_20222,c_Map_Orestrict__map(U_20224,U_20222,U_20225,U_20226)))) ),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

fof(f_4850_3,plain,
    ! [U_20226,U_20225,U_20224,U_20223,U_20222] :
      ( ( hAPP(U_20225,sK508(U_20226,U_20225,U_20224,U_20223,U_20222)) = hAPP(c_Option_Ooption_OSome(U_20222),U_20223)
        & hBOOL(hAPP(hAPP(c_member(U_20224),sK508(U_20226,U_20225,U_20224,U_20223,U_20222)),U_20226)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_20222),U_20223),c_Map_Oran(U_20224,U_20222,c_Map_Orestrict__map(U_20224,U_20222,U_20225,U_20226)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_20221,sK508(U_20226,U_20225,U_20224,U_20223,U_20222))],[f_4850_2]) ).

cnf(f_4850_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20224),sK508(U_20226,U_20225,U_20224,U_20223,U_20222)),U_20226))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20222),U_20223),c_Map_Oran(U_20224,U_20222,c_Map_Orestrict__map(U_20224,U_20222,U_20225,U_20226)))) ),
    inference(clausify,[status(thm)],[f_4850_3]) ).

cnf(f_4850_5,plain,
    ( hAPP(U_20225,sK508(U_20226,U_20225,U_20224,U_20223,U_20222)) = hAPP(c_Option_Ooption_OSome(U_20222),U_20223)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20222),U_20223),c_Map_Oran(U_20224,U_20222,c_Map_Orestrict__map(U_20224,U_20222,U_20225,U_20226)))) ),
    inference(clausify,[status(thm)],[f_4850_3]) ).

fof(f_4851_1,plain,
    ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_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_measures__lesseq]) ).

fof(f_4851_2,plain,
    ! [U_20231,U_20230,U_20229,U_20228,U_20227] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20230,U_20230)),hAPP(hAPP(c_Product__Type_OPair(U_20230,U_20230),U_20228),U_20229)),c_List_Omeasures(U_20230,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20230,tc_Nat_Onat)),U_20227),U_20231))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20230,U_20230)),hAPP(hAPP(c_Product__Type_OPair(U_20230,U_20230),U_20228),U_20229)),c_List_Omeasures(U_20230,U_20231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_20227,U_20228)),hAPP(U_20227,U_20229))) ),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

cnf(f_4851_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20230,U_20230)),hAPP(hAPP(c_Product__Type_OPair(U_20230,U_20230),U_20228),U_20229)),c_List_Omeasures(U_20230,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20230,tc_Nat_Onat)),U_20227),U_20231))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20230,U_20230)),hAPP(hAPP(c_Product__Type_OPair(U_20230,U_20230),U_20228),U_20229)),c_List_Omeasures(U_20230,U_20231)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_20227,U_20228)),hAPP(U_20227,U_20229))) ),
    inference(clausify,[status(thm)],[f_4851_2]) ).

fof(f_4852_1,plain,
    ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
            | 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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
          & 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_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J]) ).

fof(f_4852_2,plain,
    ! [U_20236,U_20235,U_20234,U_20233,U_20232] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20232,U_20232)),hAPP(hAPP(c_Product__Type_OPair(U_20232,U_20232),U_20233),U_20234)),c_List_Omeasures(U_20232,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20232,tc_Nat_Onat)),U_20235),U_20236))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20232,U_20232)),hAPP(hAPP(c_Product__Type_OPair(U_20232,U_20232),U_20233),U_20234)),c_List_Omeasures(U_20232,U_20236)))
            | hAPP(U_20235,U_20233) != hAPP(U_20235,U_20234) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20235,U_20233)),hAPP(U_20235,U_20234))) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20232,U_20232)),hAPP(hAPP(c_Product__Type_OPair(U_20232,U_20232),U_20233),U_20234)),c_List_Omeasures(U_20232,U_20236)))
          & hAPP(U_20235,U_20233) = hAPP(U_20235,U_20234) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20235,U_20233)),hAPP(U_20235,U_20234)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20232,U_20232)),hAPP(hAPP(c_Product__Type_OPair(U_20232,U_20232),U_20233),U_20234)),c_List_Omeasures(U_20232,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20232,tc_Nat_Onat)),U_20235),U_20236)))) ) ),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

fof(f_4852_3,plain,
    ( ! [U_20246,U_20244,U_20242,U_20240,U_20238] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20238,U_20238)),hAPP(hAPP(c_Product__Type_OPair(U_20238,U_20238),U_20240),U_20242)),c_List_Omeasures(U_20238,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20238,tc_Nat_Onat)),U_20244),U_20246))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20238,U_20238)),hAPP(hAPP(c_Product__Type_OPair(U_20238,U_20238),U_20240),U_20242)),c_List_Omeasures(U_20238,U_20246)))
            | hAPP(U_20244,U_20240) != hAPP(U_20244,U_20242) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20244,U_20240)),hAPP(U_20244,U_20242))) ) )
    & ! [U_20245,U_20243,U_20241,U_20239,U_20237] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20237,U_20237)),hAPP(hAPP(c_Product__Type_OPair(U_20237,U_20237),U_20239),U_20241)),c_List_Omeasures(U_20237,U_20245)))
          & hAPP(U_20243,U_20239) = hAPP(U_20243,U_20241) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20243,U_20239)),hAPP(U_20243,U_20241)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20237,U_20237)),hAPP(hAPP(c_Product__Type_OPair(U_20237,U_20237),U_20239),U_20241)),c_List_Omeasures(U_20237,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20237,tc_Nat_Onat)),U_20243),U_20245)))) ) ),
    inference(miniscope,[status(thm)],[f_4852_2]) ).

cnf(f_4852_4,plain,
    ( hAPP(U_20243,U_20239) = hAPP(U_20243,U_20241)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20243,U_20239)),hAPP(U_20243,U_20241)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20237,U_20237)),hAPP(hAPP(c_Product__Type_OPair(U_20237,U_20237),U_20239),U_20241)),c_List_Omeasures(U_20237,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20237,tc_Nat_Onat)),U_20243),U_20245)))) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

cnf(f_4852_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20237,U_20237)),hAPP(hAPP(c_Product__Type_OPair(U_20237,U_20237),U_20239),U_20241)),c_List_Omeasures(U_20237,U_20245)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20243,U_20239)),hAPP(U_20243,U_20241)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20237,U_20237)),hAPP(hAPP(c_Product__Type_OPair(U_20237,U_20237),U_20239),U_20241)),c_List_Omeasures(U_20237,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20237,tc_Nat_Onat)),U_20243),U_20245)))) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

cnf(f_4852_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20244,U_20240)),hAPP(U_20244,U_20242)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_20238,U_20238)),hAPP(hAPP(c_Product__Type_OPair(U_20238,U_20238),U_20240),U_20242)),c_List_Omeasures(U_20238,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20238,tc_Nat_Onat)),U_20244),U_20246)))) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

cnf(f_4852_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20238,U_20238)),hAPP(hAPP(c_Product__Type_OPair(U_20238,U_20238),U_20240),U_20242)),c_List_Omeasures(U_20238,U_20246)))
    | hAPP(U_20244,U_20240) != hAPP(U_20244,U_20242)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_20238,U_20238)),hAPP(hAPP(c_Product__Type_OPair(U_20238,U_20238),U_20240),U_20242)),c_List_Omeasures(U_20238,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20238,tc_Nat_Onat)),U_20244),U_20246)))) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

fof(f_4853_1,plain,
    ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__measures]) ).

fof(f_4853_2,plain,
    ! [U_20248,U_20247] : c_Wellfounded_Owf(U_20247,c_List_Omeasures(U_20247,U_20248)),
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

cnf(f_4853_3,plain,
    c_Wellfounded_Owf(U_20247,c_List_Omeasures(U_20247,U_20248)),
    inference(clausify,[status(thm)],[f_4853_2]) ).

fof(f_4854_1,plain,
    ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))),
    inference(fof_nnf,[status(thm)],[fact_in__measures_I1_J]) ).

fof(f_4854_2,plain,
    ! [U_20251,U_20250,U_20249] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20249,U_20249)),hAPP(hAPP(c_Product__Type_OPair(U_20249,U_20249),U_20250),U_20251)),c_List_Omeasures(U_20249,c_List_Olist_ONil(tc_fun(U_20249,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

cnf(f_4854_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20249,U_20249)),hAPP(hAPP(c_Product__Type_OPair(U_20249,U_20249),U_20250),U_20251)),c_List_Omeasures(U_20249,c_List_Olist_ONil(tc_fun(U_20249,tc_Nat_Onat))))),
    inference(clausify,[status(thm)],[f_4854_2]) ).

fof(f_4855_1,plain,
    ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)),
    inference(fof_nnf,[status(thm)],[fact_measures__def]) ).

fof(f_4855_2,plain,
    ! [U_20253,U_20252] : c_List_Omeasures(U_20252,U_20253) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_20252),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_20252,tc_List_Olist(tc_fun(U_20252,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_20252,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_20252,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_20252),c_List_Omap(tc_fun(U_20252,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_20252,tc_Nat_Onat),U_20252,tc_Nat_Onat),c_COMBI(tc_fun(U_20252,tc_Nat_Onat))))),U_20253)),
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

cnf(f_4855_3,plain,
    c_List_Omeasures(U_20252,U_20253) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_20252),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_20252,tc_List_Olist(tc_fun(U_20252,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_20252,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_20252,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_20252),c_List_Omap(tc_fun(U_20252,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_20252,tc_Nat_Onat),U_20252,tc_Nat_Onat),c_COMBI(tc_fun(U_20252,tc_Nat_Onat))))),U_20253)),
    inference(clausify,[status(thm)],[f_4855_2]) ).

fof(f_4856_1,plain,
    ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_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_measures__less]) ).

fof(f_4856_2,plain,
    ! [U_20258,U_20257,U_20256,U_20255,U_20254] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20257,U_20257)),hAPP(hAPP(c_Product__Type_OPair(U_20257,U_20257),U_20255),U_20256)),c_List_Omeasures(U_20257,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20257,tc_Nat_Onat)),U_20254),U_20258))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20254,U_20255)),hAPP(U_20254,U_20256))) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

cnf(f_4856_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20257,U_20257)),hAPP(hAPP(c_Product__Type_OPair(U_20257,U_20257),U_20255),U_20256)),c_List_Omeasures(U_20257,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_20257,tc_Nat_Onat)),U_20254),U_20258))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20254,U_20255)),hAPP(U_20254,U_20256))) ),
    inference(clausify,[status(thm)],[f_4856_2]) ).

fof(f_4857_1,plain,
    ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
      ( hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2))
      | ? [B_x] :
          ( hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) != hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__apply]) ).

fof(f_4857_2,plain,
    ! [U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260] :
      ( hAPP(c_List_Ofoldl(U_20262,U_20260,hAPP(c_COMBC(U_20260,U_20262,U_20262),U_20264),hAPP(U_20265,U_20267)),U_20261) = hAPP(U_20265,hAPP(c_List_Ofoldl(U_20263,U_20260,hAPP(c_COMBC(U_20260,U_20263,U_20263),U_20266),U_20267),U_20261))
      | ? [U_20259] :
          ( hAPP(c_Fun_Ocomp(U_20262,U_20262,U_20263,hAPP(U_20264,U_20259)),U_20265) != hAPP(c_Fun_Ocomp(U_20263,U_20262,U_20263,U_20265),hAPP(U_20266,U_20259))
          & hBOOL(hAPP(hAPP(c_member(U_20260),U_20259),hAPP(c_List_Oset(U_20260),U_20261))) ) ),
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

fof(f_4857_3,plain,
    ! [U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260] :
      ( hAPP(c_List_Ofoldl(U_20262,U_20260,hAPP(c_COMBC(U_20260,U_20262,U_20262),U_20264),hAPP(U_20265,U_20267)),U_20261) = hAPP(U_20265,hAPP(c_List_Ofoldl(U_20263,U_20260,hAPP(c_COMBC(U_20260,U_20263,U_20263),U_20266),U_20267),U_20261))
      | ( hAPP(c_Fun_Ocomp(U_20262,U_20262,U_20263,hAPP(U_20264,sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260))),U_20265) != hAPP(c_Fun_Ocomp(U_20263,U_20262,U_20263,U_20265),hAPP(U_20266,sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260)))
        & hBOOL(hAPP(hAPP(c_member(U_20260),sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260)),hAPP(c_List_Oset(U_20260),U_20261))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK509]),skolemize(U_20259,sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260))],[f_4857_2]) ).

cnf(f_4857_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20260),sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260)),hAPP(c_List_Oset(U_20260),U_20261)))
    | hAPP(c_List_Ofoldl(U_20262,U_20260,hAPP(c_COMBC(U_20260,U_20262,U_20262),U_20264),hAPP(U_20265,U_20267)),U_20261) = hAPP(U_20265,hAPP(c_List_Ofoldl(U_20263,U_20260,hAPP(c_COMBC(U_20260,U_20263,U_20263),U_20266),U_20267),U_20261)) ),
    inference(clausify,[status(thm)],[f_4857_3]) ).

cnf(f_4857_5,plain,
    ( hAPP(c_Fun_Ocomp(U_20262,U_20262,U_20263,hAPP(U_20264,sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260))),U_20265) != hAPP(c_Fun_Ocomp(U_20263,U_20262,U_20263,U_20265),hAPP(U_20266,sK509(U_20267,U_20266,U_20265,U_20264,U_20263,U_20262,U_20261,U_20260)))
    | hAPP(c_List_Ofoldl(U_20262,U_20260,hAPP(c_COMBC(U_20260,U_20262,U_20262),U_20264),hAPP(U_20265,U_20267)),U_20261) = hAPP(U_20265,hAPP(c_List_Ofoldl(U_20263,U_20260,hAPP(c_COMBC(U_20260,U_20263,U_20263),U_20266),U_20267),U_20261)) ),
    inference(clausify,[status(thm)],[f_4857_3]) ).

fof(f_4858_1,plain,
    ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))
      | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2))))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length]) ).

fof(f_4858_2,plain,
    ! [U_20272,U_20271,U_20270,U_20269,U_20268] :
      ( hBOOL(hAPP(U_20272,hAPP(hAPP(c_List_Ozip(U_20268,U_20270),U_20269),U_20271)))
      | ( ~ hBOOL(hAPP(U_20272,hAPP(hAPP(c_List_Ozip(U_20268,U_20270),hAPP(hAPP(c_List_Otake(U_20268),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20269)),hAPP(hAPP(c_List_Otake(U_20270),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20271))))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),hAPP(hAPP(c_List_Otake(U_20268),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20269)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),hAPP(hAPP(c_List_Otake(U_20270),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20271)) ) ),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

cnf(f_4858_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),hAPP(hAPP(c_List_Otake(U_20268),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20269)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),hAPP(hAPP(c_List_Otake(U_20270),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20271))
    | hBOOL(hAPP(U_20272,hAPP(hAPP(c_List_Ozip(U_20268,U_20270),U_20269),U_20271))) ),
    inference(clausify,[status(thm)],[f_4858_2]) ).

cnf(f_4858_4,plain,
    ( ~ hBOOL(hAPP(U_20272,hAPP(hAPP(c_List_Ozip(U_20268,U_20270),hAPP(hAPP(c_List_Otake(U_20268),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20269)),hAPP(hAPP(c_List_Otake(U_20270),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20268)),U_20269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),U_20271))),U_20271))))
    | hBOOL(hAPP(U_20272,hAPP(hAPP(c_List_Ozip(U_20268,U_20270),U_20269),U_20271))) ),
    inference(clausify,[status(thm)],[f_4858_2]) ).

fof(f_4859_1,plain,
    ! [V_ys_2,V_xs_2,T_b,T_a] :
      ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
      | ? [B_x] :
          ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) != hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))) )
      | hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) != hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__of__eqI]) ).

fof(f_4859_2,plain,
    ! [U_20277,U_20276,U_20275,U_20274] :
      ( hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276) = hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277)
      | ? [U_20273] :
          ( hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276),U_20273) != hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277),U_20273)
          & hBOOL(hAPP(hAPP(c_member(U_20274),U_20273),hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)))) )
      | hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)) != hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20277)) ),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

fof(f_4859_3,plain,
    ! [U_20277,U_20276,U_20275,U_20274] :
      ( hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276) = hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277)
      | ( hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276),sK510(U_20277,U_20276,U_20275,U_20274)) != hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277),sK510(U_20277,U_20276,U_20275,U_20274))
        & hBOOL(hAPP(hAPP(c_member(U_20274),sK510(U_20277,U_20276,U_20275,U_20274)),hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)))) )
      | hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)) != hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20277)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK510]),skolemize(U_20273,sK510(U_20277,U_20276,U_20275,U_20274))],[f_4859_2]) ).

cnf(f_4859_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20274),sK510(U_20277,U_20276,U_20275,U_20274)),hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276))))
    | hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276) = hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277)
    | hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)) != hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20277)) ),
    inference(clausify,[status(thm)],[f_4859_3]) ).

cnf(f_4859_5,plain,
    ( hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276),sK510(U_20277,U_20276,U_20275,U_20274)) != hAPP(hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277),sK510(U_20277,U_20276,U_20275,U_20274))
    | hAPP(c_Map_Omap__of(U_20274,U_20275),U_20276) = hAPP(c_Map_Omap__of(U_20274,U_20275),U_20277)
    | hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20276)) != hAPP(c_List_Oset(U_20274),hAPP(hAPP(c_List_Omap(tc_prod(U_20274,U_20275),U_20274),c_Product__Type_Ofst(U_20274,U_20275)),U_20277)) ),
    inference(clausify,[status(thm)],[f_4859_3]) ).

fof(f_4860_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_4860_2,plain,
    ! [U_20281,U_20280,U_20279,U_20278] : c_New__Random__Sequence_Opos__not__random__dseq(U_20278,U_20279,U_20280,U_20281) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_20278,U_20279),U_20280),U_20281)),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

cnf(f_4860_3,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_20278,U_20279,U_20280,U_20281) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_20278,U_20279),U_20280),U_20281)),
    inference(clausify,[status(thm)],[f_4860_2]) ).

fof(f_4861_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_a] :
      ( c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__append2]) ).

fof(f_4861_2,plain,
    ! [U_20286,U_20285,U_20284,U_20283] :
      ( c_List_OdropWhile(U_20283,U_20285,hAPP(hAPP(c_List_Oappend(U_20283),U_20284),U_20286)) = c_List_OdropWhile(U_20283,U_20285,U_20286)
      | ? [U_20282] :
          ( ~ hBOOL(hAPP(U_20285,U_20282))
          & hBOOL(hAPP(hAPP(c_member(U_20283),U_20282),hAPP(c_List_Oset(U_20283),U_20284))) ) ),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

fof(f_4861_3,plain,
    ! [U_20286,U_20285,U_20284,U_20283] :
      ( c_List_OdropWhile(U_20283,U_20285,hAPP(hAPP(c_List_Oappend(U_20283),U_20284),U_20286)) = c_List_OdropWhile(U_20283,U_20285,U_20286)
      | ( ~ hBOOL(hAPP(U_20285,sK511(U_20286,U_20285,U_20284,U_20283)))
        & hBOOL(hAPP(hAPP(c_member(U_20283),sK511(U_20286,U_20285,U_20284,U_20283)),hAPP(c_List_Oset(U_20283),U_20284))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK511]),skolemize(U_20282,sK511(U_20286,U_20285,U_20284,U_20283))],[f_4861_2]) ).

cnf(f_4861_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20283),sK511(U_20286,U_20285,U_20284,U_20283)),hAPP(c_List_Oset(U_20283),U_20284)))
    | c_List_OdropWhile(U_20283,U_20285,hAPP(hAPP(c_List_Oappend(U_20283),U_20284),U_20286)) = c_List_OdropWhile(U_20283,U_20285,U_20286) ),
    inference(clausify,[status(thm)],[f_4861_3]) ).

cnf(f_4861_5,plain,
    ( ~ hBOOL(hAPP(U_20285,sK511(U_20286,U_20285,U_20284,U_20283)))
    | c_List_OdropWhile(U_20283,U_20285,hAPP(hAPP(c_List_Oappend(U_20283),U_20284),U_20286)) = c_List_OdropWhile(U_20283,U_20285,U_20286) ),
    inference(clausify,[status(thm)],[f_4861_3]) ).

fof(f_4862_1,plain,
    ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
      ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
      | ? [B_n] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_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_a)),V_a_2))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__all__nthI]) ).

fof(f_4862_2,plain,
    ! [U_20292,U_20291,U_20290,U_20289,U_20288] :
      ( c_List_Olist__all2(U_20288,U_20290,U_20292,U_20289,U_20291)
      | ? [U_20287] :
          ( ~ hBOOL(hAPP(hAPP(U_20292,hAPP(hAPP(c_List_Onth(U_20288),U_20289),U_20287)),hAPP(hAPP(c_List_Onth(U_20290),U_20291),U_20287)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20287),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20291) ),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

fof(f_4862_3,plain,
    ! [U_20292,U_20291,U_20290,U_20289,U_20288] :
      ( c_List_Olist__all2(U_20288,U_20290,U_20292,U_20289,U_20291)
      | ( ~ hBOOL(hAPP(hAPP(U_20292,hAPP(hAPP(c_List_Onth(U_20288),U_20289),sK512(U_20292,U_20291,U_20290,U_20289,U_20288))),hAPP(hAPP(c_List_Onth(U_20290),U_20291),sK512(U_20292,U_20291,U_20290,U_20289,U_20288))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK512(U_20292,U_20291,U_20290,U_20289,U_20288)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20291) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK512]),skolemize(U_20287,sK512(U_20292,U_20291,U_20290,U_20289,U_20288))],[f_4862_2]) ).

cnf(f_4862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK512(U_20292,U_20291,U_20290,U_20289,U_20288)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289)))
    | c_List_Olist__all2(U_20288,U_20290,U_20292,U_20289,U_20291)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20291) ),
    inference(clausify,[status(thm)],[f_4862_3]) ).

cnf(f_4862_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_20292,hAPP(hAPP(c_List_Onth(U_20288),U_20289),sK512(U_20292,U_20291,U_20290,U_20289,U_20288))),hAPP(hAPP(c_List_Onth(U_20290),U_20291),sK512(U_20292,U_20291,U_20290,U_20289,U_20288))))
    | c_List_Olist__all2(U_20288,U_20290,U_20292,U_20289,U_20291)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20288)),U_20289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20291) ),
    inference(clausify,[status(thm)],[f_4862_3]) ).

fof(f_4863_1,plain,
    ! [V_f_2,T_b,T_a] :
      ( ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__map__freshness]) ).

fof(f_4863_2,plain,
    ! [U_20296,U_20295,U_20294] :
      ( ? [U_20293] : hAPP(U_20296,U_20293) = c_Option_Ooption_ONone(U_20295)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Orderings_Otop__class_Otop(tc_fun(U_20294,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Map_Odom(U_20294,U_20295,U_20296))) ),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

fof(f_4863_3,plain,
    ! [U_20296,U_20295,U_20294] :
      ( hAPP(U_20296,sK513(U_20296,U_20295,U_20294)) = c_Option_Ooption_ONone(U_20295)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Orderings_Otop__class_Otop(tc_fun(U_20294,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Map_Odom(U_20294,U_20295,U_20296))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK513]),skolemize(U_20293,sK513(U_20296,U_20295,U_20294))],[f_4863_2]) ).

cnf(f_4863_4,plain,
    ( hAPP(U_20296,sK513(U_20296,U_20295,U_20294)) = c_Option_Ooption_ONone(U_20295)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Orderings_Otop__class_Otop(tc_fun(U_20294,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20294),c_Map_Odom(U_20294,U_20295,U_20296))) ),
    inference(clausify,[status(thm)],[f_4863_3]) ).

fof(f_4864_1,plain,
    ! [V_A_2,T_a] :
      ( ? [B_x] :
          ( ! [B_y] :
              ( B_y = B_x
              | ~ hBOOL(hAPP(c_List_Odistinct(T_a),B_y))
              | ~ c_List_Olinorder__class_Osorted(T_a,B_y)
              | hAPP(c_List_Oset(T_a),B_y) != V_A_2 )
          & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
          & c_List_Olinorder__class_Osorted(T_a,B_x)
          & hAPP(c_List_Oset(T_a),B_x) = V_A_2 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_finite__sorted__distinct__unique]) ).

fof(f_4864_2,plain,
    ! [U_20300,U_20299] :
      ( ? [U_20298] :
          ( ! [U_20297] :
              ( U_20297 = U_20298
              | ~ hBOOL(hAPP(c_List_Odistinct(U_20299),U_20297))
              | ~ c_List_Olinorder__class_Osorted(U_20299,U_20297)
              | hAPP(c_List_Oset(U_20299),U_20297) != U_20300 )
          & hBOOL(hAPP(c_List_Odistinct(U_20299),U_20298))
          & c_List_Olinorder__class_Osorted(U_20299,U_20298)
          & hAPP(c_List_Oset(U_20299),U_20298) = U_20300 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
      | ~ class_Orderings_Olinorder(U_20299) ),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

fof(f_4864_3,plain,
    ! [U_20300,U_20299] :
      ( ( ! [U_20297] :
            ( U_20297 = sK514(U_20300,U_20299)
            | ~ hBOOL(hAPP(c_List_Odistinct(U_20299),U_20297))
            | ~ c_List_Olinorder__class_Osorted(U_20299,U_20297)
            | hAPP(c_List_Oset(U_20299),U_20297) != U_20300 )
        & hBOOL(hAPP(c_List_Odistinct(U_20299),sK514(U_20300,U_20299)))
        & c_List_Olinorder__class_Osorted(U_20299,sK514(U_20300,U_20299))
        & hAPP(c_List_Oset(U_20299),sK514(U_20300,U_20299)) = U_20300 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
      | ~ class_Orderings_Olinorder(U_20299) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK514]),skolemize(U_20298,sK514(U_20300,U_20299))],[f_4864_2]) ).

cnf(f_4864_4,plain,
    ( hAPP(c_List_Oset(U_20299),sK514(U_20300,U_20299)) = U_20300
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
    | ~ class_Orderings_Olinorder(U_20299) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

cnf(f_4864_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20299,sK514(U_20300,U_20299))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
    | ~ class_Orderings_Olinorder(U_20299) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

cnf(f_4864_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20299),sK514(U_20300,U_20299)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
    | ~ class_Orderings_Olinorder(U_20299) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

cnf(f_4864_7,plain,
    ( U_20297 = sK514(U_20300,U_20299)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20299),U_20297))
    | ~ c_List_Olinorder__class_Osorted(U_20299,U_20297)
    | hAPP(c_List_Oset(U_20299),U_20297) != U_20300
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20299),U_20300))
    | ~ class_Orderings_Olinorder(U_20299) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

fof(f_4865_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_a] :
      ( c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append2]) ).

fof(f_4865_2,plain,
    ! [U_20305,U_20304,U_20303,U_20302] :
      ( c_List_OtakeWhile(U_20302,U_20304,hAPP(hAPP(c_List_Oappend(U_20302),U_20303),U_20305)) = hAPP(hAPP(c_List_Oappend(U_20302),U_20303),c_List_OtakeWhile(U_20302,U_20304,U_20305))
      | ? [U_20301] :
          ( ~ hBOOL(hAPP(U_20304,U_20301))
          & hBOOL(hAPP(hAPP(c_member(U_20302),U_20301),hAPP(c_List_Oset(U_20302),U_20303))) ) ),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

fof(f_4865_3,plain,
    ! [U_20305,U_20304,U_20303,U_20302] :
      ( c_List_OtakeWhile(U_20302,U_20304,hAPP(hAPP(c_List_Oappend(U_20302),U_20303),U_20305)) = hAPP(hAPP(c_List_Oappend(U_20302),U_20303),c_List_OtakeWhile(U_20302,U_20304,U_20305))
      | ( ~ hBOOL(hAPP(U_20304,sK515(U_20305,U_20304,U_20303,U_20302)))
        & hBOOL(hAPP(hAPP(c_member(U_20302),sK515(U_20305,U_20304,U_20303,U_20302)),hAPP(c_List_Oset(U_20302),U_20303))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK515]),skolemize(U_20301,sK515(U_20305,U_20304,U_20303,U_20302))],[f_4865_2]) ).

cnf(f_4865_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20302),sK515(U_20305,U_20304,U_20303,U_20302)),hAPP(c_List_Oset(U_20302),U_20303)))
    | c_List_OtakeWhile(U_20302,U_20304,hAPP(hAPP(c_List_Oappend(U_20302),U_20303),U_20305)) = hAPP(hAPP(c_List_Oappend(U_20302),U_20303),c_List_OtakeWhile(U_20302,U_20304,U_20305)) ),
    inference(clausify,[status(thm)],[f_4865_3]) ).

cnf(f_4865_5,plain,
    ( ~ hBOOL(hAPP(U_20304,sK515(U_20305,U_20304,U_20303,U_20302)))
    | c_List_OtakeWhile(U_20302,U_20304,hAPP(hAPP(c_List_Oappend(U_20302),U_20303),U_20305)) = hAPP(hAPP(c_List_Oappend(U_20302),U_20303),c_List_OtakeWhile(U_20302,U_20304,U_20305)) ),
    inference(clausify,[status(thm)],[f_4865_3]) ).

fof(f_4866_1,plain,
    ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__is__Cons]) ).

fof(f_4866_2,plain,
    ! [U_20311,U_20310,U_20309,U_20308,U_20307] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20308,U_20307,U_20310),U_20311),U_20309) = hAPP(hAPP(c_List_Olist_OCons(U_20308),U_20311),U_20309)
      | ? [U_20306] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20307),hAPP(U_20310,U_20311)),hAPP(U_20310,U_20306)))
          & hBOOL(hAPP(hAPP(c_member(U_20308),U_20306),hAPP(c_List_Oset(U_20308),U_20309))) )
      | ~ class_Orderings_Olinorder(U_20307) ),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

fof(f_4866_3,plain,
    ! [U_20311,U_20310,U_20309,U_20308,U_20307] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20308,U_20307,U_20310),U_20311),U_20309) = hAPP(hAPP(c_List_Olist_OCons(U_20308),U_20311),U_20309)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20307),hAPP(U_20310,U_20311)),hAPP(U_20310,sK516(U_20311,U_20310,U_20309,U_20308,U_20307))))
        & hBOOL(hAPP(hAPP(c_member(U_20308),sK516(U_20311,U_20310,U_20309,U_20308,U_20307)),hAPP(c_List_Oset(U_20308),U_20309))) )
      | ~ class_Orderings_Olinorder(U_20307) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK516]),skolemize(U_20306,sK516(U_20311,U_20310,U_20309,U_20308,U_20307))],[f_4866_2]) ).

cnf(f_4866_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20308),sK516(U_20311,U_20310,U_20309,U_20308,U_20307)),hAPP(c_List_Oset(U_20308),U_20309)))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20308,U_20307,U_20310),U_20311),U_20309) = hAPP(hAPP(c_List_Olist_OCons(U_20308),U_20311),U_20309)
    | ~ class_Orderings_Olinorder(U_20307) ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

cnf(f_4866_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20307),hAPP(U_20310,U_20311)),hAPP(U_20310,sK516(U_20311,U_20310,U_20309,U_20308,U_20307))))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20308,U_20307,U_20310),U_20311),U_20309) = hAPP(hAPP(c_List_Olist_OCons(U_20308),U_20311),U_20309)
    | ~ class_Orderings_Olinorder(U_20307) ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

fof(f_4867_1,plain,
    ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
      ( ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
        | ! [B_us,B_vs] :
            ( V_xs_2 != hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
            | ~ hBOOL(hAPP(V_P_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_P_2,B_x))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) )
            | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) ) )
      & ( ? [B_us,B_vs] :
            ( V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
            & hBOOL(hAPP(V_P_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_P_2,B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) )
            & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) )
        | hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(f_4867_2,plain,
    ! [U_20322,U_20321,U_20320,U_20319,U_20318] :
      ( ( hAPP(c_List_Ofilter(U_20318,U_20319),U_20320) = hAPP(hAPP(c_List_Olist_OCons(U_20318),U_20321),U_20322)
        | ! [U_20317,U_20316] :
            ( U_20322 != hAPP(c_List_Ofilter(U_20318,U_20319),U_20316)
            | ~ hBOOL(hAPP(U_20319,U_20321))
            | ? [U_20315] :
                ( hBOOL(hAPP(U_20319,U_20315))
                & hBOOL(hAPP(hAPP(c_member(U_20318),U_20315),hAPP(c_List_Oset(U_20318),U_20317))) )
            | U_20320 != hAPP(hAPP(c_List_Oappend(U_20318),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20318),U_20321),U_20316)) ) )
      & ( ? [U_20314,U_20313] :
            ( U_20322 = hAPP(c_List_Ofilter(U_20318,U_20319),U_20313)
            & hBOOL(hAPP(U_20319,U_20321))
            & ! [U_20312] :
                ( ~ hBOOL(hAPP(U_20319,U_20312))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20318),U_20312),hAPP(c_List_Oset(U_20318),U_20314))) )
            & U_20320 = hAPP(hAPP(c_List_Oappend(U_20318),U_20314),hAPP(hAPP(c_List_Olist_OCons(U_20318),U_20321),U_20313)) )
        | hAPP(c_List_Ofilter(U_20318,U_20319),U_20320) != hAPP(hAPP(c_List_Olist_OCons(U_20318),U_20321),U_20322) ) ),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

fof(f_4867_3,plain,
    ( ! [U_20332,U_20330,U_20328,U_20326,U_20324] :
        ( hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332)
        | ! [U_20317] :
            ( ! [U_20316] :
                ( U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
                | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316)) )
            | ? [U_20315] :
                ( hBOOL(hAPP(U_20326,U_20315))
                & hBOOL(hAPP(hAPP(c_member(U_20324),U_20315),hAPP(c_List_Oset(U_20324),U_20317))) ) )
        | ~ hBOOL(hAPP(U_20326,U_20330)) )
    & ! [U_20331,U_20329,U_20327,U_20325,U_20323] :
        ( ( ? [U_20314] :
              ( ? [U_20313] :
                  ( U_20331 = hAPP(c_List_Ofilter(U_20323,U_20325),U_20313)
                  & U_20327 = hAPP(hAPP(c_List_Oappend(U_20323),U_20314),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20313)) )
              & ! [U_20312] :
                  ( ~ hBOOL(hAPP(U_20325,U_20312))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_20323),U_20312),hAPP(c_List_Oset(U_20323),U_20314))) ) )
          & hBOOL(hAPP(U_20325,U_20329)) )
        | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ) ),
    inference(miniscope,[status(thm)],[f_4867_2]) ).

fof(f_4867_4,plain,
    ( ! [U_20332,U_20330,U_20328,U_20326,U_20324] :
        ( hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332)
        | ! [U_20317] :
            ( ! [U_20316] :
                ( U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
                | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316)) )
            | ? [U_20315] :
                ( hBOOL(hAPP(U_20326,U_20315))
                & hBOOL(hAPP(hAPP(c_member(U_20324),U_20315),hAPP(c_List_Oset(U_20324),U_20317))) ) )
        | ~ hBOOL(hAPP(U_20326,U_20330)) )
    & ! [U_20331,U_20329,U_20327,U_20325,U_20323] :
        ( ( ? [U_20313] :
              ( U_20331 = hAPP(c_List_Ofilter(U_20323,U_20325),U_20313)
              & U_20327 = hAPP(hAPP(c_List_Oappend(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20313)) )
          & ! [U_20312] :
              ( ~ hBOOL(hAPP(U_20325,U_20312))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20323),U_20312),hAPP(c_List_Oset(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)))) )
          & hBOOL(hAPP(U_20325,U_20329)) )
        | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK517]),skolemize(U_20314,sK517(U_20331,U_20329,U_20327,U_20325,U_20323))],[f_4867_3]) ).

fof(f_4867_5,plain,
    ( ! [U_20332,U_20330,U_20328,U_20326,U_20324] :
        ( hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332)
        | ! [U_20317] :
            ( ! [U_20316] :
                ( U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
                | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316)) )
            | ? [U_20315] :
                ( hBOOL(hAPP(U_20326,U_20315))
                & hBOOL(hAPP(hAPP(c_member(U_20324),U_20315),hAPP(c_List_Oset(U_20324),U_20317))) ) )
        | ~ hBOOL(hAPP(U_20326,U_20330)) )
    & ! [U_20331,U_20329,U_20327,U_20325,U_20323] :
        ( ( U_20331 = hAPP(c_List_Ofilter(U_20323,U_20325),sK518(U_20331,U_20329,U_20327,U_20325,U_20323))
          & U_20327 = hAPP(hAPP(c_List_Oappend(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),sK518(U_20331,U_20329,U_20327,U_20325,U_20323)))
          & ! [U_20312] :
              ( ~ hBOOL(hAPP(U_20325,U_20312))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20323),U_20312),hAPP(c_List_Oset(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)))) )
          & hBOOL(hAPP(U_20325,U_20329)) )
        | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK518]),skolemize(U_20313,sK518(U_20331,U_20329,U_20327,U_20325,U_20323))],[f_4867_4]) ).

fof(f_4867_6,plain,
    ( ! [U_20332,U_20330,U_20328,U_20326,U_20324] :
        ( hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332)
        | ! [U_20317] :
            ( ! [U_20316] :
                ( U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
                | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316)) )
            | ( hBOOL(hAPP(U_20326,sK519(U_20332,U_20330,U_20328,U_20326,U_20324,U_20317)))
              & hBOOL(hAPP(hAPP(c_member(U_20324),sK519(U_20332,U_20330,U_20328,U_20326,U_20324,U_20317)),hAPP(c_List_Oset(U_20324),U_20317))) ) )
        | ~ hBOOL(hAPP(U_20326,U_20330)) )
    & ! [U_20331,U_20329,U_20327,U_20325,U_20323] :
        ( ( U_20331 = hAPP(c_List_Ofilter(U_20323,U_20325),sK518(U_20331,U_20329,U_20327,U_20325,U_20323))
          & U_20327 = hAPP(hAPP(c_List_Oappend(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),sK518(U_20331,U_20329,U_20327,U_20325,U_20323)))
          & ! [U_20312] :
              ( ~ hBOOL(hAPP(U_20325,U_20312))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20323),U_20312),hAPP(c_List_Oset(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)))) )
          & hBOOL(hAPP(U_20325,U_20329)) )
        | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK519]),skolemize(U_20315,sK519(U_20332,U_20330,U_20328,U_20326,U_20324,U_20317))],[f_4867_5]) ).

cnf(f_4867_7,plain,
    ( hBOOL(hAPP(U_20325,U_20329))
    | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

cnf(f_4867_8,plain,
    ( ~ hBOOL(hAPP(U_20325,U_20312))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20323),U_20312),hAPP(c_List_Oset(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323))))
    | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

cnf(f_4867_9,plain,
    ( U_20327 = hAPP(hAPP(c_List_Oappend(U_20323),sK517(U_20331,U_20329,U_20327,U_20325,U_20323)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),sK518(U_20331,U_20329,U_20327,U_20325,U_20323)))
    | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

cnf(f_4867_10,plain,
    ( U_20331 = hAPP(c_List_Ofilter(U_20323,U_20325),sK518(U_20331,U_20329,U_20327,U_20325,U_20323))
    | hAPP(c_List_Ofilter(U_20323,U_20325),U_20327) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20329),U_20331) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

cnf(f_4867_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20324),sK519(U_20332,U_20330,U_20328,U_20326,U_20324,U_20317)),hAPP(c_List_Oset(U_20324),U_20317)))
    | U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
    | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316))
    | ~ hBOOL(hAPP(U_20326,U_20330))
    | hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

cnf(f_4867_12,plain,
    ( hBOOL(hAPP(U_20326,sK519(U_20332,U_20330,U_20328,U_20326,U_20324,U_20317)))
    | U_20332 != hAPP(c_List_Ofilter(U_20324,U_20326),U_20316)
    | U_20328 != hAPP(hAPP(c_List_Oappend(U_20324),U_20317),hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20316))
    | ~ hBOOL(hAPP(U_20326,U_20330))
    | hAPP(c_List_Ofilter(U_20324,U_20326),U_20328) = hAPP(hAPP(c_List_Olist_OCons(U_20324),U_20330),U_20332) ),
    inference(clausify,[status(thm)],[f_4867_6]) ).

fof(f_4868_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)
        | ! [B_us,B_vs] :
            ( V_xs_2 != hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
            | ~ hBOOL(hAPP(V_P_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_P_2,B_x))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) )
            | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) ) )
      & ( ? [B_us,B_vs] :
            ( V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs)
            & hBOOL(hAPP(V_P_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_P_2,B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) )
            & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) )
        | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) != hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(f_4868_2,plain,
    ! [U_20343,U_20342,U_20341,U_20340,U_20339] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_20339),U_20340),U_20341) = hAPP(c_List_Ofilter(U_20339,U_20342),U_20343)
        | ! [U_20338,U_20337] :
            ( U_20341 != hAPP(c_List_Ofilter(U_20339,U_20342),U_20337)
            | ~ hBOOL(hAPP(U_20342,U_20340))
            | ? [U_20336] :
                ( hBOOL(hAPP(U_20342,U_20336))
                & hBOOL(hAPP(hAPP(c_member(U_20339),U_20336),hAPP(c_List_Oset(U_20339),U_20338))) )
            | U_20343 != hAPP(hAPP(c_List_Oappend(U_20339),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20339),U_20340),U_20337)) ) )
      & ( ? [U_20335,U_20334] :
            ( U_20341 = hAPP(c_List_Ofilter(U_20339,U_20342),U_20334)
            & hBOOL(hAPP(U_20342,U_20340))
            & ! [U_20333] :
                ( ~ hBOOL(hAPP(U_20342,U_20333))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20339),U_20333),hAPP(c_List_Oset(U_20339),U_20335))) )
            & U_20343 = hAPP(hAPP(c_List_Oappend(U_20339),U_20335),hAPP(hAPP(c_List_Olist_OCons(U_20339),U_20340),U_20334)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_20339),U_20340),U_20341) != hAPP(c_List_Ofilter(U_20339,U_20342),U_20343) ) ),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

fof(f_4868_3,plain,
    ( ! [U_20353,U_20351,U_20349,U_20347,U_20345] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353)
        | ! [U_20338] :
            ( ! [U_20337] :
                ( U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
                | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337)) )
            | ? [U_20336] :
                ( hBOOL(hAPP(U_20351,U_20336))
                & hBOOL(hAPP(hAPP(c_member(U_20345),U_20336),hAPP(c_List_Oset(U_20345),U_20338))) ) )
        | ~ hBOOL(hAPP(U_20351,U_20347)) )
    & ! [U_20352,U_20350,U_20348,U_20346,U_20344] :
        ( ( ? [U_20335] :
              ( ? [U_20334] :
                  ( U_20348 = hAPP(c_List_Ofilter(U_20344,U_20350),U_20334)
                  & U_20352 = hAPP(hAPP(c_List_Oappend(U_20344),U_20335),hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20334)) )
              & ! [U_20333] :
                  ( ~ hBOOL(hAPP(U_20350,U_20333))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_20344),U_20333),hAPP(c_List_Oset(U_20344),U_20335))) ) )
          & hBOOL(hAPP(U_20350,U_20346)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ) ),
    inference(miniscope,[status(thm)],[f_4868_2]) ).

fof(f_4868_4,plain,
    ( ! [U_20353,U_20351,U_20349,U_20347,U_20345] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353)
        | ! [U_20338] :
            ( ! [U_20337] :
                ( U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
                | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337)) )
            | ? [U_20336] :
                ( hBOOL(hAPP(U_20351,U_20336))
                & hBOOL(hAPP(hAPP(c_member(U_20345),U_20336),hAPP(c_List_Oset(U_20345),U_20338))) ) )
        | ~ hBOOL(hAPP(U_20351,U_20347)) )
    & ! [U_20352,U_20350,U_20348,U_20346,U_20344] :
        ( ( ? [U_20334] :
              ( U_20348 = hAPP(c_List_Ofilter(U_20344,U_20350),U_20334)
              & U_20352 = hAPP(hAPP(c_List_Oappend(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)),hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20334)) )
          & ! [U_20333] :
              ( ~ hBOOL(hAPP(U_20350,U_20333))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20344),U_20333),hAPP(c_List_Oset(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)))) )
          & hBOOL(hAPP(U_20350,U_20346)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK520]),skolemize(U_20335,sK520(U_20352,U_20350,U_20348,U_20346,U_20344))],[f_4868_3]) ).

fof(f_4868_5,plain,
    ( ! [U_20353,U_20351,U_20349,U_20347,U_20345] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353)
        | ! [U_20338] :
            ( ! [U_20337] :
                ( U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
                | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337)) )
            | ? [U_20336] :
                ( hBOOL(hAPP(U_20351,U_20336))
                & hBOOL(hAPP(hAPP(c_member(U_20345),U_20336),hAPP(c_List_Oset(U_20345),U_20338))) ) )
        | ~ hBOOL(hAPP(U_20351,U_20347)) )
    & ! [U_20352,U_20350,U_20348,U_20346,U_20344] :
        ( ( U_20348 = hAPP(c_List_Ofilter(U_20344,U_20350),sK521(U_20352,U_20350,U_20348,U_20346,U_20344))
          & U_20352 = hAPP(hAPP(c_List_Oappend(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)),hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),sK521(U_20352,U_20350,U_20348,U_20346,U_20344)))
          & ! [U_20333] :
              ( ~ hBOOL(hAPP(U_20350,U_20333))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20344),U_20333),hAPP(c_List_Oset(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)))) )
          & hBOOL(hAPP(U_20350,U_20346)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK521]),skolemize(U_20334,sK521(U_20352,U_20350,U_20348,U_20346,U_20344))],[f_4868_4]) ).

fof(f_4868_6,plain,
    ( ! [U_20353,U_20351,U_20349,U_20347,U_20345] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353)
        | ! [U_20338] :
            ( ! [U_20337] :
                ( U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
                | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337)) )
            | ( hBOOL(hAPP(U_20351,sK522(U_20353,U_20351,U_20349,U_20347,U_20345,U_20338)))
              & hBOOL(hAPP(hAPP(c_member(U_20345),sK522(U_20353,U_20351,U_20349,U_20347,U_20345,U_20338)),hAPP(c_List_Oset(U_20345),U_20338))) ) )
        | ~ hBOOL(hAPP(U_20351,U_20347)) )
    & ! [U_20352,U_20350,U_20348,U_20346,U_20344] :
        ( ( U_20348 = hAPP(c_List_Ofilter(U_20344,U_20350),sK521(U_20352,U_20350,U_20348,U_20346,U_20344))
          & U_20352 = hAPP(hAPP(c_List_Oappend(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)),hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),sK521(U_20352,U_20350,U_20348,U_20346,U_20344)))
          & ! [U_20333] :
              ( ~ hBOOL(hAPP(U_20350,U_20333))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20344),U_20333),hAPP(c_List_Oset(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)))) )
          & hBOOL(hAPP(U_20350,U_20346)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK522]),skolemize(U_20336,sK522(U_20353,U_20351,U_20349,U_20347,U_20345,U_20338))],[f_4868_5]) ).

cnf(f_4868_7,plain,
    ( hBOOL(hAPP(U_20350,U_20346))
    | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

cnf(f_4868_8,plain,
    ( ~ hBOOL(hAPP(U_20350,U_20333))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20344),U_20333),hAPP(c_List_Oset(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344))))
    | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

cnf(f_4868_9,plain,
    ( U_20352 = hAPP(hAPP(c_List_Oappend(U_20344),sK520(U_20352,U_20350,U_20348,U_20346,U_20344)),hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),sK521(U_20352,U_20350,U_20348,U_20346,U_20344)))
    | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

cnf(f_4868_10,plain,
    ( U_20348 = hAPP(c_List_Ofilter(U_20344,U_20350),sK521(U_20352,U_20350,U_20348,U_20346,U_20344))
    | hAPP(hAPP(c_List_Olist_OCons(U_20344),U_20346),U_20348) != hAPP(c_List_Ofilter(U_20344,U_20350),U_20352) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

cnf(f_4868_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20345),sK522(U_20353,U_20351,U_20349,U_20347,U_20345,U_20338)),hAPP(c_List_Oset(U_20345),U_20338)))
    | U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
    | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337))
    | ~ hBOOL(hAPP(U_20351,U_20347))
    | hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

cnf(f_4868_12,plain,
    ( hBOOL(hAPP(U_20351,sK522(U_20353,U_20351,U_20349,U_20347,U_20345,U_20338)))
    | U_20349 != hAPP(c_List_Ofilter(U_20345,U_20351),U_20337)
    | U_20353 != hAPP(hAPP(c_List_Oappend(U_20345),U_20338),hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20337))
    | ~ hBOOL(hAPP(U_20351,U_20347))
    | hAPP(hAPP(c_List_Olist_OCons(U_20345),U_20347),U_20349) = hAPP(c_List_Ofilter(U_20345,U_20351),U_20353) ),
    inference(clausify,[status(thm)],[f_4868_6]) ).

fof(f_4869_1,plain,
    ! [V_P_2,V_xs_2,T_a,V_n_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),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_a)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__ball__nth]) ).

fof(f_4869_2,plain,
    ! [U_20358,U_20357,U_20356,U_20355] :
      ( hBOOL(hAPP(U_20358,hAPP(hAPP(c_List_Onth(U_20356),U_20357),U_20355)))
      | ? [U_20354] :
          ( ~ hBOOL(hAPP(U_20358,U_20354))
          & hBOOL(hAPP(hAPP(c_member(U_20356),U_20354),hAPP(c_List_Oset(U_20356),U_20357))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20355),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20356)),U_20357))) ),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

fof(f_4869_3,plain,
    ! [U_20358,U_20357,U_20356,U_20355] :
      ( hBOOL(hAPP(U_20358,hAPP(hAPP(c_List_Onth(U_20356),U_20357),U_20355)))
      | ( ~ hBOOL(hAPP(U_20358,sK523(U_20358,U_20357,U_20356,U_20355)))
        & hBOOL(hAPP(hAPP(c_member(U_20356),sK523(U_20358,U_20357,U_20356,U_20355)),hAPP(c_List_Oset(U_20356),U_20357))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20355),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20356)),U_20357))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK523]),skolemize(U_20354,sK523(U_20358,U_20357,U_20356,U_20355))],[f_4869_2]) ).

cnf(f_4869_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20356),sK523(U_20358,U_20357,U_20356,U_20355)),hAPP(c_List_Oset(U_20356),U_20357)))
    | hBOOL(hAPP(U_20358,hAPP(hAPP(c_List_Onth(U_20356),U_20357),U_20355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20355),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20356)),U_20357))) ),
    inference(clausify,[status(thm)],[f_4869_3]) ).

cnf(f_4869_5,plain,
    ( ~ hBOOL(hAPP(U_20358,sK523(U_20358,U_20357,U_20356,U_20355)))
    | hBOOL(hAPP(U_20358,hAPP(hAPP(c_List_Onth(U_20356),U_20357),U_20355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20355),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20356)),U_20357))) ),
    inference(clausify,[status(thm)],[f_4869_3]) ).

fof(f_4870_1,plain,
    ! [V_x_2,V_xs_2,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_OCons]) ).

fof(f_4870_2,plain,
    ! [U_20362,U_20361,U_20360] :
      ( c_List_Olinorder__class_Osorted(U_20360,hAPP(hAPP(c_List_Olist_OCons(U_20360),U_20362),U_20361))
      | ~ c_List_Olinorder__class_Osorted(U_20360,U_20361)
      | ? [U_20359] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20360),U_20362),U_20359))
          & hBOOL(hAPP(hAPP(c_member(U_20360),U_20359),hAPP(c_List_Oset(U_20360),U_20361))) )
      | ~ class_Orderings_Olinorder(U_20360) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

fof(f_4870_3,plain,
    ! [U_20362,U_20361,U_20360] :
      ( c_List_Olinorder__class_Osorted(U_20360,hAPP(hAPP(c_List_Olist_OCons(U_20360),U_20362),U_20361))
      | ~ c_List_Olinorder__class_Osorted(U_20360,U_20361)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20360),U_20362),sK524(U_20362,U_20361,U_20360)))
        & hBOOL(hAPP(hAPP(c_member(U_20360),sK524(U_20362,U_20361,U_20360)),hAPP(c_List_Oset(U_20360),U_20361))) )
      | ~ class_Orderings_Olinorder(U_20360) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK524]),skolemize(U_20359,sK524(U_20362,U_20361,U_20360))],[f_4870_2]) ).

cnf(f_4870_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20360),sK524(U_20362,U_20361,U_20360)),hAPP(c_List_Oset(U_20360),U_20361)))
    | c_List_Olinorder__class_Osorted(U_20360,hAPP(hAPP(c_List_Olist_OCons(U_20360),U_20362),U_20361))
    | ~ c_List_Olinorder__class_Osorted(U_20360,U_20361)
    | ~ class_Orderings_Olinorder(U_20360) ),
    inference(clausify,[status(thm)],[f_4870_3]) ).

cnf(f_4870_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20360),U_20362),sK524(U_20362,U_20361,U_20360)))
    | c_List_Olinorder__class_Osorted(U_20360,hAPP(hAPP(c_List_Olist_OCons(U_20360),U_20362),U_20361))
    | ~ c_List_Olinorder__class_Osorted(U_20360,U_20361)
    | ~ class_Orderings_Olinorder(U_20360) ),
    inference(clausify,[status(thm)],[f_4870_3]) ).

fof(f_4871_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | ! [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_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_a)),V_xs_2))) ) )
      & ( ? [B_n] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_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_a)),V_xs_2))) )
        | ~ c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__length]) ).

fof(f_4871_2,plain,
    ! [U_20367,U_20366,U_20365] :
      ( ( c_List_Olist__ex(U_20365,U_20366,U_20367)
        | ! [U_20364] :
            ( ~ hBOOL(hAPP(U_20366,hAPP(hAPP(c_List_Onth(U_20365),U_20367),U_20364)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20364),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20365)),U_20367))) ) )
      & ( ? [U_20363] :
            ( hBOOL(hAPP(U_20366,hAPP(hAPP(c_List_Onth(U_20365),U_20367),U_20363)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20365)),U_20367))) )
        | ~ c_List_Olist__ex(U_20365,U_20366,U_20367) ) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

fof(f_4871_3,plain,
    ( ! [U_20373,U_20371,U_20369] :
        ( c_List_Olist__ex(U_20369,U_20371,U_20373)
        | ! [U_20364] :
            ( ~ hBOOL(hAPP(U_20371,hAPP(hAPP(c_List_Onth(U_20369),U_20373),U_20364)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20364),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20373))) ) )
    & ! [U_20372,U_20370,U_20368] :
        ( ? [U_20363] :
            ( hBOOL(hAPP(U_20370,hAPP(hAPP(c_List_Onth(U_20368),U_20372),U_20363)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20368)),U_20372))) )
        | ~ c_List_Olist__ex(U_20368,U_20370,U_20372) ) ),
    inference(miniscope,[status(thm)],[f_4871_2]) ).

fof(f_4871_4,plain,
    ( ! [U_20373,U_20371,U_20369] :
        ( c_List_Olist__ex(U_20369,U_20371,U_20373)
        | ! [U_20364] :
            ( ~ hBOOL(hAPP(U_20371,hAPP(hAPP(c_List_Onth(U_20369),U_20373),U_20364)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20364),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20373))) ) )
    & ! [U_20372,U_20370,U_20368] :
        ( ( hBOOL(hAPP(U_20370,hAPP(hAPP(c_List_Onth(U_20368),U_20372),sK525(U_20372,U_20370,U_20368))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK525(U_20372,U_20370,U_20368)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20368)),U_20372))) )
        | ~ c_List_Olist__ex(U_20368,U_20370,U_20372) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK525]),skolemize(U_20363,sK525(U_20372,U_20370,U_20368))],[f_4871_3]) ).

cnf(f_4871_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK525(U_20372,U_20370,U_20368)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20368)),U_20372)))
    | ~ c_List_Olist__ex(U_20368,U_20370,U_20372) ),
    inference(clausify,[status(thm)],[f_4871_4]) ).

cnf(f_4871_6,plain,
    ( hBOOL(hAPP(U_20370,hAPP(hAPP(c_List_Onth(U_20368),U_20372),sK525(U_20372,U_20370,U_20368))))
    | ~ c_List_Olist__ex(U_20368,U_20370,U_20372) ),
    inference(clausify,[status(thm)],[f_4871_4]) ).

cnf(f_4871_7,plain,
    ( c_List_Olist__ex(U_20369,U_20371,U_20373)
    | ~ hBOOL(hAPP(U_20371,hAPP(hAPP(c_List_Onth(U_20369),U_20373),U_20364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20364),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20373))) ),
    inference(clausify,[status(thm)],[f_4871_4]) ).

fof(f_4872_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
        | ! [B_ys] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys)))
            | ! [B_zs] : V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) )
      & ( ? [B_ys] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys)))
            & ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(f_4872_2,plain,
    ! [U_20380,U_20379,U_20378] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20378),U_20379),hAPP(c_List_Oset(U_20378),U_20380)))
        | ! [U_20377] :
            ( hBOOL(hAPP(hAPP(c_member(U_20378),U_20379),hAPP(c_List_Oset(U_20378),U_20377)))
            | ! [U_20376] : U_20380 != hAPP(hAPP(c_List_Oappend(U_20378),U_20377),hAPP(hAPP(c_List_Olist_OCons(U_20378),U_20379),U_20376)) ) )
      & ( ? [U_20375] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20378),U_20379),hAPP(c_List_Oset(U_20378),U_20375)))
            & ? [U_20374] : U_20380 = hAPP(hAPP(c_List_Oappend(U_20378),U_20375),hAPP(hAPP(c_List_Olist_OCons(U_20378),U_20379),U_20374)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20378),U_20379),hAPP(c_List_Oset(U_20378),U_20380))) ) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

fof(f_4872_3,plain,
    ( ! [U_20386,U_20384,U_20382] :
        ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20386)))
        | ! [U_20377] :
            ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20377)))
            | ! [U_20376] : U_20386 != hAPP(hAPP(c_List_Oappend(U_20382),U_20377),hAPP(hAPP(c_List_Olist_OCons(U_20382),U_20384),U_20376)) ) )
    & ! [U_20385,U_20383,U_20381] :
        ( ? [U_20375] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20375)))
            & ? [U_20374] : U_20385 = hAPP(hAPP(c_List_Oappend(U_20381),U_20375),hAPP(hAPP(c_List_Olist_OCons(U_20381),U_20383),U_20374)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20385))) ) ),
    inference(miniscope,[status(thm)],[f_4872_2]) ).

fof(f_4872_4,plain,
    ( ! [U_20386,U_20384,U_20382] :
        ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20386)))
        | ! [U_20377] :
            ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20377)))
            | ! [U_20376] : U_20386 != hAPP(hAPP(c_List_Oappend(U_20382),U_20377),hAPP(hAPP(c_List_Olist_OCons(U_20382),U_20384),U_20376)) ) )
    & ! [U_20385,U_20383,U_20381] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),sK526(U_20385,U_20383,U_20381))))
          & ? [U_20374] : U_20385 = hAPP(hAPP(c_List_Oappend(U_20381),sK526(U_20385,U_20383,U_20381)),hAPP(hAPP(c_List_Olist_OCons(U_20381),U_20383),U_20374)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20385))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK526]),skolemize(U_20375,sK526(U_20385,U_20383,U_20381))],[f_4872_3]) ).

fof(f_4872_5,plain,
    ( ! [U_20386,U_20384,U_20382] :
        ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20386)))
        | ! [U_20377] :
            ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20377)))
            | ! [U_20376] : U_20386 != hAPP(hAPP(c_List_Oappend(U_20382),U_20377),hAPP(hAPP(c_List_Olist_OCons(U_20382),U_20384),U_20376)) ) )
    & ! [U_20385,U_20383,U_20381] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),sK526(U_20385,U_20383,U_20381))))
          & U_20385 = hAPP(hAPP(c_List_Oappend(U_20381),sK526(U_20385,U_20383,U_20381)),hAPP(hAPP(c_List_Olist_OCons(U_20381),U_20383),sK527(U_20385,U_20383,U_20381))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20385))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK527]),skolemize(U_20374,sK527(U_20385,U_20383,U_20381))],[f_4872_4]) ).

cnf(f_4872_6,plain,
    ( U_20385 = hAPP(hAPP(c_List_Oappend(U_20381),sK526(U_20385,U_20383,U_20381)),hAPP(hAPP(c_List_Olist_OCons(U_20381),U_20383),sK527(U_20385,U_20383,U_20381)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20385))) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

cnf(f_4872_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),sK526(U_20385,U_20383,U_20381))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20381),U_20383),hAPP(c_List_Oset(U_20381),U_20385))) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

cnf(f_4872_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20386)))
    | hBOOL(hAPP(hAPP(c_member(U_20382),U_20384),hAPP(c_List_Oset(U_20382),U_20377)))
    | U_20386 != hAPP(hAPP(c_List_Oappend(U_20382),U_20377),hAPP(hAPP(c_List_Olist_OCons(U_20382),U_20384),U_20376)) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

fof(f_4873_1,plain,
    ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(f_4873_2,plain,
    ! [U_20388,U_20387] : ~ c_List_Olist__ex(U_20387,U_20388,c_List_Olist_ONil(U_20387)),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

cnf(f_4873_3,plain,
    ~ c_List_Olist__ex(U_20387,U_20388,c_List_Olist_ONil(U_20387)),
    inference(clausify,[status(thm)],[f_4873_2]) ).

fof(f_4874_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
        | ( ~ c_List_Olist__ex(T_a,V_P_2,V_ys_2)
          & ~ c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) )
      & ( c_List_Olist__ex(T_a,V_P_2,V_ys_2)
        | c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | ~ c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__append]) ).

fof(f_4874_2,plain,
    ! [U_20392,U_20391,U_20390,U_20389] :
      ( ( c_List_Olist__ex(U_20389,U_20390,hAPP(hAPP(c_List_Oappend(U_20389),U_20391),U_20392))
        | ( ~ c_List_Olist__ex(U_20389,U_20390,U_20392)
          & ~ c_List_Olist__ex(U_20389,U_20390,U_20391) ) )
      & ( c_List_Olist__ex(U_20389,U_20390,U_20392)
        | c_List_Olist__ex(U_20389,U_20390,U_20391)
        | ~ c_List_Olist__ex(U_20389,U_20390,hAPP(hAPP(c_List_Oappend(U_20389),U_20391),U_20392)) ) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

fof(f_4874_3,plain,
    ( ! [U_20400,U_20398,U_20396,U_20394] :
        ( c_List_Olist__ex(U_20394,U_20396,hAPP(hAPP(c_List_Oappend(U_20394),U_20398),U_20400))
        | ( ~ c_List_Olist__ex(U_20394,U_20396,U_20400)
          & ~ c_List_Olist__ex(U_20394,U_20396,U_20398) ) )
    & ! [U_20399,U_20397,U_20395,U_20393] :
        ( c_List_Olist__ex(U_20393,U_20395,U_20399)
        | c_List_Olist__ex(U_20393,U_20395,U_20397)
        | ~ c_List_Olist__ex(U_20393,U_20395,hAPP(hAPP(c_List_Oappend(U_20393),U_20397),U_20399)) ) ),
    inference(miniscope,[status(thm)],[f_4874_2]) ).

cnf(f_4874_4,plain,
    ( c_List_Olist__ex(U_20393,U_20395,U_20399)
    | c_List_Olist__ex(U_20393,U_20395,U_20397)
    | ~ c_List_Olist__ex(U_20393,U_20395,hAPP(hAPP(c_List_Oappend(U_20393),U_20397),U_20399)) ),
    inference(clausify,[status(thm)],[f_4874_3]) ).

cnf(f_4874_5,plain,
    ( ~ c_List_Olist__ex(U_20394,U_20396,U_20398)
    | c_List_Olist__ex(U_20394,U_20396,hAPP(hAPP(c_List_Oappend(U_20394),U_20398),U_20400)) ),
    inference(clausify,[status(thm)],[f_4874_3]) ).

cnf(f_4874_6,plain,
    ( ~ c_List_Olist__ex(U_20394,U_20396,U_20400)
    | c_List_Olist__ex(U_20394,U_20396,hAPP(hAPP(c_List_Oappend(U_20394),U_20398),U_20400)) ),
    inference(clausify,[status(thm)],[f_4874_3]) ).

fof(f_4875_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff]) ).

fof(f_4875_2,plain,
    ! [U_20405,U_20404,U_20403] :
      ( ( c_List_Olist__ex(U_20403,U_20404,U_20405)
        | ! [U_20402] :
            ( ~ hBOOL(hAPP(U_20404,U_20402))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20403),U_20402),hAPP(c_List_Oset(U_20403),U_20405))) ) )
      & ( ? [U_20401] :
            ( hBOOL(hAPP(U_20404,U_20401))
            & hBOOL(hAPP(hAPP(c_member(U_20403),U_20401),hAPP(c_List_Oset(U_20403),U_20405))) )
        | ~ c_List_Olist__ex(U_20403,U_20404,U_20405) ) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

fof(f_4875_3,plain,
    ( ! [U_20411,U_20409,U_20407] :
        ( c_List_Olist__ex(U_20407,U_20409,U_20411)
        | ! [U_20402] :
            ( ~ hBOOL(hAPP(U_20409,U_20402))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20407),U_20402),hAPP(c_List_Oset(U_20407),U_20411))) ) )
    & ! [U_20410,U_20408,U_20406] :
        ( ? [U_20401] :
            ( hBOOL(hAPP(U_20408,U_20401))
            & hBOOL(hAPP(hAPP(c_member(U_20406),U_20401),hAPP(c_List_Oset(U_20406),U_20410))) )
        | ~ c_List_Olist__ex(U_20406,U_20408,U_20410) ) ),
    inference(miniscope,[status(thm)],[f_4875_2]) ).

fof(f_4875_4,plain,
    ( ! [U_20411,U_20409,U_20407] :
        ( c_List_Olist__ex(U_20407,U_20409,U_20411)
        | ! [U_20402] :
            ( ~ hBOOL(hAPP(U_20409,U_20402))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20407),U_20402),hAPP(c_List_Oset(U_20407),U_20411))) ) )
    & ! [U_20410,U_20408,U_20406] :
        ( ( hBOOL(hAPP(U_20408,sK528(U_20410,U_20408,U_20406)))
          & hBOOL(hAPP(hAPP(c_member(U_20406),sK528(U_20410,U_20408,U_20406)),hAPP(c_List_Oset(U_20406),U_20410))) )
        | ~ c_List_Olist__ex(U_20406,U_20408,U_20410) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK528]),skolemize(U_20401,sK528(U_20410,U_20408,U_20406))],[f_4875_3]) ).

cnf(f_4875_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20406),sK528(U_20410,U_20408,U_20406)),hAPP(c_List_Oset(U_20406),U_20410)))
    | ~ c_List_Olist__ex(U_20406,U_20408,U_20410) ),
    inference(clausify,[status(thm)],[f_4875_4]) ).

cnf(f_4875_6,plain,
    ( hBOOL(hAPP(U_20408,sK528(U_20410,U_20408,U_20406)))
    | ~ c_List_Olist__ex(U_20406,U_20408,U_20410) ),
    inference(clausify,[status(thm)],[f_4875_4]) ).

cnf(f_4875_7,plain,
    ( c_List_Olist__ex(U_20407,U_20409,U_20411)
    | ~ hBOOL(hAPP(U_20409,U_20402))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20407),U_20402),hAPP(c_List_Oset(U_20407),U_20411))) ),
    inference(clausify,[status(thm)],[f_4875_4]) ).

fof(f_4876_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
        | ~ c_List_Olist__ex(T_a,V_P_2,V_xs_2) )
      & ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | ~ c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__rev]) ).

fof(f_4876_2,plain,
    ! [U_20414,U_20413,U_20412] :
      ( ( c_List_Olist__ex(U_20412,U_20413,hAPP(c_List_Orev(U_20412),U_20414))
        | ~ c_List_Olist__ex(U_20412,U_20413,U_20414) )
      & ( c_List_Olist__ex(U_20412,U_20413,U_20414)
        | ~ c_List_Olist__ex(U_20412,U_20413,hAPP(c_List_Orev(U_20412),U_20414)) ) ),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

fof(f_4876_3,plain,
    ( ! [U_20420,U_20418,U_20416] :
        ( c_List_Olist__ex(U_20416,U_20418,hAPP(c_List_Orev(U_20416),U_20420))
        | ~ c_List_Olist__ex(U_20416,U_20418,U_20420) )
    & ! [U_20419,U_20417,U_20415] :
        ( c_List_Olist__ex(U_20415,U_20417,U_20419)
        | ~ c_List_Olist__ex(U_20415,U_20417,hAPP(c_List_Orev(U_20415),U_20419)) ) ),
    inference(miniscope,[status(thm)],[f_4876_2]) ).

cnf(f_4876_4,plain,
    ( c_List_Olist__ex(U_20415,U_20417,U_20419)
    | ~ c_List_Olist__ex(U_20415,U_20417,hAPP(c_List_Orev(U_20415),U_20419)) ),
    inference(clausify,[status(thm)],[f_4876_3]) ).

cnf(f_4876_5,plain,
    ( c_List_Olist__ex(U_20416,U_20418,hAPP(c_List_Orev(U_20416),U_20420))
    | ~ c_List_Olist__ex(U_20416,U_20418,U_20420) ),
    inference(clausify,[status(thm)],[f_4876_3]) ).

fof(f_4877_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex(T_a,V_P_2,V_xs_2)
          & ~ hBOOL(hAPP(V_P_2,V_x_2)) ) )
      & ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2))
        | ~ c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J]) ).

fof(f_4877_2,plain,
    ! [U_20424,U_20423,U_20422,U_20421] :
      ( ( c_List_Olist__ex(U_20421,U_20422,hAPP(hAPP(c_List_Olist_OCons(U_20421),U_20423),U_20424))
        | ( ~ c_List_Olist__ex(U_20421,U_20422,U_20424)
          & ~ hBOOL(hAPP(U_20422,U_20423)) ) )
      & ( c_List_Olist__ex(U_20421,U_20422,U_20424)
        | hBOOL(hAPP(U_20422,U_20423))
        | ~ c_List_Olist__ex(U_20421,U_20422,hAPP(hAPP(c_List_Olist_OCons(U_20421),U_20423),U_20424)) ) ),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

fof(f_4877_3,plain,
    ( ! [U_20432,U_20430,U_20428,U_20426] :
        ( c_List_Olist__ex(U_20426,U_20428,hAPP(hAPP(c_List_Olist_OCons(U_20426),U_20430),U_20432))
        | ( ~ c_List_Olist__ex(U_20426,U_20428,U_20432)
          & ~ hBOOL(hAPP(U_20428,U_20430)) ) )
    & ! [U_20431,U_20429,U_20427,U_20425] :
        ( c_List_Olist__ex(U_20425,U_20427,U_20431)
        | hBOOL(hAPP(U_20427,U_20429))
        | ~ c_List_Olist__ex(U_20425,U_20427,hAPP(hAPP(c_List_Olist_OCons(U_20425),U_20429),U_20431)) ) ),
    inference(miniscope,[status(thm)],[f_4877_2]) ).

cnf(f_4877_4,plain,
    ( c_List_Olist__ex(U_20425,U_20427,U_20431)
    | hBOOL(hAPP(U_20427,U_20429))
    | ~ c_List_Olist__ex(U_20425,U_20427,hAPP(hAPP(c_List_Olist_OCons(U_20425),U_20429),U_20431)) ),
    inference(clausify,[status(thm)],[f_4877_3]) ).

cnf(f_4877_5,plain,
    ( ~ hBOOL(hAPP(U_20428,U_20430))
    | c_List_Olist__ex(U_20426,U_20428,hAPP(hAPP(c_List_Olist_OCons(U_20426),U_20430),U_20432)) ),
    inference(clausify,[status(thm)],[f_4877_3]) ).

cnf(f_4877_6,plain,
    ( ~ c_List_Olist__ex(U_20426,U_20428,U_20432)
    | c_List_Olist__ex(U_20426,U_20428,hAPP(hAPP(c_List_Olist_OCons(U_20426),U_20430),U_20432)) ),
    inference(clausify,[status(thm)],[f_4877_3]) ).

fof(f_4878_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
        | ! [B_ys,B_zs] : V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) )
      & ( ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs))
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp]) ).

fof(f_4878_2,plain,
    ! [U_20439,U_20438,U_20437] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20437),U_20438),hAPP(c_List_Oset(U_20437),U_20439)))
        | ! [U_20436,U_20435] : U_20439 != hAPP(hAPP(c_List_Oappend(U_20437),U_20436),hAPP(hAPP(c_List_Olist_OCons(U_20437),U_20438),U_20435)) )
      & ( ? [U_20434,U_20433] : U_20439 = hAPP(hAPP(c_List_Oappend(U_20437),U_20434),hAPP(hAPP(c_List_Olist_OCons(U_20437),U_20438),U_20433))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20437),U_20438),hAPP(c_List_Oset(U_20437),U_20439))) ) ),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

fof(f_4878_3,plain,
    ( ! [U_20445,U_20443,U_20441] :
        ( hBOOL(hAPP(hAPP(c_member(U_20441),U_20443),hAPP(c_List_Oset(U_20441),U_20445)))
        | ! [U_20436,U_20435] : U_20445 != hAPP(hAPP(c_List_Oappend(U_20441),U_20436),hAPP(hAPP(c_List_Olist_OCons(U_20441),U_20443),U_20435)) )
    & ! [U_20444,U_20442,U_20440] :
        ( ? [U_20434,U_20433] : U_20444 = hAPP(hAPP(c_List_Oappend(U_20440),U_20434),hAPP(hAPP(c_List_Olist_OCons(U_20440),U_20442),U_20433))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20440),U_20442),hAPP(c_List_Oset(U_20440),U_20444))) ) ),
    inference(miniscope,[status(thm)],[f_4878_2]) ).

fof(f_4878_4,plain,
    ( ! [U_20445,U_20443,U_20441] :
        ( hBOOL(hAPP(hAPP(c_member(U_20441),U_20443),hAPP(c_List_Oset(U_20441),U_20445)))
        | ! [U_20436,U_20435] : U_20445 != hAPP(hAPP(c_List_Oappend(U_20441),U_20436),hAPP(hAPP(c_List_Olist_OCons(U_20441),U_20443),U_20435)) )
    & ! [U_20444,U_20442,U_20440] :
        ( ? [U_20433] : U_20444 = hAPP(hAPP(c_List_Oappend(U_20440),sK529(U_20444,U_20442,U_20440)),hAPP(hAPP(c_List_Olist_OCons(U_20440),U_20442),U_20433))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20440),U_20442),hAPP(c_List_Oset(U_20440),U_20444))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK529]),skolemize(U_20434,sK529(U_20444,U_20442,U_20440))],[f_4878_3]) ).

fof(f_4878_5,plain,
    ( ! [U_20445,U_20443,U_20441] :
        ( hBOOL(hAPP(hAPP(c_member(U_20441),U_20443),hAPP(c_List_Oset(U_20441),U_20445)))
        | ! [U_20436,U_20435] : U_20445 != hAPP(hAPP(c_List_Oappend(U_20441),U_20436),hAPP(hAPP(c_List_Olist_OCons(U_20441),U_20443),U_20435)) )
    & ! [U_20444,U_20442,U_20440] :
        ( U_20444 = hAPP(hAPP(c_List_Oappend(U_20440),sK529(U_20444,U_20442,U_20440)),hAPP(hAPP(c_List_Olist_OCons(U_20440),U_20442),sK530(U_20444,U_20442,U_20440)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20440),U_20442),hAPP(c_List_Oset(U_20440),U_20444))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK530]),skolemize(U_20433,sK530(U_20444,U_20442,U_20440))],[f_4878_4]) ).

cnf(f_4878_6,plain,
    ( U_20444 = hAPP(hAPP(c_List_Oappend(U_20440),sK529(U_20444,U_20442,U_20440)),hAPP(hAPP(c_List_Olist_OCons(U_20440),U_20442),sK530(U_20444,U_20442,U_20440)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20440),U_20442),hAPP(c_List_Oset(U_20440),U_20444))) ),
    inference(clausify,[status(thm)],[f_4878_5]) ).

cnf(f_4878_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20441),U_20443),hAPP(c_List_Oset(U_20441),U_20445)))
    | U_20445 != hAPP(hAPP(c_List_Oappend(U_20441),U_20436),hAPP(hAPP(c_List_Olist_OCons(U_20441),U_20443),U_20435)) ),
    inference(clausify,[status(thm)],[f_4878_5]) ).

fof(f_4879_1,plain,
    ! [V_xs_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
        | ! [B_ys,B_zs] :
            ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs)))
            | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) )
      & ( ? [B_ys,B_zs] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs)))
            & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(f_4879_2,plain,
    ! [U_20452,U_20451,U_20450] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20450),U_20451),hAPP(c_List_Oset(U_20450),U_20452)))
        | ! [U_20449,U_20448] :
            ( hBOOL(hAPP(hAPP(c_member(U_20450),U_20451),hAPP(c_List_Oset(U_20450),U_20448)))
            | U_20452 != hAPP(hAPP(c_List_Oappend(U_20450),U_20449),hAPP(hAPP(c_List_Olist_OCons(U_20450),U_20451),U_20448)) ) )
      & ( ? [U_20447,U_20446] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20450),U_20451),hAPP(c_List_Oset(U_20450),U_20446)))
            & U_20452 = hAPP(hAPP(c_List_Oappend(U_20450),U_20447),hAPP(hAPP(c_List_Olist_OCons(U_20450),U_20451),U_20446)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20450),U_20451),hAPP(c_List_Oset(U_20450),U_20452))) ) ),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

fof(f_4879_3,plain,
    ( ! [U_20458,U_20456,U_20454] :
        ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20458)))
        | ! [U_20449,U_20448] :
            ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20448)))
            | U_20458 != hAPP(hAPP(c_List_Oappend(U_20454),U_20449),hAPP(hAPP(c_List_Olist_OCons(U_20454),U_20456),U_20448)) ) )
    & ! [U_20457,U_20455,U_20453] :
        ( ? [U_20447,U_20446] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20446)))
            & U_20457 = hAPP(hAPP(c_List_Oappend(U_20453),U_20447),hAPP(hAPP(c_List_Olist_OCons(U_20453),U_20455),U_20446)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20457))) ) ),
    inference(miniscope,[status(thm)],[f_4879_2]) ).

fof(f_4879_4,plain,
    ( ! [U_20458,U_20456,U_20454] :
        ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20458)))
        | ! [U_20449,U_20448] :
            ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20448)))
            | U_20458 != hAPP(hAPP(c_List_Oappend(U_20454),U_20449),hAPP(hAPP(c_List_Olist_OCons(U_20454),U_20456),U_20448)) ) )
    & ! [U_20457,U_20455,U_20453] :
        ( ? [U_20446] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20446)))
            & U_20457 = hAPP(hAPP(c_List_Oappend(U_20453),sK531(U_20457,U_20455,U_20453)),hAPP(hAPP(c_List_Olist_OCons(U_20453),U_20455),U_20446)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20457))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK531]),skolemize(U_20447,sK531(U_20457,U_20455,U_20453))],[f_4879_3]) ).

fof(f_4879_5,plain,
    ( ! [U_20458,U_20456,U_20454] :
        ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20458)))
        | ! [U_20449,U_20448] :
            ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20448)))
            | U_20458 != hAPP(hAPP(c_List_Oappend(U_20454),U_20449),hAPP(hAPP(c_List_Olist_OCons(U_20454),U_20456),U_20448)) ) )
    & ! [U_20457,U_20455,U_20453] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),sK532(U_20457,U_20455,U_20453))))
          & U_20457 = hAPP(hAPP(c_List_Oappend(U_20453),sK531(U_20457,U_20455,U_20453)),hAPP(hAPP(c_List_Olist_OCons(U_20453),U_20455),sK532(U_20457,U_20455,U_20453))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20457))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK532]),skolemize(U_20446,sK532(U_20457,U_20455,U_20453))],[f_4879_4]) ).

cnf(f_4879_6,plain,
    ( U_20457 = hAPP(hAPP(c_List_Oappend(U_20453),sK531(U_20457,U_20455,U_20453)),hAPP(hAPP(c_List_Olist_OCons(U_20453),U_20455),sK532(U_20457,U_20455,U_20453)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20457))) ),
    inference(clausify,[status(thm)],[f_4879_5]) ).

cnf(f_4879_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),sK532(U_20457,U_20455,U_20453))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20453),U_20455),hAPP(c_List_Oset(U_20453),U_20457))) ),
    inference(clausify,[status(thm)],[f_4879_5]) ).

cnf(f_4879_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20458)))
    | hBOOL(hAPP(hAPP(c_member(U_20454),U_20456),hAPP(c_List_Oset(U_20454),U_20448)))
    | U_20458 != hAPP(hAPP(c_List_Oappend(U_20454),U_20449),hAPP(hAPP(c_List_Olist_OCons(U_20454),U_20456),U_20448)) ),
    inference(clausify,[status(thm)],[f_4879_5]) ).

fof(f_4880_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_option_Orecs_I2_J]) ).

fof(f_4880_2,plain,
    ! [U_20463,U_20462,U_20461,U_20460,U_20459] : c_Option_Ooption_Ooption__rec(U_20459,U_20460,U_20461,U_20462,hAPP(c_Option_Ooption_OSome(U_20460),U_20463)) = hAPP(U_20462,U_20463),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

cnf(f_4880_3,plain,
    c_Option_Ooption_Ooption__rec(U_20459,U_20460,U_20461,U_20462,hAPP(c_Option_Ooption_OSome(U_20460),U_20463)) = hAPP(U_20462,U_20463),
    inference(clausify,[status(thm)],[f_4880_2]) ).

fof(f_4881_1,plain,
    ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_option_Orecs_I1_J]) ).

fof(f_4881_2,plain,
    ! [U_20467,U_20466,U_20465,U_20464] : c_Option_Ooption_Ooption__rec(U_20464,U_20465,U_20466,U_20467,c_Option_Ooption_ONone(U_20465)) = U_20466,
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

cnf(f_4881_3,plain,
    c_Option_Ooption_Ooption__rec(U_20464,U_20465,U_20466,U_20467,c_Option_Ooption_ONone(U_20465)) = U_20466,
    inference(clausify,[status(thm)],[f_4881_2]) ).

fof(f_4882_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_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_a)),V_xs_2))) ) )
      & ( ! [B_n] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_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_a)),V_xs_2))) )
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__length]) ).

fof(f_4882_2,plain,
    ! [U_20472,U_20471,U_20470] :
      ( ( c_List_Olist__all(U_20470,U_20471,U_20472)
        | ? [U_20469] :
            ( ~ hBOOL(hAPP(U_20471,hAPP(hAPP(c_List_Onth(U_20470),U_20472),U_20469)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20470)),U_20472))) ) )
      & ( ! [U_20468] :
            ( hBOOL(hAPP(U_20471,hAPP(hAPP(c_List_Onth(U_20470),U_20472),U_20468)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20470)),U_20472))) )
        | ~ c_List_Olist__all(U_20470,U_20471,U_20472) ) ),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

fof(f_4882_3,plain,
    ( ! [U_20478,U_20476,U_20474] :
        ( c_List_Olist__all(U_20474,U_20476,U_20478)
        | ? [U_20469] :
            ( ~ hBOOL(hAPP(U_20476,hAPP(hAPP(c_List_Onth(U_20474),U_20478),U_20469)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20474)),U_20478))) ) )
    & ! [U_20477,U_20475,U_20473] :
        ( ! [U_20468] :
            ( hBOOL(hAPP(U_20475,hAPP(hAPP(c_List_Onth(U_20473),U_20477),U_20468)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20473)),U_20477))) )
        | ~ c_List_Olist__all(U_20473,U_20475,U_20477) ) ),
    inference(miniscope,[status(thm)],[f_4882_2]) ).

fof(f_4882_4,plain,
    ( ! [U_20478,U_20476,U_20474] :
        ( c_List_Olist__all(U_20474,U_20476,U_20478)
        | ( ~ hBOOL(hAPP(U_20476,hAPP(hAPP(c_List_Onth(U_20474),U_20478),sK533(U_20478,U_20476,U_20474))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK533(U_20478,U_20476,U_20474)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20474)),U_20478))) ) )
    & ! [U_20477,U_20475,U_20473] :
        ( ! [U_20468] :
            ( hBOOL(hAPP(U_20475,hAPP(hAPP(c_List_Onth(U_20473),U_20477),U_20468)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20473)),U_20477))) )
        | ~ c_List_Olist__all(U_20473,U_20475,U_20477) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK533]),skolemize(U_20469,sK533(U_20478,U_20476,U_20474))],[f_4882_3]) ).

cnf(f_4882_5,plain,
    ( hBOOL(hAPP(U_20475,hAPP(hAPP(c_List_Onth(U_20473),U_20477),U_20468)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20473)),U_20477)))
    | ~ c_List_Olist__all(U_20473,U_20475,U_20477) ),
    inference(clausify,[status(thm)],[f_4882_4]) ).

cnf(f_4882_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK533(U_20478,U_20476,U_20474)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20474)),U_20478)))
    | c_List_Olist__all(U_20474,U_20476,U_20478) ),
    inference(clausify,[status(thm)],[f_4882_4]) ).

cnf(f_4882_7,plain,
    ( ~ hBOOL(hAPP(U_20476,hAPP(hAPP(c_List_Onth(U_20474),U_20478),sK533(U_20478,U_20476,U_20474))))
    | c_List_Olist__all(U_20474,U_20476,U_20478) ),
    inference(clausify,[status(thm)],[f_4882_4]) ).

fof(f_4883_1,plain,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_measure__function__int]) ).

cnf(f_4883_2,plain,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_4883_1]) ).

fof(f_4884_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
          & hBOOL(hAPP(V_P_2,V_x_2)) )
        | ~ c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J]) ).

fof(f_4884_2,plain,
    ! [U_20482,U_20481,U_20480,U_20479] :
      ( ( c_List_Olist__all(U_20479,U_20480,hAPP(hAPP(c_List_Olist_OCons(U_20479),U_20481),U_20482))
        | ~ c_List_Olist__all(U_20479,U_20480,U_20482)
        | ~ hBOOL(hAPP(U_20480,U_20481)) )
      & ( ( c_List_Olist__all(U_20479,U_20480,U_20482)
          & hBOOL(hAPP(U_20480,U_20481)) )
        | ~ c_List_Olist__all(U_20479,U_20480,hAPP(hAPP(c_List_Olist_OCons(U_20479),U_20481),U_20482)) ) ),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

fof(f_4884_3,plain,
    ( ! [U_20490,U_20488,U_20486,U_20484] :
        ( c_List_Olist__all(U_20484,U_20486,hAPP(hAPP(c_List_Olist_OCons(U_20484),U_20488),U_20490))
        | ~ c_List_Olist__all(U_20484,U_20486,U_20490)
        | ~ hBOOL(hAPP(U_20486,U_20488)) )
    & ! [U_20489,U_20487,U_20485,U_20483] :
        ( ( c_List_Olist__all(U_20483,U_20485,U_20489)
          & hBOOL(hAPP(U_20485,U_20487)) )
        | ~ c_List_Olist__all(U_20483,U_20485,hAPP(hAPP(c_List_Olist_OCons(U_20483),U_20487),U_20489)) ) ),
    inference(miniscope,[status(thm)],[f_4884_2]) ).

cnf(f_4884_4,plain,
    ( hBOOL(hAPP(U_20485,U_20487))
    | ~ c_List_Olist__all(U_20483,U_20485,hAPP(hAPP(c_List_Olist_OCons(U_20483),U_20487),U_20489)) ),
    inference(clausify,[status(thm)],[f_4884_3]) ).

cnf(f_4884_5,plain,
    ( c_List_Olist__all(U_20483,U_20485,U_20489)
    | ~ c_List_Olist__all(U_20483,U_20485,hAPP(hAPP(c_List_Olist_OCons(U_20483),U_20487),U_20489)) ),
    inference(clausify,[status(thm)],[f_4884_3]) ).

cnf(f_4884_6,plain,
    ( c_List_Olist__all(U_20484,U_20486,hAPP(hAPP(c_List_Olist_OCons(U_20484),U_20488),U_20490))
    | ~ c_List_Olist__all(U_20484,U_20486,U_20490)
    | ~ hBOOL(hAPP(U_20486,U_20488)) ),
    inference(clausify,[status(thm)],[f_4884_3]) ).

fof(f_4885_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) )
      & ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ~ c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__rev]) ).

fof(f_4885_2,plain,
    ! [U_20493,U_20492,U_20491] :
      ( ( c_List_Olist__all(U_20491,U_20492,hAPP(c_List_Orev(U_20491),U_20493))
        | ~ c_List_Olist__all(U_20491,U_20492,U_20493) )
      & ( c_List_Olist__all(U_20491,U_20492,U_20493)
        | ~ c_List_Olist__all(U_20491,U_20492,hAPP(c_List_Orev(U_20491),U_20493)) ) ),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

fof(f_4885_3,plain,
    ( ! [U_20499,U_20497,U_20495] :
        ( c_List_Olist__all(U_20495,U_20497,hAPP(c_List_Orev(U_20495),U_20499))
        | ~ c_List_Olist__all(U_20495,U_20497,U_20499) )
    & ! [U_20498,U_20496,U_20494] :
        ( c_List_Olist__all(U_20494,U_20496,U_20498)
        | ~ c_List_Olist__all(U_20494,U_20496,hAPP(c_List_Orev(U_20494),U_20498)) ) ),
    inference(miniscope,[status(thm)],[f_4885_2]) ).

cnf(f_4885_4,plain,
    ( c_List_Olist__all(U_20494,U_20496,U_20498)
    | ~ c_List_Olist__all(U_20494,U_20496,hAPP(c_List_Orev(U_20494),U_20498)) ),
    inference(clausify,[status(thm)],[f_4885_3]) ).

cnf(f_4885_5,plain,
    ( c_List_Olist__all(U_20495,U_20497,hAPP(c_List_Orev(U_20495),U_20499))
    | ~ c_List_Olist__all(U_20495,U_20497,U_20499) ),
    inference(clausify,[status(thm)],[f_4885_3]) ).

fof(f_4886_1,plain,
    ! [V_P_2,V_xs_2,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) )
      & ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Ball__set__list__all]) ).

fof(f_4886_2,plain,
    ! [U_20504,U_20503,U_20502] :
      ( ( ! [U_20501] :
            ( hBOOL(hAPP(U_20504,U_20501))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20502),U_20501),hAPP(c_List_Oset(U_20502),U_20503))) )
        | ~ c_List_Olist__all(U_20502,U_20504,U_20503) )
      & ( c_List_Olist__all(U_20502,U_20504,U_20503)
        | ? [U_20500] :
            ( ~ hBOOL(hAPP(U_20504,U_20500))
            & hBOOL(hAPP(hAPP(c_member(U_20502),U_20500),hAPP(c_List_Oset(U_20502),U_20503))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

fof(f_4886_3,plain,
    ( ! [U_20510,U_20508,U_20506] :
        ( ! [U_20501] :
            ( hBOOL(hAPP(U_20510,U_20501))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20506),U_20501),hAPP(c_List_Oset(U_20506),U_20508))) )
        | ~ c_List_Olist__all(U_20506,U_20510,U_20508) )
    & ! [U_20509,U_20507,U_20505] :
        ( c_List_Olist__all(U_20505,U_20509,U_20507)
        | ? [U_20500] :
            ( ~ hBOOL(hAPP(U_20509,U_20500))
            & hBOOL(hAPP(hAPP(c_member(U_20505),U_20500),hAPP(c_List_Oset(U_20505),U_20507))) ) ) ),
    inference(miniscope,[status(thm)],[f_4886_2]) ).

fof(f_4886_4,plain,
    ( ! [U_20510,U_20508,U_20506] :
        ( ! [U_20501] :
            ( hBOOL(hAPP(U_20510,U_20501))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20506),U_20501),hAPP(c_List_Oset(U_20506),U_20508))) )
        | ~ c_List_Olist__all(U_20506,U_20510,U_20508) )
    & ! [U_20509,U_20507,U_20505] :
        ( c_List_Olist__all(U_20505,U_20509,U_20507)
        | ( ~ hBOOL(hAPP(U_20509,sK534(U_20509,U_20507,U_20505)))
          & hBOOL(hAPP(hAPP(c_member(U_20505),sK534(U_20509,U_20507,U_20505)),hAPP(c_List_Oset(U_20505),U_20507))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK534]),skolemize(U_20500,sK534(U_20509,U_20507,U_20505))],[f_4886_3]) ).

cnf(f_4886_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20505),sK534(U_20509,U_20507,U_20505)),hAPP(c_List_Oset(U_20505),U_20507)))
    | c_List_Olist__all(U_20505,U_20509,U_20507) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

cnf(f_4886_6,plain,
    ( ~ hBOOL(hAPP(U_20509,sK534(U_20509,U_20507,U_20505)))
    | c_List_Olist__all(U_20505,U_20509,U_20507) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

cnf(f_4886_7,plain,
    ( hBOOL(hAPP(U_20510,U_20501))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20506),U_20501),hAPP(c_List_Oset(U_20506),U_20508)))
    | ~ c_List_Olist__all(U_20506,U_20510,U_20508) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

fof(f_4887_1,plain,
    ! [T_b,V_f_2,T_a] :
      ( c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b)))
      | ~ c_FunDef_Ois__measure(T_a,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_measure__fst]) ).

fof(f_4887_2,plain,
    ! [U_20513,U_20512,U_20511] :
      ( c_FunDef_Ois__measure(tc_prod(U_20511,U_20513),hAPP(hAPP(c_COMBB(U_20511,tc_Nat_Onat,tc_prod(U_20511,U_20513)),U_20512),c_Product__Type_Ofst(U_20511,U_20513)))
      | ~ c_FunDef_Ois__measure(U_20511,U_20512) ),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

cnf(f_4887_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_20511,U_20513),hAPP(hAPP(c_COMBB(U_20511,tc_Nat_Onat,tc_prod(U_20511,U_20513)),U_20512),c_Product__Type_Ofst(U_20511,U_20513)))
    | ~ c_FunDef_Ois__measure(U_20511,U_20512) ),
    inference(clausify,[status(thm)],[f_4887_2]) ).

fof(f_4888_1,plain,
    ! [T_b,V_f_2,T_a] :
      ( c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a)))
      | ~ c_FunDef_Ois__measure(T_a,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_measure__snd]) ).

fof(f_4888_2,plain,
    ! [U_20516,U_20515,U_20514] :
      ( c_FunDef_Ois__measure(tc_prod(U_20516,U_20514),hAPP(hAPP(c_COMBB(U_20514,tc_Nat_Onat,tc_prod(U_20516,U_20514)),U_20515),c_Product__Type_Osnd(U_20516,U_20514)))
      | ~ c_FunDef_Ois__measure(U_20514,U_20515) ),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

cnf(f_4888_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_20516,U_20514),hAPP(hAPP(c_COMBB(U_20514,tc_Nat_Onat,tc_prod(U_20516,U_20514)),U_20515),c_Product__Type_Osnd(U_20516,U_20514)))
    | ~ c_FunDef_Ois__measure(U_20514,U_20515) ),
    inference(clausify,[status(thm)],[f_4888_2]) ).

fof(f_4889_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff]) ).

fof(f_4889_2,plain,
    ! [U_20521,U_20520,U_20519] :
      ( ( c_List_Olist__all(U_20519,U_20520,U_20521)
        | ? [U_20518] :
            ( ~ hBOOL(hAPP(U_20520,U_20518))
            & hBOOL(hAPP(hAPP(c_member(U_20519),U_20518),hAPP(c_List_Oset(U_20519),U_20521))) ) )
      & ( ! [U_20517] :
            ( hBOOL(hAPP(U_20520,U_20517))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20519),U_20517),hAPP(c_List_Oset(U_20519),U_20521))) )
        | ~ c_List_Olist__all(U_20519,U_20520,U_20521) ) ),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ( ! [U_20527,U_20525,U_20523] :
        ( c_List_Olist__all(U_20523,U_20525,U_20527)
        | ? [U_20518] :
            ( ~ hBOOL(hAPP(U_20525,U_20518))
            & hBOOL(hAPP(hAPP(c_member(U_20523),U_20518),hAPP(c_List_Oset(U_20523),U_20527))) ) )
    & ! [U_20526,U_20524,U_20522] :
        ( ! [U_20517] :
            ( hBOOL(hAPP(U_20524,U_20517))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20522),U_20517),hAPP(c_List_Oset(U_20522),U_20526))) )
        | ~ c_List_Olist__all(U_20522,U_20524,U_20526) ) ),
    inference(miniscope,[status(thm)],[f_4889_2]) ).

fof(f_4889_4,plain,
    ( ! [U_20527,U_20525,U_20523] :
        ( c_List_Olist__all(U_20523,U_20525,U_20527)
        | ( ~ hBOOL(hAPP(U_20525,sK535(U_20527,U_20525,U_20523)))
          & hBOOL(hAPP(hAPP(c_member(U_20523),sK535(U_20527,U_20525,U_20523)),hAPP(c_List_Oset(U_20523),U_20527))) ) )
    & ! [U_20526,U_20524,U_20522] :
        ( ! [U_20517] :
            ( hBOOL(hAPP(U_20524,U_20517))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20522),U_20517),hAPP(c_List_Oset(U_20522),U_20526))) )
        | ~ c_List_Olist__all(U_20522,U_20524,U_20526) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK535]),skolemize(U_20518,sK535(U_20527,U_20525,U_20523))],[f_4889_3]) ).

cnf(f_4889_5,plain,
    ( hBOOL(hAPP(U_20524,U_20517))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20522),U_20517),hAPP(c_List_Oset(U_20522),U_20526)))
    | ~ c_List_Olist__all(U_20522,U_20524,U_20526) ),
    inference(clausify,[status(thm)],[f_4889_4]) ).

cnf(f_4889_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20523),sK535(U_20527,U_20525,U_20523)),hAPP(c_List_Oset(U_20523),U_20527)))
    | c_List_Olist__all(U_20523,U_20525,U_20527) ),
    inference(clausify,[status(thm)],[f_4889_4]) ).

cnf(f_4889_7,plain,
    ( ~ hBOOL(hAPP(U_20525,sK535(U_20527,U_20525,U_20523)))
    | c_List_Olist__all(U_20523,U_20525,U_20527) ),
    inference(clausify,[status(thm)],[f_4889_4]) ).

fof(f_4890_1,plain,
    ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Osimps]) ).

fof(f_4890_2,plain,
    ! [U_20529,U_20528] : c_FunDef_Ois__measure(U_20528,U_20529),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

cnf(f_4890_3,plain,
    c_FunDef_Ois__measure(U_20528,U_20529),
    inference(clausify,[status(thm)],[f_4890_2]) ).

fof(f_4891_1,plain,
    ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Oequations]) ).

fof(f_4891_2,plain,
    ! [U_20531,U_20530] : c_FunDef_Ois__measure(U_20530,U_20531),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

cnf(f_4891_3,plain,
    c_FunDef_Ois__measure(U_20530,U_20531),
    inference(clausify,[status(thm)],[f_4891_2]) ).

fof(f_4892_1,plain,
    ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Ointros]) ).

fof(f_4892_2,plain,
    ! [U_20533,U_20532] : c_FunDef_Ois__measure(U_20532,U_20533),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

cnf(f_4892_3,plain,
    c_FunDef_Ois__measure(U_20532,U_20533),
    inference(clausify,[status(thm)],[f_4892_2]) ).

fof(f_4893_1,plain,
    ! [T_a] :
      ( c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a))
      | ~ class_Nat_Osize(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_measure__size]) ).

fof(f_4893_2,plain,
    ! [U_20534] :
      ( c_FunDef_Ois__measure(U_20534,c_Nat_Osize__class_Osize(U_20534))
      | ~ class_Nat_Osize(U_20534) ),
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

cnf(f_4893_3,plain,
    ( c_FunDef_Ois__measure(U_20534,c_Nat_Osize__class_Osize(U_20534))
    | ~ class_Nat_Osize(U_20534) ),
    inference(clausify,[status(thm)],[f_4893_2]) ).

fof(f_4894_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
        | ~ c_List_Olist__all(T_a,V_P_2,V_ys_2)
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) )
      & ( ( c_List_Olist__all(T_a,V_P_2,V_ys_2)
          & c_List_Olist__all(T_a,V_P_2,V_xs_2) )
        | ~ c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__append]) ).

fof(f_4894_2,plain,
    ! [U_20538,U_20537,U_20536,U_20535] :
      ( ( c_List_Olist__all(U_20535,U_20536,hAPP(hAPP(c_List_Oappend(U_20535),U_20537),U_20538))
        | ~ c_List_Olist__all(U_20535,U_20536,U_20538)
        | ~ c_List_Olist__all(U_20535,U_20536,U_20537) )
      & ( ( c_List_Olist__all(U_20535,U_20536,U_20538)
          & c_List_Olist__all(U_20535,U_20536,U_20537) )
        | ~ c_List_Olist__all(U_20535,U_20536,hAPP(hAPP(c_List_Oappend(U_20535),U_20537),U_20538)) ) ),
    inference(variable_rename,[status(thm)],[f_4894_1]) ).

fof(f_4894_3,plain,
    ( ! [U_20546,U_20544,U_20542,U_20540] :
        ( c_List_Olist__all(U_20540,U_20542,hAPP(hAPP(c_List_Oappend(U_20540),U_20544),U_20546))
        | ~ c_List_Olist__all(U_20540,U_20542,U_20546)
        | ~ c_List_Olist__all(U_20540,U_20542,U_20544) )
    & ! [U_20545,U_20543,U_20541,U_20539] :
        ( ( c_List_Olist__all(U_20539,U_20541,U_20545)
          & c_List_Olist__all(U_20539,U_20541,U_20543) )
        | ~ c_List_Olist__all(U_20539,U_20541,hAPP(hAPP(c_List_Oappend(U_20539),U_20543),U_20545)) ) ),
    inference(miniscope,[status(thm)],[f_4894_2]) ).

cnf(f_4894_4,plain,
    ( c_List_Olist__all(U_20539,U_20541,U_20543)
    | ~ c_List_Olist__all(U_20539,U_20541,hAPP(hAPP(c_List_Oappend(U_20539),U_20543),U_20545)) ),
    inference(clausify,[status(thm)],[f_4894_3]) ).

cnf(f_4894_5,plain,
    ( c_List_Olist__all(U_20539,U_20541,U_20545)
    | ~ c_List_Olist__all(U_20539,U_20541,hAPP(hAPP(c_List_Oappend(U_20539),U_20543),U_20545)) ),
    inference(clausify,[status(thm)],[f_4894_3]) ).

cnf(f_4894_6,plain,
    ( c_List_Olist__all(U_20540,U_20542,hAPP(hAPP(c_List_Oappend(U_20540),U_20544),U_20546))
    | ~ c_List_Olist__all(U_20540,U_20542,U_20546)
    | ~ c_List_Olist__all(U_20540,U_20542,U_20544) ),
    inference(clausify,[status(thm)],[f_4894_3]) ).

fof(f_4895_1,plain,
    ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(f_4895_2,plain,
    ! [U_20548,U_20547] : c_List_Olist__all(U_20547,U_20548,c_List_Olist_ONil(U_20547)),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

cnf(f_4895_3,plain,
    c_List_Olist__all(U_20547,U_20548,c_List_Olist_ONil(U_20547)),
    inference(clausify,[status(thm)],[f_4895_2]) ).

fof(f_4896_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__raw]) ).

fof(f_4896_2,plain,
    ! [U_20553,U_20552,U_20551] :
      ( ( c_List_Olist__all(U_20551,U_20552,U_20553)
        | ? [U_20550] :
            ( ~ hBOOL(hAPP(U_20552,U_20550))
            & hBOOL(hAPP(hAPP(c_member(U_20551),U_20550),hAPP(c_List_Oset(U_20551),U_20553))) ) )
      & ( ! [U_20549] :
            ( hBOOL(hAPP(U_20552,U_20549))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20551),U_20549),hAPP(c_List_Oset(U_20551),U_20553))) )
        | ~ c_List_Olist__all(U_20551,U_20552,U_20553) ) ),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

fof(f_4896_3,plain,
    ( ! [U_20559,U_20557,U_20555] :
        ( c_List_Olist__all(U_20555,U_20557,U_20559)
        | ? [U_20550] :
            ( ~ hBOOL(hAPP(U_20557,U_20550))
            & hBOOL(hAPP(hAPP(c_member(U_20555),U_20550),hAPP(c_List_Oset(U_20555),U_20559))) ) )
    & ! [U_20558,U_20556,U_20554] :
        ( ! [U_20549] :
            ( hBOOL(hAPP(U_20556,U_20549))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20554),U_20549),hAPP(c_List_Oset(U_20554),U_20558))) )
        | ~ c_List_Olist__all(U_20554,U_20556,U_20558) ) ),
    inference(miniscope,[status(thm)],[f_4896_2]) ).

fof(f_4896_4,plain,
    ( ! [U_20559,U_20557,U_20555] :
        ( c_List_Olist__all(U_20555,U_20557,U_20559)
        | ( ~ hBOOL(hAPP(U_20557,sK536(U_20559,U_20557,U_20555)))
          & hBOOL(hAPP(hAPP(c_member(U_20555),sK536(U_20559,U_20557,U_20555)),hAPP(c_List_Oset(U_20555),U_20559))) ) )
    & ! [U_20558,U_20556,U_20554] :
        ( ! [U_20549] :
            ( hBOOL(hAPP(U_20556,U_20549))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20554),U_20549),hAPP(c_List_Oset(U_20554),U_20558))) )
        | ~ c_List_Olist__all(U_20554,U_20556,U_20558) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK536]),skolemize(U_20550,sK536(U_20559,U_20557,U_20555))],[f_4896_3]) ).

cnf(f_4896_5,plain,
    ( hBOOL(hAPP(U_20556,U_20549))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20554),U_20549),hAPP(c_List_Oset(U_20554),U_20558)))
    | ~ c_List_Olist__all(U_20554,U_20556,U_20558) ),
    inference(clausify,[status(thm)],[f_4896_4]) ).

cnf(f_4896_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20555),sK536(U_20559,U_20557,U_20555)),hAPP(c_List_Oset(U_20555),U_20559)))
    | c_List_Olist__all(U_20555,U_20557,U_20559) ),
    inference(clausify,[status(thm)],[f_4896_4]) ).

cnf(f_4896_7,plain,
    ( ~ hBOOL(hAPP(U_20557,sK536(U_20559,U_20557,U_20555)))
    | c_List_Olist__all(U_20555,U_20557,U_20559) ),
    inference(clausify,[status(thm)],[f_4896_4]) ).

fof(f_4897_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
          & ~ hBOOL(hAPP(V_P_2,V_x_2)) )
        | ( ~ c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
          & hBOOL(hAPP(V_P_2,V_x_2)) ) )
      & ( ( ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
            | hBOOL(hAPP(V_P_2,V_x_2)) )
          & ( c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
            | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) )
        | ~ c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(f_4897_2,plain,
    ! [U_20563,U_20562,U_20561,U_20560] :
      ( ( c_List_Olist__ex1(U_20560,U_20561,hAPP(hAPP(c_List_Olist_OCons(U_20560),U_20562),U_20563))
        | ( ~ c_List_Olist__ex1(U_20560,U_20561,U_20563)
          & ~ hBOOL(hAPP(U_20561,U_20562)) )
        | ( ~ c_List_Olist__all(U_20560,hAPP(hAPP(c_COMBS(U_20560,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20560),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20560),c_fNot),U_20561))),hAPP(c_fequal,U_20562)),U_20563)
          & hBOOL(hAPP(U_20561,U_20562)) ) )
      & ( ( ( c_List_Olist__ex1(U_20560,U_20561,U_20563)
            | hBOOL(hAPP(U_20561,U_20562)) )
          & ( c_List_Olist__all(U_20560,hAPP(hAPP(c_COMBS(U_20560,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20560),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20560),c_fNot),U_20561))),hAPP(c_fequal,U_20562)),U_20563)
            | ~ hBOOL(hAPP(U_20561,U_20562)) ) )
        | ~ c_List_Olist__ex1(U_20560,U_20561,hAPP(hAPP(c_List_Olist_OCons(U_20560),U_20562),U_20563)) ) ),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

fof(f_4897_3,plain,
    ( ! [U_20571,U_20569,U_20567,U_20565] :
        ( c_List_Olist__ex1(U_20565,U_20567,hAPP(hAPP(c_List_Olist_OCons(U_20565),U_20569),U_20571))
        | ( ~ c_List_Olist__ex1(U_20565,U_20567,U_20571)
          & ~ hBOOL(hAPP(U_20567,U_20569)) )
        | ( ~ c_List_Olist__all(U_20565,hAPP(hAPP(c_COMBS(U_20565,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20565),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20565),c_fNot),U_20567))),hAPP(c_fequal,U_20569)),U_20571)
          & hBOOL(hAPP(U_20567,U_20569)) ) )
    & ! [U_20570,U_20568,U_20566,U_20564] :
        ( ( ( c_List_Olist__ex1(U_20564,U_20566,U_20570)
            | hBOOL(hAPP(U_20566,U_20568)) )
          & ( c_List_Olist__all(U_20564,hAPP(hAPP(c_COMBS(U_20564,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20564),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20564),c_fNot),U_20566))),hAPP(c_fequal,U_20568)),U_20570)
            | ~ hBOOL(hAPP(U_20566,U_20568)) ) )
        | ~ c_List_Olist__ex1(U_20564,U_20566,hAPP(hAPP(c_List_Olist_OCons(U_20564),U_20568),U_20570)) ) ),
    inference(miniscope,[status(thm)],[f_4897_2]) ).

cnf(f_4897_4,plain,
    ( c_List_Olist__all(U_20564,hAPP(hAPP(c_COMBS(U_20564,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20564),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20564),c_fNot),U_20566))),hAPP(c_fequal,U_20568)),U_20570)
    | ~ hBOOL(hAPP(U_20566,U_20568))
    | ~ c_List_Olist__ex1(U_20564,U_20566,hAPP(hAPP(c_List_Olist_OCons(U_20564),U_20568),U_20570)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

cnf(f_4897_5,plain,
    ( c_List_Olist__ex1(U_20564,U_20566,U_20570)
    | hBOOL(hAPP(U_20566,U_20568))
    | ~ c_List_Olist__ex1(U_20564,U_20566,hAPP(hAPP(c_List_Olist_OCons(U_20564),U_20568),U_20570)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

cnf(f_4897_6,plain,
    ( ~ hBOOL(hAPP(U_20567,U_20569))
    | hBOOL(hAPP(U_20567,U_20569))
    | c_List_Olist__ex1(U_20565,U_20567,hAPP(hAPP(c_List_Olist_OCons(U_20565),U_20569),U_20571)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

cnf(f_4897_7,plain,
    ( ~ c_List_Olist__ex1(U_20565,U_20567,U_20571)
    | hBOOL(hAPP(U_20567,U_20569))
    | c_List_Olist__ex1(U_20565,U_20567,hAPP(hAPP(c_List_Olist_OCons(U_20565),U_20569),U_20571)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

cnf(f_4897_8,plain,
    ( ~ hBOOL(hAPP(U_20567,U_20569))
    | ~ c_List_Olist__all(U_20565,hAPP(hAPP(c_COMBS(U_20565,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20565),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20565),c_fNot),U_20567))),hAPP(c_fequal,U_20569)),U_20571)
    | c_List_Olist__ex1(U_20565,U_20567,hAPP(hAPP(c_List_Olist_OCons(U_20565),U_20569),U_20571)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

cnf(f_4897_9,plain,
    ( ~ c_List_Olist__ex1(U_20565,U_20567,U_20571)
    | ~ c_List_Olist__all(U_20565,hAPP(hAPP(c_COMBS(U_20565,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20565),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20565),c_fNot),U_20567))),hAPP(c_fequal,U_20569)),U_20571)
    | c_List_Olist__ex1(U_20565,U_20567,hAPP(hAPP(c_List_Olist_OCons(U_20565),U_20569),U_20571)) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

fof(f_4898_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
          | ? [B_x] :
              ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
              & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) )
        & ( ! [B_x] :
              ( hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
              | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) )
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) ) )
      | ~ class_Enum_Oenum(T_a)
      | ~ class_HOL_Oequal(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_equal__fun__def]) ).

fof(f_4898_2,plain,
    ! [U_20577,U_20576,U_20575,U_20574] :
      ( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577))
          | ? [U_20573] :
              ( hAPP(U_20576,U_20573) != hAPP(U_20577,U_20573)
              & hBOOL(hAPP(hAPP(c_member(U_20575),U_20573),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575)))) ) )
        & ( ! [U_20572] :
              ( hAPP(U_20576,U_20572) = hAPP(U_20577,U_20572)
              | ~ hBOOL(hAPP(hAPP(c_member(U_20575),U_20572),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575)))) )
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577)) ) )
      | ~ class_Enum_Oenum(U_20575)
      | ~ class_HOL_Oequal(U_20574) ),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20577,U_20576,U_20575,U_20574] :
      ( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577))
          | ( hAPP(U_20576,sK537(U_20577,U_20576,U_20575,U_20574)) != hAPP(U_20577,sK537(U_20577,U_20576,U_20575,U_20574))
            & hBOOL(hAPP(hAPP(c_member(U_20575),sK537(U_20577,U_20576,U_20575,U_20574)),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575)))) ) )
        & ( ! [U_20572] :
              ( hAPP(U_20576,U_20572) = hAPP(U_20577,U_20572)
              | ~ hBOOL(hAPP(hAPP(c_member(U_20575),U_20572),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575)))) )
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577)) ) )
      | ~ class_Enum_Oenum(U_20575)
      | ~ class_HOL_Oequal(U_20574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK537]),skolemize(U_20573,sK537(U_20577,U_20576,U_20575,U_20574))],[f_4898_2]) ).

cnf(f_4898_4,plain,
    ( hAPP(U_20576,U_20572) = hAPP(U_20577,U_20572)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20575),U_20572),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575))))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577))
    | ~ class_Enum_Oenum(U_20575)
    | ~ class_HOL_Oequal(U_20574) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

cnf(f_4898_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20575),sK537(U_20577,U_20576,U_20575,U_20574)),hAPP(c_List_Oset(U_20575),c_Enum_Oenum__class_Oenum(U_20575))))
    | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577))
    | ~ class_Enum_Oenum(U_20575)
    | ~ class_HOL_Oequal(U_20574) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

cnf(f_4898_6,plain,
    ( hAPP(U_20576,sK537(U_20577,U_20576,U_20575,U_20574)) != hAPP(U_20577,sK537(U_20577,U_20576,U_20575,U_20574))
    | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(U_20575,U_20574)),U_20576),U_20577))
    | ~ class_Enum_Oenum(U_20575)
    | ~ class_HOL_Oequal(U_20574) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

fof(f_4899_1,plain,
    ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(f_4899_2,plain,
    ! [U_20579,U_20578] : ~ c_List_Olist__ex1(U_20578,U_20579,c_List_Olist_ONil(U_20578)),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

cnf(f_4899_3,plain,
    ~ c_List_Olist__ex1(U_20578,U_20579,c_List_Olist_ONil(U_20578)),
    inference(clausify,[status(thm)],[f_4899_2]) ).

fof(f_4900_1,plain,
    ! [T_a] :
      ( c_HOL_Oequal__class_Oequal(T_a) = c_fequal
      | ~ class_HOL_Oequal(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equal]) ).

fof(f_4900_2,plain,
    ! [U_20580] :
      ( c_HOL_Oequal__class_Oequal(U_20580) = c_fequal
      | ~ class_HOL_Oequal(U_20580) ),
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

cnf(f_4900_3,plain,
    ( c_HOL_Oequal__class_Oequal(U_20580) = c_fequal
    | ~ class_HOL_Oequal(U_20580) ),
    inference(clausify,[status(thm)],[f_4900_2]) ).

fof(f_4901_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x))
      | ~ class_HOL_Oequal(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equal__refl]) ).

fof(f_4901_2,plain,
    ! [U_20582,U_20581] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20581),U_20582),U_20582))
      | ~ class_HOL_Oequal(U_20581) ),
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

cnf(f_4901_3,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20581),U_20582),U_20582))
    | ~ class_HOL_Oequal(U_20581) ),
    inference(clausify,[status(thm)],[f_4901_2]) ).

fof(f_4902_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) ) )
      | ~ class_HOL_Oequal(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equal__eq]) ).

fof(f_4902_2,plain,
    ! [U_20585,U_20584,U_20583] :
      ( ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20583),U_20584),U_20585))
          | U_20584 != U_20585 )
        & ( U_20584 = U_20585
          | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20583),U_20584),U_20585)) ) )
      | ~ class_HOL_Oequal(U_20583) ),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

cnf(f_4902_3,plain,
    ( U_20584 = U_20585
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20583),U_20584),U_20585))
    | ~ class_HOL_Oequal(U_20583) ),
    inference(clausify,[status(thm)],[f_4902_2]) ).

cnf(f_4902_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(U_20583),U_20584),U_20585))
    | U_20584 != U_20585
    | ~ class_HOL_Oequal(U_20583) ),
    inference(clausify,[status(thm)],[f_4902_2]) ).

fof(f_4903_1,plain,
    ! [T_a] :
      ( c_fequal = c_HOL_Oequal__class_Oequal(T_a)
      | ~ class_HOL_Oequal(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equal]) ).

fof(f_4903_2,plain,
    ! [U_20586] :
      ( c_fequal = c_HOL_Oequal__class_Oequal(U_20586)
      | ~ class_HOL_Oequal(U_20586) ),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

cnf(f_4903_3,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(U_20586)
    | ~ class_HOL_Oequal(U_20586) ),
    inference(clausify,[status(thm)],[f_4903_2]) ).

fof(f_4904_1,plain,
    ! [V_P_2,T_a] :
      ( ( ( ? [B_x] :
              ( ! [B_y] :
                  ( B_y = B_x
                  | ~ hBOOL(hAPP(V_P_2,B_y)) )
              & hBOOL(hAPP(V_P_2,B_x)) )
          | ~ c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) )
        & ( c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a))
          | ! [B_x] :
              ( ? [B_y] :
                  ( B_y != B_x
                  & hBOOL(hAPP(V_P_2,B_y)) )
              | ~ hBOOL(hAPP(V_P_2,B_x)) ) ) )
      | ~ class_Enum_Oenum(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_exists1__code]) ).

fof(f_4904_2,plain,
    ! [U_20592,U_20591] :
      ( ( ( ? [U_20590] :
              ( ! [U_20589] :
                  ( U_20589 = U_20590
                  | ~ hBOOL(hAPP(U_20592,U_20589)) )
              & hBOOL(hAPP(U_20592,U_20590)) )
          | ~ c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591)) )
        & ( c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
          | ! [U_20588] :
              ( ? [U_20587] :
                  ( U_20587 != U_20588
                  & hBOOL(hAPP(U_20592,U_20587)) )
              | ~ hBOOL(hAPP(U_20592,U_20588)) ) ) )
      | ~ class_Enum_Oenum(U_20591) ),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

fof(f_4904_3,plain,
    ! [U_20592,U_20591] :
      ( ( ( ? [U_20590] :
              ( ! [U_20589] :
                  ( U_20589 = U_20590
                  | ~ hBOOL(hAPP(U_20592,U_20589)) )
              & hBOOL(hAPP(U_20592,U_20590)) )
          | ~ c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591)) )
        & ( c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
          | ! [U_20588] :
              ( ( sK538(U_20592,U_20591,U_20588) != U_20588
                & hBOOL(hAPP(U_20592,sK538(U_20592,U_20591,U_20588))) )
              | ~ hBOOL(hAPP(U_20592,U_20588)) ) ) )
      | ~ class_Enum_Oenum(U_20591) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK538]),skolemize(U_20587,sK538(U_20592,U_20591,U_20588))],[f_4904_2]) ).

fof(f_4904_4,plain,
    ! [U_20592,U_20591] :
      ( ( ( ( ! [U_20589] :
                ( U_20589 = sK539(U_20592,U_20591)
                | ~ hBOOL(hAPP(U_20592,U_20589)) )
            & hBOOL(hAPP(U_20592,sK539(U_20592,U_20591))) )
          | ~ c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591)) )
        & ( c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
          | ! [U_20588] :
              ( ( sK538(U_20592,U_20591,U_20588) != U_20588
                & hBOOL(hAPP(U_20592,sK538(U_20592,U_20591,U_20588))) )
              | ~ hBOOL(hAPP(U_20592,U_20588)) ) ) )
      | ~ class_Enum_Oenum(U_20591) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK539]),skolemize(U_20590,sK539(U_20592,U_20591))],[f_4904_3]) ).

cnf(f_4904_5,plain,
    ( hBOOL(hAPP(U_20592,sK538(U_20592,U_20591,U_20588)))
    | ~ hBOOL(hAPP(U_20592,U_20588))
    | c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
    | ~ class_Enum_Oenum(U_20591) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

cnf(f_4904_6,plain,
    ( sK538(U_20592,U_20591,U_20588) != U_20588
    | ~ hBOOL(hAPP(U_20592,U_20588))
    | c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
    | ~ class_Enum_Oenum(U_20591) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

cnf(f_4904_7,plain,
    ( hBOOL(hAPP(U_20592,sK539(U_20592,U_20591)))
    | ~ c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
    | ~ class_Enum_Oenum(U_20591) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

cnf(f_4904_8,plain,
    ( U_20589 = sK539(U_20592,U_20591)
    | ~ hBOOL(hAPP(U_20592,U_20589))
    | ~ c_List_Olist__ex1(U_20591,U_20592,c_Enum_Oenum__class_Oenum(U_20591))
    | ~ class_Enum_Oenum(U_20591) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

fof(f_4905_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I3_J]) ).

cnf(f_4905_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4905_1]) ).

fof(f_4906_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I4_J]) ).

cnf(f_4906_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4906_1]) ).

fof(f_4907_1,plain,
    ! [V_xs_2,V_P_2,T_a] :
      ( ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) )
            | ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) ) )
      & ( ? [B_x] :
            ( ! [B_y] :
                ( B_y = B_x
                | ~ hBOOL(hAPP(V_P_2,B_y))
                | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) )
            & hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) )
        | ~ c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__iff]) ).

fof(f_4907_2,plain,
    ! [U_20599,U_20598,U_20597] :
      ( ( c_List_Olist__ex1(U_20597,U_20598,U_20599)
        | ! [U_20596] :
            ( ? [U_20595] :
                ( U_20595 != U_20596
                & hBOOL(hAPP(U_20598,U_20595))
                & hBOOL(hAPP(hAPP(c_member(U_20597),U_20595),hAPP(c_List_Oset(U_20597),U_20599))) )
            | ~ hBOOL(hAPP(U_20598,U_20596))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20597),U_20596),hAPP(c_List_Oset(U_20597),U_20599))) ) )
      & ( ? [U_20594] :
            ( ! [U_20593] :
                ( U_20593 = U_20594
                | ~ hBOOL(hAPP(U_20598,U_20593))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20597),U_20593),hAPP(c_List_Oset(U_20597),U_20599))) )
            & hBOOL(hAPP(U_20598,U_20594))
            & hBOOL(hAPP(hAPP(c_member(U_20597),U_20594),hAPP(c_List_Oset(U_20597),U_20599))) )
        | ~ c_List_Olist__ex1(U_20597,U_20598,U_20599) ) ),
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ( ! [U_20605,U_20603,U_20601] :
        ( c_List_Olist__ex1(U_20601,U_20603,U_20605)
        | ! [U_20596] :
            ( ? [U_20595] :
                ( U_20595 != U_20596
                & hBOOL(hAPP(U_20603,U_20595))
                & hBOOL(hAPP(hAPP(c_member(U_20601),U_20595),hAPP(c_List_Oset(U_20601),U_20605))) )
            | ~ hBOOL(hAPP(U_20603,U_20596))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605))) ) )
    & ! [U_20604,U_20602,U_20600] :
        ( ? [U_20594] :
            ( ! [U_20593] :
                ( U_20593 = U_20594
                | ~ hBOOL(hAPP(U_20602,U_20593))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20600),U_20593),hAPP(c_List_Oset(U_20600),U_20604))) )
            & hBOOL(hAPP(U_20602,U_20594))
            & hBOOL(hAPP(hAPP(c_member(U_20600),U_20594),hAPP(c_List_Oset(U_20600),U_20604))) )
        | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ) ),
    inference(miniscope,[status(thm)],[f_4907_2]) ).

fof(f_4907_4,plain,
    ( ! [U_20605,U_20603,U_20601] :
        ( c_List_Olist__ex1(U_20601,U_20603,U_20605)
        | ! [U_20596] :
            ( ? [U_20595] :
                ( U_20595 != U_20596
                & hBOOL(hAPP(U_20603,U_20595))
                & hBOOL(hAPP(hAPP(c_member(U_20601),U_20595),hAPP(c_List_Oset(U_20601),U_20605))) )
            | ~ hBOOL(hAPP(U_20603,U_20596))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605))) ) )
    & ! [U_20604,U_20602,U_20600] :
        ( ( ! [U_20593] :
              ( U_20593 = sK540(U_20604,U_20602,U_20600)
              | ~ hBOOL(hAPP(U_20602,U_20593))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20600),U_20593),hAPP(c_List_Oset(U_20600),U_20604))) )
          & hBOOL(hAPP(U_20602,sK540(U_20604,U_20602,U_20600)))
          & hBOOL(hAPP(hAPP(c_member(U_20600),sK540(U_20604,U_20602,U_20600)),hAPP(c_List_Oset(U_20600),U_20604))) )
        | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK540]),skolemize(U_20594,sK540(U_20604,U_20602,U_20600))],[f_4907_3]) ).

fof(f_4907_5,plain,
    ( ! [U_20605,U_20603,U_20601] :
        ( c_List_Olist__ex1(U_20601,U_20603,U_20605)
        | ! [U_20596] :
            ( ( sK541(U_20605,U_20603,U_20601,U_20596) != U_20596
              & hBOOL(hAPP(U_20603,sK541(U_20605,U_20603,U_20601,U_20596)))
              & hBOOL(hAPP(hAPP(c_member(U_20601),sK541(U_20605,U_20603,U_20601,U_20596)),hAPP(c_List_Oset(U_20601),U_20605))) )
            | ~ hBOOL(hAPP(U_20603,U_20596))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605))) ) )
    & ! [U_20604,U_20602,U_20600] :
        ( ( ! [U_20593] :
              ( U_20593 = sK540(U_20604,U_20602,U_20600)
              | ~ hBOOL(hAPP(U_20602,U_20593))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20600),U_20593),hAPP(c_List_Oset(U_20600),U_20604))) )
          & hBOOL(hAPP(U_20602,sK540(U_20604,U_20602,U_20600)))
          & hBOOL(hAPP(hAPP(c_member(U_20600),sK540(U_20604,U_20602,U_20600)),hAPP(c_List_Oset(U_20600),U_20604))) )
        | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK541]),skolemize(U_20595,sK541(U_20605,U_20603,U_20601,U_20596))],[f_4907_4]) ).

cnf(f_4907_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20600),sK540(U_20604,U_20602,U_20600)),hAPP(c_List_Oset(U_20600),U_20604)))
    | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

cnf(f_4907_7,plain,
    ( hBOOL(hAPP(U_20602,sK540(U_20604,U_20602,U_20600)))
    | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

cnf(f_4907_8,plain,
    ( U_20593 = sK540(U_20604,U_20602,U_20600)
    | ~ hBOOL(hAPP(U_20602,U_20593))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20600),U_20593),hAPP(c_List_Oset(U_20600),U_20604)))
    | ~ c_List_Olist__ex1(U_20600,U_20602,U_20604) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

cnf(f_4907_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20601),sK541(U_20605,U_20603,U_20601,U_20596)),hAPP(c_List_Oset(U_20601),U_20605)))
    | ~ hBOOL(hAPP(U_20603,U_20596))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605)))
    | c_List_Olist__ex1(U_20601,U_20603,U_20605) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

cnf(f_4907_10,plain,
    ( hBOOL(hAPP(U_20603,sK541(U_20605,U_20603,U_20601,U_20596)))
    | ~ hBOOL(hAPP(U_20603,U_20596))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605)))
    | c_List_Olist__ex1(U_20601,U_20603,U_20605) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

cnf(f_4907_11,plain,
    ( sK541(U_20605,U_20603,U_20601,U_20596) != U_20596
    | ~ hBOOL(hAPP(U_20603,U_20596))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20601),U_20596),hAPP(c_List_Oset(U_20601),U_20605)))
    | c_List_Olist__ex1(U_20601,U_20603,U_20605) ),
    inference(clausify,[status(thm)],[f_4907_5]) ).

fof(f_4908_1,plain,
    ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_size__code]) ).

fof(f_4908_2,plain,
    ! [U_20607,U_20606] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20606)),U_20607) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_20606,tc_Lazy__Sequence_Olazy__sequence(U_20606)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_20606,tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat),U_20606),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_20606)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20606)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(U_20606),U_20607)),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

cnf(f_4908_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20606)),U_20607) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_20606,tc_Lazy__Sequence_Olazy__sequence(U_20606)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_20606,tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat),U_20606),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_20606),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_20606)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20606)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(U_20606),U_20607)),
    inference(clausify,[status(thm)],[f_4908_2]) ).

fof(f_4909_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]) ).

cnf(f_4909_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(clausify,[status(thm)],[f_4909_1]) ).

fof(f_4910_1,plain,
    ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I7_J]) ).

fof(f_4910_2,plain,
    ! [U_20608] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_20608))),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

cnf(f_4910_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_20608))),
    inference(clausify,[status(thm)],[f_4910_2]) ).

fof(f_4911_1,plain,
    ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I11_J]) ).

fof(f_4911_2,plain,
    ! [U_20609] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20609)),c_Int_OMin)),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

cnf(f_4911_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20609)),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_4911_2]) ).

fof(f_4912_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I13_J]) ).

fof(f_4912_2,plain,
    ! [U_20611,U_20610] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20610)),c_Int_OBit0(U_20611)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20610),U_20611)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20610),U_20611))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20610)),c_Int_OBit0(U_20611))) ) ),
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ( ! [U_20615,U_20613] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20613)),c_Int_OBit0(U_20615)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20613),U_20615)) )
    & ! [U_20614,U_20612] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20612),U_20614))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20612)),c_Int_OBit0(U_20614))) ) ),
    inference(miniscope,[status(thm)],[f_4912_2]) ).

cnf(f_4912_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20612),U_20614))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20612)),c_Int_OBit0(U_20614))) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

cnf(f_4912_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20613)),c_Int_OBit0(U_20615)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20613),U_20615)) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

fof(f_4913_1,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I1_J]) ).

cnf(f_4913_2,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_4913_1]) ).

fof(f_4914_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I16_J]) ).

fof(f_4914_2,plain,
    ! [U_20617,U_20616] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20616)),c_Int_OBit1(U_20617)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20616),U_20617)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20616),U_20617))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20616)),c_Int_OBit1(U_20617))) ) ),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

fof(f_4914_3,plain,
    ( ! [U_20621,U_20619] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20619)),c_Int_OBit1(U_20621)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20619),U_20621)) )
    & ! [U_20620,U_20618] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20618),U_20620))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20618)),c_Int_OBit1(U_20620))) ) ),
    inference(miniscope,[status(thm)],[f_4914_2]) ).

cnf(f_4914_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20618),U_20620))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20618)),c_Int_OBit1(U_20620))) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

cnf(f_4914_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20619)),c_Int_OBit1(U_20621)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20619),U_20621)) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

fof(f_4915_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_eq__number__of__int__code]) ).

fof(f_4915_2,plain,
    ! [U_20623,U_20622] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20622)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20623)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20622),U_20623)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20622),U_20623))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20622)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20623))) ) ),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

fof(f_4915_3,plain,
    ( ! [U_20627,U_20625] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20625)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20627)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20625),U_20627)) )
    & ! [U_20626,U_20624] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20624),U_20626))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20624)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20626))) ) ),
    inference(miniscope,[status(thm)],[f_4915_2]) ).

cnf(f_4915_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20624),U_20626))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20624)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20626))) ),
    inference(clausify,[status(thm)],[f_4915_3]) ).

cnf(f_4915_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20625)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_20627)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20625),U_20627)) ),
    inference(clausify,[status(thm)],[f_4915_3]) ).

fof(f_4916_1,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I6_J]) ).

cnf(f_4916_2,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_4916_1]) ).

fof(f_4917_1,plain,
    ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I4_J]) ).

fof(f_4917_2,plain,
    ! [U_20628] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_20628))),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

cnf(f_4917_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_20628))),
    inference(clausify,[status(thm)],[f_4917_2]) ).

fof(f_4918_1,plain,
    ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I10_J]) ).

fof(f_4918_2,plain,
    ! [U_20629] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20629)),c_Int_OPls)),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

cnf(f_4918_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20629)),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_4918_2]) ).

fof(f_4919_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) != c_Groups_Ozero__class_Ozero(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_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_equal__int__def]) ).

fof(f_4919_2,plain,
    ! [U_20631,U_20630] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20630),U_20631))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20630),U_20631) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20630),U_20631) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20630),U_20631)) ) ),
    inference(variable_rename,[status(thm)],[f_4919_1]) ).

fof(f_4919_3,plain,
    ( ! [U_20635,U_20633] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20633),U_20635))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20633),U_20635) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_20634,U_20632] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20632),U_20634) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20632),U_20634)) ) ),
    inference(miniscope,[status(thm)],[f_4919_2]) ).

cnf(f_4919_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20632),U_20634) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20632),U_20634)) ),
    inference(clausify,[status(thm)],[f_4919_3]) ).

cnf(f_4919_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20633),U_20635))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_20633),U_20635) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_4919_3]) ).

fof(f_4920_1,plain,
    ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I14_J]) ).

fof(f_4920_2,plain,
    ! [U_20637,U_20636] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20636)),c_Int_OBit1(U_20637))),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

cnf(f_4920_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20636)),c_Int_OBit1(U_20637))),
    inference(clausify,[status(thm)],[f_4920_2]) ).

fof(f_4921_1,plain,
    ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I15_J]) ).

fof(f_4921_2,plain,
    ! [U_20639,U_20638] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20638)),c_Int_OBit0(U_20639))),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

cnf(f_4921_3,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20638)),c_Int_OBit0(U_20639))),
    inference(clausify,[status(thm)],[f_4921_2]) ).

fof(f_4922_1,plain,
    ! [V_k2_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J]) ).

fof(f_4922_2,plain,
    ! [U_20640] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20640)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20640)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20640))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20640))) ) ),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ( ! [U_20642] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20642)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20642)) )
    & ! [U_20641] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20641))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20641))) ) ),
    inference(miniscope,[status(thm)],[f_4922_2]) ).

cnf(f_4922_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20641))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20641))) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_20642)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),U_20642)) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

fof(f_4923_1,plain,
    ! [V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I9_J]) ).

fof(f_4923_2,plain,
    ! [U_20643] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20643)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20643),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20643),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20643)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

fof(f_4923_3,plain,
    ( ! [U_20645] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20645)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20645),c_Int_OPls)) )
    & ! [U_20644] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20644),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20644)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_4923_2]) ).

cnf(f_4923_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20644),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20644)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_4923_3]) ).

cnf(f_4923_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(U_20645)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20645),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_4923_3]) ).

fof(f_4924_1,plain,
    ! [V_k2_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I8_J]) ).

fof(f_4924_2,plain,
    ! [U_20646] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20646)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20646)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20646))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20646))) ) ),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

fof(f_4924_3,plain,
    ( ! [U_20648] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20648)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20648)) )
    & ! [U_20647] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20647))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20647))) ) ),
    inference(miniscope,[status(thm)],[f_4924_2]) ).

cnf(f_4924_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20647))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20647))) ),
    inference(clausify,[status(thm)],[f_4924_3]) ).

cnf(f_4924_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_20648)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),U_20648)) ),
    inference(clausify,[status(thm)],[f_4924_3]) ).

fof(f_4925_1,plain,
    ! [V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I12_J]) ).

fof(f_4925_2,plain,
    ! [U_20649] :
      ( ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20649)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20649),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20649),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20649)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ( ! [U_20651] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20651)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20651),c_Int_OMin)) )
    & ! [U_20650] :
        ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20650),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20650)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_4925_2]) ).

cnf(f_4925_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20650),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20650)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

cnf(f_4925_5,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(U_20651)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20651),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

fof(f_4926_1,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I5_J]) ).

cnf(f_4926_2,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_4926_1]) ).

fof(f_4927_1,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__code_I2_J]) ).

cnf(f_4927_2,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_4927_1]) ).

fof(f_4928_1,plain,
    ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(f_4928_2,plain,
    ! [U_20654,U_20653,U_20652] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20652,U_20653),U_20654) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_20652,tc_Lazy__Sequence_Olazy__sequence(U_20652)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_20652,tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_20652,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),U_20652),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_20652),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_20652)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_20652,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),U_20652),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_20652))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_20652),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_20653))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20652,U_20653))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_20652),U_20654)),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

cnf(f_4928_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20652,U_20653),U_20654) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_20652,tc_Lazy__Sequence_Olazy__sequence(U_20652)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_20652,tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_20652,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),U_20652),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_20652),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_20652)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_20652,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_20652),tc_Nat_Onat)),U_20652),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_20652))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_20652),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_20653))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20652,U_20653))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_20652),U_20654)),
    inference(clausify,[status(thm)],[f_4928_2]) ).

fof(f_4929_1,plain,
    ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_seq__case]) ).

fof(f_4929_2,plain,
    ! [U_20659,U_20658,U_20657,U_20656,U_20655] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_20655,U_20656,U_20657,U_20658,U_20659) = hAPP(c_Option_Ooption_Ooption__case(U_20655,tc_prod(U_20656,tc_Lazy__Sequence_Olazy__sequence(U_20656)),U_20657,hAPP(c_Product__Type_Oprod_Oprod__case(U_20656,tc_Lazy__Sequence_Olazy__sequence(U_20656),U_20655),U_20658)),hAPP(c_Lazy__Sequence_Oyield(U_20656),U_20659)),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

cnf(f_4929_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_20655,U_20656,U_20657,U_20658,U_20659) = hAPP(c_Option_Ooption_Ooption__case(U_20655,tc_prod(U_20656,tc_Lazy__Sequence_Olazy__sequence(U_20656)),U_20657,hAPP(c_Product__Type_Oprod_Oprod__case(U_20656,tc_Lazy__Sequence_Olazy__sequence(U_20656),U_20655),U_20658)),hAPP(c_Lazy__Sequence_Oyield(U_20656),U_20659)),
    inference(clausify,[status(thm)],[f_4929_2]) ).

fof(f_4930_1,plain,
    ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)),
    inference(fof_nnf,[status(thm)],[fact_eq__int__refl]) ).

fof(f_4930_2,plain,
    ! [U_20660] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20660),U_20660)),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

cnf(f_4930_3,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),U_20660),U_20660)),
    inference(clausify,[status(thm)],[f_4930_2]) ).

fof(f_4931_1,plain,
    ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)),
    inference(fof_nnf,[status(thm)],[fact_yieldn__def]) ).

fof(f_4931_2,plain,
    ! [U_20661] : c_Lazy__Sequence_Oyieldn(U_20661) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_20661),U_20661,c_Lazy__Sequence_Oyield(U_20661)),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

cnf(f_4931_3,plain,
    c_Lazy__Sequence_Oyieldn(U_20661) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_20661),U_20661,c_Lazy__Sequence_Oyield(U_20661)),
    inference(clausify,[status(thm)],[f_4931_2]) ).

fof(f_4932_1,plain,
    ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_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(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I2_J]) ).

fof(f_4932_2,plain,
    ! [U_20665,U_20664,U_20663,U_20662] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20662,U_20663),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20662,U_20664,U_20665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_20663,U_20664)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20662,U_20663),U_20665))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

cnf(f_4932_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20662,U_20663),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20662,U_20664,U_20665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_20663,U_20664)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_20662,U_20663),U_20665))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4932_2]) ).

fof(f_4933_1,plain,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(f_4933_2,plain,
    ! [U_20671,U_20670,U_20669,U_20668,U_20667,U_20666] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_20666,U_20667,U_20668,U_20669,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20667,U_20670,U_20671)) = hAPP(hAPP(U_20669,U_20670),U_20671),
    inference(variable_rename,[status(thm)],[f_4933_1]) ).

cnf(f_4933_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_20666,U_20667,U_20668,U_20669,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20667,U_20670,U_20671)) = hAPP(hAPP(U_20669,U_20670),U_20671),
    inference(clausify,[status(thm)],[f_4933_2]) ).

fof(f_4934_1,plain,
    ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
      ( ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2)
        | V_lazy__sequence_2 != V_lazy__sequence_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_lazy__sequence_2 = V_lazy__sequence_H_2
          & V_a_2 = V_a_H_2 )
        | c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject]) ).

fof(f_4934_2,plain,
    ! [U_20676,U_20675,U_20674,U_20673,U_20672] :
      ( ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_20672,U_20673,U_20674) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20672,U_20675,U_20676)
        | U_20674 != U_20676
        | U_20673 != U_20675 )
      & ( ( U_20674 = U_20676
          & U_20673 = U_20675 )
        | c_Lazy__Sequence_Olazy__sequence_OInsert(U_20672,U_20673,U_20674) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_20672,U_20675,U_20676) ) ),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

fof(f_4934_3,plain,
    ( ! [U_20686,U_20684,U_20682,U_20680] :
        ( ! [U_20678] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_20678,U_20680,U_20682) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20678,U_20684,U_20686)
        | U_20682 != U_20686
        | U_20680 != U_20684 )
    & ! [U_20685,U_20683,U_20681,U_20679] :
        ( ! [U_20677] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20679,U_20681) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20683,U_20685)
        | ( U_20681 = U_20685
          & U_20679 = U_20683 ) ) ),
    inference(miniscope,[status(thm)],[f_4934_2]) ).

cnf(f_4934_4,plain,
    ( U_20679 = U_20683
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20679,U_20681) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20683,U_20685) ),
    inference(clausify,[status(thm)],[f_4934_3]) ).

cnf(f_4934_5,plain,
    ( U_20681 = U_20685
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20679,U_20681) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_20677,U_20683,U_20685) ),
    inference(clausify,[status(thm)],[f_4934_3]) ).

cnf(f_4934_6,plain,
    ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_20678,U_20680,U_20682) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20678,U_20684,U_20686)
    | U_20682 != U_20686
    | U_20680 != U_20684 ),
    inference(clausify,[status(thm)],[f_4934_3]) ).

fof(f_4935_1,plain,
    ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)),
    inference(fof_nnf,[status(thm)],[fact__01]) ).

fof(f_4935_2,plain,
    ! [U_20689,U_20688,U_20687] : hAPP(c_Lazy__Sequence_Oyield(U_20687),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20687,U_20688,U_20689)) = hAPP(c_Option_Ooption_OSome(tc_prod(U_20687,tc_Lazy__Sequence_Olazy__sequence(U_20687))),hAPP(hAPP(c_Product__Type_OPair(U_20687,tc_Lazy__Sequence_Olazy__sequence(U_20687)),U_20688),U_20689)),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

cnf(f_4935_3,plain,
    hAPP(c_Lazy__Sequence_Oyield(U_20687),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20687,U_20688,U_20689)) = hAPP(c_Option_Ooption_OSome(tc_prod(U_20687,tc_Lazy__Sequence_Olazy__sequence(U_20687))),hAPP(hAPP(c_Product__Type_OPair(U_20687,tc_Lazy__Sequence_Olazy__sequence(U_20687)),U_20688),U_20689)),
    inference(clausify,[status(thm)],[f_4935_2]) ).

fof(f_4936_1,plain,
    ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I4_J]) ).

fof(f_4936_2,plain,
    ! [U_20692,U_20691,U_20690] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20690)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20690,U_20691,U_20692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20690)),U_20692)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

cnf(f_4936_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20690)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_20690,U_20691,U_20692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20690)),U_20692)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4936_2]) ).

fof(f_4937_1,plain,
    ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,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_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),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_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a)
        | 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_4937_2,plain,
    ! [U_20697,U_20696,U_20695,U_20694,U_20693] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_20694,U_20695,U_20696,U_20697),U_20693) = hAPP(c_Lazy__Sequence_Obind(U_20694,U_20695,hAPP(U_20696,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20693),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_20694,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_20695)),U_20697),U_20693))
        | U_20693 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_20694,U_20695,U_20696,U_20697),U_20693) = c_Lazy__Sequence_Oempty(U_20695)
        | U_20693 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

fof(f_4937_3,plain,
    ( ! [U_20707,U_20705,U_20703,U_20701,U_20699] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_20701,U_20703,U_20705,U_20707),U_20699) = hAPP(c_Lazy__Sequence_Obind(U_20701,U_20703,hAPP(U_20705,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20699),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_20701,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_20703)),U_20707),U_20699))
        | U_20699 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_20706,U_20704,U_20702,U_20700,U_20698] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_20700,U_20702,U_20704,U_20706),U_20698) = c_Lazy__Sequence_Oempty(U_20702)
        | U_20698 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4937_2]) ).

cnf(f_4937_4,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_20700,U_20702,U_20704,U_20706),U_20698) = c_Lazy__Sequence_Oempty(U_20702)
    | U_20698 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4937_3]) ).

cnf(f_4937_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_20701,U_20703,U_20705,U_20707),U_20699) = hAPP(c_Lazy__Sequence_Obind(U_20701,U_20703,hAPP(U_20705,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20699),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_20701,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_20703)),U_20707),U_20699))
    | U_20699 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4937_3]) ).

fof(f_4938_1,plain,
    ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,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_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),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_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a)
        | 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_4938_2,plain,
    ! [U_20712,U_20711,U_20710,U_20709,U_20708] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20709,U_20710,U_20711,U_20712),U_20708) = c_Lazy__Sequence_Ohb__bind(U_20709,U_20710,hAPP(U_20711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20708),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_20709,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_20710))),U_20712),U_20708))
        | U_20708 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20709,U_20710,U_20711,U_20712),U_20708) = c_Lazy__Sequence_Ohit__bound(U_20710)
        | U_20708 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

fof(f_4938_3,plain,
    ( ! [U_20722,U_20720,U_20718,U_20716,U_20714] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20716,U_20718,U_20720,U_20722),U_20714) = c_Lazy__Sequence_Ohb__bind(U_20716,U_20718,hAPP(U_20720,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20714),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_20716,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_20718))),U_20722),U_20714))
        | U_20714 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_20721,U_20719,U_20717,U_20715,U_20713] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20715,U_20717,U_20719,U_20721),U_20713) = c_Lazy__Sequence_Ohit__bound(U_20717)
        | U_20713 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4938_2]) ).

cnf(f_4938_4,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20715,U_20717,U_20719,U_20721),U_20713) = c_Lazy__Sequence_Ohit__bound(U_20717)
    | U_20713 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

cnf(f_4938_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_20716,U_20718,U_20720,U_20722),U_20714) = c_Lazy__Sequence_Ohb__bind(U_20716,U_20718,hAPP(U_20720,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_20714),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_20716,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_20718))),U_20722),U_20714))
    | U_20714 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

fof(f_4939_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),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_4939_2,plain,
    ! [U_20729,U_20728,U_20727,U_20726,U_20725,U_20724,U_20723] : c_New__Random__Sequence_Opos__decr__bind(U_20723,U_20724,U_20725,U_20726,U_20727,U_20728,U_20729) = c_New__DSequence_Opos__decr__bind(U_20723,U_20724,hAPP(hAPP(hAPP(U_20725,U_20727),U_20728),U_20729),hAPP(hAPP(c_COMBC(U_20723,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_20724))),hAPP(hAPP(c_COMBC(U_20723,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_20724)))),hAPP(hAPP(c_COMBC(U_20723,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_20724))))),U_20726),U_20727)),U_20728)),U_20729)),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

cnf(f_4939_3,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_20723,U_20724,U_20725,U_20726,U_20727,U_20728,U_20729) = c_New__DSequence_Opos__decr__bind(U_20723,U_20724,hAPP(hAPP(hAPP(U_20725,U_20727),U_20728),U_20729),hAPP(hAPP(c_COMBC(U_20723,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_20724))),hAPP(hAPP(c_COMBC(U_20723,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_20724)))),hAPP(hAPP(c_COMBC(U_20723,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_20724))))),U_20726),U_20727)),U_20728)),U_20729)),
    inference(clausify,[status(thm)],[f_4939_2]) ).

fof(f_4940_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),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_4940_2,plain,
    ! [U_20736,U_20735,U_20734,U_20733,U_20732,U_20731,U_20730] : c_New__Random__Sequence_Oneg__decr__bind(U_20730,U_20731,U_20732,U_20733,U_20734,U_20735,U_20736) = c_New__DSequence_Oneg__decr__bind(U_20730,U_20731,hAPP(hAPP(hAPP(U_20732,U_20734),U_20735),U_20736),hAPP(hAPP(c_COMBC(U_20730,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_20731)))),hAPP(hAPP(c_COMBC(U_20730,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_20731))))),hAPP(hAPP(c_COMBC(U_20730,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_20731)))))),U_20733),U_20734)),U_20735)),U_20736)),
    inference(variable_rename,[status(thm)],[f_4940_1]) ).

cnf(f_4940_3,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_20730,U_20731,U_20732,U_20733,U_20734,U_20735,U_20736) = c_New__DSequence_Oneg__decr__bind(U_20730,U_20731,hAPP(hAPP(hAPP(U_20732,U_20734),U_20735),U_20736),hAPP(hAPP(c_COMBC(U_20730,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_20731)))),hAPP(hAPP(c_COMBC(U_20730,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_20731))))),hAPP(hAPP(c_COMBC(U_20730,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_20731)))))),U_20733),U_20734)),U_20735)),U_20736)),
    inference(clausify,[status(thm)],[f_4940_2]) ).

fof(f_4941_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(f_4941_2,plain,
    ! [U_20741,U_20740,U_20739,U_20738,U_20737] : hAPP(c_New__DSequence_Oneg__bind(U_20737,U_20738,U_20739,U_20740),U_20741) = c_Lazy__Sequence_Ohb__bind(U_20737,U_20738,hAPP(U_20739,U_20741),hAPP(hAPP(c_COMBC(U_20737,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_20738))),U_20740),U_20741)),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

cnf(f_4941_3,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_20737,U_20738,U_20739,U_20740),U_20741) = c_Lazy__Sequence_Ohb__bind(U_20737,U_20738,hAPP(U_20739,U_20741),hAPP(hAPP(c_COMBC(U_20737,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_20738))),U_20740),U_20741)),
    inference(clausify,[status(thm)],[f_4941_2]) ).

fof(f_4942_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_4942_2,plain,
    ! [U_20743,U_20742] : hAPP(c_New__DSequence_Opos__empty(U_20742),U_20743) = c_Lazy__Sequence_Oempty(U_20742),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

cnf(f_4942_3,plain,
    hAPP(c_New__DSequence_Opos__empty(U_20742),U_20743) = c_Lazy__Sequence_Oempty(U_20742),
    inference(clausify,[status(thm)],[f_4942_2]) ).

fof(f_4943_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a),
    inference(fof_nnf,[status(thm)],[fact_pos__empty__def]) ).

fof(f_4943_2,plain,
    ! [U_20747,U_20746,U_20745,U_20744] : c_New__Random__Sequence_Opos__empty(U_20744,U_20745,U_20746,U_20747) = c_New__DSequence_Opos__empty(U_20744),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

cnf(f_4943_3,plain,
    c_New__Random__Sequence_Opos__empty(U_20744,U_20745,U_20746,U_20747) = c_New__DSequence_Opos__empty(U_20744),
    inference(clausify,[status(thm)],[f_4943_2]) ).

fof(f_4944_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__bind__def]) ).

fof(f_4944_2,plain,
    ! [U_20754,U_20753,U_20752,U_20751,U_20750,U_20749,U_20748] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_20748,U_20749,U_20750,U_20751),U_20752),U_20753),U_20754) = c_New__DSequence_Oneg__bind(U_20748,U_20749,hAPP(hAPP(hAPP(U_20750,U_20752),U_20753),U_20754),hAPP(hAPP(c_COMBC(U_20748,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_20749)))),hAPP(hAPP(c_COMBC(U_20748,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_20749))))),hAPP(hAPP(c_COMBC(U_20748,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_20749)))))),U_20751),U_20752)),U_20753)),U_20754)),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

cnf(f_4944_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_20748,U_20749,U_20750,U_20751),U_20752),U_20753),U_20754) = c_New__DSequence_Oneg__bind(U_20748,U_20749,hAPP(hAPP(hAPP(U_20750,U_20752),U_20753),U_20754),hAPP(hAPP(c_COMBC(U_20748,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_20749)))),hAPP(hAPP(c_COMBC(U_20748,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_20749))))),hAPP(hAPP(c_COMBC(U_20748,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_20749)))))),U_20751),U_20752)),U_20753)),U_20754)),
    inference(clausify,[status(thm)],[f_4944_2]) ).

fof(f_4945_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(f_4945_2,plain,
    ! [U_20759,U_20758,U_20757,U_20756,U_20755] : hAPP(c_New__DSequence_Opos__bind(U_20755,U_20756,U_20757,U_20758),U_20759) = hAPP(c_Lazy__Sequence_Obind(U_20755,U_20756,hAPP(U_20757,U_20759)),hAPP(hAPP(c_COMBC(U_20755,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_20756)),U_20758),U_20759)),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

cnf(f_4945_3,plain,
    hAPP(c_New__DSequence_Opos__bind(U_20755,U_20756,U_20757,U_20758),U_20759) = hAPP(c_Lazy__Sequence_Obind(U_20755,U_20756,hAPP(U_20757,U_20759)),hAPP(hAPP(c_COMBC(U_20755,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_20756)),U_20758),U_20759)),
    inference(clausify,[status(thm)],[f_4945_2]) ).

fof(f_4946_1,plain,
    ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__map__def]) ).

fof(f_4946_2,plain,
    ! [U_20763,U_20762,U_20761,U_20760] : c_New__Random__Sequence_Oneg__map(U_20760,U_20761,U_20762,U_20763) = c_New__Random__Sequence_Oneg__bind(U_20760,U_20761,U_20763,hAPP(c_Fun_Ocomp(U_20761,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_20761)))))),U_20760,c_New__Random__Sequence_Oneg__single(U_20761)),U_20762)),
    inference(variable_rename,[status(thm)],[f_4946_1]) ).

cnf(f_4946_3,plain,
    c_New__Random__Sequence_Oneg__map(U_20760,U_20761,U_20762,U_20763) = c_New__Random__Sequence_Oneg__bind(U_20760,U_20761,U_20763,hAPP(c_Fun_Ocomp(U_20761,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_20761)))))),U_20760,c_New__Random__Sequence_Oneg__single(U_20761)),U_20762)),
    inference(clausify,[status(thm)],[f_4946_2]) ).

fof(f_4947_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_neg__single__def]) ).

fof(f_4947_2,plain,
    ! [U_20768,U_20767,U_20766,U_20765,U_20764] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_20764),U_20765),U_20766),U_20767),U_20768) = c_New__DSequence_Oneg__single(U_20764,U_20765),
    inference(variable_rename,[status(thm)],[f_4947_1]) ).

cnf(f_4947_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_20764),U_20765),U_20766),U_20767),U_20768) = c_New__DSequence_Oneg__single(U_20764,U_20765),
    inference(clausify,[status(thm)],[f_4947_2]) ).

fof(f_4948_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__bind__def]) ).

fof(f_4948_2,plain,
    ! [U_20775,U_20774,U_20773,U_20772,U_20771,U_20770,U_20769] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_20769,U_20770,U_20771,U_20772),U_20773),U_20774),U_20775) = c_New__DSequence_Opos__bind(U_20769,U_20770,hAPP(hAPP(hAPP(U_20771,U_20773),U_20774),U_20775),hAPP(hAPP(c_COMBC(U_20769,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_20770))),hAPP(hAPP(c_COMBC(U_20769,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_20770)))),hAPP(hAPP(c_COMBC(U_20769,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_20770))))),U_20772),U_20773)),U_20774)),U_20775)),
    inference(variable_rename,[status(thm)],[f_4948_1]) ).

cnf(f_4948_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_20769,U_20770,U_20771,U_20772),U_20773),U_20774),U_20775) = c_New__DSequence_Opos__bind(U_20769,U_20770,hAPP(hAPP(hAPP(U_20771,U_20773),U_20774),U_20775),hAPP(hAPP(c_COMBC(U_20769,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_20770))),hAPP(hAPP(c_COMBC(U_20769,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_20770)))),hAPP(hAPP(c_COMBC(U_20769,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_20770))))),U_20772),U_20773)),U_20774)),U_20775)),
    inference(clausify,[status(thm)],[f_4948_2]) ).

fof(f_4949_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_4949_2,plain,
    ! [U_20778,U_20777,U_20776] : hAPP(c_New__DSequence_Oneg__single(U_20776,U_20777),U_20778) = c_Lazy__Sequence_Ohb__single(U_20776,U_20777),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

cnf(f_4949_3,plain,
    hAPP(c_New__DSequence_Oneg__single(U_20776,U_20777),U_20778) = c_Lazy__Sequence_Ohb__single(U_20776,U_20777),
    inference(clausify,[status(thm)],[f_4949_2]) ).

fof(f_4950_1,plain,
    ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__map__def]) ).

fof(f_4950_2,plain,
    ! [U_20782,U_20781,U_20780,U_20779] : c_New__Random__Sequence_Opos__map(U_20779,U_20780,U_20781,U_20782) = c_New__Random__Sequence_Opos__bind(U_20779,U_20780,U_20782,hAPP(c_Fun_Ocomp(U_20780,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_20780))))),U_20779,c_New__Random__Sequence_Opos__single(U_20780)),U_20781)),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

cnf(f_4950_3,plain,
    c_New__Random__Sequence_Opos__map(U_20779,U_20780,U_20781,U_20782) = c_New__Random__Sequence_Opos__bind(U_20779,U_20780,U_20782,hAPP(c_Fun_Ocomp(U_20780,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_20780))))),U_20779,c_New__Random__Sequence_Opos__single(U_20780)),U_20781)),
    inference(clausify,[status(thm)],[f_4950_2]) ).

fof(f_4951_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_pos__single__def]) ).

fof(f_4951_2,plain,
    ! [U_20787,U_20786,U_20785,U_20784,U_20783] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_20783),U_20784),U_20785),U_20786),U_20787) = c_New__DSequence_Opos__single(U_20783,U_20784),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

cnf(f_4951_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_20783),U_20784),U_20785),U_20786),U_20787) = c_New__DSequence_Opos__single(U_20783,U_20784),
    inference(clausify,[status(thm)],[f_4951_2]) ).

fof(f_4952_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(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__splice]) ).

fof(f_4952_2,plain,
    ! [U_20790,U_20789,U_20788] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),c_List_Osplice(U_20788,U_20789,U_20790)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),U_20789)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),U_20790)),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

cnf(f_4952_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),c_List_Osplice(U_20788,U_20789,U_20790)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),U_20789)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20788)),U_20790)),
    inference(clausify,[status(thm)],[f_4952_2]) ).

fof(f_4953_1,plain,
    ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(f_4953_2,plain,
    ! [U_20795,U_20794,U_20793,U_20792,U_20791] : c_List_Osplice(U_20791,hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20792),U_20793),hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20794),U_20795)) = hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20792),hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20794),c_List_Osplice(U_20791,U_20793,U_20795))),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

cnf(f_4953_3,plain,
    c_List_Osplice(U_20791,hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20792),U_20793),hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20794),U_20795)) = hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20792),hAPP(hAPP(c_List_Olist_OCons(U_20791),U_20794),c_List_Osplice(U_20791,U_20793,U_20795))),
    inference(clausify,[status(thm)],[f_4953_2]) ).

fof(f_4954_1,plain,
    ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_splice__Nil2]) ).

fof(f_4954_2,plain,
    ! [U_20797,U_20796] : c_List_Osplice(U_20796,U_20797,c_List_Olist_ONil(U_20796)) = U_20797,
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

cnf(f_4954_3,plain,
    c_List_Osplice(U_20796,U_20797,c_List_Olist_ONil(U_20796)) = U_20797,
    inference(clausify,[status(thm)],[f_4954_2]) ).

fof(f_4955_1,plain,
    ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(f_4955_2,plain,
    ! [U_20799,U_20798] : c_List_Osplice(U_20798,c_List_Olist_ONil(U_20798),U_20799) = U_20799,
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

cnf(f_4955_3,plain,
    c_List_Osplice(U_20798,c_List_Olist_ONil(U_20798),U_20799) = U_20799,
    inference(clausify,[status(thm)],[f_4955_2]) ).

fof(f_4956_1,plain,
    ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(f_4956_2,plain,
    ! [U_20802,U_20801,U_20800] : c_List_Osplice(U_20800,hAPP(hAPP(c_List_Olist_OCons(U_20800),U_20801),U_20802),c_List_Olist_ONil(U_20800)) = hAPP(hAPP(c_List_Olist_OCons(U_20800),U_20801),U_20802),
    inference(variable_rename,[status(thm)],[f_4956_1]) ).

cnf(f_4956_3,plain,
    c_List_Osplice(U_20800,hAPP(hAPP(c_List_Olist_OCons(U_20800),U_20801),U_20802),c_List_Olist_ONil(U_20800)) = hAPP(hAPP(c_List_Olist_OCons(U_20800),U_20801),U_20802),
    inference(clausify,[status(thm)],[f_4956_2]) ).

fof(f_4957_1,plain,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(f_4957_2,plain,
    ! [U_20805,U_20804,U_20803] : hAPP(c_New__DSequence_Opos__single(U_20803,U_20804),U_20805) = hAPP(c_Lazy__Sequence_Osingle(U_20803),U_20804),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

cnf(f_4957_3,plain,
    hAPP(c_New__DSequence_Opos__single(U_20803,U_20804),U_20805) = hAPP(c_Lazy__Sequence_Osingle(U_20803),U_20804),
    inference(clausify,[status(thm)],[f_4957_2]) ).

fof(f_4958_1,plain,
    ! [V_r_2,T_a] :
      ( ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2))))
        | ~ c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) )
      & ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicP__converse]) ).

fof(f_4958_2,plain,
    ! [U_20807,U_20806] :
      ( ( c_Wellfounded_Oacyclic(U_20806,hAPP(c_Set_OCollect(tc_prod(U_20806,U_20806)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20806,U_20806,tc_HOL_Obool),c_Predicate_Oconversep(U_20806,U_20806,U_20807))))
        | ~ c_Wellfounded_Oacyclic(U_20806,hAPP(c_Set_OCollect(tc_prod(U_20806,U_20806)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20806,U_20806,tc_HOL_Obool),U_20807))) )
      & ( c_Wellfounded_Oacyclic(U_20806,hAPP(c_Set_OCollect(tc_prod(U_20806,U_20806)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20806,U_20806,tc_HOL_Obool),U_20807)))
        | ~ c_Wellfounded_Oacyclic(U_20806,hAPP(c_Set_OCollect(tc_prod(U_20806,U_20806)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20806,U_20806,tc_HOL_Obool),c_Predicate_Oconversep(U_20806,U_20806,U_20807)))) ) ),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

fof(f_4958_3,plain,
    ( ! [U_20811,U_20809] :
        ( c_Wellfounded_Oacyclic(U_20809,hAPP(c_Set_OCollect(tc_prod(U_20809,U_20809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20809,U_20809,tc_HOL_Obool),c_Predicate_Oconversep(U_20809,U_20809,U_20811))))
        | ~ c_Wellfounded_Oacyclic(U_20809,hAPP(c_Set_OCollect(tc_prod(U_20809,U_20809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20809,U_20809,tc_HOL_Obool),U_20811))) )
    & ! [U_20810,U_20808] :
        ( c_Wellfounded_Oacyclic(U_20808,hAPP(c_Set_OCollect(tc_prod(U_20808,U_20808)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20808,U_20808,tc_HOL_Obool),U_20810)))
        | ~ c_Wellfounded_Oacyclic(U_20808,hAPP(c_Set_OCollect(tc_prod(U_20808,U_20808)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20808,U_20808,tc_HOL_Obool),c_Predicate_Oconversep(U_20808,U_20808,U_20810)))) ) ),
    inference(miniscope,[status(thm)],[f_4958_2]) ).

cnf(f_4958_4,plain,
    ( c_Wellfounded_Oacyclic(U_20808,hAPP(c_Set_OCollect(tc_prod(U_20808,U_20808)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20808,U_20808,tc_HOL_Obool),U_20810)))
    | ~ c_Wellfounded_Oacyclic(U_20808,hAPP(c_Set_OCollect(tc_prod(U_20808,U_20808)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20808,U_20808,tc_HOL_Obool),c_Predicate_Oconversep(U_20808,U_20808,U_20810)))) ),
    inference(clausify,[status(thm)],[f_4958_3]) ).

cnf(f_4958_5,plain,
    ( c_Wellfounded_Oacyclic(U_20809,hAPP(c_Set_OCollect(tc_prod(U_20809,U_20809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20809,U_20809,tc_HOL_Obool),c_Predicate_Oconversep(U_20809,U_20809,U_20811))))
    | ~ c_Wellfounded_Oacyclic(U_20809,hAPP(c_Set_OCollect(tc_prod(U_20809,U_20809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_20809,U_20809,tc_HOL_Obool),U_20811))) ),
    inference(clausify,[status(thm)],[f_4958_3]) ).

fof(f_4959_1,plain,
    ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__meet]) ).

fof(f_4959_2,plain,
    ! [U_20815,U_20814,U_20813,U_20812] : c_Predicate_Oconversep(U_20812,U_20813,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20812,tc_fun(U_20813,tc_HOL_Obool))),U_20814),U_20815)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20813,tc_fun(U_20812,tc_HOL_Obool))),c_Predicate_Oconversep(U_20812,U_20813,U_20814)),c_Predicate_Oconversep(U_20812,U_20813,U_20815)),
    inference(variable_rename,[status(thm)],[f_4959_1]) ).

cnf(f_4959_3,plain,
    c_Predicate_Oconversep(U_20812,U_20813,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20812,tc_fun(U_20813,tc_HOL_Obool))),U_20814),U_20815)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20813,tc_fun(U_20812,tc_HOL_Obool))),c_Predicate_Oconversep(U_20812,U_20813,U_20814)),c_Predicate_Oconversep(U_20812,U_20813,U_20815)),
    inference(clausify,[status(thm)],[f_4959_2]) ).

fof(f_4960_1,plain,
    ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal,
    inference(fof_nnf,[status(thm)],[fact_conversep__eq]) ).

fof(f_4960_2,plain,
    ! [U_20816] : c_Predicate_Oconversep(U_20816,U_20816,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

cnf(f_4960_3,plain,
    c_Predicate_Oconversep(U_20816,U_20816,c_fequal) = c_fequal,
    inference(clausify,[status(thm)],[f_4960_2]) ).

fof(f_4961_1,plain,
    ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_conversep__conversep]) ).

fof(f_4961_2,plain,
    ! [U_20819,U_20818,U_20817] : c_Predicate_Oconversep(U_20817,U_20818,c_Predicate_Oconversep(U_20818,U_20817,U_20819)) = U_20819,
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

cnf(f_4961_3,plain,
    c_Predicate_Oconversep(U_20817,U_20818,c_Predicate_Oconversep(U_20818,U_20817,U_20819)) = U_20819,
    inference(clausify,[status(thm)],[f_4961_2]) ).

fof(f_4962_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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_a,T_b,V_r_2),V_a_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__iff]) ).

fof(f_4962_2,plain,
    ! [U_20824,U_20823,U_20822,U_20821,U_20820] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20820,U_20821,U_20822),U_20823),U_20824))
        | ~ hBOOL(hAPP(hAPP(U_20822,U_20824),U_20823)) )
      & ( hBOOL(hAPP(hAPP(U_20822,U_20824),U_20823))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20820,U_20821,U_20822),U_20823),U_20824)) ) ),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

fof(f_4962_3,plain,
    ( ! [U_20834,U_20832,U_20830] :
        ( ! [U_20828,U_20826] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20826,U_20828,U_20830),U_20832),U_20834))
        | ~ hBOOL(hAPP(hAPP(U_20830,U_20834),U_20832)) )
    & ! [U_20833,U_20831,U_20829] :
        ( ! [U_20827,U_20825] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20825,U_20827,U_20829),U_20831),U_20833))
        | hBOOL(hAPP(hAPP(U_20829,U_20833),U_20831)) ) ),
    inference(miniscope,[status(thm)],[f_4962_2]) ).

cnf(f_4962_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20825,U_20827,U_20829),U_20831),U_20833))
    | hBOOL(hAPP(hAPP(U_20829,U_20833),U_20831)) ),
    inference(clausify,[status(thm)],[f_4962_3]) ).

cnf(f_4962_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20826,U_20828,U_20830),U_20832),U_20834))
    | ~ hBOOL(hAPP(hAPP(U_20830,U_20834),U_20832)) ),
    inference(clausify,[status(thm)],[f_4962_3]) ).

fof(f_4963_1,plain,
    ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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_a,T_b,V_r_2),V_a2_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep_Oequations]) ).

fof(f_4963_2,plain,
    ! [U_20839,U_20838,U_20837,U_20836,U_20835] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20835,U_20836,U_20837),U_20838),U_20839))
        | ~ hBOOL(hAPP(hAPP(U_20837,U_20839),U_20838)) )
      & ( hBOOL(hAPP(hAPP(U_20837,U_20839),U_20838))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20835,U_20836,U_20837),U_20838),U_20839)) ) ),
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

fof(f_4963_3,plain,
    ( ! [U_20849,U_20847,U_20845] :
        ( ! [U_20843,U_20841] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20841,U_20843,U_20845),U_20847),U_20849))
        | ~ hBOOL(hAPP(hAPP(U_20845,U_20849),U_20847)) )
    & ! [U_20848,U_20846,U_20844] :
        ( ! [U_20842,U_20840] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20840,U_20842,U_20844),U_20846),U_20848))
        | hBOOL(hAPP(hAPP(U_20844,U_20848),U_20846)) ) ),
    inference(miniscope,[status(thm)],[f_4963_2]) ).

cnf(f_4963_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20840,U_20842,U_20844),U_20846),U_20848))
    | hBOOL(hAPP(hAPP(U_20844,U_20848),U_20846)) ),
    inference(clausify,[status(thm)],[f_4963_3]) ).

cnf(f_4963_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20841,U_20843,U_20845),U_20847),U_20849))
    | ~ hBOOL(hAPP(hAPP(U_20845,U_20849),U_20847)) ),
    inference(clausify,[status(thm)],[f_4963_3]) ).

fof(f_4964_1,plain,
    ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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_4964_2,plain,
    ! [U_20854,U_20853,U_20852,U_20851,U_20850] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20853,U_20854,U_20850),U_20852),U_20851))
      | ~ hBOOL(hAPP(hAPP(U_20850,U_20851),U_20852)) ),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

cnf(f_4964_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20853,U_20854,U_20850),U_20852),U_20851))
    | ~ hBOOL(hAPP(hAPP(U_20850,U_20851),U_20852)) ),
    inference(clausify,[status(thm)],[f_4964_2]) ).

fof(f_4965_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conversepD]) ).

fof(f_4965_2,plain,
    ! [U_20859,U_20858,U_20857,U_20856,U_20855] :
      ( hBOOL(hAPP(hAPP(U_20857,U_20859),U_20858))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20855,U_20856,U_20857),U_20858),U_20859)) ),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

fof(f_4965_3,plain,
    ! [U_20859,U_20858,U_20857] :
      ( ! [U_20856,U_20855] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20855,U_20856,U_20857),U_20858),U_20859))
      | hBOOL(hAPP(hAPP(U_20857,U_20859),U_20858)) ),
    inference(miniscope,[status(thm)],[f_4965_2]) ).

cnf(f_4965_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20855,U_20856,U_20857),U_20858),U_20859))
    | hBOOL(hAPP(hAPP(U_20857,U_20859),U_20858)) ),
    inference(clausify,[status(thm)],[f_4965_3]) ).

fof(f_4966_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),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_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__noteq]) ).

fof(f_4966_2,plain,
    ! [U_20862,U_20861,U_20860] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20860,U_20860,hAPP(hAPP(c_COMBB(tc_fun(U_20860,tc_HOL_Obool),tc_fun(U_20860,tc_HOL_Obool),U_20860),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20860),c_fNot)),c_fequal)),U_20861),U_20862))
        | U_20861 = U_20862 )
      & ( U_20861 != U_20862
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20860,U_20860,hAPP(hAPP(c_COMBB(tc_fun(U_20860,tc_HOL_Obool),tc_fun(U_20860,tc_HOL_Obool),U_20860),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20860),c_fNot)),c_fequal)),U_20861),U_20862)) ) ),
    inference(variable_rename,[status(thm)],[f_4966_1]) ).

fof(f_4966_3,plain,
    ( ! [U_20868,U_20866] :
        ( ! [U_20864] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20864,U_20864,hAPP(hAPP(c_COMBB(tc_fun(U_20864,tc_HOL_Obool),tc_fun(U_20864,tc_HOL_Obool),U_20864),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20864),c_fNot)),c_fequal)),U_20866),U_20868))
        | U_20866 = U_20868 )
    & ! [U_20867,U_20865] :
        ( ! [U_20863] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20863,U_20863,hAPP(hAPP(c_COMBB(tc_fun(U_20863,tc_HOL_Obool),tc_fun(U_20863,tc_HOL_Obool),U_20863),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20863),c_fNot)),c_fequal)),U_20865),U_20867))
        | U_20865 != U_20867 ) ),
    inference(miniscope,[status(thm)],[f_4966_2]) ).

cnf(f_4966_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20863,U_20863,hAPP(hAPP(c_COMBB(tc_fun(U_20863,tc_HOL_Obool),tc_fun(U_20863,tc_HOL_Obool),U_20863),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20863),c_fNot)),c_fequal)),U_20865),U_20867))
    | U_20865 != U_20867 ),
    inference(clausify,[status(thm)],[f_4966_3]) ).

cnf(f_4966_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20864,U_20864,hAPP(hAPP(c_COMBB(tc_fun(U_20864,tc_HOL_Obool),tc_fun(U_20864,tc_HOL_Obool),U_20864),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20864),c_fNot)),c_fequal)),U_20866),U_20868))
    | U_20866 = U_20868 ),
    inference(clausify,[status(thm)],[f_4966_3]) ).

fof(f_4967_1,plain,
    ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__pred__comp]) ).

fof(f_4967_2,plain,
    ! [U_20873,U_20872,U_20871,U_20870,U_20869] : c_Predicate_Oconversep(U_20869,U_20870,c_Predicate_Opred__comp(U_20869,U_20871,U_20870,U_20872,U_20873)) = c_Predicate_Opred__comp(U_20870,U_20871,U_20869,c_Predicate_Oconversep(U_20871,U_20870,U_20873),c_Predicate_Oconversep(U_20869,U_20871,U_20872)),
    inference(variable_rename,[status(thm)],[f_4967_1]) ).

cnf(f_4967_3,plain,
    c_Predicate_Oconversep(U_20869,U_20870,c_Predicate_Opred__comp(U_20869,U_20871,U_20870,U_20872,U_20873)) = c_Predicate_Opred__comp(U_20870,U_20871,U_20869,c_Predicate_Oconversep(U_20871,U_20870,U_20873),c_Predicate_Oconversep(U_20869,U_20871,U_20872)),
    inference(clausify,[status(thm)],[f_4967_2]) ).

fof(f_4968_1,plain,
    ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__join]) ).

fof(f_4968_2,plain,
    ! [U_20877,U_20876,U_20875,U_20874] : c_Predicate_Oconversep(U_20874,U_20875,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20874,tc_fun(U_20875,tc_HOL_Obool))),U_20876),U_20877)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20875,tc_fun(U_20874,tc_HOL_Obool))),c_Predicate_Oconversep(U_20874,U_20875,U_20876)),c_Predicate_Oconversep(U_20874,U_20875,U_20877)),
    inference(variable_rename,[status(thm)],[f_4968_1]) ).

cnf(f_4968_3,plain,
    c_Predicate_Oconversep(U_20874,U_20875,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20874,tc_fun(U_20875,tc_HOL_Obool))),U_20876),U_20877)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20875,tc_fun(U_20874,tc_HOL_Obool))),c_Predicate_Oconversep(U_20874,U_20875,U_20876)),c_Predicate_Oconversep(U_20874,U_20875,U_20877)),
    inference(clausify,[status(thm)],[f_4968_2]) ).

fof(f_4969_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq]) ).

fof(f_4969_2,plain,
    ! [U_20882,U_20881,U_20880,U_20879,U_20878] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20878,U_20879,hAPP(hAPP(c_COMBC(U_20878,tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_fun(U_20879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20879,tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_fun(U_20879,tc_HOL_Obool)),U_20878),c_COMBC(U_20879,tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20879,tc_prod(U_20878,U_20879)),tc_fun(U_20879,tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),U_20878),hAPP(c_COMBB(tc_prod(U_20878,U_20879),tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool),U_20879),c_member(tc_prod(U_20878,U_20879)))),c_Product__Type_OPair(U_20878,U_20879)))),U_20880)),U_20881),U_20882))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20879,U_20878)),hAPP(hAPP(c_Product__Type_OPair(U_20879,U_20878),U_20881),U_20882)),hAPP(c_Relation_Oconverse(U_20878,U_20879),U_20880))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20879,U_20878)),hAPP(hAPP(c_Product__Type_OPair(U_20879,U_20878),U_20881),U_20882)),hAPP(c_Relation_Oconverse(U_20878,U_20879),U_20880)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20878,U_20879,hAPP(hAPP(c_COMBC(U_20878,tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_fun(U_20879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20879,tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_fun(U_20879,tc_HOL_Obool)),U_20878),c_COMBC(U_20879,tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20879,tc_prod(U_20878,U_20879)),tc_fun(U_20879,tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool)),U_20878),hAPP(c_COMBB(tc_prod(U_20878,U_20879),tc_fun(tc_fun(tc_prod(U_20878,U_20879),tc_HOL_Obool),tc_HOL_Obool),U_20879),c_member(tc_prod(U_20878,U_20879)))),c_Product__Type_OPair(U_20878,U_20879)))),U_20880)),U_20881),U_20882)) ) ),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

fof(f_4969_3,plain,
    ( ! [U_20892,U_20890,U_20888,U_20886,U_20884] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20884,U_20886,hAPP(hAPP(c_COMBC(U_20884,tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_fun(U_20886,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20886,tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_fun(U_20886,tc_HOL_Obool)),U_20884),c_COMBC(U_20886,tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20886,tc_prod(U_20884,U_20886)),tc_fun(U_20886,tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),U_20884),hAPP(c_COMBB(tc_prod(U_20884,U_20886),tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool),U_20886),c_member(tc_prod(U_20884,U_20886)))),c_Product__Type_OPair(U_20884,U_20886)))),U_20888)),U_20890),U_20892))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20886,U_20884)),hAPP(hAPP(c_Product__Type_OPair(U_20886,U_20884),U_20890),U_20892)),hAPP(c_Relation_Oconverse(U_20884,U_20886),U_20888))) )
    & ! [U_20891,U_20889,U_20887,U_20885,U_20883] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20885,U_20883)),hAPP(hAPP(c_Product__Type_OPair(U_20885,U_20883),U_20889),U_20891)),hAPP(c_Relation_Oconverse(U_20883,U_20885),U_20887)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20883,U_20885,hAPP(hAPP(c_COMBC(U_20883,tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_fun(U_20885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20885,tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_fun(U_20885,tc_HOL_Obool)),U_20883),c_COMBC(U_20885,tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20885,tc_prod(U_20883,U_20885)),tc_fun(U_20885,tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),U_20883),hAPP(c_COMBB(tc_prod(U_20883,U_20885),tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool),U_20885),c_member(tc_prod(U_20883,U_20885)))),c_Product__Type_OPair(U_20883,U_20885)))),U_20887)),U_20889),U_20891)) ) ),
    inference(miniscope,[status(thm)],[f_4969_2]) ).

cnf(f_4969_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20885,U_20883)),hAPP(hAPP(c_Product__Type_OPair(U_20885,U_20883),U_20889),U_20891)),hAPP(c_Relation_Oconverse(U_20883,U_20885),U_20887)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20883,U_20885,hAPP(hAPP(c_COMBC(U_20883,tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_fun(U_20885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20885,tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_fun(U_20885,tc_HOL_Obool)),U_20883),c_COMBC(U_20885,tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20885,tc_prod(U_20883,U_20885)),tc_fun(U_20885,tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool)),U_20883),hAPP(c_COMBB(tc_prod(U_20883,U_20885),tc_fun(tc_fun(tc_prod(U_20883,U_20885),tc_HOL_Obool),tc_HOL_Obool),U_20885),c_member(tc_prod(U_20883,U_20885)))),c_Product__Type_OPair(U_20883,U_20885)))),U_20887)),U_20889),U_20891)) ),
    inference(clausify,[status(thm)],[f_4969_3]) ).

cnf(f_4969_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_20884,U_20886,hAPP(hAPP(c_COMBC(U_20884,tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_fun(U_20886,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20886,tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_fun(U_20886,tc_HOL_Obool)),U_20884),c_COMBC(U_20886,tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_20886,tc_prod(U_20884,U_20886)),tc_fun(U_20886,tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool)),U_20884),hAPP(c_COMBB(tc_prod(U_20884,U_20886),tc_fun(tc_fun(tc_prod(U_20884,U_20886),tc_HOL_Obool),tc_HOL_Obool),U_20886),c_member(tc_prod(U_20884,U_20886)))),c_Product__Type_OPair(U_20884,U_20886)))),U_20888)),U_20890),U_20892))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20886,U_20884)),hAPP(hAPP(c_Product__Type_OPair(U_20886,U_20884),U_20890),U_20892)),hAPP(c_Relation_Oconverse(U_20884,U_20886),U_20888))) ),
    inference(clausify,[status(thm)],[f_4969_3]) ).

fof(f_4970_1,plain,
    ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),
    inference(fof_nnf,[status(thm)],[fact__02]) ).

fof(f_4970_2,plain,
    ! [U_20896,U_20895,U_20894,U_20893] : c_Lazy__Sequence_Oproduct(U_20893,U_20894,U_20895,U_20896) = hAPP(c_Lazy__Sequence_Obind(U_20893,tc_prod(U_20893,U_20894),U_20895),hAPP(hAPP(c_COMBB(tc_fun(U_20894,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894)),U_20893),c_Lazy__Sequence_Obind(U_20894,tc_prod(U_20893,U_20894),U_20896)),hAPP(hAPP(c_COMBB(tc_fun(U_20894,tc_prod(U_20893,U_20894)),tc_fun(U_20894,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894))),U_20893),hAPP(c_COMBB(tc_prod(U_20893,U_20894),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894)),U_20894),c_Lazy__Sequence_Osingle(tc_prod(U_20893,U_20894)))),c_Product__Type_OPair(U_20893,U_20894)))),
    inference(variable_rename,[status(thm)],[f_4970_1]) ).

cnf(f_4970_3,plain,
    c_Lazy__Sequence_Oproduct(U_20893,U_20894,U_20895,U_20896) = hAPP(c_Lazy__Sequence_Obind(U_20893,tc_prod(U_20893,U_20894),U_20895),hAPP(hAPP(c_COMBB(tc_fun(U_20894,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894)),U_20893),c_Lazy__Sequence_Obind(U_20894,tc_prod(U_20893,U_20894),U_20896)),hAPP(hAPP(c_COMBB(tc_fun(U_20894,tc_prod(U_20893,U_20894)),tc_fun(U_20894,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894))),U_20893),hAPP(c_COMBB(tc_prod(U_20893,U_20894),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_20893,U_20894)),U_20894),c_Lazy__Sequence_Osingle(tc_prod(U_20893,U_20894)))),c_Product__Type_OPair(U_20893,U_20894)))),
    inference(clausify,[status(thm)],[f_4970_2]) ).

fof(f_4971_1,plain,
    ! [V_x,T_a,V_n] :
      ( hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_tl__replicate]) ).

fof(f_4971_2,plain,
    ! [U_20899,U_20898,U_20897] :
      ( hAPP(c_List_Otl(U_20898),c_List_Oreplicate(U_20898,U_20897,U_20899)) = c_List_Oreplicate(U_20898,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20897),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20899)
      | U_20897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

cnf(f_4971_3,plain,
    ( hAPP(c_List_Otl(U_20898),c_List_Oreplicate(U_20898,U_20897,U_20899)) = c_List_Oreplicate(U_20898,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20897),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20899)
    | U_20897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4971_2]) ).

fof(f_4972_1,plain,
    ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_zip__replicate]) ).

fof(f_4972_2,plain,
    ! [U_20905,U_20904,U_20903,U_20902,U_20901,U_20900] : hAPP(hAPP(c_List_Ozip(U_20900,U_20901),c_List_Oreplicate(U_20900,U_20902,U_20903)),c_List_Oreplicate(U_20901,U_20904,U_20905)) = c_List_Oreplicate(tc_prod(U_20900,U_20901),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_20902),U_20904),hAPP(hAPP(c_Product__Type_OPair(U_20900,U_20901),U_20903),U_20905)),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

cnf(f_4972_3,plain,
    hAPP(hAPP(c_List_Ozip(U_20900,U_20901),c_List_Oreplicate(U_20900,U_20902,U_20903)),c_List_Oreplicate(U_20901,U_20904,U_20905)) = c_List_Oreplicate(tc_prod(U_20900,U_20901),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_20902),U_20904),hAPP(hAPP(c_Product__Type_OPair(U_20900,U_20901),U_20903),U_20905)),
    inference(clausify,[status(thm)],[f_4972_2]) ).

fof(f_4973_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),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_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(f_4973_2,plain,
    ! [U_20909,U_20908,U_20907,U_20906] : hAPP(hAPP(c_List_Oappend(U_20906),c_List_Oreplicate(U_20906,U_20907,U_20908)),hAPP(hAPP(c_List_Olist_OCons(U_20906),U_20908),U_20909)) = hAPP(hAPP(c_List_Olist_OCons(U_20906),U_20908),hAPP(hAPP(c_List_Oappend(U_20906),c_List_Oreplicate(U_20906,U_20907,U_20908)),U_20909)),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

cnf(f_4973_3,plain,
    hAPP(hAPP(c_List_Oappend(U_20906),c_List_Oreplicate(U_20906,U_20907,U_20908)),hAPP(hAPP(c_List_Olist_OCons(U_20906),U_20908),U_20909)) = hAPP(hAPP(c_List_Olist_OCons(U_20906),U_20908),hAPP(hAPP(c_List_Oappend(U_20906),c_List_Oreplicate(U_20906,U_20907,U_20908)),U_20909)),
    inference(clausify,[status(thm)],[f_4973_2]) ).

fof(f_4974_1,plain,
    ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
    inference(fof_nnf,[status(thm)],[fact_replicate__Suc]) ).

fof(f_4974_2,plain,
    ! [U_20912,U_20911,U_20910] : c_List_Oreplicate(U_20910,hAPP(c_Nat_OSuc,U_20911),U_20912) = hAPP(hAPP(c_List_Olist_OCons(U_20910),U_20912),c_List_Oreplicate(U_20910,U_20911,U_20912)),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

cnf(f_4974_3,plain,
    c_List_Oreplicate(U_20910,hAPP(c_Nat_OSuc,U_20911),U_20912) = hAPP(hAPP(c_List_Olist_OCons(U_20910),U_20912),c_List_Oreplicate(U_20910,U_20911,U_20912)),
    inference(clausify,[status(thm)],[f_4974_2]) ).

fof(f_4975_1,plain,
    ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
    inference(fof_nnf,[status(thm)],[fact_rev__replicate]) ).

fof(f_4975_2,plain,
    ! [U_20915,U_20914,U_20913] : hAPP(c_List_Orev(U_20913),c_List_Oreplicate(U_20913,U_20914,U_20915)) = c_List_Oreplicate(U_20913,U_20914,U_20915),
    inference(variable_rename,[status(thm)],[f_4975_1]) ).

cnf(f_4975_3,plain,
    hAPP(c_List_Orev(U_20913),c_List_Oreplicate(U_20913,U_20914,U_20915)) = c_List_Oreplicate(U_20913,U_20914,U_20915),
    inference(clausify,[status(thm)],[f_4975_2]) ).

fof(f_4976_1,plain,
    ! [V_x,T_a,V_n] :
      ( c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_last__replicate]) ).

fof(f_4976_2,plain,
    ! [U_20918,U_20917,U_20916] :
      ( c_List_Olast(U_20917,c_List_Oreplicate(U_20917,U_20916,U_20918)) = U_20918
      | U_20916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

cnf(f_4976_3,plain,
    ( c_List_Olast(U_20917,c_List_Oreplicate(U_20917,U_20916,U_20918)) = U_20918
    | U_20916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4976_2]) ).

fof(f_4977_1,plain,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
    inference(fof_nnf,[status(thm)],[fact_drop__replicate]) ).

fof(f_4977_2,plain,
    ! [U_20922,U_20921,U_20920,U_20919] : hAPP(hAPP(c_List_Odrop(U_20919),U_20920),c_List_Oreplicate(U_20919,U_20921,U_20922)) = c_List_Oreplicate(U_20919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20921),U_20920),U_20922),
    inference(variable_rename,[status(thm)],[f_4977_1]) ).

cnf(f_4977_3,plain,
    hAPP(hAPP(c_List_Odrop(U_20919),U_20920),c_List_Oreplicate(U_20919,U_20921,U_20922)) = c_List_Oreplicate(U_20919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20921),U_20920),U_20922),
    inference(clausify,[status(thm)],[f_4977_2]) ).

fof(f_4978_1,plain,
    ! [V_x,T_a,V_n] :
      ( hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_hd__replicate]) ).

fof(f_4978_2,plain,
    ! [U_20925,U_20924,U_20923] :
      ( hAPP(c_List_Ohd(U_20924),c_List_Oreplicate(U_20924,U_20923,U_20925)) = U_20925
      | U_20923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4978_1]) ).

cnf(f_4978_3,plain,
    ( hAPP(c_List_Ohd(U_20924),c_List_Oreplicate(U_20924,U_20923,U_20925)) = U_20925
    | U_20923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4978_2]) ).

fof(f_4979_1,plain,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
    inference(fof_nnf,[status(thm)],[fact_take__replicate]) ).

fof(f_4979_2,plain,
    ! [U_20929,U_20928,U_20927,U_20926] : hAPP(hAPP(c_List_Otake(U_20926),U_20927),c_List_Oreplicate(U_20926,U_20928,U_20929)) = c_List_Oreplicate(U_20926,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_20927),U_20928),U_20929),
    inference(variable_rename,[status(thm)],[f_4979_1]) ).

cnf(f_4979_3,plain,
    hAPP(hAPP(c_List_Otake(U_20926),U_20927),c_List_Oreplicate(U_20926,U_20928,U_20929)) = c_List_Oreplicate(U_20926,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_20927),U_20928),U_20929),
    inference(clausify,[status(thm)],[f_4979_2]) ).

fof(f_4980_1,plain,
    ! [V_P_2,V_a_2,V_n_2,T_a] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) )
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(V_P_2,V_a_2)) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_P_2,V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Ball__set__replicate]) ).

fof(f_4980_2,plain,
    ! [U_20935,U_20934,U_20933,U_20932] :
      ( ( ! [U_20931] :
            ( hBOOL(hAPP(U_20935,U_20931))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20932),U_20931),hAPP(c_List_Oset(U_20932),c_List_Oreplicate(U_20932,U_20933,U_20934)))) )
        | ( U_20933 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_20935,U_20934)) ) )
      & ( U_20933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_20935,U_20934))
        | ? [U_20930] :
            ( ~ hBOOL(hAPP(U_20935,U_20930))
            & hBOOL(hAPP(hAPP(c_member(U_20932),U_20930),hAPP(c_List_Oset(U_20932),c_List_Oreplicate(U_20932,U_20933,U_20934)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

fof(f_4980_3,plain,
    ( ! [U_20943,U_20941,U_20939] :
        ( ! [U_20937,U_20931] :
            ( hBOOL(hAPP(U_20943,U_20931))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20937),U_20931),hAPP(c_List_Oset(U_20937),c_List_Oreplicate(U_20937,U_20939,U_20941)))) )
        | ( U_20939 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_20943,U_20941)) ) )
    & ! [U_20942,U_20940,U_20938] :
        ( ! [U_20936] :
          ? [U_20930] :
            ( ~ hBOOL(hAPP(U_20942,U_20930))
            & hBOOL(hAPP(hAPP(c_member(U_20936),U_20930),hAPP(c_List_Oset(U_20936),c_List_Oreplicate(U_20936,U_20938,U_20940)))) )
        | U_20938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_20942,U_20940)) ) ),
    inference(miniscope,[status(thm)],[f_4980_2]) ).

fof(f_4980_4,plain,
    ( ! [U_20943,U_20941,U_20939] :
        ( ! [U_20937,U_20931] :
            ( hBOOL(hAPP(U_20943,U_20931))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20937),U_20931),hAPP(c_List_Oset(U_20937),c_List_Oreplicate(U_20937,U_20939,U_20941)))) )
        | ( U_20939 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_20943,U_20941)) ) )
    & ! [U_20942,U_20940,U_20938] :
        ( ! [U_20936] :
            ( ~ hBOOL(hAPP(U_20942,sK542(U_20942,U_20940,U_20938,U_20936)))
            & hBOOL(hAPP(hAPP(c_member(U_20936),sK542(U_20942,U_20940,U_20938,U_20936)),hAPP(c_List_Oset(U_20936),c_List_Oreplicate(U_20936,U_20938,U_20940)))) )
        | U_20938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_20942,U_20940)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK542]),skolemize(U_20930,sK542(U_20942,U_20940,U_20938,U_20936))],[f_4980_3]) ).

cnf(f_4980_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20936),sK542(U_20942,U_20940,U_20938,U_20936)),hAPP(c_List_Oset(U_20936),c_List_Oreplicate(U_20936,U_20938,U_20940))))
    | U_20938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_20942,U_20940)) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

cnf(f_4980_6,plain,
    ( ~ hBOOL(hAPP(U_20942,sK542(U_20942,U_20940,U_20938,U_20936)))
    | U_20938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_20942,U_20940)) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

cnf(f_4980_7,plain,
    ( ~ hBOOL(hAPP(U_20943,U_20941))
    | hBOOL(hAPP(U_20943,U_20931))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20937),U_20931),hAPP(c_List_Oset(U_20937),c_List_Oreplicate(U_20937,U_20939,U_20941)))) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

cnf(f_4980_8,plain,
    ( U_20939 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_20943,U_20931))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20937),U_20931),hAPP(c_List_Oset(U_20937),c_List_Oreplicate(U_20937,U_20939,U_20941)))) ),
    inference(clausify,[status(thm)],[f_4980_4]) ).

fof(f_4981_1,plain,
    ! [V_P_2,V_a_2,V_n_2,T_a] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) )
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(V_P_2,V_a_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Bex__set__replicate]) ).

fof(f_4981_2,plain,
    ! [U_20949,U_20948,U_20947,U_20946] :
      ( ( ? [U_20945] :
            ( hBOOL(hAPP(U_20949,U_20945))
            & hBOOL(hAPP(hAPP(c_member(U_20946),U_20945),hAPP(c_List_Oset(U_20946),c_List_Oreplicate(U_20946,U_20947,U_20948)))) )
        | U_20947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_20949,U_20948)) )
      & ( ( U_20947 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_20949,U_20948)) )
        | ! [U_20944] :
            ( ~ hBOOL(hAPP(U_20949,U_20944))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20946),U_20944),hAPP(c_List_Oset(U_20946),c_List_Oreplicate(U_20946,U_20947,U_20948)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

fof(f_4981_3,plain,
    ( ! [U_20957,U_20955,U_20953] :
        ( ! [U_20951] :
          ? [U_20945] :
            ( hBOOL(hAPP(U_20957,U_20945))
            & hBOOL(hAPP(hAPP(c_member(U_20951),U_20945),hAPP(c_List_Oset(U_20951),c_List_Oreplicate(U_20951,U_20953,U_20955)))) )
        | U_20953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_20957,U_20955)) )
    & ! [U_20956,U_20954,U_20952] :
        ( ! [U_20950,U_20944] :
            ( ~ hBOOL(hAPP(U_20956,U_20944))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20950),U_20944),hAPP(c_List_Oset(U_20950),c_List_Oreplicate(U_20950,U_20952,U_20954)))) )
        | ( U_20952 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_20956,U_20954)) ) ) ),
    inference(miniscope,[status(thm)],[f_4981_2]) ).

fof(f_4981_4,plain,
    ( ! [U_20957,U_20955,U_20953] :
        ( ! [U_20951] :
            ( hBOOL(hAPP(U_20957,sK543(U_20957,U_20955,U_20953,U_20951)))
            & hBOOL(hAPP(hAPP(c_member(U_20951),sK543(U_20957,U_20955,U_20953,U_20951)),hAPP(c_List_Oset(U_20951),c_List_Oreplicate(U_20951,U_20953,U_20955)))) )
        | U_20953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_20957,U_20955)) )
    & ! [U_20956,U_20954,U_20952] :
        ( ! [U_20950,U_20944] :
            ( ~ hBOOL(hAPP(U_20956,U_20944))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20950),U_20944),hAPP(c_List_Oset(U_20950),c_List_Oreplicate(U_20950,U_20952,U_20954)))) )
        | ( U_20952 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_20956,U_20954)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK543]),skolemize(U_20945,sK543(U_20957,U_20955,U_20953,U_20951))],[f_4981_3]) ).

cnf(f_4981_5,plain,
    ( hBOOL(hAPP(U_20956,U_20954))
    | ~ hBOOL(hAPP(U_20956,U_20944))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20950),U_20944),hAPP(c_List_Oset(U_20950),c_List_Oreplicate(U_20950,U_20952,U_20954)))) ),
    inference(clausify,[status(thm)],[f_4981_4]) ).

cnf(f_4981_6,plain,
    ( U_20952 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_20956,U_20944))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20950),U_20944),hAPP(c_List_Oset(U_20950),c_List_Oreplicate(U_20950,U_20952,U_20954)))) ),
    inference(clausify,[status(thm)],[f_4981_4]) ).

cnf(f_4981_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20951),sK543(U_20957,U_20955,U_20953,U_20951)),hAPP(c_List_Oset(U_20951),c_List_Oreplicate(U_20951,U_20953,U_20955))))
    | U_20953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_20957,U_20955)) ),
    inference(clausify,[status(thm)],[f_4981_4]) ).

cnf(f_4981_8,plain,
    ( hBOOL(hAPP(U_20957,sK543(U_20957,U_20955,U_20953,U_20951)))
    | U_20953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_20957,U_20955)) ),
    inference(clausify,[status(thm)],[f_4981_4]) ).

fof(f_4982_1,plain,
    ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] :
      ( ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2)
        | ( V_x_2 != V_y_2
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | V_m_2 != V_n_2 )
      & ( ( ( V_x_2 = V_y_2
            | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & V_m_2 = V_n_2 )
        | c_List_Oreplicate(T_a,V_m_2,V_x_2) != c_List_Oreplicate(T_a,V_n_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate]) ).

fof(f_4982_2,plain,
    ! [U_20962,U_20961,U_20960,U_20959,U_20958] :
      ( ( c_List_Oreplicate(U_20958,U_20959,U_20960) = c_List_Oreplicate(U_20958,U_20961,U_20962)
        | ( U_20960 != U_20962
          & U_20959 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_20959 != U_20961 )
      & ( ( ( U_20960 = U_20962
            | U_20959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_20959 = U_20961 )
        | c_List_Oreplicate(U_20958,U_20959,U_20960) != c_List_Oreplicate(U_20958,U_20961,U_20962) ) ),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

fof(f_4982_3,plain,
    ( ! [U_20972,U_20970,U_20968,U_20966] :
        ( ! [U_20964] : c_List_Oreplicate(U_20964,U_20966,U_20968) = c_List_Oreplicate(U_20964,U_20970,U_20972)
        | ( U_20968 != U_20972
          & U_20966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_20966 != U_20970 )
    & ! [U_20971,U_20969,U_20967,U_20965] :
        ( ! [U_20963] : c_List_Oreplicate(U_20963,U_20965,U_20967) != c_List_Oreplicate(U_20963,U_20969,U_20971)
        | ( ( U_20967 = U_20971
            | U_20965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_20965 = U_20969 ) ) ),
    inference(miniscope,[status(thm)],[f_4982_2]) ).

cnf(f_4982_4,plain,
    ( U_20965 = U_20969
    | c_List_Oreplicate(U_20963,U_20965,U_20967) != c_List_Oreplicate(U_20963,U_20969,U_20971) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

cnf(f_4982_5,plain,
    ( U_20967 = U_20971
    | U_20965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oreplicate(U_20963,U_20965,U_20967) != c_List_Oreplicate(U_20963,U_20969,U_20971) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

cnf(f_4982_6,plain,
    ( U_20966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_20966 != U_20970
    | c_List_Oreplicate(U_20964,U_20966,U_20968) = c_List_Oreplicate(U_20964,U_20970,U_20972) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

cnf(f_4982_7,plain,
    ( U_20968 != U_20972
    | U_20966 != U_20970
    | c_List_Oreplicate(U_20964,U_20966,U_20968) = c_List_Oreplicate(U_20964,U_20970,U_20972) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

fof(f_4983_1,plain,
    ! [V_x,T_a,V_n,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__replicate]) ).

fof(f_4983_2,plain,
    ! [U_20976,U_20975,U_20974,U_20973] :
      ( hAPP(hAPP(c_List_Onth(U_20975),c_List_Oreplicate(U_20975,U_20974,U_20976)),U_20973) = U_20976
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20973),U_20974)) ),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

cnf(f_4983_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_20975),c_List_Oreplicate(U_20975,U_20974,U_20976)),U_20973) = U_20976
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20973),U_20974)) ),
    inference(clausify,[status(thm)],[f_4983_2]) ).

fof(f_4984_1,plain,
    ! [V_y_2,V_n_2,V_x_2,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2))))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != V_y_2 )
      & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_x_2 = V_y_2 )
        | ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__replicate]) ).

fof(f_4984_2,plain,
    ! [U_20980,U_20979,U_20978,U_20977] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20977),U_20978),hAPP(c_List_Oset(U_20977),c_List_Oreplicate(U_20977,U_20979,U_20980))))
        | U_20979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_20978 != U_20980 )
      & ( ( U_20979 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_20978 = U_20980 )
        | ~ hBOOL(hAPP(hAPP(c_member(U_20977),U_20978),hAPP(c_List_Oset(U_20977),c_List_Oreplicate(U_20977,U_20979,U_20980)))) ) ),
    inference(variable_rename,[status(thm)],[f_4984_1]) ).

fof(f_4984_3,plain,
    ( ! [U_20988,U_20986,U_20984] :
        ( ! [U_20982] : hBOOL(hAPP(hAPP(c_member(U_20982),U_20984),hAPP(c_List_Oset(U_20982),c_List_Oreplicate(U_20982,U_20986,U_20988))))
        | U_20986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_20984 != U_20988 )
    & ! [U_20987,U_20985,U_20983] :
        ( ! [U_20981] : ~ hBOOL(hAPP(hAPP(c_member(U_20981),U_20983),hAPP(c_List_Oset(U_20981),c_List_Oreplicate(U_20981,U_20985,U_20987))))
        | ( U_20985 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_20983 = U_20987 ) ) ),
    inference(miniscope,[status(thm)],[f_4984_2]) ).

cnf(f_4984_4,plain,
    ( U_20983 = U_20987
    | ~ hBOOL(hAPP(hAPP(c_member(U_20981),U_20983),hAPP(c_List_Oset(U_20981),c_List_Oreplicate(U_20981,U_20985,U_20987)))) ),
    inference(clausify,[status(thm)],[f_4984_3]) ).

cnf(f_4984_5,plain,
    ( U_20985 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20981),U_20983),hAPP(c_List_Oset(U_20981),c_List_Oreplicate(U_20981,U_20985,U_20987)))) ),
    inference(clausify,[status(thm)],[f_4984_3]) ).

cnf(f_4984_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20982),U_20984),hAPP(c_List_Oset(U_20982),c_List_Oreplicate(U_20982,U_20986,U_20988))))
    | U_20986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_20984 != U_20988 ),
    inference(clausify,[status(thm)],[f_4984_3]) ).

fof(f_4985_1,plain,
    ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)),
    inference(fof_nnf,[status(thm)],[fact_replicate__add]) ).

fof(f_4985_2,plain,
    ! [U_20992,U_20991,U_20990,U_20989] : c_List_Oreplicate(U_20989,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20990),U_20991),U_20992) = hAPP(hAPP(c_List_Oappend(U_20989),c_List_Oreplicate(U_20989,U_20990,U_20992)),c_List_Oreplicate(U_20989,U_20991,U_20992)),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

cnf(f_4985_3,plain,
    c_List_Oreplicate(U_20989,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20990),U_20991),U_20992) = hAPP(hAPP(c_List_Oappend(U_20989),c_List_Oreplicate(U_20989,U_20990,U_20992)),c_List_Oreplicate(U_20989,U_20991,U_20992)),
    inference(clausify,[status(thm)],[f_4985_2]) ).

fof(f_4986_1,plain,
    ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)),
    inference(fof_nnf,[status(thm)],[fact_append__replicate__commute]) ).

fof(f_4986_2,plain,
    ! [U_20996,U_20995,U_20994,U_20993] : hAPP(hAPP(c_List_Oappend(U_20993),c_List_Oreplicate(U_20993,U_20994,U_20995)),c_List_Oreplicate(U_20993,U_20996,U_20995)) = hAPP(hAPP(c_List_Oappend(U_20993),c_List_Oreplicate(U_20993,U_20996,U_20995)),c_List_Oreplicate(U_20993,U_20994,U_20995)),
    inference(variable_rename,[status(thm)],[f_4986_1]) ).

cnf(f_4986_3,plain,
    hAPP(hAPP(c_List_Oappend(U_20993),c_List_Oreplicate(U_20993,U_20994,U_20995)),c_List_Oreplicate(U_20993,U_20996,U_20995)) = hAPP(hAPP(c_List_Oappend(U_20993),c_List_Oreplicate(U_20993,U_20996,U_20995)),c_List_Oreplicate(U_20993,U_20994,U_20995)),
    inference(clausify,[status(thm)],[f_4986_2]) ).

fof(f_4987_1,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]) ).

cnf(f_4987_2,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_4987_1]) ).

fof(f_4988_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_4988_2,plain,
    ! [U_20998,U_20997] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20998,U_20997))
      | ~ class_Lattices_Obounded__lattice(U_20997) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

cnf(f_4988_3,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20998,U_20997))
    | ~ class_Lattices_Obounded__lattice(U_20997) ),
    inference(clausify,[status(thm)],[f_4988_2]) ).

fof(f_4989_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_4989_2,plain,
    ! [U_21000,U_20999] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_21000,U_20999))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20999) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

cnf(f_4989_3,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_21000,U_20999))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20999) ),
    inference(clausify,[status(thm)],[f_4989_2]) ).

fof(f_4990_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_4990_2,plain,
    ! [U_21002,U_21001] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_21002,U_21001))
      | ~ class_Lattices_Obounded__lattice(U_21001) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

cnf(f_4990_3,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_21002,U_21001))
    | ~ class_Lattices_Obounded__lattice(U_21001) ),
    inference(clausify,[status(thm)],[f_4990_2]) ).

fof(f_4991_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_4991_2,plain,
    ! [U_21004,U_21003] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_21004,U_21003))
      | ~ class_Lattices_Obounded__lattice(U_21003) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

cnf(f_4991_3,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_21004,U_21003))
    | ~ class_Lattices_Obounded__lattice(U_21003) ),
    inference(clausify,[status(thm)],[f_4991_2]) ).

fof(f_4992_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_4992_2,plain,
    ! [U_21006,U_21005] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_21006,U_21005))
      | ~ class_Lattices_Olattice(U_21005) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

cnf(f_4992_3,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_21006,U_21005))
    | ~ class_Lattices_Olattice(U_21005) ),
    inference(clausify,[status(thm)],[f_4992_2]) ).

fof(f_4993_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_4993_2,plain,
    ! [U_21008,U_21007] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_21008,U_21007))
      | ~ class_Lattices_Olattice(U_21007) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

cnf(f_4993_3,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_21008,U_21007))
    | ~ class_Lattices_Olattice(U_21007) ),
    inference(clausify,[status(thm)],[f_4993_2]) ).

fof(f_4994_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_4994_2,plain,
    ! [U_21010,U_21009] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_21010,U_21009))
      | ~ class_Lattices_Odistrib__lattice(U_21009) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

cnf(f_4994_3,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_21010,U_21009))
    | ~ class_Lattices_Odistrib__lattice(U_21009) ),
    inference(clausify,[status(thm)],[f_4994_2]) ).

fof(f_4995_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_4995_2,plain,
    ! [U_21012,U_21011] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_21012,U_21011))
      | ~ class_Lattices_Oboolean__algebra(U_21011) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

cnf(f_4995_3,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_21012,U_21011))
    | ~ class_Lattices_Oboolean__algebra(U_21011) ),
    inference(clausify,[status(thm)],[f_4995_2]) ).

fof(f_4996_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_4996_2,plain,
    ! [U_21014,U_21013] :
      ( class_Orderings_Opreorder(tc_fun(U_21014,U_21013))
      | ~ class_Orderings_Opreorder(U_21013) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

cnf(f_4996_3,plain,
    ( class_Orderings_Opreorder(tc_fun(U_21014,U_21013))
    | ~ class_Orderings_Opreorder(U_21013) ),
    inference(clausify,[status(thm)],[f_4996_2]) ).

fof(f_4997_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_4997_2,plain,
    ! [U_21016,U_21015] :
      ( class_Finite__Set_Ofinite(tc_fun(U_21015,U_21016))
      | ~ class_Finite__Set_Ofinite(U_21016)
      | ~ class_Finite__Set_Ofinite(U_21015) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

cnf(f_4997_3,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_21015,U_21016))
    | ~ class_Finite__Set_Ofinite(U_21016)
    | ~ class_Finite__Set_Ofinite(U_21015) ),
    inference(clausify,[status(thm)],[f_4997_2]) ).

fof(f_4998_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_4998_2,plain,
    ! [U_21018,U_21017] :
      ( class_Lattices_Olattice(tc_fun(U_21018,U_21017))
      | ~ class_Lattices_Olattice(U_21017) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

cnf(f_4998_3,plain,
    ( class_Lattices_Olattice(tc_fun(U_21018,U_21017))
    | ~ class_Lattices_Olattice(U_21017) ),
    inference(clausify,[status(thm)],[f_4998_2]) ).

fof(f_4999_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_4999_2,plain,
    ! [U_21020,U_21019] :
      ( class_Orderings_Oorder(tc_fun(U_21020,U_21019))
      | ~ class_Orderings_Oorder(U_21019) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

cnf(f_4999_3,plain,
    ( class_Orderings_Oorder(tc_fun(U_21020,U_21019))
    | ~ class_Orderings_Oorder(U_21019) ),
    inference(clausify,[status(thm)],[f_4999_2]) ).

fof(f_5000_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_5000_2,plain,
    ! [U_21022,U_21021] :
      ( class_Orderings_Otop(tc_fun(U_21022,U_21021))
      | ~ class_Orderings_Otop(U_21021) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

cnf(f_5000_3,plain,
    ( class_Orderings_Otop(tc_fun(U_21022,U_21021))
    | ~ class_Orderings_Otop(U_21021) ),
    inference(clausify,[status(thm)],[f_5000_2]) ).

fof(f_5001_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_5001_2,plain,
    ! [U_21024,U_21023] :
      ( class_Orderings_Oord(tc_fun(U_21024,U_21023))
      | ~ class_Orderings_Oord(U_21023) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

cnf(f_5001_3,plain,
    ( class_Orderings_Oord(tc_fun(U_21024,U_21023))
    | ~ class_Orderings_Oord(U_21023) ),
    inference(clausify,[status(thm)],[f_5001_2]) ).

fof(f_5002_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_5002_2,plain,
    ! [U_21026,U_21025] :
      ( class_Orderings_Obot(tc_fun(U_21026,U_21025))
      | ~ class_Orderings_Obot(U_21025) ),
    inference(variable_rename,[status(thm)],[f_5002_1]) ).

cnf(f_5002_3,plain,
    ( class_Orderings_Obot(tc_fun(U_21026,U_21025))
    | ~ class_Orderings_Obot(U_21025) ),
    inference(clausify,[status(thm)],[f_5002_2]) ).

fof(f_5003_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_5003_2,plain,
    ! [U_21028,U_21027] :
      ( class_Groups_Ouminus(tc_fun(U_21028,U_21027))
      | ~ class_Groups_Ouminus(U_21027) ),
    inference(variable_rename,[status(thm)],[f_5003_1]) ).

cnf(f_5003_3,plain,
    ( class_Groups_Ouminus(tc_fun(U_21028,U_21027))
    | ~ class_Groups_Ouminus(U_21027) ),
    inference(clausify,[status(thm)],[f_5003_2]) ).

fof(f_5004_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_5004_2,plain,
    ! [U_21030,U_21029] :
      ( class_Groups_Ominus(tc_fun(U_21030,U_21029))
      | ~ class_Groups_Ominus(U_21029) ),
    inference(variable_rename,[status(thm)],[f_5004_1]) ).

cnf(f_5004_3,plain,
    ( class_Groups_Ominus(tc_fun(U_21030,U_21029))
    | ~ class_Groups_Ominus(U_21029) ),
    inference(clausify,[status(thm)],[f_5004_2]) ).

fof(f_5005_1,plain,
    ! [T_1,T_2] :
      ( class_HOL_Oequal(tc_fun(T_2,T_1))
      | ~ class_HOL_Oequal(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_fun__HOL_Oequal]) ).

fof(f_5005_2,plain,
    ! [U_21032,U_21031] :
      ( class_HOL_Oequal(tc_fun(U_21031,U_21032))
      | ~ class_HOL_Oequal(U_21032)
      | ~ class_Enum_Oenum(U_21031) ),
    inference(variable_rename,[status(thm)],[f_5005_1]) ).

cnf(f_5005_3,plain,
    ( class_HOL_Oequal(tc_fun(U_21031,U_21032))
    | ~ class_HOL_Oequal(U_21032)
    | ~ class_Enum_Oenum(U_21031) ),
    inference(clausify,[status(thm)],[f_5005_2]) ).

fof(f_5006_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_fun(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum]) ).

fof(f_5006_2,plain,
    ! [U_21034,U_21033] :
      ( class_Enum_Oenum(tc_fun(U_21033,U_21034))
      | ~ class_Enum_Oenum(U_21034)
      | ~ class_Enum_Oenum(U_21033) ),
    inference(variable_rename,[status(thm)],[f_5006_1]) ).

cnf(f_5006_3,plain,
    ( class_Enum_Oenum(tc_fun(U_21033,U_21034))
    | ~ class_Enum_Oenum(U_21034)
    | ~ class_Enum_Oenum(U_21033) ),
    inference(clausify,[status(thm)],[f_5006_2]) ).

fof(f_5007_1,plain,
    class_HOL_Oequal(tc_Com_Ocom),
    inference(fof_nnf,[status(thm)],[arity_Com__Ocom__HOL_Oequal]) ).

cnf(f_5007_2,plain,
    class_HOL_Oequal(tc_Com_Ocom),
    inference(clausify,[status(thm)],[f_5007_1]) ).

fof(f_5008_1,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(fof_nnf,[status(thm)],[arity_Com__Ocom__Nat_Osize]) ).

cnf(f_5008_2,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(clausify,[status(thm)],[f_5008_1]) ).

fof(f_5009_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]) ).

cnf(f_5009_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5009_1]) ).

fof(f_5010_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]) ).

cnf(f_5010_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5010_1]) ).

fof(f_5011_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]) ).

cnf(f_5011_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5011_1]) ).

fof(f_5012_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_5012_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5012_1]) ).

fof(f_5013_1,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).

cnf(f_5013_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5013_1]) ).

fof(f_5014_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]) ).

cnf(f_5014_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5014_1]) ).

fof(f_5015_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

cnf(f_5015_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5015_1]) ).

fof(f_5016_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).

cnf(f_5016_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5016_1]) ).

fof(f_5017_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]) ).

cnf(f_5017_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5017_1]) ).

fof(f_5018_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).

cnf(f_5018_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5018_1]) ).

fof(f_5019_1,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).

cnf(f_5019_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5019_1]) ).

fof(f_5020_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_5020_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5020_1]) ).

fof(f_5021_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]) ).

cnf(f_5021_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5021_1]) ).

fof(f_5022_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

cnf(f_5022_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5022_1]) ).

fof(f_5023_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

cnf(f_5023_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5023_1]) ).

fof(f_5024_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).

cnf(f_5024_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5024_1]) ).

fof(f_5025_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

cnf(f_5025_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5025_1]) ).

fof(f_5026_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

cnf(f_5026_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5026_1]) ).

fof(f_5027_1,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).

cnf(f_5027_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5027_1]) ).

fof(f_5028_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

cnf(f_5028_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5028_1]) ).

fof(f_5029_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

cnf(f_5029_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5029_1]) ).

fof(f_5030_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

cnf(f_5030_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5030_1]) ).

fof(f_5031_1,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]) ).

cnf(f_5031_2,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5031_1]) ).

fof(f_5032_1,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]) ).

cnf(f_5032_2,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5032_1]) ).

fof(f_5033_1,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]) ).

cnf(f_5033_2,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5033_1]) ).

fof(f_5034_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

cnf(f_5034_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5034_1]) ).

fof(f_5035_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

cnf(f_5035_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5035_1]) ).

fof(f_5036_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

cnf(f_5036_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5036_1]) ).

fof(f_5037_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

cnf(f_5037_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5037_1]) ).

fof(f_5038_1,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).

cnf(f_5038_2,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5038_1]) ).

fof(f_5039_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

cnf(f_5039_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5039_1]) ).

fof(f_5040_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

cnf(f_5040_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5040_1]) ).

fof(f_5041_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

cnf(f_5041_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5041_1]) ).

fof(f_5042_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

cnf(f_5042_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5042_1]) ).

fof(f_5043_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

cnf(f_5043_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5043_1]) ).

fof(f_5044_1,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]) ).

cnf(f_5044_2,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5044_1]) ).

fof(f_5045_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

cnf(f_5045_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5045_1]) ).

fof(f_5046_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

cnf(f_5046_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5046_1]) ).

fof(f_5047_1,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]) ).

cnf(f_5047_2,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5047_1]) ).

fof(f_5048_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

cnf(f_5048_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5048_1]) ).

fof(f_5049_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

cnf(f_5049_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5049_1]) ).

fof(f_5050_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

cnf(f_5050_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5050_1]) ).

fof(f_5051_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

cnf(f_5051_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5051_1]) ).

fof(f_5052_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

cnf(f_5052_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5052_1]) ).

fof(f_5053_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

cnf(f_5053_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5053_1]) ).

fof(f_5054_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

cnf(f_5054_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5054_1]) ).

fof(f_5055_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

cnf(f_5055_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5055_1]) ).

fof(f_5056_1,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]) ).

cnf(f_5056_2,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5056_1]) ).

fof(f_5057_1,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).

cnf(f_5057_2,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5057_1]) ).

fof(f_5058_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

cnf(f_5058_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5058_1]) ).

fof(f_5059_1,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Olattice]) ).

cnf(f_5059_2,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5059_1]) ).

fof(f_5060_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

cnf(f_5060_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5060_1]) ).

fof(f_5061_1,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).

cnf(f_5061_2,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5061_1]) ).

fof(f_5062_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

cnf(f_5062_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5062_1]) ).

fof(f_5063_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

cnf(f_5063_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5063_1]) ).

fof(f_5064_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

cnf(f_5064_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5064_1]) ).

fof(f_5065_1,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).

cnf(f_5065_2,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5065_1]) ).

fof(f_5066_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

cnf(f_5066_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5066_1]) ).

fof(f_5067_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

cnf(f_5067_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5067_1]) ).

fof(f_5068_1,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).

cnf(f_5068_2,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5068_1]) ).

fof(f_5069_1,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).

cnf(f_5069_2,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5069_1]) ).

fof(f_5070_1,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).

cnf(f_5070_2,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5070_1]) ).

fof(f_5071_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

cnf(f_5071_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5071_1]) ).

fof(f_5072_1,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).

cnf(f_5072_2,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5072_1]) ).

fof(f_5073_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

cnf(f_5073_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5073_1]) ).

fof(f_5074_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

cnf(f_5074_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5074_1]) ).

fof(f_5075_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

cnf(f_5075_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5075_1]) ).

fof(f_5076_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

cnf(f_5076_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5076_1]) ).

fof(f_5077_1,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).

cnf(f_5077_2,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5077_1]) ).

fof(f_5078_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

cnf(f_5078_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5078_1]) ).

fof(f_5079_1,plain,
    class_HOL_Oequal(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__HOL_Oequal]) ).

cnf(f_5079_2,plain,
    class_HOL_Oequal(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5079_1]) ).

fof(f_5080_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]) ).

cnf(f_5080_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5080_1]) ).

fof(f_5081_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]) ).

cnf(f_5081_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5081_1]) ).

fof(f_5082_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]) ).

cnf(f_5082_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5082_1]) ).

fof(f_5083_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_5083_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5083_1]) ).

fof(f_5084_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]) ).

cnf(f_5084_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5084_1]) ).

fof(f_5085_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

cnf(f_5085_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5085_1]) ).

fof(f_5086_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).

cnf(f_5086_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5086_1]) ).

fof(f_5087_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).

cnf(f_5087_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5087_1]) ).

fof(f_5088_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_5088_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5088_1]) ).

fof(f_5089_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

cnf(f_5089_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5089_1]) ).

fof(f_5090_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

cnf(f_5090_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5090_1]) ).

fof(f_5091_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

cnf(f_5091_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5091_1]) ).

fof(f_5092_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

cnf(f_5092_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5092_1]) ).

fof(f_5093_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

cnf(f_5093_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5093_1]) ).

fof(f_5094_1,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]) ).

cnf(f_5094_2,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5094_1]) ).

fof(f_5095_1,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).

cnf(f_5095_2,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5095_1]) ).

fof(f_5096_1,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]) ).

cnf(f_5096_2,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5096_1]) ).

fof(f_5097_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

cnf(f_5097_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5097_1]) ).

fof(f_5098_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

cnf(f_5098_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5098_1]) ).

fof(f_5099_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

cnf(f_5099_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5099_1]) ).

fof(f_5100_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

cnf(f_5100_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5100_1]) ).

fof(f_5101_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

cnf(f_5101_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5101_1]) ).

fof(f_5102_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

cnf(f_5102_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5102_1]) ).

fof(f_5103_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

cnf(f_5103_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5103_1]) ).

fof(f_5104_1,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]) ).

cnf(f_5104_2,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5104_1]) ).

fof(f_5105_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

cnf(f_5105_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5105_1]) ).

fof(f_5106_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

cnf(f_5106_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5106_1]) ).

fof(f_5107_1,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]) ).

cnf(f_5107_2,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5107_1]) ).

fof(f_5108_1,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]) ).

cnf(f_5108_2,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5108_1]) ).

fof(f_5109_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

cnf(f_5109_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5109_1]) ).

fof(f_5110_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

cnf(f_5110_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5110_1]) ).

fof(f_5111_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

cnf(f_5111_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5111_1]) ).

fof(f_5112_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

cnf(f_5112_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5112_1]) ).

fof(f_5113_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

cnf(f_5113_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5113_1]) ).

fof(f_5114_1,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).

cnf(f_5114_2,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5114_1]) ).

fof(f_5115_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

cnf(f_5115_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5115_1]) ).

fof(f_5116_1,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).

cnf(f_5116_2,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5116_1]) ).

fof(f_5117_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

cnf(f_5117_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5117_1]) ).

fof(f_5118_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

cnf(f_5118_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5118_1]) ).

fof(f_5119_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

cnf(f_5119_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5119_1]) ).

fof(f_5120_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

cnf(f_5120_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5120_1]) ).

fof(f_5121_1,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Obot]) ).

cnf(f_5121_2,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5121_1]) ).

fof(f_5122_1,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).

cnf(f_5122_2,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5122_1]) ).

fof(f_5123_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

cnf(f_5123_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5123_1]) ).

fof(f_5124_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

cnf(f_5124_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5124_1]) ).

fof(f_5125_1,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).

cnf(f_5125_2,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5125_1]) ).

fof(f_5126_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

cnf(f_5126_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5126_1]) ).

fof(f_5127_1,plain,
    class_HOL_Oequal(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__HOL_Oequal]) ).

cnf(f_5127_2,plain,
    class_HOL_Oequal(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5127_1]) ).

fof(f_5128_1,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osize]) ).

cnf(f_5128_2,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5128_1]) ).

fof(f_5129_1,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]) ).

cnf(f_5129_2,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5129_1]) ).

fof(f_5130_1,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).

cnf(f_5130_2,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5130_1]) ).

fof(f_5131_1,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).

cnf(f_5131_2,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5131_1]) ).

fof(f_5132_1,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]) ).

cnf(f_5132_2,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5132_1]) ).

fof(f_5133_1,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).

cnf(f_5133_2,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5133_1]) ).

fof(f_5134_1,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]) ).

cnf(f_5134_2,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5134_1]) ).

fof(f_5135_1,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).

cnf(f_5135_2,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5135_1]) ).

fof(f_5136_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

cnf(f_5136_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5136_1]) ).

fof(f_5137_1,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]) ).

cnf(f_5137_2,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5137_1]) ).

fof(f_5138_1,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).

cnf(f_5138_2,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5138_1]) ).

fof(f_5139_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

cnf(f_5139_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5139_1]) ).

fof(f_5140_1,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).

cnf(f_5140_2,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5140_1]) ).

fof(f_5141_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

cnf(f_5141_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5141_1]) ).

fof(f_5142_1,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).

cnf(f_5142_2,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5142_1]) ).

fof(f_5143_1,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).

cnf(f_5143_2,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5143_1]) ).

fof(f_5144_1,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).

cnf(f_5144_2,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5144_1]) ).

fof(f_5145_1,plain,
    class_HOL_Oequal(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__HOL_Oequal]) ).

cnf(f_5145_2,plain,
    class_HOL_Oequal(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5145_1]) ).

fof(f_5146_1,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Enum_Oenum]) ).

cnf(f_5146_2,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5146_1]) ).

fof(f_5147_1,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Nat_Osize]) ).

cnf(f_5147_2,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5147_1]) ).

fof(f_5148_1,plain,
    class_HOL_Oequal(tc_Com_Ostate),
    inference(fof_nnf,[status(thm)],[arity_Com__Ostate__HOL_Oequal]) ).

cnf(f_5148_2,plain,
    class_HOL_Oequal(tc_Com_Ostate),
    inference(clausify,[status(thm)],[f_5148_1]) ).

fof(f_5149_1,plain,
    class_Nat_Osize(tc_Com_Ostate),
    inference(fof_nnf,[status(thm)],[arity_Com__Ostate__Nat_Osize]) ).

cnf(f_5149_2,plain,
    class_Nat_Osize(tc_Com_Ostate),
    inference(clausify,[status(thm)],[f_5149_1]) ).

fof(f_5150_1,plain,
    ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)),
    inference(fof_nnf,[status(thm)],[arity_List__Olist__HOL_Oequal]) ).

fof(f_5150_2,plain,
    ! [U_21035] : class_HOL_Oequal(tc_List_Olist(U_21035)),
    inference(variable_rename,[status(thm)],[f_5150_1]) ).

cnf(f_5150_3,plain,
    class_HOL_Oequal(tc_List_Olist(U_21035)),
    inference(clausify,[status(thm)],[f_5150_2]) ).

fof(f_5151_1,plain,
    ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
    inference(fof_nnf,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(f_5151_2,plain,
    ! [U_21036] : class_Nat_Osize(tc_List_Olist(U_21036)),
    inference(variable_rename,[status(thm)],[f_5151_1]) ).

cnf(f_5151_3,plain,
    class_Nat_Osize(tc_List_Olist(U_21036)),
    inference(clausify,[status(thm)],[f_5151_2]) ).

fof(f_5152_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_5152_2,plain,
    ! [U_21038,U_21037] :
      ( class_Finite__Set_Ofinite(tc_sum(U_21037,U_21038))
      | ~ class_Finite__Set_Ofinite(U_21038)
      | ~ class_Finite__Set_Ofinite(U_21037) ),
    inference(variable_rename,[status(thm)],[f_5152_1]) ).

cnf(f_5152_3,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_21037,U_21038))
    | ~ class_Finite__Set_Ofinite(U_21038)
    | ~ class_Finite__Set_Ofinite(U_21037) ),
    inference(clausify,[status(thm)],[f_5152_2]) ).

fof(f_5153_1,plain,
    ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_sum__HOL_Oequal]) ).

fof(f_5153_2,plain,
    ! [U_21040,U_21039] : class_HOL_Oequal(tc_sum(U_21039,U_21040)),
    inference(variable_rename,[status(thm)],[f_5153_1]) ).

cnf(f_5153_3,plain,
    class_HOL_Oequal(tc_sum(U_21039,U_21040)),
    inference(clausify,[status(thm)],[f_5153_2]) ).

fof(f_5154_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_sum(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum]) ).

fof(f_5154_2,plain,
    ! [U_21042,U_21041] :
      ( class_Enum_Oenum(tc_sum(U_21041,U_21042))
      | ~ class_Enum_Oenum(U_21042)
      | ~ class_Enum_Oenum(U_21041) ),
    inference(variable_rename,[status(thm)],[f_5154_1]) ).

cnf(f_5154_3,plain,
    ( class_Enum_Oenum(tc_sum(U_21041,U_21042))
    | ~ class_Enum_Oenum(U_21042)
    | ~ class_Enum_Oenum(U_21041) ),
    inference(clausify,[status(thm)],[f_5154_2]) ).

fof(f_5155_1,plain,
    ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(f_5155_2,plain,
    ! [U_21044,U_21043] : class_Nat_Osize(tc_sum(U_21043,U_21044)),
    inference(variable_rename,[status(thm)],[f_5155_1]) ).

cnf(f_5155_3,plain,
    class_Nat_Osize(tc_sum(U_21043,U_21044)),
    inference(clausify,[status(thm)],[f_5155_2]) ).

fof(f_5156_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_5156_2,plain,
    ! [U_21045] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_21045))
      | ~ class_Finite__Set_Ofinite(U_21045) ),
    inference(variable_rename,[status(thm)],[f_5156_1]) ).

cnf(f_5156_3,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_21045))
    | ~ class_Finite__Set_Ofinite(U_21045) ),
    inference(clausify,[status(thm)],[f_5156_2]) ).

fof(f_5157_1,plain,
    ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__HOL_Oequal]) ).

fof(f_5157_2,plain,
    ! [U_21046] : class_HOL_Oequal(tc_Option_Ooption(U_21046)),
    inference(variable_rename,[status(thm)],[f_5157_1]) ).

cnf(f_5157_3,plain,
    class_HOL_Oequal(tc_Option_Ooption(U_21046)),
    inference(clausify,[status(thm)],[f_5157_2]) ).

fof(f_5158_1,plain,
    ! [T_1] :
      ( class_Enum_Oenum(tc_Option_Ooption(T_1))
      | ~ class_Enum_Oenum(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum]) ).

fof(f_5158_2,plain,
    ! [U_21047] :
      ( class_Enum_Oenum(tc_Option_Ooption(U_21047))
      | ~ class_Enum_Oenum(U_21047) ),
    inference(variable_rename,[status(thm)],[f_5158_1]) ).

cnf(f_5158_3,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(U_21047))
    | ~ class_Enum_Oenum(U_21047) ),
    inference(clausify,[status(thm)],[f_5158_2]) ).

fof(f_5159_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(f_5159_2,plain,
    ! [U_21048] : class_Nat_Osize(tc_Option_Ooption(U_21048)),
    inference(variable_rename,[status(thm)],[f_5159_1]) ).

cnf(f_5159_3,plain,
    class_Nat_Osize(tc_Option_Ooption(U_21048)),
    inference(clausify,[status(thm)],[f_5159_2]) ).

fof(f_5160_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_5160_2,plain,
    ! [U_21050,U_21049] :
      ( class_Finite__Set_Ofinite(tc_prod(U_21049,U_21050))
      | ~ class_Finite__Set_Ofinite(U_21050)
      | ~ class_Finite__Set_Ofinite(U_21049) ),
    inference(variable_rename,[status(thm)],[f_5160_1]) ).

cnf(f_5160_3,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_21049,U_21050))
    | ~ class_Finite__Set_Ofinite(U_21050)
    | ~ class_Finite__Set_Ofinite(U_21049) ),
    inference(clausify,[status(thm)],[f_5160_2]) ).

fof(f_5161_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_5161_2,plain,
    ! [U_21052,U_21051] :
      ( class_Smallcheck_Osmall(tc_prod(U_21051,U_21052))
      | ~ class_Smallcheck_Osmall(U_21052)
      | ~ class_Smallcheck_Osmall(U_21051) ),
    inference(variable_rename,[status(thm)],[f_5161_1]) ).

cnf(f_5161_3,plain,
    ( class_Smallcheck_Osmall(tc_prod(U_21051,U_21052))
    | ~ class_Smallcheck_Osmall(U_21052)
    | ~ class_Smallcheck_Osmall(U_21051) ),
    inference(clausify,[status(thm)],[f_5161_2]) ).

fof(f_5162_1,plain,
    ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_prod__HOL_Oequal]) ).

fof(f_5162_2,plain,
    ! [U_21054,U_21053] : class_HOL_Oequal(tc_prod(U_21053,U_21054)),
    inference(variable_rename,[status(thm)],[f_5162_1]) ).

cnf(f_5162_3,plain,
    class_HOL_Oequal(tc_prod(U_21053,U_21054)),
    inference(clausify,[status(thm)],[f_5162_2]) ).

fof(f_5163_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_prod(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum]) ).

fof(f_5163_2,plain,
    ! [U_21056,U_21055] :
      ( class_Enum_Oenum(tc_prod(U_21055,U_21056))
      | ~ class_Enum_Oenum(U_21056)
      | ~ class_Enum_Oenum(U_21055) ),
    inference(variable_rename,[status(thm)],[f_5163_1]) ).

cnf(f_5163_3,plain,
    ( class_Enum_Oenum(tc_prod(U_21055,U_21056))
    | ~ class_Enum_Oenum(U_21056)
    | ~ class_Enum_Oenum(U_21055) ),
    inference(clausify,[status(thm)],[f_5163_2]) ).

fof(f_5164_1,plain,
    ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(f_5164_2,plain,
    ! [U_21058,U_21057] : class_Nat_Osize(tc_prod(U_21057,U_21058)),
    inference(variable_rename,[status(thm)],[f_5164_1]) ).

cnf(f_5164_3,plain,
    class_Nat_Osize(tc_prod(U_21057,U_21058)),
    inference(clausify,[status(thm)],[f_5164_2]) ).

fof(f_5165_1,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).

cnf(f_5165_2,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5165_1]) ).

fof(f_5166_1,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]) ).

cnf(f_5166_2,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5166_1]) ).

fof(f_5167_1,plain,
    class_HOL_Oequal(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__HOL_Oequal]) ).

cnf(f_5167_2,plain,
    class_HOL_Oequal(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5167_1]) ).

fof(f_5168_1,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]) ).

cnf(f_5168_2,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5168_1]) ).

fof(f_5169_1,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]) ).

cnf(f_5169_2,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5169_1]) ).

fof(f_5170_1,plain,
    class_HOL_Oequal(tc_Code__Evaluation_Oterm),
    inference(fof_nnf,[status(thm)],[arity_Code____Evaluation__Oterm__HOL_Oequal]) ).

cnf(f_5170_2,plain,
    class_HOL_Oequal(tc_Code__Evaluation_Oterm),
    inference(clausify,[status(thm)],[f_5170_1]) ).

fof(f_5171_1,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(fof_nnf,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]) ).

cnf(f_5171_2,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(clausify,[status(thm)],[f_5171_1]) ).

fof(f_5172_1,plain,
    ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Hoare____Mirabelle__Otriple__HOL_Oequal]) ).

fof(f_5172_2,plain,
    ! [U_21059] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(U_21059)),
    inference(variable_rename,[status(thm)],[f_5172_1]) ).

cnf(f_5172_3,plain,
    class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(U_21059)),
    inference(clausify,[status(thm)],[f_5172_2]) ).

fof(f_5173_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize]) ).

fof(f_5173_2,plain,
    ! [U_21060] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_21060)),
    inference(variable_rename,[status(thm)],[f_5173_1]) ).

cnf(f_5173_3,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_21060)),
    inference(clausify,[status(thm)],[f_5173_2]) ).

fof(f_5174_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]) ).

cnf(f_5174_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5174_1]) ).

fof(f_5175_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]) ).

cnf(f_5175_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5175_1]) ).

fof(f_5176_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]) ).

cnf(f_5176_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5176_1]) ).

fof(f_5177_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]) ).

cnf(f_5177_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5177_1]) ).

fof(f_5178_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]) ).

cnf(f_5178_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5178_1]) ).

fof(f_5179_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]) ).

cnf(f_5179_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5179_1]) ).

fof(f_5180_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]) ).

cnf(f_5180_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5180_1]) ).

fof(f_5181_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]) ).

cnf(f_5181_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5181_1]) ).

fof(f_5182_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]) ).

cnf(f_5182_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5182_1]) ).

fof(f_5183_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]) ).

cnf(f_5183_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5183_1]) ).

fof(f_5184_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]) ).

cnf(f_5184_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5184_1]) ).

fof(f_5185_1,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]) ).

cnf(f_5185_2,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5185_1]) ).

fof(f_5186_1,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]) ).

cnf(f_5186_2,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5186_1]) ).

fof(f_5187_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]) ).

cnf(f_5187_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5187_1]) ).

fof(f_5188_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]) ).

cnf(f_5188_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5188_1]) ).

fof(f_5189_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]) ).

cnf(f_5189_2,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5189_1]) ).

fof(f_5190_1,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]) ).

cnf(f_5190_2,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5190_1]) ).

fof(f_5191_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]) ).

cnf(f_5191_2,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5191_1]) ).

fof(f_5192_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]) ).

cnf(f_5192_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5192_1]) ).

fof(f_5193_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]) ).

cnf(f_5193_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5193_1]) ).

fof(f_5194_1,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]) ).

cnf(f_5194_2,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5194_1]) ).

fof(f_5195_1,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]) ).

cnf(f_5195_2,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5195_1]) ).

fof(f_5196_1,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]) ).

cnf(f_5196_2,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5196_1]) ).

fof(f_5197_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]) ).

cnf(f_5197_2,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5197_1]) ).

fof(f_5198_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]) ).

cnf(f_5198_2,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5198_1]) ).

fof(f_5199_1,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]) ).

cnf(f_5199_2,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5199_1]) ).

fof(f_5200_1,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]) ).

cnf(f_5200_2,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5200_1]) ).

fof(f_5201_1,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]) ).

cnf(f_5201_2,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5201_1]) ).

fof(f_5202_1,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]) ).

cnf(f_5202_2,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5202_1]) ).

fof(f_5203_1,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]) ).

cnf(f_5203_2,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5203_1]) ).

fof(f_5204_1,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]) ).

cnf(f_5204_2,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5204_1]) ).

fof(f_5205_1,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]) ).

cnf(f_5205_2,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5205_1]) ).

fof(f_5206_1,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]) ).

cnf(f_5206_2,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5206_1]) ).

fof(f_5207_1,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]) ).

cnf(f_5207_2,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5207_1]) ).

fof(f_5208_1,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]) ).

cnf(f_5208_2,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5208_1]) ).

fof(f_5209_1,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]) ).

cnf(f_5209_2,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5209_1]) ).

fof(f_5210_1,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]) ).

cnf(f_5210_2,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5210_1]) ).

fof(f_5211_1,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]) ).

cnf(f_5211_2,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5211_1]) ).

fof(f_5212_1,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]) ).

cnf(f_5212_2,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5212_1]) ).

fof(f_5213_1,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]) ).

cnf(f_5213_2,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5213_1]) ).

fof(f_5214_1,plain,
    class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__HOL_Oequal]) ).

cnf(f_5214_2,plain,
    class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5214_1]) ).

fof(f_5215_1,plain,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]) ).

cnf(f_5215_2,plain,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5215_1]) ).

fof(f_5216_1,plain,
    ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal]) ).

fof(f_5216_2,plain,
    ! [U_21061] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(U_21061)),
    inference(variable_rename,[status(thm)],[f_5216_1]) ).

cnf(f_5216_3,plain,
    class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(U_21061)),
    inference(clausify,[status(thm)],[f_5216_2]) ).

fof(f_5217_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(f_5217_2,plain,
    ! [U_21062] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_21062)),
    inference(variable_rename,[status(thm)],[f_5217_1]) ).

cnf(f_5217_3,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_21062)),
    inference(clausify,[status(thm)],[f_5217_2]) ).

fof(f_5218_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_5218_2,plain,
    ! [U_21064,U_21063] : hAPP(c_COMBI(U_21063),U_21064) = U_21064,
    inference(variable_rename,[status(thm)],[f_5218_1]) ).

cnf(f_5218_3,plain,
    hAPP(c_COMBI(U_21063),U_21064) = U_21064,
    inference(clausify,[status(thm)],[f_5218_2]) ).

fof(f_5219_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_5219_2,plain,
    ! [U_21068,U_21067,U_21066,U_21065] : hAPP(hAPP(c_COMBK(U_21065,U_21066),U_21067),U_21068) = U_21067,
    inference(variable_rename,[status(thm)],[f_5219_1]) ).

cnf(f_5219_3,plain,
    hAPP(hAPP(c_COMBK(U_21065,U_21066),U_21067),U_21068) = U_21067,
    inference(clausify,[status(thm)],[f_5219_2]) ).

fof(f_5220_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).

fof(f_5220_2,plain,
    ! [U_21074,U_21073,U_21072,U_21071,U_21070,U_21069] : hAPP(hAPP(hAPP(c_COMBB(U_21069,U_21070,U_21071),U_21072),U_21073),U_21074) = hAPP(U_21072,hAPP(U_21073,U_21074)),
    inference(variable_rename,[status(thm)],[f_5220_1]) ).

cnf(f_5220_3,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_21069,U_21070,U_21071),U_21072),U_21073),U_21074) = hAPP(U_21072,hAPP(U_21073,U_21074)),
    inference(clausify,[status(thm)],[f_5220_2]) ).

fof(f_5221_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).

fof(f_5221_2,plain,
    ! [U_21080,U_21079,U_21078,U_21077,U_21076,U_21075] : hAPP(hAPP(hAPP(c_COMBC(U_21075,U_21076,U_21077),U_21078),U_21079),U_21080) = hAPP(hAPP(U_21078,U_21080),U_21079),
    inference(variable_rename,[status(thm)],[f_5221_1]) ).

cnf(f_5221_3,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_21075,U_21076,U_21077),U_21078),U_21079),U_21080) = hAPP(hAPP(U_21078,U_21080),U_21079),
    inference(clausify,[status(thm)],[f_5221_2]) ).

fof(f_5222_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).

fof(f_5222_2,plain,
    ! [U_21086,U_21085,U_21084,U_21083,U_21082,U_21081] : hAPP(hAPP(hAPP(c_COMBS(U_21081,U_21082,U_21083),U_21084),U_21085),U_21086) = hAPP(hAPP(U_21084,U_21086),hAPP(U_21085,U_21086)),
    inference(variable_rename,[status(thm)],[f_5222_1]) ).

cnf(f_5222_3,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_21081,U_21082,U_21083),U_21084),U_21085),U_21086) = hAPP(hAPP(U_21084,U_21086),hAPP(U_21085,U_21086)),
    inference(clausify,[status(thm)],[f_5222_2]) ).

fof(f_5223_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_5223_2,plain,
    ! [U_21088,U_21087] :
      ( U_21087 = U_21088
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_21087),U_21088)) ),
    inference(variable_rename,[status(thm)],[f_5223_1]) ).

cnf(f_5223_3,plain,
    ( U_21087 = U_21088
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_21087),U_21088)) ),
    inference(clausify,[status(thm)],[f_5223_2]) ).

fof(f_5224_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_5224_2,plain,
    ! [U_21090,U_21089] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_21089),U_21090))
      | U_21089 != U_21090 ),
    inference(variable_rename,[status(thm)],[f_5224_1]) ).

cnf(f_5224_3,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_21089),U_21090))
    | U_21089 != U_21090 ),
    inference(clausify,[status(thm)],[f_5224_2]) ).

fof(f_5225_1,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_nnf,[status(thm)],[help_c__fFalse__1]) ).

cnf(f_5225_2,plain,
    ~ hBOOL(c_fFalse),
    inference(clausify,[status(thm)],[f_5225_1]) ).

fof(f_5226_1,plain,
    hBOOL(c_fTrue),
    inference(fof_nnf,[status(thm)],[help_c__fTrue__1]) ).

cnf(f_5226_2,plain,
    hBOOL(c_fTrue),
    inference(clausify,[status(thm)],[f_5226_1]) ).

fof(f_5227_1,plain,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).

fof(f_5227_2,plain,
    ! [U_21091] :
      ( ~ hBOOL(U_21091)
      | ~ hBOOL(hAPP(c_fNot,U_21091)) ),
    inference(variable_rename,[status(thm)],[f_5227_1]) ).

cnf(f_5227_3,plain,
    ( ~ hBOOL(U_21091)
    | ~ hBOOL(hAPP(c_fNot,U_21091)) ),
    inference(clausify,[status(thm)],[f_5227_2]) ).

fof(f_5228_1,plain,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).

fof(f_5228_2,plain,
    ! [U_21092] :
      ( hBOOL(hAPP(c_fNot,U_21092))
      | hBOOL(U_21092) ),
    inference(variable_rename,[status(thm)],[f_5228_1]) ).

cnf(f_5228_3,plain,
    ( hBOOL(hAPP(c_fNot,U_21092))
    | hBOOL(U_21092) ),
    inference(clausify,[status(thm)],[f_5228_2]) ).

fof(f_5229_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).

fof(f_5229_2,plain,
    ! [U_21094,U_21093] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_21093),U_21094))
      | ~ hBOOL(U_21094)
      | ~ hBOOL(U_21093) ),
    inference(variable_rename,[status(thm)],[f_5229_1]) ).

fof(f_5229_3,plain,
    ! [U_21094] :
      ( ! [U_21093] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_21093),U_21094))
          | ~ hBOOL(U_21093) )
      | ~ hBOOL(U_21094) ),
    inference(miniscope,[status(thm)],[f_5229_2]) ).

cnf(f_5229_4,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_21093),U_21094))
    | ~ hBOOL(U_21093)
    | ~ hBOOL(U_21094) ),
    inference(clausify,[status(thm)],[f_5229_3]) ).

fof(f_5230_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).

fof(f_5230_2,plain,
    ! [U_21096,U_21095] :
      ( hBOOL(U_21095)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_21095),U_21096)) ),
    inference(variable_rename,[status(thm)],[f_5230_1]) ).

cnf(f_5230_3,plain,
    ( hBOOL(U_21095)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_21095),U_21096)) ),
    inference(clausify,[status(thm)],[f_5230_2]) ).

fof(f_5231_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).

fof(f_5231_2,plain,
    ! [U_21098,U_21097] :
      ( hBOOL(U_21098)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_21097),U_21098)) ),
    inference(variable_rename,[status(thm)],[f_5231_1]) ).

fof(f_5231_3,plain,
    ! [U_21098] :
      ( ! [U_21097] : ~ hBOOL(hAPP(hAPP(c_fconj,U_21097),U_21098))
      | hBOOL(U_21098) ),
    inference(miniscope,[status(thm)],[f_5231_2]) ).

cnf(f_5231_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_21097),U_21098))
    | hBOOL(U_21098) ),
    inference(clausify,[status(thm)],[f_5231_3]) ).

fof(f_5232_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__1]) ).

fof(f_5232_2,plain,
    ! [U_21100,U_21099] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_21099),U_21100))
      | ~ hBOOL(U_21099) ),
    inference(variable_rename,[status(thm)],[f_5232_1]) ).

cnf(f_5232_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_21099),U_21100))
    | ~ hBOOL(U_21099) ),
    inference(clausify,[status(thm)],[f_5232_2]) ).

fof(f_5233_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__2]) ).

fof(f_5233_2,plain,
    ! [U_21102,U_21101] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_21102),U_21101))
      | ~ hBOOL(U_21101) ),
    inference(variable_rename,[status(thm)],[f_5233_1]) ).

cnf(f_5233_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_21102),U_21101))
    | ~ hBOOL(U_21101) ),
    inference(clausify,[status(thm)],[f_5233_2]) ).

fof(f_5234_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__3]) ).

fof(f_5234_2,plain,
    ! [U_21104,U_21103] :
      ( hBOOL(U_21104)
      | hBOOL(U_21103)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_21103),U_21104)) ),
    inference(variable_rename,[status(thm)],[f_5234_1]) ).

fof(f_5234_3,plain,
    ! [U_21104] :
      ( ! [U_21103] :
          ( hBOOL(U_21103)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_21103),U_21104)) )
      | hBOOL(U_21104) ),
    inference(miniscope,[status(thm)],[f_5234_2]) ).

cnf(f_5234_4,plain,
    ( hBOOL(U_21103)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_21103),U_21104))
    | hBOOL(U_21104) ),
    inference(clausify,[status(thm)],[f_5234_3]) ).

fof(f_5235_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__1]) ).

fof(f_5235_2,plain,
    ! [U_21106,U_21105] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_21105),U_21106))
      | hBOOL(U_21105) ),
    inference(variable_rename,[status(thm)],[f_5235_1]) ).

cnf(f_5235_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_21105),U_21106))
    | hBOOL(U_21105) ),
    inference(clausify,[status(thm)],[f_5235_2]) ).

fof(f_5236_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__2]) ).

fof(f_5236_2,plain,
    ! [U_21108,U_21107] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_21108),U_21107))
      | ~ hBOOL(U_21107) ),
    inference(variable_rename,[status(thm)],[f_5236_1]) ).

cnf(f_5236_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_21108),U_21107))
    | ~ hBOOL(U_21107) ),
    inference(clausify,[status(thm)],[f_5236_2]) ).

fof(f_5237_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__3]) ).

fof(f_5237_2,plain,
    ! [U_21110,U_21109] :
      ( hBOOL(U_21110)
      | ~ hBOOL(U_21109)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21109),U_21110)) ),
    inference(variable_rename,[status(thm)],[f_5237_1]) ).

fof(f_5237_3,plain,
    ! [U_21110] :
      ( ! [U_21109] :
          ( ~ hBOOL(U_21109)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21109),U_21110)) )
      | hBOOL(U_21110) ),
    inference(miniscope,[status(thm)],[f_5237_2]) ).

cnf(f_5237_4,plain,
    ( ~ hBOOL(U_21109)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21109),U_21110))
    | hBOOL(U_21110) ),
    inference(clausify,[status(thm)],[f_5237_3]) ).

fof(f_5238_1,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),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))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),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_Procs)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

cnf(f_5238_2,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),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))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),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_Procs)),
    inference(clausify,[status(thm)],[f_5238_1]) ).

fof(f_5239_1,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

cnf(f_5239_2,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_5239_1]) ).

fof(f_5240_1,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    inference(negate,[status(cth)],[conj_2]) ).

cnf(f_5240_2,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_5240_1]) ).

cnf(f_23_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_23_3]) ).

cnf(f_23_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_23_6]) ).

cnf(f_125_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_125_8]) ).

cnf(f_191_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_191_3]) ).

cnf(f_197_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_197_4]) ).

cnf(f_198_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_198_4]) ).

cnf(f_790_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_4]) ).

cnf(f_790_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_5]) ).

cnf(f_790_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_6]) ).

cnf(f_790_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_7]) ).

cnf(f_790_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_8]) ).

cnf(f_790_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_9]) ).

cnf(f_790_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_790_10]) ).

cnf(f_1013_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1013_7]) ).

cnf(f_1013_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1013_8]) ).

cnf(f_1013_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1013_13]) ).

cnf(f_1022_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1022_3]) ).

cnf(f_1153_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1153_8]) ).

cnf(f_1159_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1159_4]) ).

cnf(f_1160_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1160_4]) ).

cnf(f_1271_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1271_6]) ).

cnf(f_1674_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1674_6]) ).

cnf(f_1675_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1675_6]) ).

cnf(f_2409_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2409_6]) ).

cnf(f_2409_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2409_7]) ).

cnf(f_2409_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2409_12]) ).

cnf(f_2410_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2410_6]) ).

cnf(f_2410_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2410_7]) ).

cnf(f_2410_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2410_12]) ).

cnf(f_2429_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2429_5]) ).

cnf(f_2430_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2430_5]) ).

cnf(f_2450_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2450_6]) ).

cnf(f_2450_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2450_7]) ).

cnf(f_2450_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2450_12]) ).

cnf(f_2451_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2451_6]) ).

cnf(f_2451_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2451_7]) ).

cnf(f_2451_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2451_12]) ).

cnf(f_2535_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2535_3]) ).

cnf(f_2556_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2556_8]) ).

cnf(f_2656_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2656_3]) ).

cnf(f_2701_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2701_8]) ).

cnf(f_2755_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2755_5]) ).

cnf(f_2756_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2756_5]) ).

cnf(f_2757_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2757_5]) ).

cnf(f_2758_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2758_5]) ).

cnf(f_2762_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2762_6]) ).

cnf(f_2762_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2762_7]) ).

cnf(f_2762_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2762_12]) ).

cnf(f_2763_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2763_6]) ).

cnf(f_2763_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2763_7]) ).

cnf(f_2763_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2763_12]) ).

cnf(f_2764_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2764_6]) ).

cnf(f_2764_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2764_7]) ).

cnf(f_2764_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2764_12]) ).

cnf(f_2765_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2765_6]) ).

cnf(f_2765_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2765_7]) ).

cnf(f_2765_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2765_12]) ).

cnf(f_2768_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2768_6]) ).

cnf(f_2768_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2768_7]) ).

cnf(f_2768_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2768_12]) ).

cnf(f_2769_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2769_6]) ).

cnf(f_2769_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2769_7]) ).

cnf(f_2769_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2769_12]) ).

cnf(f_2770_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2770_6]) ).

cnf(f_2770_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2770_7]) ).

cnf(f_2770_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2770_12]) ).

cnf(f_2771_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2771_6]) ).

cnf(f_2771_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2771_7]) ).

cnf(f_2771_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2771_12]) ).

cnf(f_2800_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2800_7]) ).

cnf(f_2800_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2800_8]) ).

cnf(f_2800_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2800_13]) ).

cnf(f_2849_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2849_6]) ).

cnf(f_3133_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3133_3]) ).

cnf(f_3261_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3261_10]) ).

cnf(f_3261_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3261_11]) ).

cnf(f_3261_16_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3261_16]) ).

cnf(f_3739_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3739_3]) ).

cnf(f_3741_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3741_4]) ).

cnf(f_3839_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3839_6]) ).

cnf(f_3839_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3839_7]) ).

cnf(f_4155_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4155_4]) ).

cnf(f_4200_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4200_8]) ).

cnf(f_4897_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4897_6]) ).

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,
    ( 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_6,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_7,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_8,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple(Eq_x_0) = c_Hoare__Mirabelle_Otriple_Otriple(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( c_Set_Oinsert(Eq_x_0) = c_Set_Oinsert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,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_11,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_12,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_13,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_14,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_15,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_16,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_17,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,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_98,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_99,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_100,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_101,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_102,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_103,axiom,
    ( c_Orderings_Oord_Omax(Eq_x_0,Eq_x_1) = c_Orderings_Oord_Omax(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( c_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_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,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_113,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_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,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_136,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_137,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_138,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_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_152,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_153,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_154,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_155,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_156,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_157,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_158,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_159,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_160,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_161,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_162,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_163,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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,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_183,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_184,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_185,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_186,axiom,
    ( c_Hilbert__Choice_OLeastM(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hilbert__Choice_OLeastM(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( c_Hilbert__Choice_OGreatestM(Eq_x_0,Eq_x_1,Eq_x_2) = c_Hilbert__Choice_OGreatestM(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( c_Hilbert__Choice_OGreatest(Eq_x_0) = c_Hilbert__Choice_OGreatest(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_189,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_190,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_191,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_192,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_193,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_194,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_195,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_196,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_197,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_198,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_199,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_200,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_201,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_202,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_203,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_204,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_205,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_206,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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,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_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,axiom,
    ( c_Lazy__Sequence_Oanamorph(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Oanamorph(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_241,axiom,
    ( c_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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,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_254,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_255,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_256,axiom,
    ( c_Map_Omap__of(Eq_x_0,Eq_x_1) = c_Map_Omap__of(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_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_258,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_259,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_260,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_261,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_262,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_263,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_264,axiom,
    ( c_List_Olistsp(Eq_x_0,Eq_x_1) = c_List_Olistsp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_265,axiom,
    ( c_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_266,axiom,
    ( c_Enum_Oproduct(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Enum_Oproduct(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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_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_268,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_269,axiom,
    ( c_Enum_Oenum__the(Eq_x_0,Eq_x_1) = c_Enum_Oenum__the(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_270,axiom,
    ( c_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_271,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_272,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_273,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_274,axiom,
    ( c_Enum_Oenum__class_Oenum(Eq_x_0) = c_Enum_Oenum__class_Oenum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_275,axiom,
    ( c_Enum_Oenum__class_Oenum__all(Eq_x_0) = c_Enum_Oenum__class_Oenum__all(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_276,axiom,
    ( c_Enum_Oenum__class_Oenum__ex(Eq_x_0) = c_Enum_Oenum__class_Oenum__ex(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_277,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_278,axiom,
    ( c_List_OremoveAll(Eq_x_0,Eq_x_1) = c_List_OremoveAll(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_279,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_280,axiom,
    ( c_List_Olinorder__class_Osort__key(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Olinorder__class_Osort__key(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_281,axiom,
    ( c_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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,axiom,
    ( c_List_Oinsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oinsert(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_295,axiom,
    ( c_List_Omaps(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Omaps(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_296,axiom,
    ( c_List_Omeasures(Eq_x_0,Eq_x_1) = c_List_Omeasures(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_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_298,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_299,axiom,
    ( c_HOL_Oequal__class_Oequal(Eq_x_0) = c_HOL_Oequal__class_Oequal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,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_301,axiom,
    ( c_Lazy__Sequence_Oyield(Eq_x_0) = c_Lazy__Sequence_Oyield(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_302,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_303,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__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_304,axiom,
    ( c_Lazy__Sequence_Oyieldn(Eq_x_0) = c_Lazy__Sequence_Oyieldn(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_305,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_OInsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_306,axiom,
    ( c_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_307,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_308,axiom,
    ( c_Lazy__Sequence_Obind(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Obind(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,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_318,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_319,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_320,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_321,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_322,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_323,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_324,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_325,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_326,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_327,axiom,
    ( c_List_Osplice(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osplice(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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_Lazy__Sequence_Osingle(Eq_x_0) = c_Lazy__Sequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_329,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_330,axiom,
    ( c_Lazy__Sequence_Oproduct(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Oproduct(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( c_List_Oreplicate(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oreplicate(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,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_333,axiom,
    ( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_334,axiom,
    ( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_335,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_336,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_337,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_342,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_344,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK16(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_348,axiom,
    ( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK22(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) = sK22(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_354,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_355,axiom,
    ( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK36(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_368,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_369,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_370,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_372,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK46(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_378,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_382,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_383,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_385,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_389,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK59(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_391,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK61(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_393,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_396,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK65(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_397,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK68(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_400,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK69(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_401,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_402,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_404,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK73(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_405,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK74(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_406,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK81(Eq_x_0) = sK81(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_413,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_414,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_415,axiom,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_416,axiom,
    ( sK85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_418,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_419,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_420,axiom,
    ( sK89(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_423,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_424,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK93(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK94(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_426,axiom,
    ( sK95(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_428,axiom,
    ( sK97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_430,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_431,axiom,
    ( sK100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_432,axiom,
    ( sK101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_434,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_435,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_436,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_437,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_438,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_439,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_440,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK109(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK112(Eq_x_0) = sK112(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_444,axiom,
    ( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_445,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_446,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_448,axiom,
    ( sK117(Eq_x_0,Eq_x_1) = sK117(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,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_450,axiom,
    ( sK119(Eq_x_0) = sK119(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_451,axiom,
    ( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_452,axiom,
    ( sK121(Eq_x_0,Eq_x_1) = sK121(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_453,axiom,
    ( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_454,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_455,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_456,axiom,
    ( sK125(Eq_x_0) = sK125(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_457,axiom,
    ( sK126(Eq_x_0) = sK126(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_458,axiom,
    ( sK127(Eq_x_0) = sK127(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_459,axiom,
    ( sK128(Eq_x_0) = sK128(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_460,axiom,
    ( sK129(Eq_x_0,Eq_x_1) = sK129(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_461,axiom,
    ( sK130(Eq_x_0,Eq_x_1) = sK130(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_462,axiom,
    ( sK131(Eq_x_0,Eq_x_1) = sK131(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_463,axiom,
    ( sK132(Eq_x_0,Eq_x_1) = sK132(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_464,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_465,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_466,axiom,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2) = sK135(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_467,axiom,
    ( sK136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_468,axiom,
    ( sK137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK137(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_469,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2) = sK138(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_470,axiom,
    ( sK139(Eq_x_0,Eq_x_1) = sK139(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,
    ( 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_472,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_473,axiom,
    ( sK142(Eq_x_0,Eq_x_1) = sK142(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_474,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2) = sK143(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_475,axiom,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2) = sK144(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2) = sK145(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_477,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_478,axiom,
    ( sK147(Eq_x_0) = sK147(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_479,axiom,
    ( sK148(Eq_x_0) = sK148(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_480,axiom,
    ( sK149(Eq_x_0) = sK149(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_481,axiom,
    ( sK150(Eq_x_0) = sK150(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_482,axiom,
    ( sK151(Eq_x_0,Eq_x_1) = sK151(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_483,axiom,
    ( sK152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_484,axiom,
    ( sK153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_486,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_488,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_489,axiom,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_490,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_491,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2) = sK160(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_492,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2) = sK161(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_494,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_495,axiom,
    ( sK164(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_496,axiom,
    ( sK165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_497,axiom,
    ( sK166(Eq_x_0) = sK166(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_498,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_499,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_500,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_504,axiom,
    ( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_505,axiom,
    ( sK174(Eq_x_0,Eq_x_1) = sK174(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_506,axiom,
    ( sK175(Eq_x_0,Eq_x_1) = sK175(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_507,axiom,
    ( sK176(Eq_x_0,Eq_x_1) = sK176(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_508,axiom,
    ( sK177(Eq_x_0,Eq_x_1) = sK177(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_509,axiom,
    ( sK178(Eq_x_0,Eq_x_1) = sK178(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_510,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_511,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_514,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_515,axiom,
    ( sK184(Eq_x_0,Eq_x_1) = sK184(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_516,axiom,
    ( sK185(Eq_x_0) = sK185(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_517,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK186(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK188(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK189(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK190(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK192(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_525,axiom,
    ( sK194(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK194(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_526,axiom,
    ( sK195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK197(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_529,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_530,axiom,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK199(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_532,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2) = sK201(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_533,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2) = sK202(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_534,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2) = sK203(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_535,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_536,axiom,
    ( sK205(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK205(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_537,axiom,
    ( sK206(Eq_x_0,Eq_x_1) = sK206(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_538,axiom,
    ( sK207(Eq_x_0) = sK207(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_539,axiom,
    ( sK208(Eq_x_0) = sK208(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_540,axiom,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK209(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_541,axiom,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK210(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_542,axiom,
    ( sK211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_543,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_544,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_545,axiom,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK214(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_546,axiom,
    ( sK215(Eq_x_0,Eq_x_1,Eq_x_2) = sK215(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK216(Eq_x_0,Eq_x_1,Eq_x_2) = sK216(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2) = sK217(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_550,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_551,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2) = sK220(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2) = sK221(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_553,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2) = sK222(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_554,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2) = sK223(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2) = sK224(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2) = sK225(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK226(Eq_x_0,Eq_x_1) = sK226(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_558,axiom,
    ( sK227(Eq_x_0,Eq_x_1) = sK227(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_559,axiom,
    ( sK228(Eq_x_0,Eq_x_1) = sK228(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_560,axiom,
    ( sK229(Eq_x_0,Eq_x_1) = sK229(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_561,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_562,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_563,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_564,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_565,axiom,
    ( sK234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_566,axiom,
    ( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2) = sK237(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2) = sK238(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2) = sK239(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_571,axiom,
    ( sK240(Eq_x_0,Eq_x_1,Eq_x_2) = sK240(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_572,axiom,
    ( sK241(Eq_x_0,Eq_x_1,Eq_x_2) = sK241(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_573,axiom,
    ( sK242(Eq_x_0,Eq_x_1,Eq_x_2) = sK242(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_574,axiom,
    ( sK243(Eq_x_0,Eq_x_1,Eq_x_2) = sK243(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK244(Eq_x_0,Eq_x_1,Eq_x_2) = sK244(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2) = sK245(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2) = sK246(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2) = sK247(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2) = sK248(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2) = sK249(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK250(Eq_x_0,Eq_x_1,Eq_x_2) = sK250(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK251(Eq_x_0,Eq_x_1,Eq_x_2) = sK251(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK252(Eq_x_0) = sK252(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_584,axiom,
    ( sK253(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK253(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_585,axiom,
    ( sK254(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK254(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2) = sK256(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK257(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_589,axiom,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2) = sK258(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2) = sK259(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_591,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2) = sK260(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK261(Eq_x_0,Eq_x_1,Eq_x_2) = sK261(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK262(Eq_x_0,Eq_x_1) = sK262(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_594,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2) = sK263(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2) = sK264(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_596,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2) = sK265(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_597,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2) = sK266(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_598,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_599,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK268(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_600,axiom,
    ( sK269(Eq_x_0,Eq_x_1) = sK269(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_601,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2) = sK270(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_602,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2) = sK271(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK272(Eq_x_0,Eq_x_1) = sK272(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_604,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_605,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2) = sK274(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_606,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_607,axiom,
    ( sK276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_608,axiom,
    ( sK277(Eq_x_0,Eq_x_1,Eq_x_2) = sK277(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_609,axiom,
    ( sK278(Eq_x_0,Eq_x_1,Eq_x_2) = sK278(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_610,axiom,
    ( sK279(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK279(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_611,axiom,
    ( sK280(Eq_x_0,Eq_x_1,Eq_x_2) = sK280(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK281(Eq_x_0,Eq_x_1,Eq_x_2) = sK281(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_614,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_615,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK284(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2) = sK285(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK286(Eq_x_0,Eq_x_1,Eq_x_2) = sK286(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK287(Eq_x_0,Eq_x_1,Eq_x_2) = sK287(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK288(Eq_x_0,Eq_x_1) = sK288(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_620,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2) = sK289(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2) = sK290(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_622,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2) = sK291(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_623,axiom,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2) = sK292(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_624,axiom,
    ( sK293(Eq_x_0,Eq_x_1,Eq_x_2) = sK293(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_625,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2) = sK294(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_626,axiom,
    ( sK295(Eq_x_0,Eq_x_1) = sK295(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_627,axiom,
    ( sK296(Eq_x_0,Eq_x_1,Eq_x_2) = sK296(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2) = sK297(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2) = sK298(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2) = sK299(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_632,axiom,
    ( sK301(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK301(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_633,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_634,axiom,
    ( sK303(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) = sK303(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_635,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_636,axiom,
    ( sK305(Eq_x_0) = sK305(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_637,axiom,
    ( sK306(Eq_x_0) = sK306(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_638,axiom,
    ( sK307(Eq_x_0) = sK307(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_639,axiom,
    ( sK308(Eq_x_0) = sK308(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_640,axiom,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK309(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK310(Eq_x_0) = sK310(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_642,axiom,
    ( sK311(Eq_x_0) = sK311(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_643,axiom,
    ( sK312(Eq_x_0,Eq_x_1,Eq_x_2) = sK312(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_644,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2) = sK313(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_645,axiom,
    ( sK314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK314(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK315(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_647,axiom,
    ( sK316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK316(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK317(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK317(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK318(Eq_x_0,Eq_x_1) = sK318(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_650,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2) = sK319(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_651,axiom,
    ( sK320(Eq_x_0,Eq_x_1) = sK320(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_652,axiom,
    ( sK321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK321(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK322(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK322(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK323(Eq_x_0,Eq_x_1) = sK323(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_655,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_656,axiom,
    ( sK325(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK325(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK326(Eq_x_0,Eq_x_1) = sK326(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_658,axiom,
    ( 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_659,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_660,axiom,
    ( sK329(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK329(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_661,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK330(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_662,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_663,axiom,
    ( sK332(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK332(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK333(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK334(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK335(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_667,axiom,
    ( sK336(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK336(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK337(Eq_x_0,Eq_x_1) = sK337(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_669,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK338(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_670,axiom,
    ( sK339(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK339(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_671,axiom,
    ( sK340(Eq_x_0,Eq_x_1,Eq_x_2) = sK340(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_672,axiom,
    ( sK341(Eq_x_0,Eq_x_1,Eq_x_2) = sK341(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK342(Eq_x_0,Eq_x_1) = sK342(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,
    ( sK343(Eq_x_0) = sK343(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_675,axiom,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2) = sK344(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_676,axiom,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2) = sK345(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK346(Eq_x_0,Eq_x_1) = sK346(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_678,axiom,
    ( sK347(Eq_x_0,Eq_x_1) = sK347(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_679,axiom,
    ( sK348(Eq_x_0) = sK348(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_680,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2) = sK349(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK350(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK351(Eq_x_0) = sK351(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_683,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_684,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_685,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_686,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2) = sK355(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK356(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_688,axiom,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2) = sK357(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_689,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2) = sK358(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_690,axiom,
    ( sK359(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK359(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_691,axiom,
    ( sK360(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK360(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_692,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK361(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_693,axiom,
    ( sK362(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK362(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_694,axiom,
    ( sK363(Eq_x_0,Eq_x_1) = sK363(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_695,axiom,
    ( sK364(Eq_x_0,Eq_x_1) = sK364(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_696,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK365(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_697,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2) = sK366(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_698,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_699,axiom,
    ( sK368(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK368(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_700,axiom,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK369(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2) = sK370(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_702,axiom,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK371(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_703,axiom,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK372(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_704,axiom,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK373(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK374(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK375(Eq_x_0,Eq_x_1) = sK375(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_707,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK376(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_709,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_710,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_711,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2) = sK380(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_712,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2) = sK381(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK382(Eq_x_0,Eq_x_1) = sK382(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_714,axiom,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2) = sK383(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_715,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2) = sK384(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_717,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_718,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_719,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_720,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_721,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_722,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_723,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK392(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_724,axiom,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK393(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK394(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK395(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK395(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_727,axiom,
    ( sK396(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK396(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK397(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK398(Eq_x_0,Eq_x_1) = sK398(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_730,axiom,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2) = sK399(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_731,axiom,
    ( sK400(Eq_x_0,Eq_x_1) = sK400(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_732,axiom,
    ( sK401(Eq_x_0,Eq_x_1) = sK401(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_733,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_734,axiom,
    ( sK403(Eq_x_0,Eq_x_1) = sK403(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_735,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK404(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_736,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK405(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_737,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK406(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_738,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK407(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_739,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_740,axiom,
    ( sK409(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK409(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK410(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK411(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_743,axiom,
    ( sK412(Eq_x_0,Eq_x_1) = sK412(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_744,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2) = sK413(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_745,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK414(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK415(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK416(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK416(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK417(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK417(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_749,axiom,
    ( sK418(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK418(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK419(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK420(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_753,axiom,
    ( sK422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK422(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_754,axiom,
    ( sK423(Eq_x_0,Eq_x_1,Eq_x_2) = sK423(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_756,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_757,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2) = sK426(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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) = sK428(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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) = sK429(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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) = sK430(Eq_y_0)
    | 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,Eq_x_3) = sK432(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_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) = sK434(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_765,axiom,
    ( sK435(Eq_x_0,Eq_x_1) = sK435(Eq_y_0,Eq_y_1)
    | 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,Eq_x_3) = sK436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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) = sK437(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_768,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2) = sK438(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_769,axiom,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK439(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_770,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_771,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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) = sK442(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_773,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK443(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_774,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK444(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_775,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK445(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_776,axiom,
    ( sK446(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK446(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_777,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = 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_778,axiom,
    ( sK448(Eq_x_0) = sK448(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_779,axiom,
    ( sK449(Eq_x_0) = sK449(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_780,axiom,
    ( sK450(Eq_x_0,Eq_x_1) = sK450(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_781,axiom,
    ( sK451(Eq_x_0,Eq_x_1,Eq_x_2) = sK451(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2) = sK452(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2) = sK453(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_784,axiom,
    ( sK454(Eq_x_0,Eq_x_1,Eq_x_2) = sK454(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_785,axiom,
    ( sK455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK455(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_786,axiom,
    ( sK456(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK456(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_787,axiom,
    ( sK457(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK457(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_788,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK458(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_789,axiom,
    ( sK459(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK459(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_790,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_791,axiom,
    ( sK461(Eq_x_0,Eq_x_1) = sK461(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_792,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_793,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2) = sK463(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_794,axiom,
    ( sK464(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK464(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK465(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK465(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK466(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK467(Eq_x_0,Eq_x_1,Eq_x_2) = sK467(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_798,axiom,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2) = sK468(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_799,axiom,
    ( sK469(Eq_x_0,Eq_x_1) = sK469(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_800,axiom,
    ( sK470(Eq_x_0,Eq_x_1) = sK470(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_801,axiom,
    ( sK471(Eq_x_0,Eq_x_1) = sK471(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_802,axiom,
    ( sK472(Eq_x_0,Eq_x_1) = sK472(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_803,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_804,axiom,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK474(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_805,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK475(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_806,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK476(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_807,axiom,
    ( sK477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK477(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_808,axiom,
    ( sK478(Eq_x_0,Eq_x_1) = sK478(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_809,axiom,
    ( sK479(Eq_x_0,Eq_x_1) = sK479(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_810,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_811,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2) = sK481(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK482(Eq_x_0,Eq_x_1,Eq_x_2) = sK482(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK483(Eq_x_0,Eq_x_1,Eq_x_2) = sK483(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_814,axiom,
    ( sK484(Eq_x_0,Eq_x_1) = sK484(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_815,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_816,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_817,axiom,
    ( sK487(Eq_x_0,Eq_x_1,Eq_x_2) = sK487(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK488(Eq_x_0,Eq_x_1,Eq_x_2) = sK488(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_819,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_820,axiom,
    ( sK490(Eq_x_0,Eq_x_1) = sK490(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,
    ( 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_822,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_823,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_824,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK494(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK495(Eq_x_0,Eq_x_1) = sK495(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,
    ( 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_827,axiom,
    ( sK497(Eq_x_0,Eq_x_1,Eq_x_2) = sK497(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_828,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK498(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_829,axiom,
    ( sK499(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK499(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_830,axiom,
    ( 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_831,axiom,
    ( sK501(Eq_x_0,Eq_x_1) = sK501(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_832,axiom,
    ( sK502(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK502(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK503(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK503(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_834,axiom,
    ( sK504(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK504(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_835,axiom,
    ( sK505(Eq_x_0,Eq_x_1) = sK505(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_836,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_837,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_838,axiom,
    ( sK508(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK508(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_839,axiom,
    ( sK509(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK509(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_840,axiom,
    ( sK510(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK510(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_841,axiom,
    ( sK511(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK511(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_842,axiom,
    ( sK512(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK512(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_843,axiom,
    ( sK513(Eq_x_0,Eq_x_1,Eq_x_2) = sK513(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_844,axiom,
    ( sK514(Eq_x_0,Eq_x_1) = sK514(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_845,axiom,
    ( sK515(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK515(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_846,axiom,
    ( sK516(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK516(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_847,axiom,
    ( sK517(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK517(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_848,axiom,
    ( sK518(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK518(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_849,axiom,
    ( sK519(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK519(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_850,axiom,
    ( sK520(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK520(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_851,axiom,
    ( sK521(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK521(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_852,axiom,
    ( sK522(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK522(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_853,axiom,
    ( sK523(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK523(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_854,axiom,
    ( sK524(Eq_x_0,Eq_x_1,Eq_x_2) = sK524(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_855,axiom,
    ( sK525(Eq_x_0,Eq_x_1,Eq_x_2) = sK525(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_856,axiom,
    ( sK526(Eq_x_0,Eq_x_1,Eq_x_2) = sK526(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_857,axiom,
    ( sK527(Eq_x_0,Eq_x_1,Eq_x_2) = sK527(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_858,axiom,
    ( sK528(Eq_x_0,Eq_x_1,Eq_x_2) = sK528(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_859,axiom,
    ( sK529(Eq_x_0,Eq_x_1,Eq_x_2) = sK529(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_860,axiom,
    ( sK530(Eq_x_0,Eq_x_1,Eq_x_2) = sK530(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_861,axiom,
    ( sK531(Eq_x_0,Eq_x_1,Eq_x_2) = sK531(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_862,axiom,
    ( sK532(Eq_x_0,Eq_x_1,Eq_x_2) = sK532(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_863,axiom,
    ( sK533(Eq_x_0,Eq_x_1,Eq_x_2) = sK533(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_864,axiom,
    ( sK534(Eq_x_0,Eq_x_1,Eq_x_2) = sK534(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_865,axiom,
    ( sK535(Eq_x_0,Eq_x_1,Eq_x_2) = sK535(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_866,axiom,
    ( sK536(Eq_x_0,Eq_x_1,Eq_x_2) = sK536(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_867,axiom,
    ( sK537(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK537(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_868,axiom,
    ( sK538(Eq_x_0,Eq_x_1,Eq_x_2) = sK538(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_869,axiom,
    ( sK539(Eq_x_0,Eq_x_1) = sK539(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_870,axiom,
    ( sK540(Eq_x_0,Eq_x_1,Eq_x_2) = sK540(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_871,axiom,
    ( sK541(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK541(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_872,axiom,
    ( sK542(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK542(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_873,axiom,
    ( sK543(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK543(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_874,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_875,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_876,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_877,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_878,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_879,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_880,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_881,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_882,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_883,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_884,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_885,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_886,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_887,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_888,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_889,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_890,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_891,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_892,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_893,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_894,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_895,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_896,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_897,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_898,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_899,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_900,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_901,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_902,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_903,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_904,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_905,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_906,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_907,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_908,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_909,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_910,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_911,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_912,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_913,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_914,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_915,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_916,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_917,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_918,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_919,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_920,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_921,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_922,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_923,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_924,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_925,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_926,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_927,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_928,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_929,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_930,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_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,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_939,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_940,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_941,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_942,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_943,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_944,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_945,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_946,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_947,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_948,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_949,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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,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_961,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_962,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_963,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_964,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_965,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_966,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_967,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_968,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_969,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_970,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_971,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_972,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_973,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_974,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_975,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_976,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_977,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_978,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_979,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_980,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_981,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_982,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_983,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_984,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_985,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_986,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_987,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_988,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_989,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_990,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_991,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_992,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_993,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_994,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_995,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_996,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_997,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_998,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_999,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_1000,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_1001,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_1002,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_1003,axiom,
    ( class_Enum_Oenum(Eq_y_0)
    | ~ class_Enum_Oenum(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1004,axiom,
    ( class_HOL_Oequal(Eq_y_0)
    | ~ class_HOL_Oequal(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1005,axiom,
    ( c_Enum_Oall__n__lists(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Enum_Oall__n__lists(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( c_Enum_Oex__n__lists(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Enum_Oex__n__lists(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( c_List_Olist__all2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_List_Olist__all2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1009,axiom,
    ( c_List_Olist__ex(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__ex(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( c_List_Olist__all(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__all(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( c_FunDef_Ois__measure(Eq_y_0,Eq_y_1)
    | ~ c_FunDef_Ois__measure(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1012,axiom,
    ( class_Nat_Osize(Eq_y_0)
    | ~ class_Nat_Osize(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1013,axiom,
    ( c_List_Olist__ex1(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__ex1(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW379+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04  This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.38  % Computer : n015.cluster.edu
% 0.13/5.38  % Model    : x86_64 x86_64
% 0.13/5.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.38  % Memory   : 8046.5625MB
% 0.13/5.38  % OS       : Linux 6.8.0-71-generic
% 0.13/5.38  % CPULimit : 300
% 0.13/5.38  % WCLimit  : 300
% 0.13/5.38  % DateTime : Sun Sep 20 05:30:55 UTC 2026
% 0.13/5.38  % CPUTime  : 
% 257.54/262.89  % SZS status Theorem for theBenchmark
% 257.54/262.89  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------